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Aberrisma

2026-11-04T10:35:17Z

Inthar:

{{Proposed}}

An '''aberrisma''' is an interval representing some comma as an additional type of melodic step smaller than a semitone. Its name originates from the comparison of its sound to a chromatic aberration, with the -isma suffix often used for commas. Although they are typically between 20 and 55 cents (around 81/80 to half of 16/15) and often inflated commas about the size of a diesis, the aberrisma is a melodic function and not an interval size. Larger and smaller sizes can function as aberrismas depending on the scale tuning. '''Aberrismic theory''' is the subset of microtonal theory pioneered by [[User:Ground|Ground]] and [[User:Inthar|Inthar]] that deals with aberrismas. See [[straddle primes]] for aberrismas equated to 1/1 without being tempered out.

Ground's '''aberrismic thesis''' is that intervals an audible distance apart can be broadly used together in the same scale framework while merely registering as detunings of the same interval. {{adv|One way to operationalize this thesis into a scientific hypothesis: In a specific test case, trained and untrained 12edo listeners may notice aberrismic steps in a 27edo blackdye melody (against a control 12edo melody) but consider them to correspond to the same diatonic degree. To our knowledge this hasn't been scientifically tested yet.}} Straddle theory applies the thesis to definite ratios, whereas in the original aberrismic scales, it's applied to diatonic scale degrees. Commas have been described as a type of unison in other contexts, but rarely as distinct steps vital to the structure of a scale, or as intervals that are represented by the same ratio. An aberrisma is categorically a unison but doesn't sound like one when isolated, which represents both observed RTT commas and the difference between straddled intervals; it is a unison widened into a melodic step. Aberrismic theory is a collection of the effects of applying the aberrismic thesis to scale theory and RTT.

The aberrisma is used as one of the parameters in constructing an aberrismic scale, a type of ternary scale. For example, blackdye is a 10-note aberrismic superset of the 7-note nicetone, but with a more distinctive set of three step sizes and added opportunities to avoid pythagorean and wolf intervals. Aberrismas may also appear in MOS scales, such as Garibaldi[17]. Superpyth[12] is a good example of the distinction between interval function and size. The diatonic semitone, a deflated 256/243, is equated to the inflated 81/80. Despite being the same size, the former represents a narrow semitone, the latter is an aberrisma, and a stack of the two is a classic semitone.

== The "why" of aberrismic theory ==
=== Adding comma steps to Pyth diatonic ===
81/80 and 64/63 are the canonical choices for 2.3.5 and 2.3.7 formal commas for modifications to Pythagorean (2.3) JI ratios — 81/80 separates 5/4 from 81/64, 10/9 from 9/8, and so on; and 64/63 separates 7/4 from 16/9, 9/7 from 81/64, and so on. Aberrismic theory asks: what if we made 81/80 or 64/63 into scale steps, so that we can use both of the intervals separated by the formal comma in one scale? Indeed, doing this to 2.3 diatonic to make a ternary scale, in a way that best preserves the fifth-generated structure, results in (2.3.5) blackdye and (2.3.7) diasem, respectively.

==== Example: Blackdye ====
The Zarlino diatonic is chiral — there are two different, equally valid second degrees of the Ionian mode. Both are useful, as the sharp one forms a perfect fifth with the fifth degree but a wolf fifth with the sixth degree, and the flat one forms a perfect fifth with the sixth degree but a wolf fifth with the fifth degree.
[[File:Blackdye.png|thumb|510x510px|The construction of blackdye from Zarlino diatonic]]
One way to make it achiral is to temper out 81/80, the difference between these two steps, resulting in [[Meantone]] diatonic; intuitively this requires flattening the fifth and sharpening the sixth somewhat. However, an alternative way, if you wish to observe 81/80 or to use just intonation, is to include both varieties of whole tone over the unison, treating 81/80 as a melodic step between them. This can be thought of as dividing up a 9/8 into a 10/9 and an 81/80. It is then reasonable to extend this action to all instances of 9/8 in the scale (as, for instance, the Didymic diatonic has 27/16 as opposed to 5/3). The result is a 10-note ternary scale called '''blackdye'''.

=== Stylistic compositional features for aberrismic theory ===
This section will attempt to describe the principles and stylistic features of a specific style of music that justify using aberrismic scales in a composition. It is not an attempt to present aberrismic theory as absolute truth.
* A style of music that is melodic and heavy in modulations benefits from
** Multiple step sizes for melodic interest, for example diesis-sized steps that are below conventional semitones, specifically ones large enough to be melodically distinct but small enough to represent intonational changes.
** A set of modulatory intervals, including fifths.
** A system that allows unlimited modulation.
* It is widely agreed that lower primes are more robust to detuning. Hence for approximating JI with edos, we use lower prime temperaments, and which also represent either 81/80 or 64/63 steps for greater accuracy.
The above suggests temperaments, in particular edos, that use tempered lower primes, and edos large enough to have small diesis-sized steps. In the context of fifth-based modulation, scales also benefit from having offset arcs of fifths. One simple way to have this is to detemper MOS scales into ternary scales with an additional smaller melodic step size, which have a generator arc with fifths or a generator arc that stacks to fifths via a detempered generator chain.

{{UserTag|g_|Ground|7766ff|I assert that ~40¢ is the ideal point between "categorical unison" and "clear step"; context pushes it one way or the other, like in 27edo Superpyth diatonic and blackdye.}}

== List of aberrismic scales ==
* {{Adv|"GS(...)[n]" is [[generator sequence]] notation.}}
* {{adv|"subst ax(bycz)" denotes [[MOS substitution]].}}
* {{adv|"Almost" a cross-set means that one or two notes may be missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}
* {{adv|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}
=== Quasi-diatonic aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!|pinedye / dia1s (5L2m1s) {{adv|{{nowrap|subst 5L(2m1s)}}}}
||1sC: LLsLLmLm 1sR: LLmLLmLs 1sL: LLmLLsLm
||2.3.5 [L, m, s] = [10/9, 27/25, 81/80]
||{{adv|GS(3/2)[3] and GS(10/9)[3]}}
||1sC has 4 fifths and 1sR/1sL have 5
|-
!class="thl"|diasem / dia2s (5L2m2s) {{adv|{{nowrap|subst 5L(2m2s)}}}}
||2sR: LmLsLmLsL 2sL: LsLmLsLmL
||2.3.7 [L, m, s] = [9/8, 28/27, 64/63]
||{{adv|GS(3/2)[5] and 7/6}}
||Aggregate generator is 4/3, thus has fifth arcs of 5 and 4 notes respectively.
''See also: [[Chthonic harmony#Diasem|Diasem]]''
|-
!class="thl"|blackdye / dia3s (5L2m3s) {{adv|{{nowrap|subst 5L(2m3s)}}}}
||sLmLsLmLsL
||2.3.5 [L, m, s] = [10/9, 16/15, 81/80]
||{{adv|''GS(3/2)[5] and 10/9''}}
||Two interleaved 3-limit pentatonics
''See also: [[10-form#Blackdye|Blackdye]]''
|-
!|diaslen / dia4s (5L2m4s) {{adv|{{nowrap|subst 5L(2m4s)}}}}
||4sC: LmLsLsLmLss 4sR: LsLmLsLsLms 4sL: LsLsLmLsLsm
||2.3.7 [L, m, s] = [9/8, 49/48, 64/63]
||{{adv|GS(3/2)[4] and GS(8/7)[3]}}
||Fifth arcs with 4 notes, 4 notes, and 3 notes, with offset 8/7. Tempered to the slentonic {5L6s) MOS by [[Slendric]]. {{adv|Detempered Slendric[11] generator structure, aggregate generator is 3/2}}
|-
!|diachrome / chromedye / dia5s (5L2m5s)
||5sC: LsLsLmsLsLsm {{adv|{{nowrap|(subst 2m(5L5s))}}}} 5sR: LmsLsLsLmsLs 5sL: LsLsLsmLsLsm
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 256/243, 81/80]
||{{adv|5sC: ''GS(3/2)[6] and 40/27''}}
||Fifth-generated but with a 6-step offset
|-
!|whitedye / dia7s (5L2m7s) {{adv|{{nowrap|subst 7s(5L2m)}}}}
||LsLsLsmsLsLsms
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 28/27, 81/80]
||{{adv|''GS(3/2)[7] and 81/80''}}
||Two interleaved diatonics
|}
See [[Ground's composition theory#Quasi-diatonic scales]] for more tunings of diasem and blackdye.

=== Other aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI/[[erac]] interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!class="thl"|[[penslen]] / slen5m (5L5m6s) {{adv|{{nowrap|subst 6s(5L5m)}}}}
||LmsLmsLsmLsmLsms
||2.3.5.7.11[41 & 46] [L, m, s] = [12/11, 33/32, 64/63]
||{{adv|''GS(8/7)[8] and 11/8''}}
|| Has two aberrisma sizes, s and m.
|-
!|prejubilic / citro3s (4L2m3s) {{adv|{{nowrap|subst 2m(4L3s)}}}}
||C: LLsmLsLms R: LmLsLmsLs L: LmLsLsmLs
||2.5.7 [L, m, s] = [28/25, 35/32, 50/49]
||{{adv|GS(5/4)[3] and GS(7/5)[3] (exact for C)}}
||Didacus tempering makes L = m + s.
|-
!|arm5s (7L2m5s) {{adv|{{nowrap|subst 7L(2m5s)}}}}
||LmLsLsLmLsLsLs
||2.x<3.5.7.11.13[37edo] (4:2:1)
||{{adv|''GS(<<3/2)[7] and 14/13''}}
||An interleaving of two antidiatonic scales.
|-
!|mosh3s (3L4m3s) {{adv|{{nowrap|subst 4m(3L3s)}}}}
||LmsLmsmLsm
||2.x<3.7.11.13[37edo] (5:4:2)
||{{adv|''GS(16/13)[5] and 11/8''}}
||
|-
!|smi2s (4L3m2s) {{adv|{{nowrap|subst 2s(4L3m)}}}}
||C: LLmsLmLsm R: LmLmsLmLs L: LmLsLmLsm
||2.9.7.11.17[46edo] (8:4:1)
||{{adv|GS(17/14)[3] and GS(11/8)[3] (exact for C)}}
||
|-
!|sleneiro / oneiro3s (5L3m3s) {{adv|{{nowrap|subst 5L(3m3s)}}}}
||R: LmLsLmLsLms L: LsLmLsLmLsm
||2.(13:15:17:19)[5 & 18 & 44]
||{{adv|GS(13:15:17)}}
||An [[odd-regular]] aberrismic version of [[oneirotonic]].
|}

=== Systematic naming ===
Basic systematic names for aberrismic scales are of the form

[mos_prefix]n[added_step_size] (e.g. dia2s for diasem).

Any systematic name can be used for a scale as long as the scale satisfies the deletion-MOS subcondition for the added step size.

This is subject to change as aberrismic theory nomenclature is updated in the future.

== Notation ==
The [[generator gronut]] is an aberrismic extension of the circle of fifths.

=== Quasi-diatonic ===
Quasi-diatonic aberrismic notation restricts to [[diatonic notation]] on the tempered 3-limit.

Aberrismic/straddle-prime accidentals:
* Plus / Minus +/- : These tune a note sharp or flat by a small aberrisma. They reference Johnston notation because 81/80 is a common aberrisma, but they can also represent 64/63 or any other interval of similar function. 
* Duplus / Duminus ≠/= : Short for ++/--, most often representing 36/35~33/32~1053/1024, which is the large aberrisma in scales like penslen, or two small aberrismas in Akea temperament. Of all options, this set of characters is the easiest to type, looks the best in various fonts, and is least likely to be confused for the similar semisharp accidental (although they happen to represent the same size of interval).
* [[Erac|Eracs]] may be used to represent the inflating of commas typically found in aberrismic scales, although they represent a specific unit of error.

== Aberrismic theory and RTT ==
Aberrismic theory often applies RTT to ternary LCJI scales with comma steps. Certain scales with aberrismas may thus be endowed with JI interpretations via [[RTT]] temperaments, which may be used in suitable [[equal temperament]]s. Under Ground's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become a [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers out neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]]. Tempering is important in aberrismic theory as a way to improve the function of commas (frequently [[81/80]] or [[64/63]]) as aberrismas in ternary LCJI scales by tempering them larger than just.

At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or [[Ultrapyth]] temperament.

There are two choices involved in interpreting a given ternary scale, namely the choice of temperament and the choice of where to map the scale steps. The assignment of scale steps to tempered intervals is chosen to improve coverage of important LCJI intervals.

=== Example: Blackdye ===
The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth respectively.
* ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists an exact JI tuning.
* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one. Ground once termed the tuning of blackdye that makes aberrisma-altered Pyth thirds 13/11 and 14/11 ''Flutterpyth blackdye''.

{| class="wikitable right-2 right-3 right-4 right-5"
|+ style="font-size: 105%;" | Blackdye intervals in two temperaments
|-
! Interval class
! Sizes
! Untempered 2.3.5
! 2.3.7.11.13 Flutterpyth (extended to 13-limit Ultrapyth)
|-
! 1-step
| s m L
| 81/80 16/15 10/9
| 143/140 22/21 160/143
|-
! 2-step
| L + s L + m
| 9/8 32/27
| 8/7, 9/8 7/6
|-
! 3-step
| L + 2s L + m + s 2L + s 2L + m
| 729/640 6/5 5/4 320/243
| 7/6 13/11 14/11 13/10
|-
! 4-step
| 2L + 2s 2L + m + s
| 81/64 4/3
| 13/10 4/3
|-
! 5-step
| 2L + m + 2s 2L + 2m + s 3L + 2s 3L + m + s
| 27/20 64/45 45/32 40/27
| 66/49 11/8 16/11 49/33
|-
! 6-step
| 3L + m + 2s 3L + 2m + s
| 3/2 128/81
| 3/2 20/13
|-
! 7-step
| 3L + m + 3s 3L + 2m + 2s 4L + m + 2s 4L + 2m + s
| 243/160 8/5 5/3 1280/729
| 20/13 11/7 22/13 12/7
|-
! 8-step
| 4L + m + 3s 4L + 2m + 2s
| 27/16 16/9
| 12/7 7/4, 16/9
|-
! 9-step
| 5L + 2m + s 5L + m + 2s 4L + 2m + 2s
| 9/5 15/8 160/81
| 143/80 21/11 280/143
|}

== Glossary ==
* '''Aberration scale''': A scale made by interleaving aberrismas into a binary scale and stretching or compressing, usually a [[MOS substitution]] scale of type {{nowrap|[a+b+1]s(aLbm)}} (compression, called '''tractaberrated''') or {{nowrap|[a+b-1]s(aLbm)}} (stretching, called '''tensaberrated'''). For example, sLsmsLsLsLsmsLs is an aberration scale made from diatonic (a MOS substitution scale of type 8s(5L2m)), also called trackdye.
* '''Aberrisma''': The smallest interval region that melodically sounds like a step.
* '''Magnitone''': The melodic function of L + s in quasi-diatonic aberrismic scales.
* '''Monotone-MOS''': A ternary scale is ''monotone-MOS'' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy a monotone-MOS subcondition''. For example, diasem (LmLsLmLsL) satisfies all three monotone-MOS subconditions, but blackdye (sLmLsLmLsL) satisfies only the m = s and s = 0 monotone-MOS subconditions. An aberrismic scale is required to satisfy the s = 0 monotone-MOS subcondition.
* '''Solitone''': The melodic function of the L step in quasi-diatonic aberrismic scales.
* '''Subaberrisma''': A step so small (smaller than the typical limit for an aberrisma) that its status as a melodic step is unclear.

== Extension to higher ranks ==
Aberrismic theory is typically concerned with ternary scales, especially those with two chains of generators of the same length or differing by one, meaning that they have a [[GS]] with only two intervals. This is because they are not much harder to navigate than an MOS while offering significantly more flexibility.

{{UserTag|g_|Ground|7766ff|I propose that we call this type of scale '''bicatenary'''.}}

However, this is often not enough to accurately represent a larger JI subgroup. Portent penslen (5L5m6s) is a somewhat unique counterexample, being bicatenary yet microtempered in the 11-limit. The solution is to add more step sizes while maintaining as much lower-rank structure as possible. For example, while penslen is found in edos like 41 and 46, the equivalent in the similarly LCJI-accurate 53 and 58 is 5L2m3s4t, a quaternary subset of Buzzard[28] with a JI tuning of 35/32 : 21/20 : 36/35 : 64/63. [[Ground's composition theory#Interval logic deviation theory|ILD]] is a simple way to access notes outside of a scale with a higher rank.

A common tempering of blackdye involves a sharper 3 to significantly inflate 81/80, both for melodic utility and to equate 27/20 to a superfourth like 15/11 or 11/8. It also becomes natural to temper out 64/63. Possibly the most common ratio representation of an aberrisma is 36/35, but few ternary scales use it without tempering out 81/80 or 64/63.

(81/80)^2 = 43¢ is notably in the middle of the usual aberrisma size range as well. This does not exist in blackdye, but becomes accessible in certain variants of 5L2m8s as well as numerous quaternary scales with even more options for available intervals.

== Compositional examples ==
Some compositional snippets using aberrismic scales:

* The Art of It makes almost exclusive use of 31edo diasem: [[File:A New Dusk-02 The Art of It.mp3]]
* A fugue using aberrismic scales: [[File:Inthar - Fugue in 32edo and 33edo.mp3]]
* A 34edo blackdye fugue exposition: [[File:Blackdye-fugue-expo.mp3]]

== External links ==
* [https://turbofishcrow.github.io/tern Tern: aberrismic-focused ternary scale analysis]
{{cat|
Terms
Aberrismic terms
Ternary scales
}}

Oneirotonic

2026-11-04T03:01:49Z

Inthar: /* "Corvic" */

'''Oneirotonic''' (often shortened to '''oneiro''') is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.

=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (my Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
==== Table of oneirotonic tunings ====
{| class="wikitable"
|+Oneirotonic Tunings, Edo ≤ 53, Cents
| colspan="2" |Range:
! colspan="6" |Corvic (Ammonite)
! colspan="4" |Corvic (Petrtri Extension) (d3s within ~15¢ of 5/4)
! colspan="9" |A-strad (m2s within ~10¢ of 7/6)
! colspan="7" |Buzzard (highlighted diatonic fifth)
|-
| colspan="2" |Mediant Depth:
|
|¦¦¦
|<nowiki>¦¦|</nowiki>
|¦¦
|<nowiki>¦|</nowiki>
|¦¦
|¦
|<nowiki>¦|</nowiki>
|¦¦
| colspan="2" |<nowiki>|</nowiki>
|¦¦
|<nowiki>¦|</nowiki>
|¦¦
|¦
|¦¦
|<nowiki>¦|</nowiki>
|<nowiki>¦¦|</nowiki>
| colspan="2" |¦¦
|<nowiki>¦¦|</nowiki>
|¦¦¦
|<nowiki>¦¦¦|</nowiki>
|¦¦¦¦
|<nowiki>¦¦¦¦|</nowiki>
|
|-
|Interval
|Gens
!3\8
!20\53
!17\45
!14\37
!11\29
!19\50
!8\21
!13\34
!18\47
! colspan="2" |5\13
!17\44
!12\31
!19\49
!7\18
!16\41
!9\23
!20\51
! colspan="2" |11\28
!13\33
!15\38
!17\43
!19\48
!21\53
!2\5
|-
! style="white-space:nowrap;" |Diminished 3-Step
! -7
|450
|430
|427
|422
|414
|408
| class="thl" |'''400'''
| class="thl" |'''388'''
| class="thl" |'''383'''
| class="thl" colspan="2" |'''369'''
|355
|348
|343
|333
|322
|313
|306
| colspan="2" |300
|291
|284
|279
|275
|272
|240
|-
! style="white-space:nowrap;" |Minor 6-Step
! -6
|900
|883
|880
|876
|869
|864
|857
|847
|843
| colspan="2" |831
|818
|813
|808
|800
|790
|783
|776
| colspan="2" |771
|764
|758
|753
|750
|747
|720
|-
! style="white-space:nowrap;" |Minor 1-Step
! -5
|150
|136
|133
|130
|124
|120
|114
|106
|102
| colspan="2" |92
|82
|77
|73
|67
|59
|52
|47
| colspan="2" |43
|36
|32
|28
|25
|23
|0
|-
! style="white-space:nowrap;" |Minor 4-Step
! -4
|600
|589
|587
|584
|579
|576
|571
|565
|562
| colspan="2" |554
|545
|542
|539
|533
|527
|522
|518
| colspan="2" |514
|509
|505
|502
|500
|498
|480
|-
! style="white-space:nowrap;" |Minor 7-Step
! -3
|1050
|1042
|1040
|1038
|1034
|1032
|1029
|1024
|1021
| colspan="2" |1015
|1009
|1006
|1004
|1000
|995
|991
|988
| colspan="2" |986
|982
|979
|977
|975
|974
|960
|-
! style="white-space:nowrap;" |Minor 2-Step
! -2
|300
|294
|293
|292
|290
|288
|286
|282
|281
| colspan="2" class="acc0" |'''277'''
| class="acc0" |'''273'''
| class="acc0" |'''271'''
| class="acc0" |'''269'''
| class="acc0" |'''267'''
| class="acc0" |'''263'''
| class="acc0" |'''261'''
| class="acc0" |'''259'''
| colspan="2" class="acc0" |'''257'''
|255
|253
|251
|250
|249
|240
|-
! style="white-space:nowrap;" |Perfect 5-Step
! -1
|750
|747
|747
|746
|745
|744
|743
|741
|740
| colspan="2" |738
|736
|735
|735
|733
|732
|730
|729
| colspan="2" |729
|727
|726
|726
|725
|725
|720
|-
! style="white-space:nowrap;" |Perfect 0-Step
!0
|0
|0
|0
|0
|0
|0
|0
|0
|0
| colspan="2" |0
|0
|0
|0
|0
|0
|0
|0
| colspan="2" |0
|0
|0
|0
|0
|0
|0
|-
! style="white-space:nowrap;" |Perfect 3-Step
!1
|450
|453
|453
|454
|455
|456
|457
|459
|460
| colspan="2" |462
|464
|465
|465
|467
|468
|470
|471
| colspan="2" |471
|473
|474
|474
|475
|475
|480
|-
! style="white-space:nowrap;" |Major 6-Step
!2
|900
|906
|907
|908
|910
|912
|914
|918
|919
| colspan="2" |923
|927
|929
|931
|933
|937
|939
|941
| colspan="2" |943
|945
|947
|949
|950
|951
|960
|-
! style="white-space:nowrap;" |Major 1-Step
!3
|150
|158
|160
|162
|166
|168
|171
|176
|179
| colspan="2" |185
|191
|194
|196
|200
|205
|209
|212
| colspan="2" |214
|218
|221
|223
|225
|226
|240
|-
! style="white-space:nowrap;" |Major 4-Step
!4
|600
|611
|613
|616
|621
|624
|629
|635
|638
| colspan="2" |646
|655
|658
|661
|667
|673
|678
|682
| colspan="2" class="acc1" |'''686'''
| class="acc1" |'''691'''
| class="acc1" |'''695'''
| class="acc1" |'''698'''
| class="acc1" |'''700'''
| class="acc1" |'''702'''
| class="acc1" |'''720'''
|-
! style="white-space:nowrap;" |Major 7-Step
!5
|1050
|1064
|1067
|1070
|1076
|1080
|1086
|1094
|1098
| colspan="2" |1108
|1118
|1123
|1127
|1133
|1141
|1148
|1153
| colspan="2" |1157
|1164
|1168
|1172
|1175
|1177
|0
|-
! style="white-space:nowrap;" |Major 2-Step
!6
|300
|317
|320
|324
|331
|336
|343
|353
|357
| colspan="2" |369
|382
|387
|392
|400
|410
|417
|424
| colspan="2" |429
|436
|442
|447
|450
|453
|480
|-
! style="white-space:nowrap;" |Augmented 5-Step
!7
|750
|770
|773
|778
|786
|792
|800
|812
|817
| colspan="2" |831
|845
|852
|857
|867
|878
|887
|894
| colspan="2" |900
|909
|916
|921
|925
|928
|960
|}
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneirotonic 3-step generator in frequency space (splitting the interval into an [[isodifferential]] chord). One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneirotonic tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo are some tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Isodifferential

2026-11-03T17:03:19Z

Inthar: Changed redirect target from Delta-rational to Delta-rational chord

#redirect [[Delta-rational chord]]

Isodifferential

2026-11-03T17:03:13Z

Inthar: Redirected page to Delta-rational

#redirect [[Delta-rational]]

Oneirotonic

2026-11-03T17:02:57Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' (often shortened to '''oneiro''') is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneirotonic 3-step generator in frequency space (splitting the interval into an [[isodifferential]] chord). One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneirotonic tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo are some tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T16:59:55Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' (often shortened to '''oneiro''') is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneirotonic 3-step generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneirotonic tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo are some tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T16:59:08Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' (often shortened to '''oneiro''') is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneirotonic 3-step generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneirotonic tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T16:58:39Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' (often shortened to '''oneiro''') is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneirotonic naiadic-to-subfourth generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneirotonic tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T16:57:46Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' (often shortened to '''oneiro''') is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneirotonic subfourth generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneirotonic tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneiro

2026-11-03T16:57:15Z

Inthar: Redirected page to Oneirotonic

#redirect [[oneirotonic]]

Oneirotonic

2026-11-03T16:56:57Z

Inthar:

'''Oneirotonic''' (often shortened to '''oneiro''') is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneiro subfourth generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T15:41:39Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneiro subfourth generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate edo tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

MOS substitution

2026-11-03T09:00:16Z

Inthar:

'''MOS substitution''' is a procedure for obtaining a ternary (3 step sizes) scale from two [[MOS]] patterns. It consists of taking one MOS pattern (called the ''template MOS''), choosing a step size, and overwriting all instances of that step size using the step pattern of another MOS pattern (called the ''filling MOS''), step size for step size. A MOS substitution scale may have any combination of step sizes and is meant as a way to somewhat evenly distribute three step sizes, even when "perfectly" even distribution (in the sense of every step size occupying "maximally even" MOS positions, the best approximation of an equal division of a circle in a more dense equal division) may be impossible.

== Convention ==
MOS substitution scales are described using the notation "subst a'''x'''(b'''y'''c'''z''')" or just "a'''x'''(b'''y'''c'''z''')", called the scale's ''(MOS substitution) type''. Here the template MOS is a'''x'''(b+c)'''X''' where '''X''' is the slot letter, and the filling MOS is (a mode of) b'''y'''c'''z'''. A specific MOS substitution scale may be denoted {{nowrap|template_MOS_with_slot_letter_X(filling_MOS)}}.

{| class="wikitable"
|+ style="font-size: 105%;" | The three subst 2'''L'''(1'''m'''2'''s''') scales
|-
! rowspan="2" | [[Simplified UDP]] for filling MOS
! rowspan="2" | Filling MOS
! colspan="2" | Step pattern
! rowspan="2" | Denoted as
|-
! Template MOS:
| <code>LXLXX</code>
|-
| 2{{pipe}}0
| style="text-align: right;" | <code>mss</code>
| colspan="2" style="text-align: right;" | <code>LmLss</code>
| LXLXX(mss)
|-
| 1{{pipe}}1
| style="text-align: right;" | <code>sms</code>
| colspan="2" style="text-align: right;" | <code>LsLms</code>
| LXLXX(sms)
|-
| 0{{pipe}}2
| style="text-align: right;" | <code>ssm</code>
| colspan="2" style="text-align: right;" | <code>LsLsm</code>
| LXLXX(ssm)
|}

== Examples ==
=== Simple examples ===
Many familiar ternary scales can be constructed as MOS substitutions.

LMsLMLs = XXsXXXs(LMLML), LXXLXLX(MsMs), XMXXMXX(LsLLs)

LLmLLLs = LLXLLLX(ms)

LMsLM = XXsXX(LMLM)

=== Aberrismic scales ===
Diasem: LmLsLmLsL = LXLXLXLXL(msms)

Blackdye: sLmLsLmLsL = XLXLXLXLXL(smsms)

The three standard [[diaslen]] scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via MOS substitution, giving [[generator sequence]]s for the three scales:

{| class="wikitable"
|+ diaslen scales as MOS substitution scales
|-
! rowspan="2" | chirality
! rowspan="2" | filling MOS
! colspan="2" | step pattern
! colspan="2" | [[generator sequence]]
|-
!| template MOS:
|| <code>LXLXLXLXLXX</code>
!| intvl. class of gen.:
|| 2-steps
|-
| 4sC || <code>mssmss</code>
| colspan="2" style="text-align:right;" | <code>LmLsLsLmLss</code>
| colspan="2" | GS(L+m, L+s, L+s)
|-
| 4sR || <code>smssms</code>
| colspan="2" style="text-align:right;" | <code>LsLmLsLsLms</code>
| colspan="2" | GS(L+s, L+m, L+s)
|-
| 4sL || <code>ssmssm</code>
| colspan="2" style="text-align:right;" | <code>LsLsLmLsLsm</code>
| colspan="2" | GS(L+s, L+s, L+m)
|}

For more examples, see [[Aberrisma#List of aberrismic scales]].

=== Some classes of MOS substitutions ===
* Ternary [[Interleaving|interleaved]]-MOS scales such as blackdye (5L2m3s, sLmLsLmLsL) and whitedye (5L2m7s, sLsLsLsmsLsLsm) are MOS substitution scales. In those particular examples, the template MOS is of the form ky kz.
* {{adv|MOS substitution scales where the ''filling'' MOS is of the form ky kz are of the following two types:}}
** {{adv|''Odd-regular'' MV3 scales are subst ax(ky kz){{angbr|something}} scales where a is odd. Such scales come in a chiral pair.}}
*** {{adv|Example: Diasem (5L(2m2s)) has chiral variants LmLsLmLsL and LsLmLsLmL.}}
** {{adv|''Even-regular'' MV3 scales (such as 5sC diachrome) are subst ax(ky kz){{angbr|something}} scales where a is even and gcd(a, k) {{=}} 1. These scales are achiral. In this case, "ax(ky kz)" specifies the scale uniquely.}}
*** {{adv|Example: 5sC diachrome is a subst 2m(5L5s): LsLsLmsLsLsm.}}
* {{adv|A ternary scale is always a MOS substitution scale if the L {{=}} m and s {{=}} 0 [[monotone-MOS property|monotone-MOS]] properties are satisfied.}}

== Properties ==
If the template MOS is single-period, the MOS substitution scale has a [[generator sequence]] using only two distinct intervals. The length of this GS is the length of the period of the filling MOS. Hence if you want a ''short'' generator sequence, you should use a multiperiod filling MOS, like for diaslen.

=== Parallelogram substring scales ===
MOS substitution scales in general still have somewhat messy pitch-class lattices (or they may not have one at all, due to the equave being equally divided). However, some have nicer lattices in the sense that they are [[parallelogram substring scale|substrings of a row-by-row parallelogram traversal]]. That is, the pitch classes form a parallelogram {{adv|(a rectangle under some basis)}}
# with all rows traversed in the same direction
# with some number (possibly zero) of full middle rows
# the first row is not required to be full but must be a suffix of a full row
# the last row is not required to be full but must be a prefix of a full row.
We call such scales "parallelogram substring scales". Not all ternary parallelogram substring scales are MOS substitution scales. However, fully parallelogram (PS scales with full first and last rows) ternary scales are always MOS substitution scales.

{{adv|If the template MOS is single-period and the number of slot letters in a template MOS's generator is a generator interval class of the filling MOS (e.g. diaslen), the MOS substitution scale is a parallelogram substring scale. What other MOS substitution scales satisfy the parallelogram substring property is still being investigated.}}
{{cat|
Ternary scales
Scale construction
}}

MOS substitution

2026-11-03T08:37:13Z

Inthar:

'''MOS substitution''' is a procedure for obtaining a ternary (3 step sizes) scale from two [[MOS]] patterns. It consists of taking one MOS pattern (called the ''template MOS''), choosing a step size, and overwriting all instances of that step size using the step pattern of another MOS pattern (called the ''filling MOS''), step size for step size. A MOS substitution scale may have any combination of step sizes and is meant as a way to somewhat evenly distribute three step sizes, even when "perfectly" even distribution (in the sense of every step size occupying "maximally even" MOS positions) may be impossible.

== Convention ==
MOS substitution scales are described using the notation "subst a'''x'''(b'''y'''c'''z''')" or just "a'''x'''(b'''y'''c'''z''')", called the scale's ''(MOS substitution) type''. Here the template MOS is a'''x'''(b+c)'''X''' where '''X''' is the slot letter, and the filling MOS is (a mode of) b'''y'''c'''z'''. A specific MOS substitution scale may be denoted {{nowrap|template_MOS_with_slot_letter_X(filling_MOS)}}.

{| class="wikitable"
|+ style="font-size: 105%;" | The three subst 2'''L'''(1'''m'''2'''s''') scales
|-
! rowspan="2" | [[Simplified UDP]] for filling MOS
! rowspan="2" | Filling MOS
! colspan="2" | Step pattern
! rowspan="2" | Denoted as
|-
! Template MOS:
| <code>LXLXX</code>
|-
| 2{{pipe}}0
| style="text-align: right;" | <code>mss</code>
| colspan="2" style="text-align: right;" | <code>LmLss</code>
| LXLXX(mss)
|-
| 1{{pipe}}1
| style="text-align: right;" | <code>sms</code>
| colspan="2" style="text-align: right;" | <code>LsLms</code>
| LXLXX(sms)
|-
| 0{{pipe}}2
| style="text-align: right;" | <code>ssm</code>
| colspan="2" style="text-align: right;" | <code>LsLsm</code>
| LXLXX(ssm)
|}

== Examples ==
=== Simple examples ===
Many familiar ternary scales can be constructed as MOS substitutions.

LMsLMLs = XXsXXXs(LMLML), LXXLXLX(MsMs), XMXXMXX(LsLLs)

LLmLLLs = LLXLLLX(ms)

LMsLM = XXsXX(LMLM)

=== Aberrismic scales ===
Diasem: LmLsLmLsL = LXLXLXLXL(msms)

Blackdye: sLmLsLmLsL = XLXLXLXLXL(smsms)

The three standard [[diaslen]] scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via MOS substitution, giving [[generator sequence]]s for the three scales:

{| class="wikitable"
|+ diaslen scales as MOS substitution scales
|-
! rowspan="2" | chirality
! rowspan="2" | filling MOS
! colspan="2" | step pattern
! colspan="2" | [[generator sequence]]
|-
!| template MOS:
|| <code>LXLXLXLXLXX</code>
!| intvl. class of gen.:
|| 2-steps
|-
| 4sC || <code>mssmss</code>
| colspan="2" style="text-align:right;" | <code>LmLsLsLmLss</code>
| colspan="2" | GS(L+m, L+s, L+s)
|-
| 4sR || <code>smssms</code>
| colspan="2" style="text-align:right;" | <code>LsLmLsLsLms</code>
| colspan="2" | GS(L+s, L+m, L+s)
|-
| 4sL || <code>ssmssm</code>
| colspan="2" style="text-align:right;" | <code>LsLsLmLsLsm</code>
| colspan="2" | GS(L+s, L+s, L+m)
|}

For more examples, see [[Aberrisma#List of aberrismic scales]].

=== Some classes of MOS substitutions ===
* Ternary [[Interleaving|interleaved]]-MOS scales such as blackdye (5L2m3s, sLmLsLmLsL) and whitedye (5L2m7s, sLsLsLsmsLsLsm) are MOS substitution scales. In those particular examples, the template MOS is of the form ky kz.
* {{adv|MOS substitution scales where the ''filling'' MOS is of the form ky kz are of the following two types:}}
** {{adv|''Odd-regular'' MV3 scales are subst ax(ky kz){{angbr|something}} scales where a is odd. Such scales come in a chiral pair.}}
*** {{adv|Example: Diasem (5L(2m2s)) has chiral variants LmLsLmLsL and LsLmLsLmL.}}
** {{adv|''Even-regular'' MV3 scales (such as 5sC diachrome) are subst ax(ky kz){{angbr|something}} scales where a is even and gcd(a, k) {{=}} 1. These scales are achiral. In this case, "ax(ky kz)" specifies the scale uniquely.}}
*** {{adv|Example: 5sC diachrome is a subst 2m(5L5s): LsLsLmsLsLsm.}}
* {{adv|A ternary scale is always a MOS substitution scale if the L {{=}} m and s {{=}} 0 [[monotone-MOS property|monotone-MOS]] properties are satisfied.}}

== Properties ==
If the template MOS is single-period, the MOS substitution scale has a [[generator sequence]] using only two distinct intervals. The length of this GS is the length of the period of the filling MOS. Hence if you want a ''short'' generator sequence, you should use a multiperiod filling MOS, like for diaslen.

=== Parallelogram substring scales ===
MOS substitution scales in general still have somewhat messy pitch-class lattices (or they may not have one at all, due to the equave being equally divided). However, some have nicer lattices in the sense that they are [[parallelogram substring scale|substrings of a row-by-row parallelogram traversal]]. That is, the pitch classes form a parallelogram {{adv|(a rectangle under some basis)}}
# with all rows traversed in the same direction
# with some number (possibly zero) of full middle rows
# the first row is not required to be full but must be a suffix of a full row
# the last row is not required to be full but must be a prefix of a full row.
We call such scales "parallelogram substring scales". Not all ternary parallelogram substring scales are MOS substitution scales. However, fully parallelogram (PS scales with full first and last rows) ternary scales are always MOS substitution scales.

{{adv|If the template MOS is single-period and the number of slot letters in a template MOS's generator is a generator interval class of the filling MOS (e.g. diaslen), the MOS substitution scale is a parallelogram substring scale. What other MOS substitution scales satisfy the parallelogram substring property is still being investigated.}}
{{cat|
Ternary scales
Scale construction
}}

Oneirotonic

2026-11-03T08:18:57Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneiro subfourth generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T08:18:00Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by halving a JI oneiro generator in frequency space. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T08:17:34Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|JI interpretations for sleneiro can be created by arithmetically dividing a JI oneiro generator into two. One obvious example is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T07:54:32Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 50edo and 74edo have accurate tunings of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T07:52:41Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45];}} 74edo has an accurate tuning of this temperament.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T07:48:11Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23)[21 & 29 & 45].}}
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Generator sequence

2026-11-03T07:46:27Z

Inthar:

{{Expert}}

A '''generator sequence''' ('''GS''') is a cyclically repeating sequence of stacked intervals called ''generators''. A GS can be denoted:

GS(interval1, interval2, interval3, ..., intervaln),

which means: stack interval2 on top of interval1, interval3 on top of interval2, etc. up to intervaln, then stack interval1 again and repeat.

In the simplest case, GS(interval) denotes stacking that interval repeatedly. For example, Pythagorean diatonic is GS(3/2)[7].

The ''aggregate generator'' is the stack of all intervals in the GS.

This wiki adopts a convention where an enumerated chord can be used instead for part or whole of the argument, where the chord's steps are generators, for example writing [[Ptolemy's intense diatonic]] as GS(4:5:6)[7], which is abbreviation for GS(5/4, 6/5)[7].

For example: GS(6:7:8) = GS(7/6, 8/7) means an alternating stack of 7/6 and 8/7 (where the first interval is 7/6). Like for temperaments, [n] can be used to mean "octave reduce at each step and stop stacking at n notes", so GS(7/6, 8/7)[9] denotes the 2.3.7 (right-hand) diasem scale. The aggregate generator is 4/3.

Generator sequences generalize [[MOS]] scales, and GSes are often used to create higher-rank scales.

{{Cat|Scale construction}}

Oneirotonic

2026-11-03T07:45:19Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is {{nowrap|[[GS]](13:15:17)[11]}} in the {{nowrap|2.(13:15:17)}} subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to {{nowrap|2.(13:15:17:19).}} The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is {{nowrap|2.(5:7:11:13:23:29)[21 & 29 & 45].}}
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T07:43:44Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range. The definitive high-accuracy interpretation for this scale is 2.(5:7:11:13:23:29)[21 & 29 & 45].
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T07:30:53Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup, which resembles Mothra A-Team. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings. {{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}

For something more resembling softer oneiro tunings we may consider GS(20:23:26), which is within the Corvic temperament range.
}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T07:18:33Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS subconditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T07:17:28Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
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I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

==== 5L3m3s quasi-oneirotonic ====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Aberrisma

2026-11-03T06:57:54Z

Inthar:

{{Proposed}}

An '''aberrisma''' is an interval representing some comma as an additional type of melodic step smaller than a semitone. Its name originates from the comparison of its sound to a chromatic aberration, with the -isma suffix often used for commas. Although they are typically between 20 and 55 cents (around 81/80 to half of 16/15) and often inflated commas about the size of a diesis, the aberrisma is a melodic function and not an interval size. Larger and smaller sizes can function as aberrismas depending on the scale tuning. '''Aberrismic theory''' is the subset of microtonal theory pioneered by [[User:Ground|Ground]] and [[User:Inthar|Inthar]] that deals with aberrismas. See [[straddle primes]] for aberrismas equated to 1/1 without being tempered out.

Ground's '''aberrismic hypothesis''' is that intervals an audible distance apart can be broadly used together in the same scale framework while merely registering as detunings of the same interval. {{adv|One way to operationalize this hypothesis: In a specific test case, trained and untrained 12edo listeners may notice aberrismic steps in a 27edo blackdye melody (against a control 12edo melody) but consider them to correspond to the same diatonic degree. To our knowledge this hasn't been scientifically tested yet.}} Straddle theory applies the hypothesis to definite ratios, whereas in the original aberrismic scales, it's applied to diatonic scale degrees. Commas have been described as a type of unison in other contexts, but rarely as distinct steps vital to the structure of a scale, or as intervals that are represented by the same ratio. An aberrisma is categorically a unison but doesn't sound like one when isolated, which represents both observed RTT commas and the difference between straddled intervals; it is a unison widened into a melodic step. Aberrismic theory is a collection of the effects of applying the aberrismic hypothesis to scale theory and RTT.

The aberrisma is used as one of the parameters in constructing an aberrismic scale, a type of ternary scale. For example, blackdye is a 10-note aberrismic superset of the 7-note nicetone, but with a more distinctive set of three step sizes and added opportunities to avoid pythagorean and wolf intervals. Aberrismas may also appear in MOS scales, such as Garibaldi[17]. Superpyth[12] is a good example of the distinction between interval function and size. The diatonic semitone, a deflated 256/243, is equated to the inflated 81/80. Despite being the same size, the former represents a narrow semitone, the latter is an aberrisma, and a stack of the two is a classic semitone.

== The "why" of aberrismic theory ==
=== Adding comma steps to Pyth diatonic ===
81/80 and 64/63 are the canonical choices for 2.3.5 and 2.3.7 formal commas for modifications to Pythagorean (2.3) JI ratios — 81/80 separates 5/4 from 81/64, 10/9 from 9/8, and so on; and 64/63 separates 7/4 from 16/9, 9/7 from 81/64, and so on. Aberrismic theory asks: what if we made 81/80 or 64/63 into scale steps, so that we can use both of the intervals separated by the formal comma in one scale? Indeed, doing this to 2.3 diatonic to make a ternary scale, in a way that best preserves the fifth-generated structure, results in (2.3.5) blackdye and (2.3.7) diasem, respectively.

==== Example: Blackdye ====
The Zarlino diatonic is chiral — there are two different, equally valid second degrees of the Ionian mode. Both are useful, as the sharp one forms a perfect fifth with the fifth degree but a wolf fifth with the sixth degree, and the flat one forms a perfect fifth with the sixth degree but a wolf fifth with the fifth degree.
[[File:Blackdye.png|thumb|510x510px|The construction of blackdye from Zarlino diatonic]]
One way to make it achiral is to temper out 81/80, the difference between these two steps, resulting in [[Meantone]] diatonic; intuitively this requires flattening the fifth and sharpening the sixth somewhat. However, an alternative way, if you wish to observe 81/80 or to use just intonation, is to include both varieties of whole tone over the unison, treating 81/80 as a melodic step between them. This can be thought of as dividing up a 9/8 into a 10/9 and an 81/80. It is then reasonable to extend this action to all instances of 9/8 in the scale (as, for instance, the Didymic diatonic has 27/16 as opposed to 5/3). The result is a 10-note ternary scale called '''blackdye'''.

=== Stylistic compositional features for aberrismic theory ===
This section will attempt to describe the principles and stylistic features of a specific style of music that justify using aberrismic scales in a composition. It is not an attempt to present aberrismic theory as absolute truth.
* A style of music that is melodic and heavy in modulations benefits from
** Multiple step sizes for melodic interest, for example diesis-sized steps that are below conventional semitones, specifically ones large enough to be melodically distinct but small enough to represent intonational changes.
** A set of modulatory intervals, including fifths.
** A system that allows unlimited modulation.
* It is widely agreed that lower primes are more robust to detuning. Hence for approximating JI with edos, we use lower prime temperaments, and which also represent either 81/80 or 64/63 steps for greater accuracy.
The above suggests temperaments, in particular edos, that use tempered lower primes, and edos large enough to have small diesis-sized steps. In the context of fifth-based modulation, scales also benefit from having offset arcs of fifths. One simple way to have this is to detemper MOS scales into ternary scales with an additional smaller melodic step size, which have a generator arc with fifths or a generator arc that stacks to fifths via a detempered generator chain.

{{UserTag|g_|Ground|7766ff|I assert that ~40¢ is the ideal point between "categorical unison" and "clear step"; context pushes it one way or the other, like in 27edo Superpyth diatonic and blackdye.}}

== List of aberrismic scales ==
* {{Adv|"GS(...)[n]" is [[generator sequence]] notation.}}
* {{adv|"subst ax(bycz)" denotes [[MOS substitution]].}}
* {{adv|"Almost" a cross-set means that one or two notes may be missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}
* {{adv|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}
=== Quasi-diatonic aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!|pinedye / dia1s (5L2m1s) {{adv|{{nowrap|subst 5L(2m1s)}}}}
||1sC: LLsLLmLm 1sR: LLmLLmLs 1sL: LLmLLsLm
||2.3.5 [L, m, s] = [10/9, 27/25, 81/80]
||{{adv|GS(3/2)[3] and GS(10/9)[3]}}
||1sC has 4 fifths and 1sR/1sL have 5
|-
!class="thl"|diasem / dia2s (5L2m2s) {{adv|{{nowrap|subst 5L(2m2s)}}}}
||2sR: LmLsLmLsL 2sL: LsLmLsLmL
||2.3.7 [L, m, s] = [9/8, 28/27, 64/63]
||{{adv|GS(3/2)[5] and 7/6}}
||Aggregate generator is 4/3, thus has fifth arcs of 5 and 4 notes respectively.
''See also: [[Chthonic harmony#Diasem|Diasem]]''
|-
!class="thl"|blackdye / dia3s (5L2m3s) {{adv|{{nowrap|subst 5L(2m3s)}}}}
||sLmLsLmLsL
||2.3.5 [L, m, s] = [10/9, 16/15, 81/80]
||{{adv|''GS(3/2)[5] and 10/9''}}
||Two interleaved 3-limit pentatonics
''See also: [[10-form#Blackdye|Blackdye]]''
|-
!|diaslen / dia4s (5L2m4s) {{adv|{{nowrap|subst 5L(2m4s)}}}}
||4sC: LmLsLsLmLss 4sR: LsLmLsLsLms 4sL: LsLsLmLsLsm
||2.3.7 [L, m, s] = [9/8, 49/48, 64/63]
||{{adv|GS(3/2)[4] and GS(8/7)[3]}}
||Fifth arcs with 4 notes, 4 notes, and 3 notes, with offset 8/7. Tempered to the slentonic {5L6s) MOS by [[Slendric]]. {{adv|Detempered Slendric[11] generator structure, aggregate generator is 3/2}}
|-
!|diachrome / chromedye / dia5s (5L2m5s)
||5sC: LsLsLmsLsLsm {{adv|{{nowrap|(subst 2m(5L5s))}}}} 5sR: LmsLsLsLmsLs 5sL: LsLsLsmLsLsm
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 256/243, 81/80]
||{{adv|5sC: ''GS(3/2)[6] and 40/27''}}
||Fifth-generated but with a 6-step offset
|-
!|whitedye / dia7s (5L2m7s) {{adv|{{nowrap|subst 7s(5L2m)}}}}
||LsLsLsmsLsLsms
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 28/27, 81/80]
||{{adv|''GS(3/2)[7] and 81/80''}}
||Two interleaved diatonics
|}
See [[Ground's composition theory#Quasi-diatonic scales]] for more tunings of diasem and blackdye.

=== Other aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI/[[erac]] interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!class="thl"|[[penslen]] / slen5m (5L5m6s) {{adv|{{nowrap|subst 6s(5L5m)}}}}
||LmsLmsLsmLsmLsms
||2.3.5.7.11[41 & 46] [L, m, s] = [12/11, 33/32, 64/63]
||{{adv|''GS(8/7)[8] and 11/8''}}
|| Has two aberrisma sizes, s and m.
|-
!|prejubilic / citro3s (4L2m3s) {{adv|{{nowrap|subst 2m(4L3s)}}}}
||C: LLsmLsLms R: LmLsLmsLs L: LmLsLsmLs
||2.5.7 [L, m, s] = [28/25, 35/32, 50/49]
||{{adv|GS(5/4)[3] and GS(7/5)[3] (exact for C)}}
||Didacus tempering makes L = m + s.
|-
!|arm5s (7L2m5s) {{adv|{{nowrap|subst 7L(2m5s)}}}}
||LmLsLsLmLsLsLs
||2.x<3.5.7.11.13[37edo] (4:2:1)
||{{adv|''GS(<<3/2)[7] and 14/13''}}
||An interleaving of two antidiatonic scales.
|-
!|mosh3s (3L4m3s) {{adv|{{nowrap|subst 4m(3L3s)}}}}
||LmsLmsmLsm
||2.x<3.7.11.13[37edo] (5:4:2)
||{{adv|''GS(16/13)[5] and 11/8''}}
||
|-
!|smi2s (4L3m2s) {{adv|{{nowrap|subst 2s(4L3m)}}}}
||C: LLmsLmLsm R: LmLmsLmLs L: LmLsLmLsm
||2.9.7.11.17[46edo] (8:4:1)
||{{adv|GS(17/14)[3] and GS(11/8)[3] (exact for C)}}
||
|-
!|sleneiro / oneiro3s (5L3m3s) {{adv|{{nowrap|subst 5L(3m3s)}}}}
||R: LmLsLmLsLms L: LsLmLsLmLsm
||2.(13:15:17:19)[5 & 18 & 44]
||{{adv|GS(13:15:17)}}
||An [[odd-regular]] aberrismic version of [[oneirotonic]].
|}

=== Systematic naming ===
Basic systematic names for aberrismic scales are of the form

[mos_prefix]n[added_step_size] (e.g. dia2s for diasem).

Any systematic name can be used for a scale as long as the scale satisfies the deletion-MOS subcondition for the added step size.

This is subject to change as aberrismic theory nomenclature is updated in the future.

== Notation ==
The [[generator gronut]] is an aberrismic extension of the circle of fifths.

=== Quasi-diatonic ===
Quasi-diatonic aberrismic notation restricts to [[diatonic notation]] on the tempered 3-limit.

Aberrismic/straddle-prime accidentals:
* Plus / Minus +/- : These tune a note sharp or flat by a small aberrisma. They reference Johnston notation because 81/80 is a common aberrisma, but they can also represent 64/63 or any other interval of similar function. 
* Duplus / Duminus ≠/= : Short for ++/--, most often representing 36/35~33/32~1053/1024, which is the large aberrisma in scales like penslen, or two small aberrismas in Akea temperament. Of all options, this set of characters is the easiest to type, looks the best in various fonts, and is least likely to be confused for the similar semisharp accidental (although they happen to represent the same size of interval).
* [[Erac|Eracs]] may be used to represent the inflating of commas typically found in aberrismic scales, although they represent a specific unit of error.

== Aberrismic theory and RTT ==
Aberrismic theory often applies RTT to ternary LCJI scales with comma steps. Certain scales with aberrismas may thus be endowed with JI interpretations via [[RTT]] temperaments, which may be used in suitable [[equal temperament]]s. Under Ground's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become a [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers out neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]]. Tempering is important in aberrismic theory as a way to improve the function of commas (frequently [[81/80]] or [[64/63]]) as aberrismas in ternary LCJI scales by tempering them larger than just.

At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or [[Ultrapyth]] temperament.

There are two choices involved in interpreting a given ternary scale, namely the choice of temperament and the choice of where to map the scale steps. The assignment of scale steps to tempered intervals is chosen to improve coverage of important LCJI intervals.

=== Example: Blackdye ===
The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth respectively.
* ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists an exact JI tuning.
* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one. Ground once termed the tuning of blackdye that makes aberrisma-altered Pyth thirds 13/11 and 14/11 ''Flutterpyth blackdye''.

{| class="wikitable right-2 right-3 right-4 right-5"
|+ style="font-size: 105%;" | Blackdye intervals in two temperaments
|-
! Interval class
! Sizes
! Untempered 2.3.5
! 2.3.7.11.13 Flutterpyth (extended to 13-limit Ultrapyth)
|-
! 1-step
| s m L
| 81/80 16/15 10/9
| 143/140 22/21 160/143
|-
! 2-step
| L + s L + m
| 9/8 32/27
| 8/7, 9/8 7/6
|-
! 3-step
| L + 2s L + m + s 2L + s 2L + m
| 729/640 6/5 5/4 320/243
| 7/6 13/11 14/11 13/10
|-
! 4-step
| 2L + 2s 2L + m + s
| 81/64 4/3
| 13/10 4/3
|-
! 5-step
| 2L + m + 2s 2L + 2m + s 3L + 2s 3L + m + s
| 27/20 64/45 45/32 40/27
| 66/49 11/8 16/11 49/33
|-
! 6-step
| 3L + m + 2s 3L + 2m + s
| 3/2 128/81
| 3/2 20/13
|-
! 7-step
| 3L + m + 3s 3L + 2m + 2s 4L + m + 2s 4L + 2m + s
| 243/160 8/5 5/3 1280/729
| 20/13 11/7 22/13 12/7
|-
! 8-step
| 4L + m + 3s 4L + 2m + 2s
| 27/16 16/9
| 12/7 7/4, 16/9
|-
! 9-step
| 5L + 2m + s 5L + m + 2s 4L + 2m + 2s
| 9/5 15/8 160/81
| 143/80 21/11 280/143
|}

== Glossary ==
* '''Aberration scale''': A scale made by interleaving aberrismas into a binary scale and stretching or compressing, usually a [[MOS substitution]] scale of type {{nowrap|[a+b+1]s(aLbm)}} (compression, called '''tractaberrated''') or {{nowrap|[a+b-1]s(aLbm)}} (stretching, called '''tensaberrated'''). For example, sLsmsLsLsLsmsLs is an aberration scale made from diatonic (a MOS substitution scale of type 8s(5L2m)), also called trackdye.
* '''Aberrisma''': The smallest interval region that melodically sounds like a step.
* '''Magnitone''': The melodic function of L + s in quasi-diatonic aberrismic scales.
* '''Monotone-MOS''': A ternary scale is ''monotone-MOS'' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy a monotone-MOS subcondition''. For example, diasem (LmLsLmLsL) satisfies all three monotone-MOS subconditions, but blackdye (sLmLsLmLsL) satisfies only the m = s and s = 0 monotone-MOS subconditions. An aberrismic scale is required to satisfy the s = 0 monotone-MOS subcondition.
* '''Solitone''': The melodic function of the L step in quasi-diatonic aberrismic scales.
* '''Subaberrisma''': A step so small (smaller than the typical limit for an aberrisma) that its status as a melodic step is unclear.

== Extension to higher ranks ==
Aberrismic theory is typically concerned with ternary scales, especially those with two chains of generators of the same length or differing by one, meaning that they have a [[GS]] with only two intervals. This is because they are not much harder to navigate than an MOS while offering significantly more flexibility.

{{UserTag|g_|Ground|7766ff|I propose that we call this type of scale '''bicatenary'''.}}

However, this is often not enough to accurately represent a larger JI subgroup. Portent penslen (5L5m6s) is a somewhat unique counterexample, being bicatenary yet microtempered in the 11-limit. The solution is to add more step sizes while maintaining as much lower-rank structure as possible. For example, while penslen is found in edos like 41 and 46, the equivalent in the similarly LCJI-accurate 53 and 58 is 5L2m3s4t, a quaternary subset of Buzzard[28] with a JI tuning of 35/32 : 21/20 : 36/35 : 64/63. [[Ground's composition theory#Interval logic deviation theory|ILD]] is a simple way to access notes outside of a scale with a higher rank.

A common tempering of blackdye involves a sharper 3 to significantly inflate 81/80, both for melodic utility and to equate 27/20 to a superfourth like 15/11 or 11/8. It also becomes natural to temper out 64/63. Possibly the most common ratio representation of an aberrisma is 36/35, but few ternary scales use it without tempering out 81/80 or 64/63.

(81/80)^2 = 43¢ is notably in the middle of the usual aberrisma size range as well. This does not exist in blackdye, but becomes accessible in certain variants of 5L2m8s as well as numerous quaternary scales with even more options for available intervals.

== Compositional examples ==
Some compositional snippets using aberrismic scales:

* The Art of It makes almost exclusive use of 31edo diasem: [[File:A New Dusk-02 The Art of It.mp3]]
* A fugue using aberrismic scales: [[File:Inthar - Fugue in 32edo and 33edo.mp3]]
* A 34edo blackdye fugue exposition: [[File:Blackdye-fugue-expo.mp3]]

== External links ==
* [https://turbofishcrow.github.io/tern Tern: aberrismic-focused ternary scale analysis]
{{cat|
Terms
Aberrismic terms
Ternary scales
}}

Ternary scale

2026-11-03T06:09:11Z

Inthar: /* See also */

A '''ternary scale''' is a scale with exactly 3 step sizes. This article is an overview of the theory of ternary scale patterns.

== Relationship with rank ==
Ternary scales with [[independent]] step sizes are rank-3. However, rank-3 scales need not be ternary. Duodene (16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1) is an example of a rank-3 (2.3.5) quaternary scale.

== MV3 ternary scales ==
A maximum variety 3 (MV3) scale is a scale whose [[ordinal]]s come in at most 3 sizes.

Single-period MV3 ternary scale patterns come in the following types:
# '''pairwise-MOS''': scales such that making any two kinds of steps the same size always results in a MOS (an example is Zarlino, where LMsLMLs gives LssLsLs, LLsLLLs, and LsLLsLL)
#* '''abacaba''' scales where '''a''', '''b''', and '''c''' are three distinct step sizes: for example, LmLsLmL
#* '''odd-regular''' scales: [[MOS substitution]] scales of type a'''x'''(b'''y'''b'''z''') where a is odd and gcd(a, b) = 1 (example: [[diasem]])
#* '''even-regular''' scales: [[MOS substitution]] scales of type a'''x'''(b'''y'''b'''z''') where a is even and gcd(a, b) = 1 (example: [[penslen]])
# '''abcba''' scales where '''a''', '''b''', and '''c''' are three distinct step sizes: a finite family of non-pairwise-MOS MV3 ternary patterns
# '''twisted MV3''' scales (see below): an infinite family of non-pairwise-MOS MV3 ternary scales

=== Odd-regular scales ===
'''Odd-regular scales''' have a structure where the generator chain of a 1-period MOS is detempered into a [[generator sequence]] (GS) of two alternating generators, g1 and g2, with a "bad" generator different from both on only one note. Odd-regular scales are chiral; switching g1 and g2 in the GS corresponds to using the other chirality.

Example: zarlino (RH LmsLmLs and LH LsmLsLm, 3L(2m2s)) is an odd-regular scale pattern; GS(5/4, 6/5) generates RH and GS(6/5, 5/4) generates LH.

=== Even-regular scales ===
'''Even-regular scales''' have two parallel generator chains offset by a len(scale)/2-step interval, with "bad" generators only occurring on 1 note per chain. This generator comes from detempering a generator of ax2bX (a 2-period MOS) for an even-regular scale of MOS substitution type ax(bybz). For example, achiral diachrome (LsLsLmsLsLsm, 2m(5L5s)) has a 5-step interval 2L + m + 2s (interpreted as 4/3) as a generator, and m + 4X (period-complement of X) is a generator of the MOS 2m10X. Even-regular scales are achiral.

Even-regular scales have an interleaving structure: if n > 4, an n-note even-regular scale is an [[interleaving]] of two copies of an n/2-note even-regular scale if n is a multiple of 4, and is an interleaving of the two opposite chiralities of an n/2-note odd-regular scale otherwise. Examples:
* Mosh3s (4m(3L3s), LmsLmsmLsm) is an interleaving of (Lm)(sL)(ms)(mL)(sm) = LmsLs and (ms)(Lm)(sm)(Ls)(mL) = sLsmL
* Penslen (6s(5L5m), msLsmLsmLsmsLmsL) is an interleaving of (ms)(Ls)(mL)(sm)(Ls)(ms)(Lm)(sL) = smLsmsLm and (sL)(sm)(Ls)(mL)(sm)(sL)(ms)(Lm) = msmLsmsL

=== Twisted MV3 scales ===
'''Twisted MV3 scales''' are much like MOS substitution scales, but the "template MOS" is not actually a MOS, but a "twisted" multiMOS, which is constructed as follows:
# Take the ''brightest'' (or ''darkest'') mode of a multiMOS, where the period (one MOS unit) has exactly one step count X even (e.g. 2X 1s, XXs -> 6X 3s, XXsXXsXXs)
# Mark borders between units: XXs|XXs|XXs
# Change s|X -> X|s (or vice versa) at some of the borders: XXX|sXs|XXs
Now do the letterwise substitution procedure, as in [[MOS substitution]], with X as the slot letter, with filling MOS alternating: LmLsmsLms = XXXsXsXXs(LmLmLm).

Twisted MV3 scales always have step signature ka'''x'''ka'''y'''kb'''z''' with k > 1.

== Interleaving ==
If ''w''('''x''', '''y''') (a sequence of step sizes '''x''' and '''y''') is a binary scale, then the ternary scale ''w''('''z'''('''x'''-'''z'''), '''z'''('''y'''-'''z''')) (the same sequence but with substitutions '''x''' -> '''z'''('''x'''-'''z'''), '''y''' -> '''z'''('''y'''-'''z''')) is an [[interleaving]], namely cross-set(''w''('''x''', '''y'''), '''z''').

Blackdye (sLmLsLmLsL, 5L(2m3s)) is an example: it is w(L+s, m+s) where w = 2L3s.

== MOS substitution ==
: ''Main article: [[MOS substitution]]''
MOS substitution generalizes odd-regular and even-regular scales (as well as the above interleaving construction).

== See also ==
* [[Aberrisma|Aberrismic theory]]: A theory of ternary scales where the small step is meant to be audible yet small enough to separate two intervals that are categorically "the same"
{{cat|Scales
Ternary scales{{!}}*}}

Ternary scale

2026-11-03T06:08:50Z

Inthar: /* See also */

A '''ternary scale''' is a scale with exactly 3 step sizes. This article is an overview of the theory of ternary scale patterns.

== Relationship with rank ==
Ternary scales with [[independent]] step sizes are rank-3. However, rank-3 scales need not be ternary. Duodene (16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1) is an example of a rank-3 (2.3.5) quaternary scale.

== MV3 ternary scales ==
A maximum variety 3 (MV3) scale is a scale whose [[ordinal]]s come in at most 3 sizes.

Single-period MV3 ternary scale patterns come in the following types:
# '''pairwise-MOS''': scales such that making any two kinds of steps the same size always results in a MOS (an example is Zarlino, where LMsLMLs gives LssLsLs, LLsLLLs, and LsLLsLL)
#* '''abacaba''' scales where '''a''', '''b''', and '''c''' are three distinct step sizes: for example, LmLsLmL
#* '''odd-regular''' scales: [[MOS substitution]] scales of type a'''x'''(b'''y'''b'''z''') where a is odd and gcd(a, b) = 1 (example: [[diasem]])
#* '''even-regular''' scales: [[MOS substitution]] scales of type a'''x'''(b'''y'''b'''z''') where a is even and gcd(a, b) = 1 (example: [[penslen]])
# '''abcba''' scales where '''a''', '''b''', and '''c''' are three distinct step sizes: a finite family of non-pairwise-MOS MV3 ternary patterns
# '''twisted MV3''' scales (see below): an infinite family of non-pairwise-MOS MV3 ternary scales

=== Odd-regular scales ===
'''Odd-regular scales''' have a structure where the generator chain of a 1-period MOS is detempered into a [[generator sequence]] (GS) of two alternating generators, g1 and g2, with a "bad" generator different from both on only one note. Odd-regular scales are chiral; switching g1 and g2 in the GS corresponds to using the other chirality.

Example: zarlino (RH LmsLmLs and LH LsmLsLm, 3L(2m2s)) is an odd-regular scale pattern; GS(5/4, 6/5) generates RH and GS(6/5, 5/4) generates LH.

=== Even-regular scales ===
'''Even-regular scales''' have two parallel generator chains offset by a len(scale)/2-step interval, with "bad" generators only occurring on 1 note per chain. This generator comes from detempering a generator of ax2bX (a 2-period MOS) for an even-regular scale of MOS substitution type ax(bybz). For example, achiral diachrome (LsLsLmsLsLsm, 2m(5L5s)) has a 5-step interval 2L + m + 2s (interpreted as 4/3) as a generator, and m + 4X (period-complement of X) is a generator of the MOS 2m10X. Even-regular scales are achiral.

Even-regular scales have an interleaving structure: if n > 4, an n-note even-regular scale is an [[interleaving]] of two copies of an n/2-note even-regular scale if n is a multiple of 4, and is an interleaving of the two opposite chiralities of an n/2-note odd-regular scale otherwise. Examples:
* Mosh3s (4m(3L3s), LmsLmsmLsm) is an interleaving of (Lm)(sL)(ms)(mL)(sm) = LmsLs and (ms)(Lm)(sm)(Ls)(mL) = sLsmL
* Penslen (6s(5L5m), msLsmLsmLsmsLmsL) is an interleaving of (ms)(Ls)(mL)(sm)(Ls)(ms)(Lm)(sL) = smLsmsLm and (sL)(sm)(Ls)(mL)(sm)(sL)(ms)(Lm) = msmLsmsL

=== Twisted MV3 scales ===
'''Twisted MV3 scales''' are much like MOS substitution scales, but the "template MOS" is not actually a MOS, but a "twisted" multiMOS, which is constructed as follows:
# Take the ''brightest'' (or ''darkest'') mode of a multiMOS, where the period (one MOS unit) has exactly one step count X even (e.g. 2X 1s, XXs -> 6X 3s, XXsXXsXXs)
# Mark borders between units: XXs|XXs|XXs
# Change s|X -> X|s (or vice versa) at some of the borders: XXX|sXs|XXs
Now do the letterwise substitution procedure, as in [[MOS substitution]], with X as the slot letter, with filling MOS alternating: LmLsmsLms = XXXsXsXXs(LmLmLm).

Twisted MV3 scales always have step signature ka'''x'''ka'''y'''kb'''z''' with k > 1.

== Interleaving ==
If ''w''('''x''', '''y''') (a sequence of step sizes '''x''' and '''y''') is a binary scale, then the ternary scale ''w''('''z'''('''x'''-'''z'''), '''z'''('''y'''-'''z''')) (the same sequence but with substitutions '''x''' -> '''z'''('''x'''-'''z'''), '''y''' -> '''z'''('''y'''-'''z''')) is an [[interleaving]], namely cross-set(''w''('''x''', '''y'''), '''z''').

Blackdye (sLmLsLmLsL, 5L(2m3s)) is an example: it is w(L+s, m+s) where w = 2L3s.

== MOS substitution ==
: ''Main article: [[MOS substitution]]''
MOS substitution generalizes odd-regular and even-regular scales (as well as the above interleaving construction).

== See also ==
* [[Aberrisma|Aberrismic theory]]: A tuning theory of ternary scales where the small step is meant to be audible yet small enough to separate two intervals that are categorically "the same"
{{cat|Scales
Ternary scales{{!}}*}}

Ternary scale

2026-11-03T06:08:36Z

Inthar: /* See also */

Ternary scale

2026-11-03T06:06:12Z

Inthar: /* Odd-regular scales */

A '''ternary scale''' is a scale with exactly 3 step sizes. This article is an overview of the theory of ternary scale patterns.

== Relationship with rank ==
Ternary scales with [[independent]] step sizes are rank-3. However, rank-3 scales need not be ternary. Duodene (16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1) is an example of a rank-3 (2.3.5) quaternary scale.

== MV3 ternary scales ==
A maximum variety 3 (MV3) scale is a scale whose [[ordinal]]s come in at most 3 sizes.

Single-period MV3 ternary scale patterns come in the following types:
# '''pairwise-MOS''': scales such that making any two kinds of steps the same size always results in a MOS (an example is Zarlino, where LMsLMLs gives LssLsLs, LLsLLLs, and LsLLsLL)
#* '''abacaba''' scales where '''a''', '''b''', and '''c''' are three distinct step sizes: for example, LmLsLmL
#* '''odd-regular''' scales: [[MOS substitution]] scales of type a'''x'''(b'''y'''b'''z''') where a is odd and gcd(a, b) = 1 (example: [[diasem]])
#* '''even-regular''' scales: [[MOS substitution]] scales of type a'''x'''(b'''y'''b'''z''') where a is even and gcd(a, b) = 1 (example: [[penslen]])
# '''abcba''' scales where '''a''', '''b''', and '''c''' are three distinct step sizes: a finite family of non-pairwise-MOS MV3 ternary patterns
# '''twisted MV3''' scales (see below): an infinite family of non-pairwise-MOS MV3 ternary scales

=== Odd-regular scales ===
'''Odd-regular scales''' have a structure where the generator chain of a 1-period MOS is detempered into a [[generator sequence]] (GS) of two alternating generators, g1 and g2, with a "bad" generator different from both on only one note. Odd-regular scales are chiral; switching g1 and g2 in the GS corresponds to using the other chirality.

Example: zarlino (RH LmsLmLs and LH LsmLsLm, 3L(2m2s)) is an odd-regular scale pattern; GS(5/4, 6/5) generates RH and GS(6/5, 5/4) generates LH.

=== Even-regular scales ===
'''Even-regular scales''' have two parallel generator chains offset by a len(scale)/2-step interval, with "bad" generators only occurring on 1 note per chain. This generator comes from detempering a generator of ax2bX (a 2-period MOS) for an even-regular scale of MOS substitution type ax(bybz). For example, achiral diachrome (LsLsLmsLsLsm, 2m(5L5s)) has a 5-step interval 2L + m + 2s (interpreted as 4/3) as a generator, and m + 4X (period-complement of X) is a generator of the MOS 2m10X. Even-regular scales are achiral.

Even-regular scales have an interleaving structure: if n > 4, an n-note even-regular scale is an [[interleaving]] of two copies of an n/2-note even-regular scale if n is a multiple of 4, and is an interleaving of the two opposite chiralities of an n/2-note odd-regular scale otherwise. Examples:
* Mosh3s (4m(3L3s), LmsLmsmLsm) is an interleaving of (Lm)(sL)(ms)(mL)(sm) = LmsLs and (ms)(Lm)(sm)(Ls)(mL) = sLsmL
* Penslen (6s(5L5m), msLsmLsmLsmsLmsL) is an interleaving of (ms)(Ls)(mL)(sm)(Ls)(ms)(Lm)(sL) = smLsmsLm and (sL)(sm)(Ls)(mL)(sm)(sL)(ms)(Lm) = msmLsmsL

=== Twisted MV3 scales ===
'''Twisted MV3 scales''' are much like MOS substitution scales, but the "template MOS" is not actually a MOS, but a "twisted" multiMOS, which is constructed as follows:
# Take the ''brightest'' (or ''darkest'') mode of a multiMOS, where the period (one MOS unit) has exactly one step count X even (e.g. 2X 1s, XXs -> 6X 3s, XXsXXsXXs)
# Mark borders between units: XXs|XXs|XXs
# Change s|X -> X|s (or vice versa) at some of the borders: XXX|sXs|XXs
Now do the letterwise substitution procedure, as in [[MOS substitution]], with X as the slot letter, with filling MOS alternating: LmLsmsLms = XXXsXsXXs(LmLmLm).

Twisted MV3 scales always have step signature ka'''x'''ka'''y'''kb'''z''' with k > 1.

== Interleaving ==
If ''w''('''x''', '''y''') (a sequence of step sizes '''x''' and '''y''') is a binary scale, then the ternary scale ''w''('''z'''('''x'''-'''z'''), '''z'''('''y'''-'''z''')) (the same sequence but with substitutions '''x''' -> '''z'''('''x'''-'''z'''), '''y''' -> '''z'''('''y'''-'''z''')) is an [[interleaving]], namely cross-set(''w''('''x''', '''y'''), '''z''').

Blackdye (sLmLsLmLsL, 5L(2m3s)) is an example: it is w(L+s, m+s) where w = 2L3s.

== MOS substitution ==
: ''Main article: [[MOS substitution]]''
MOS substitution generalizes odd-regular and even-regular scales (as well as the above interleaving construction).

== See also ==
* [[Aberrisma|Aberrismic theory]]: A compositional theory using ternary scales
{{cat|Scales
Ternary scales{{!}}*}}

Oneirotonic

2026-11-03T06:02:22Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an [[odd-regular]] MV3 scale, there are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Aberrisma

2026-11-03T06:01:48Z

Inthar: /* Other aberrismic scales */

{{Proposed}}

An '''aberrisma''' is an interval representing some comma as an additional type of melodic step smaller than a semitone. Its name originates from the comparison of its sound to a chromatic aberration, with the -isma suffix often used for commas. Although they are typically between 20 and 55 cents (around 81/80 to half of 16/15) and often inflated commas about the size of a diesis, the aberrisma is a melodic function and not an interval size. Larger and smaller sizes can function as aberrismas depending on the scale tuning. '''Aberrismic theory''' is the subset of microtonal theory pioneered by [[User:Ground|Ground]] and [[User:Inthar|Inthar]] that deals with aberrismas. See [[straddle primes]] for aberrismas equated to 1/1 without being tempered out.

Ground's '''aberrismic hypothesis''' is that intervals an audible distance apart can be broadly used together in the same scale framework while merely registering as detunings of the same interval. {{adv|In a specific test case, trained and untrained 12edo listeners may notice aberrismic steps in a 27edo blackdye melody (against a control 12edo melody) but consider them to correspond to the same diatonic degree. To our knowledge this hasn't been scientifically tested yet.}} Straddle theory applies the hypothesis to definite ratios, whereas in the original aberrismic scales, it's applied to diatonic scale degrees. Commas have been described as a type of unison in other contexts, but rarely as distinct steps vital to the structure of a scale, or as intervals that are represented by the same ratio. An aberrisma is categorically a unison but doesn't sound like one when isolated, which represents both observed RTT commas and the difference between straddled intervals; it is a unison widened into a melodic step. Aberrismic theory is a collection of the effects of applying the aberrismic hypothesis to scale theory and RTT.

The aberrisma is used as one of the parameters in constructing an aberrismic scale, a type of ternary scale. For example, blackdye is a 10-note aberrismic superset of the 7-note nicetone, but with a more distinctive set of three step sizes and added opportunities to avoid pythagorean and wolf intervals. Aberrismas may also appear in MOS scales, such as Garibaldi[17]. Superpyth[12] is a good example of the distinction between interval function and size. The diatonic semitone, a deflated 256/243, is equated to the inflated 81/80. Despite being the same size, the former represents a narrow semitone, the latter is an aberrisma, and a stack of the two is a classic semitone.

== The "why" of aberrismic theory ==
=== Adding comma steps to Pyth diatonic ===
81/80 and 64/63 are the canonical choices for 2.3.5 and 2.3.7 formal commas for modifications to Pythagorean (2.3) JI ratios — 81/80 separates 5/4 from 81/64, 10/9 from 9/8, and so on; and 64/63 separates 7/4 from 16/9, 9/7 from 81/64, and so on. Aberrismic theory asks: what if we made 81/80 or 64/63 into scale steps, so that we can use both of the intervals separated by the formal comma in one scale? Indeed, doing this to 2.3 diatonic to make a ternary scale, in a way that best preserves the fifth-generated structure, results in (2.3.5) blackdye and (2.3.7) diasem, respectively.

==== Example: Blackdye ====
The Zarlino diatonic is chiral — there are two different, equally valid second degrees of the Ionian mode. Both are useful, as the sharp one forms a perfect fifth with the fifth degree but a wolf fifth with the sixth degree, and the flat one forms a perfect fifth with the sixth degree but a wolf fifth with the fifth degree.
[[File:Blackdye.png|thumb|510x510px|The construction of blackdye from Zarlino diatonic]]
One way to make it achiral is to temper out 81/80, the difference between these two steps, resulting in [[Meantone]] diatonic; intuitively this requires flattening the fifth and sharpening the sixth somewhat. However, an alternative way, if you wish to observe 81/80 or to use just intonation, is to include both varieties of whole tone over the unison, treating 81/80 as a melodic step between them. This can be thought of as dividing up a 9/8 into a 10/9 and an 81/80. It is then reasonable to extend this action to all instances of 9/8 in the scale (as, for instance, the Didymic diatonic has 27/16 as opposed to 5/3). The result is a 10-note ternary scale called '''blackdye'''.

=== Stylistic compositional features for aberrismic theory ===
This section will attempt to describe the principles and stylistic features of a specific style of music that justify using aberrismic scales in a composition. It is not an attempt to present aberrismic theory as absolute truth.
* A style of music that is melodic and heavy in modulations benefits from
** Multiple step sizes for melodic interest, for example diesis-sized steps that are below conventional semitones, specifically ones large enough to be melodically distinct but small enough to represent intonational changes.
** A set of modulatory intervals, including fifths.
** A system that allows unlimited modulation.
* It is widely agreed that lower primes are more robust to detuning. Hence for approximating JI with edos, we use lower prime temperaments, and which also represent either 81/80 or 64/63 steps for greater accuracy.
The above suggests temperaments, in particular edos, that use tempered lower primes, and edos large enough to have small diesis-sized steps. In the context of fifth-based modulation, scales also benefit from having offset arcs of fifths. One simple way to have this is to detemper MOS scales into ternary scales with an additional smaller melodic step size, which have a generator arc with fifths or a generator arc that stacks to fifths via a detempered generator chain.

{{UserTag|g_|Ground|7766ff|I assert that ~40¢ is the ideal point between "categorical unison" and "clear step"; context pushes it one way or the other, like in 27edo Superpyth diatonic and blackdye.}}

== List of aberrismic scales ==
* {{Adv|"GS(...)[n]" is [[generator sequence]] notation.}}
* {{adv|"subst ax(bycz)" denotes [[MOS substitution]].}}
* {{adv|"Almost" a cross-set means that one or two notes may be missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}
* {{adv|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}
=== Quasi-diatonic aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!|pinedye / dia1s (5L2m1s) {{adv|{{nowrap|subst 5L(2m1s)}}}}
||1sC: LLsLLmLm 1sR: LLmLLmLs 1sL: LLmLLsLm
||2.3.5 [L, m, s] = [10/9, 27/25, 81/80]
||{{adv|GS(3/2)[3] and GS(10/9)[3]}}
||1sC has 4 fifths and 1sR/1sL have 5
|-
!class="thl"|diasem / dia2s (5L2m2s) {{adv|{{nowrap|subst 5L(2m2s)}}}}
||2sR: LmLsLmLsL 2sL: LsLmLsLmL
||2.3.7 [L, m, s] = [9/8, 28/27, 64/63]
||{{adv|GS(3/2)[5] and 7/6}}
||Aggregate generator is 4/3, thus has fifth arcs of 5 and 4 notes respectively.
''See also: [[Chthonic harmony#Diasem|Diasem]]''
|-
!class="thl"|blackdye / dia3s (5L2m3s) {{adv|{{nowrap|subst 5L(2m3s)}}}}
||sLmLsLmLsL
||2.3.5 [L, m, s] = [10/9, 16/15, 81/80]
||{{adv|''GS(3/2)[5] and 10/9''}}
||Two interleaved 3-limit pentatonics
''See also: [[10-form#Blackdye|Blackdye]]''
|-
!|diaslen / dia4s (5L2m4s) {{adv|{{nowrap|subst 5L(2m4s)}}}}
||4sC: LmLsLsLmLss 4sR: LsLmLsLsLms 4sL: LsLsLmLsLsm
||2.3.7 [L, m, s] = [9/8, 49/48, 64/63]
||{{adv|GS(3/2)[4] and GS(8/7)[3]}}
||Fifth arcs with 4 notes, 4 notes, and 3 notes, with offset 8/7. Tempered to the slentonic {5L6s) MOS by [[Slendric]]. {{adv|Detempered Slendric[11] generator structure, aggregate generator is 3/2}}
|-
!|diachrome / chromedye / dia5s (5L2m5s)
||5sC: LsLsLmsLsLsm {{adv|{{nowrap|(subst 2m(5L5s))}}}} 5sR: LmsLsLsLmsLs 5sL: LsLsLsmLsLsm
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 256/243, 81/80]
||{{adv|5sC: ''GS(3/2)[6] and 40/27''}}
||Fifth-generated but with a 6-step offset
|-
!|whitedye / dia7s (5L2m7s) {{adv|{{nowrap|subst 7s(5L2m)}}}}
||LsLsLsmsLsLsms
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 28/27, 81/80]
||{{adv|''GS(3/2)[7] and 81/80''}}
||Two interleaved diatonics
|}
See [[Ground's composition theory#Quasi-diatonic scales]] for more tunings of diasem and blackdye.

=== Other aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI/[[erac]] interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!class="thl"|[[penslen]] / slen5m (5L5m6s) {{adv|{{nowrap|subst 6s(5L5m)}}}}
||LmsLmsLsmLsmLsms
||2.3.5.7.11[41 & 46] [L, m, s] = [12/11, 33/32, 64/63]
||{{adv|''GS(8/7)[8] and 11/8''}}
|| Has two aberrisma sizes, s and m.
|-
!|prejubilic / citro3s (4L2m3s) {{adv|{{nowrap|subst 2m(4L3s)}}}}
||C: LLsmLsLms R: LmLsLmsLs L: LmLsLsmLs
||2.5.7 [L, m, s] = [28/25, 35/32, 50/49]
||{{adv|GS(5/4)[3] and GS(7/5)[3] (exact for C)}}
||Didacus tempering makes L = m + s.
|-
!|arm5s (7L2m5s) {{adv|{{nowrap|subst 7L(2m5s)}}}}
||LmLsLsLmLsLsLs
||2.x<3.5.7.11.13[37edo] (4:2:1)
||{{adv|''GS(<<3/2)[7] and 14/13''}}
||An interleaving of two antidiatonic scales.
|-
!|mosh3s (3L4m3s) {{adv|{{nowrap|subst 4m(3L3s)}}}}
||LmsLmsmLsm
||2.x<3.7.11.13[37edo] (5:4:2)
||{{adv|''GS(16/13)[5] and 11/8''}}
||
|-
!|smi2s (4L3m2s) {{adv|{{nowrap|subst 2s(4L3m)}}}}
||C: LLmsLmLsm R: LmLmsLmLs L: LmLsLmLsm
||2.9.7.11.17[46edo] (8:4:1)
||{{adv|GS(17/14)[3] and GS(11/8)[3] (exact for C)}}
||
|-
!|sleneiro / oneiro3s (5L3m3s) {{adv|{{nowrap|subst 5L(3m3s)}}}}
||R: LmLsLmLsLms L: LsLmLsLmLsm
||2.(13:15:17:19)[5 & 18 & 44]
||{{adv|GS(13:15:17)}}
||An [[odd-regular]] aberrismic version of [[oneirotonic]].
|}

=== Systematic naming ===
Basic systematic names for aberrismic scales are of the form

[mos_prefix]n[added_step_size] (e.g. dia2s for diasem).

Any systematic name can be used for a scale as long as the scale satisfies the deletion-MOS subcondition for the added step size.

This is subject to change as aberrismic theory nomenclature is updated in the future.

== Notation ==
The [[generator gronut]] is an aberrismic extension of the circle of fifths.

=== Quasi-diatonic ===
Quasi-diatonic aberrismic notation restricts to [[diatonic notation]] on the tempered 3-limit.

Aberrismic/straddle-prime accidentals:
* Plus / Minus +/- : These tune a note sharp or flat by a small aberrisma. They reference Johnston notation because 81/80 is a common aberrisma, but they can also represent 64/63 or any other interval of similar function. 
* Duplus / Duminus ≠/= : Short for ++/--, most often representing 36/35~33/32~1053/1024, which is the large aberrisma in scales like penslen, or two small aberrismas in Akea temperament. Of all options, this set of characters is the easiest to type, looks the best in various fonts, and is least likely to be confused for the similar semisharp accidental (although they happen to represent the same size of interval).
* [[Erac|Eracs]] may be used to represent the inflating of commas typically found in aberrismic scales, although they represent a specific unit of error.

== Aberrismic theory and RTT ==
Aberrismic theory often applies RTT to ternary LCJI scales with comma steps. Certain scales with aberrismas may thus be endowed with JI interpretations via [[RTT]] temperaments, which may be used in suitable [[equal temperament]]s. Under Ground's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become a [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers out neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]]. Tempering is important in aberrismic theory as a way to improve the function of commas (frequently [[81/80]] or [[64/63]]) as aberrismas in ternary LCJI scales by tempering them larger than just.

At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or [[Ultrapyth]] temperament.

There are two choices involved in interpreting a given ternary scale, namely the choice of temperament and the choice of where to map the scale steps. The assignment of scale steps to tempered intervals is chosen to improve coverage of important LCJI intervals.

=== Example: Blackdye ===
The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth respectively.
* ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists an exact JI tuning.
* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one. Ground once termed the tuning of blackdye that makes aberrisma-altered Pyth thirds 13/11 and 14/11 ''Flutterpyth blackdye''.

{| class="wikitable right-2 right-3 right-4 right-5"
|+ style="font-size: 105%;" | Blackdye intervals in two temperaments
|-
! Interval class
! Sizes
! Untempered 2.3.5
! 2.3.7.11.13 Flutterpyth (extended to 13-limit Ultrapyth)
|-
! 1-step
| s m L
| 81/80 16/15 10/9
| 143/140 22/21 160/143
|-
! 2-step
| L + s L + m
| 9/8 32/27
| 8/7, 9/8 7/6
|-
! 3-step
| L + 2s L + m + s 2L + s 2L + m
| 729/640 6/5 5/4 320/243
| 7/6 13/11 14/11 13/10
|-
! 4-step
| 2L + 2s 2L + m + s
| 81/64 4/3
| 13/10 4/3
|-
! 5-step
| 2L + m + 2s 2L + 2m + s 3L + 2s 3L + m + s
| 27/20 64/45 45/32 40/27
| 66/49 11/8 16/11 49/33
|-
! 6-step
| 3L + m + 2s 3L + 2m + s
| 3/2 128/81
| 3/2 20/13
|-
! 7-step
| 3L + m + 3s 3L + 2m + 2s 4L + m + 2s 4L + 2m + s
| 243/160 8/5 5/3 1280/729
| 20/13 11/7 22/13 12/7
|-
! 8-step
| 4L + m + 3s 4L + 2m + 2s
| 27/16 16/9
| 12/7 7/4, 16/9
|-
! 9-step
| 5L + 2m + s 5L + m + 2s 4L + 2m + 2s
| 9/5 15/8 160/81
| 143/80 21/11 280/143
|}

== Glossary ==
* '''Aberration scale''': A scale made by interleaving aberrismas into a binary scale and stretching or compressing, usually a [[MOS substitution]] scale of type {{nowrap|[a+b+1]s(aLbm)}} (compression, called '''tractaberrated''') or {{nowrap|[a+b-1]s(aLbm)}} (stretching, called '''tensaberrated'''). For example, sLsmsLsLsLsmsLs is an aberration scale made from diatonic (a MOS substitution scale of type 8s(5L2m)), also called trackdye.
* '''Aberrisma''': The smallest interval region that melodically sounds like a step.
* '''Magnitone''': The melodic function of L + s in quasi-diatonic aberrismic scales.
* '''Monotone-MOS''': A ternary scale is ''monotone-MOS'' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy a monotone-MOS subcondition''. For example, diasem (LmLsLmLsL) satisfies all three monotone-MOS subconditions, but blackdye (sLmLsLmLsL) satisfies only the m = s and s = 0 monotone-MOS subconditions. An aberrismic scale is required to satisfy the s = 0 monotone-MOS subcondition.
* '''Solitone''': The melodic function of the L step in quasi-diatonic aberrismic scales.
* '''Subaberrisma''': A step so small (smaller than the typical limit for an aberrisma) that its status as a melodic step is unclear.

== Extension to higher ranks ==
Aberrismic theory is typically concerned with ternary scales, especially those with two chains of generators of the same length or differing by one, meaning that they have a [[GS]] with only two intervals. This is because they are not much harder to navigate than an MOS while offering significantly more flexibility.

{{UserTag|g_|Ground|7766ff|I propose that we call this type of scale '''bicatenary'''.}}

However, this is often not enough to accurately represent a larger JI subgroup. Portent penslen (5L5m6s) is a somewhat unique counterexample, being bicatenary yet microtempered in the 11-limit. The solution is to add more step sizes while maintaining as much lower-rank structure as possible. For example, while penslen is found in edos like 41 and 46, the equivalent in the similarly LCJI-accurate 53 and 58 is 5L2m3s4t, a quaternary subset of Buzzard[28] with a JI tuning of 35/32 : 21/20 : 36/35 : 64/63. [[Ground's composition theory#Interval logic deviation theory|ILD]] is a simple way to access notes outside of a scale with a higher rank.

A common tempering of blackdye involves a sharper 3 to significantly inflate 81/80, both for melodic utility and to equate 27/20 to a superfourth like 15/11 or 11/8. It also becomes natural to temper out 64/63. Possibly the most common ratio representation of an aberrisma is 36/35, but few ternary scales use it without tempering out 81/80 or 64/63.

(81/80)^2 = 43¢ is notably in the middle of the usual aberrisma size range as well. This does not exist in blackdye, but becomes accessible in certain variants of 5L2m8s as well as numerous quaternary scales with even more options for available intervals.

== Compositional examples ==
Some compositional snippets using aberrismic scales:

* The Art of It makes almost exclusive use of 31edo diasem: [[File:A New Dusk-02 The Art of It.mp3]]
* A fugue using aberrismic scales: [[File:Inthar - Fugue in 32edo and 33edo.mp3]]
* A 34edo blackdye fugue exposition: [[File:Blackdye-fugue-expo.mp3]]

== External links ==
* [https://turbofishcrow.github.io/tern Tern: aberrismic-focused ternary scale analysis]
{{cat|
Terms
Aberrismic terms
Ternary scales
}}

Aberrisma

2026-11-03T06:01:08Z

Inthar: /* Other aberrismic scales */

{{Proposed}}

An '''aberrisma''' is an interval representing some comma as an additional type of melodic step smaller than a semitone. Its name originates from the comparison of its sound to a chromatic aberration, with the -isma suffix often used for commas. Although they are typically between 20 and 55 cents (around 81/80 to half of 16/15) and often inflated commas about the size of a diesis, the aberrisma is a melodic function and not an interval size. Larger and smaller sizes can function as aberrismas depending on the scale tuning. '''Aberrismic theory''' is the subset of microtonal theory pioneered by [[User:Ground|Ground]] and [[User:Inthar|Inthar]] that deals with aberrismas. See [[straddle primes]] for aberrismas equated to 1/1 without being tempered out.

Ground's '''aberrismic hypothesis''' is that intervals an audible distance apart can be broadly used together in the same scale framework while merely registering as detunings of the same interval. {{adv|In a specific test case, trained and untrained 12edo listeners may notice aberrismic steps in a 27edo blackdye melody (against a control 12edo melody) but consider them to correspond to the same diatonic degree. To our knowledge this hasn't been scientifically tested yet.}} Straddle theory applies the hypothesis to definite ratios, whereas in the original aberrismic scales, it's applied to diatonic scale degrees. Commas have been described as a type of unison in other contexts, but rarely as distinct steps vital to the structure of a scale, or as intervals that are represented by the same ratio. An aberrisma is categorically a unison but doesn't sound like one when isolated, which represents both observed RTT commas and the difference between straddled intervals; it is a unison widened into a melodic step. Aberrismic theory is a collection of the effects of applying the aberrismic hypothesis to scale theory and RTT.

The aberrisma is used as one of the parameters in constructing an aberrismic scale, a type of ternary scale. For example, blackdye is a 10-note aberrismic superset of the 7-note nicetone, but with a more distinctive set of three step sizes and added opportunities to avoid pythagorean and wolf intervals. Aberrismas may also appear in MOS scales, such as Garibaldi[17]. Superpyth[12] is a good example of the distinction between interval function and size. The diatonic semitone, a deflated 256/243, is equated to the inflated 81/80. Despite being the same size, the former represents a narrow semitone, the latter is an aberrisma, and a stack of the two is a classic semitone.

== The "why" of aberrismic theory ==
=== Adding comma steps to Pyth diatonic ===
81/80 and 64/63 are the canonical choices for 2.3.5 and 2.3.7 formal commas for modifications to Pythagorean (2.3) JI ratios — 81/80 separates 5/4 from 81/64, 10/9 from 9/8, and so on; and 64/63 separates 7/4 from 16/9, 9/7 from 81/64, and so on. Aberrismic theory asks: what if we made 81/80 or 64/63 into scale steps, so that we can use both of the intervals separated by the formal comma in one scale? Indeed, doing this to 2.3 diatonic to make a ternary scale, in a way that best preserves the fifth-generated structure, results in (2.3.5) blackdye and (2.3.7) diasem, respectively.

==== Example: Blackdye ====
The Zarlino diatonic is chiral — there are two different, equally valid second degrees of the Ionian mode. Both are useful, as the sharp one forms a perfect fifth with the fifth degree but a wolf fifth with the sixth degree, and the flat one forms a perfect fifth with the sixth degree but a wolf fifth with the fifth degree.
[[File:Blackdye.png|thumb|510x510px|The construction of blackdye from Zarlino diatonic]]
One way to make it achiral is to temper out 81/80, the difference between these two steps, resulting in [[Meantone]] diatonic; intuitively this requires flattening the fifth and sharpening the sixth somewhat. However, an alternative way, if you wish to observe 81/80 or to use just intonation, is to include both varieties of whole tone over the unison, treating 81/80 as a melodic step between them. This can be thought of as dividing up a 9/8 into a 10/9 and an 81/80. It is then reasonable to extend this action to all instances of 9/8 in the scale (as, for instance, the Didymic diatonic has 27/16 as opposed to 5/3). The result is a 10-note ternary scale called '''blackdye'''.

=== Stylistic compositional features for aberrismic theory ===
This section will attempt to describe the principles and stylistic features of a specific style of music that justify using aberrismic scales in a composition. It is not an attempt to present aberrismic theory as absolute truth.
* A style of music that is melodic and heavy in modulations benefits from
** Multiple step sizes for melodic interest, for example diesis-sized steps that are below conventional semitones, specifically ones large enough to be melodically distinct but small enough to represent intonational changes.
** A set of modulatory intervals, including fifths.
** A system that allows unlimited modulation.
* It is widely agreed that lower primes are more robust to detuning. Hence for approximating JI with edos, we use lower prime temperaments, and which also represent either 81/80 or 64/63 steps for greater accuracy.
The above suggests temperaments, in particular edos, that use tempered lower primes, and edos large enough to have small diesis-sized steps. In the context of fifth-based modulation, scales also benefit from having offset arcs of fifths. One simple way to have this is to detemper MOS scales into ternary scales with an additional smaller melodic step size, which have a generator arc with fifths or a generator arc that stacks to fifths via a detempered generator chain.

{{UserTag|g_|Ground|7766ff|I assert that ~40¢ is the ideal point between "categorical unison" and "clear step"; context pushes it one way or the other, like in 27edo Superpyth diatonic and blackdye.}}

== List of aberrismic scales ==
* {{Adv|"GS(...)[n]" is [[generator sequence]] notation.}}
* {{adv|"subst ax(bycz)" denotes [[MOS substitution]].}}
* {{adv|"Almost" a cross-set means that one or two notes may be missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}
* {{adv|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}
=== Quasi-diatonic aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!|pinedye / dia1s (5L2m1s) {{adv|{{nowrap|subst 5L(2m1s)}}}}
||1sC: LLsLLmLm 1sR: LLmLLmLs 1sL: LLmLLsLm
||2.3.5 [L, m, s] = [10/9, 27/25, 81/80]
||{{adv|GS(3/2)[3] and GS(10/9)[3]}}
||1sC has 4 fifths and 1sR/1sL have 5
|-
!class="thl"|diasem / dia2s (5L2m2s) {{adv|{{nowrap|subst 5L(2m2s)}}}}
||2sR: LmLsLmLsL 2sL: LsLmLsLmL
||2.3.7 [L, m, s] = [9/8, 28/27, 64/63]
||{{adv|GS(3/2)[5] and 7/6}}
||Aggregate generator is 4/3, thus has fifth arcs of 5 and 4 notes respectively.
''See also: [[Chthonic harmony#Diasem|Diasem]]''
|-
!class="thl"|blackdye / dia3s (5L2m3s) {{adv|{{nowrap|subst 5L(2m3s)}}}}
||sLmLsLmLsL
||2.3.5 [L, m, s] = [10/9, 16/15, 81/80]
||{{adv|''GS(3/2)[5] and 10/9''}}
||Two interleaved 3-limit pentatonics
''See also: [[10-form#Blackdye|Blackdye]]''
|-
!|diaslen / dia4s (5L2m4s) {{adv|{{nowrap|subst 5L(2m4s)}}}}
||4sC: LmLsLsLmLss 4sR: LsLmLsLsLms 4sL: LsLsLmLsLsm
||2.3.7 [L, m, s] = [9/8, 49/48, 64/63]
||{{adv|GS(3/2)[4] and GS(8/7)[3]}}
||Fifth arcs with 4 notes, 4 notes, and 3 notes, with offset 8/7. Tempered to the slentonic {5L6s) MOS by [[Slendric]]. {{adv|Detempered Slendric[11] generator structure, aggregate generator is 3/2}}
|-
!|diachrome / chromedye / dia5s (5L2m5s)
||5sC: LsLsLmsLsLsm {{adv|{{nowrap|(subst 2m(5L5s))}}}} 5sR: LmsLsLsLmsLs 5sL: LsLsLsmLsLsm
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 256/243, 81/80]
||{{adv|5sC: ''GS(3/2)[6] and 40/27''}}
||Fifth-generated but with a 6-step offset
|-
!|whitedye / dia7s (5L2m7s) {{adv|{{nowrap|subst 7s(5L2m)}}}}
||LsLsLsmsLsLsms
||5120/5103-tempered 2.3.5.7 [L, m, s] = [10/9, 28/27, 81/80]
||{{adv|''GS(3/2)[7] and 81/80''}}
||Two interleaved diatonics
|}
See [[Ground's composition theory#Quasi-diatonic scales]] for more tunings of diasem and blackdye.

=== Other aberrismic scales ===
{|class="wikitable"
|-
!|Name / Signature
!|Pattern(s)
!|Possible JI/[[erac]] interp.
!|{{adv|Almost a [[cross-set]] of... (interpreted)}}
!|Notes
|-
!class="thl"|[[penslen]] / slen5m (5L5m6s) {{adv|{{nowrap|subst 6s(5L5m)}}}}
||LmsLmsLsmLsmLsms
||2.3.5.7.11[41 & 46] [L, m, s] = [12/11, 33/32, 64/63]
||{{adv|''GS(8/7)[8] and 11/8''}}
|| Has two aberrisma sizes, s and m.
|-
!|prejubilic / citro3s (4L2m3s) {{adv|{{nowrap|subst 2m(4L3s)}}}}
||C: LLsmLsLms R: LmLsLmsLs L: LmLsLsmLs
||2.5.7 [L, m, s] = [28/25, 35/32, 50/49]
||{{adv|GS(5/4)[3] and GS(7/5)[3] (exact for C)}}
||Didacus tempering makes L = m + s.
|-
!|arm5s (7L2m5s) {{adv|{{nowrap|subst 7L(2m5s)}}}}
||LmLsLsLmLsLsLs
||2.x<3.5.7.11.13[37edo] (4:2:1)
||{{adv|''GS(<<3/2)[7] and 14/13''}}
||An interleaving of two antidiatonic scales.
|-
!|mosh3s (3L4m3s) {{adv|{{nowrap|subst 4m(3L3s)}}}}
||LmsLmsmLsm
||2.x<3.7.11.13[37edo] (5:4:2)
||{{adv|''GS(16/13)[5] and 11/8''}}
||
|-
!|smi2s (4L3m2s) {{adv|{{nowrap|subst 2s(4L3m)}}}}
||C: LLmsLmLsm R: LmLmsLmLs L: LmLsLmLsm
||2.9.7.11.17[46edo] (8:4:1)
||{{adv|GS(17/14)[3] and GS(11/8)[3] (exact for C)}}
||
|-
!|sleneiro / oneiro3s (5L3m3s) {{adv|{{nowrap|subst 5L(3m3s)}}}}
||R: LmLsLmLsLms L: LsLmLsLmLsm
||2.(13:15:17:19)[5 & 18 & 44]
||{{adv|GS(13:15:17)}}
||An odd-regular aberrismic version of [[oneirotonic]].
|}

=== Systematic naming ===
Basic systematic names for aberrismic scales are of the form

[mos_prefix]n[added_step_size] (e.g. dia2s for diasem).

Any systematic name can be used for a scale as long as the scale satisfies the deletion-MOS subcondition for the added step size.

This is subject to change as aberrismic theory nomenclature is updated in the future.

== Notation ==
The [[generator gronut]] is an aberrismic extension of the circle of fifths.

=== Quasi-diatonic ===
Quasi-diatonic aberrismic notation restricts to [[diatonic notation]] on the tempered 3-limit.

Aberrismic/straddle-prime accidentals:
* Plus / Minus +/- : These tune a note sharp or flat by a small aberrisma. They reference Johnston notation because 81/80 is a common aberrisma, but they can also represent 64/63 or any other interval of similar function. 
* Duplus / Duminus ≠/= : Short for ++/--, most often representing 36/35~33/32~1053/1024, which is the large aberrisma in scales like penslen, or two small aberrismas in Akea temperament. Of all options, this set of characters is the easiest to type, looks the best in various fonts, and is least likely to be confused for the similar semisharp accidental (although they happen to represent the same size of interval).
* [[Erac|Eracs]] may be used to represent the inflating of commas typically found in aberrismic scales, although they represent a specific unit of error.

== Aberrismic theory and RTT ==
Aberrismic theory often applies RTT to ternary LCJI scales with comma steps. Certain scales with aberrismas may thus be endowed with JI interpretations via [[RTT]] temperaments, which may be used in suitable [[equal temperament]]s. Under Ground's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become a [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers out neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]]. Tempering is important in aberrismic theory as a way to improve the function of commas (frequently [[81/80]] or [[64/63]]) as aberrismas in ternary LCJI scales by tempering them larger than just.

At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or [[Ultrapyth]] temperament.

There are two choices involved in interpreting a given ternary scale, namely the choice of temperament and the choice of where to map the scale steps. The assignment of scale steps to tempered intervals is chosen to improve coverage of important LCJI intervals.

=== Example: Blackdye ===
The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth respectively.
* ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists an exact JI tuning.
* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one. Ground once termed the tuning of blackdye that makes aberrisma-altered Pyth thirds 13/11 and 14/11 ''Flutterpyth blackdye''.

{| class="wikitable right-2 right-3 right-4 right-5"
|+ style="font-size: 105%;" | Blackdye intervals in two temperaments
|-
! Interval class
! Sizes
! Untempered 2.3.5
! 2.3.7.11.13 Flutterpyth (extended to 13-limit Ultrapyth)
|-
! 1-step
| s m L
| 81/80 16/15 10/9
| 143/140 22/21 160/143
|-
! 2-step
| L + s L + m
| 9/8 32/27
| 8/7, 9/8 7/6
|-
! 3-step
| L + 2s L + m + s 2L + s 2L + m
| 729/640 6/5 5/4 320/243
| 7/6 13/11 14/11 13/10
|-
! 4-step
| 2L + 2s 2L + m + s
| 81/64 4/3
| 13/10 4/3
|-
! 5-step
| 2L + m + 2s 2L + 2m + s 3L + 2s 3L + m + s
| 27/20 64/45 45/32 40/27
| 66/49 11/8 16/11 49/33
|-
! 6-step
| 3L + m + 2s 3L + 2m + s
| 3/2 128/81
| 3/2 20/13
|-
! 7-step
| 3L + m + 3s 3L + 2m + 2s 4L + m + 2s 4L + 2m + s
| 243/160 8/5 5/3 1280/729
| 20/13 11/7 22/13 12/7
|-
! 8-step
| 4L + m + 3s 4L + 2m + 2s
| 27/16 16/9
| 12/7 7/4, 16/9
|-
! 9-step
| 5L + 2m + s 5L + m + 2s 4L + 2m + 2s
| 9/5 15/8 160/81
| 143/80 21/11 280/143
|}

== Glossary ==
* '''Aberration scale''': A scale made by interleaving aberrismas into a binary scale and stretching or compressing, usually a [[MOS substitution]] scale of type {{nowrap|[a+b+1]s(aLbm)}} (compression, called '''tractaberrated''') or {{nowrap|[a+b-1]s(aLbm)}} (stretching, called '''tensaberrated'''). For example, sLsmsLsLsLsmsLs is an aberration scale made from diatonic (a MOS substitution scale of type 8s(5L2m)), also called trackdye.
* '''Aberrisma''': The smallest interval region that melodically sounds like a step.
* '''Magnitone''': The melodic function of L + s in quasi-diatonic aberrismic scales.
* '''Monotone-MOS''': A ternary scale is ''monotone-MOS'' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy a monotone-MOS subcondition''. For example, diasem (LmLsLmLsL) satisfies all three monotone-MOS subconditions, but blackdye (sLmLsLmLsL) satisfies only the m = s and s = 0 monotone-MOS subconditions. An aberrismic scale is required to satisfy the s = 0 monotone-MOS subcondition.
* '''Solitone''': The melodic function of the L step in quasi-diatonic aberrismic scales.
* '''Subaberrisma''': A step so small (smaller than the typical limit for an aberrisma) that its status as a melodic step is unclear.

== Extension to higher ranks ==
Aberrismic theory is typically concerned with ternary scales, especially those with two chains of generators of the same length or differing by one, meaning that they have a [[GS]] with only two intervals. This is because they are not much harder to navigate than an MOS while offering significantly more flexibility.

{{UserTag|g_|Ground|7766ff|I propose that we call this type of scale '''bicatenary'''.}}

However, this is often not enough to accurately represent a larger JI subgroup. Portent penslen (5L5m6s) is a somewhat unique counterexample, being bicatenary yet microtempered in the 11-limit. The solution is to add more step sizes while maintaining as much lower-rank structure as possible. For example, while penslen is found in edos like 41 and 46, the equivalent in the similarly LCJI-accurate 53 and 58 is 5L2m3s4t, a quaternary subset of Buzzard[28] with a JI tuning of 35/32 : 21/20 : 36/35 : 64/63. [[Ground's composition theory#Interval logic deviation theory|ILD]] is a simple way to access notes outside of a scale with a higher rank.

A common tempering of blackdye involves a sharper 3 to significantly inflate 81/80, both for melodic utility and to equate 27/20 to a superfourth like 15/11 or 11/8. It also becomes natural to temper out 64/63. Possibly the most common ratio representation of an aberrisma is 36/35, but few ternary scales use it without tempering out 81/80 or 64/63.

(81/80)^2 = 43¢ is notably in the middle of the usual aberrisma size range as well. This does not exist in blackdye, but becomes accessible in certain variants of 5L2m8s as well as numerous quaternary scales with even more options for available intervals.

== Compositional examples ==
Some compositional snippets using aberrismic scales:

* The Art of It makes almost exclusive use of 31edo diasem: [[File:A New Dusk-02 The Art of It.mp3]]
* A fugue using aberrismic scales: [[File:Inthar - Fugue in 32edo and 33edo.mp3]]
* A 34edo blackdye fugue exposition: [[File:Blackdye-fugue-expo.mp3]]

== External links ==
* [https://turbofishcrow.github.io/tern Tern: aberrismic-focused ternary scale analysis]
{{cat|
Terms
Aberrismic terms
Ternary scales
}}

Oneirotonic

2026-11-03T06:00:01Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This [[aberrismic]] scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an odd-regular scale, there are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:59:10Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an odd-regular scale, there are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}} If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:56:12Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an odd-regular scale, there are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is [[GS]](13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}}}}

{{Adv|If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:55:02Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. Since sleneiro is an odd-regular scale, there are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}}}}

{{Adv|If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:52:38Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44; arguably 39edo and 44edo are the first reasonably accurate tunings.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}}}}

{{Adv|If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:44:37Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). The corresponding edo join is 5 & 18 & 44.

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}}}}

{{Adv|If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:40:33Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). 

{{Adv|In fact, the JI scale suggests a whole host of efficient temperings, resulting in the rank-3 temperament {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}}}}

{{Adv|If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:38:20Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). 

{{Adv|In fact, the JI scale suggests many efficient temperings, resulting in the rank-3 temperament {{nowrap|2.27.31.49.53.(13:15:17:19)[5 & 44 & 62].}}}}

{{Adv|Extending to prime 5 by tempering out 2601/2600 results in {{nowrap|2.5.27.31.49.53.(3:13:17:19)[44 & 62 & 93].}}}}

{{Adv|If we then extend to prime 3 by tempering out 676/675, we obtain {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:26:09Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). 

{{Adv|In fact, the JI scale suggests many efficient temperings, resulting in the rank-3 temperament {{nowrap|2.27.31.49.53.(13:15:17:19)[5 & 44 & 62].}} Extending to prime 3 and tempering out 676/675 and 2601/2600 results in {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by a flattened ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:23:54Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). 

{{Adv|In fact, the JI scale suggests many efficient temperings, resulting in the rank-3 temperament {{nowrap|2.27.31.49.53.(13:15:17:19)[5 & 44 & 62].}} Extending to prime 3 and tempering out 676/675 and 2601/2600 results in {{nowrap|2.3.5.13.17.19.31.49.53[106 & 111],}} generated by ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:16:24Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates four stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). 

{{Adv|In fact, the JI scale suggests many efficient temperings, resulting in the rank-3 temperament {{nowrap|2.27.31.49.53.(13:15:17:19)[5 & 44 & 62].}} Extending to prime 3 and tempering out 676/675 results in {{nowrap|2.3.31.49.53.(13:15:17:19)[5 & 106],}} generated by ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:16:10Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486, which equates three stacked 17/13's to one 19/13, extends this to 2.(13:15:17:19). 

{{Adv|In fact, the JI scale suggests many efficient temperings, resulting in the rank-3 temperament {{nowrap|2.27.31.49.53.(13:15:17:19)[5 & 44 & 62].}} Extending to prime 3 and tempering out 676/675 results in {{nowrap|2.3.31.49.53.(13:15:17:19)[5 & 106],}} generated by ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:13:26Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486 extends this to 2.(13:15:17:19). 

{{Adv|In fact, the JI scale suggests many efficient temperings, resulting in the rank-3 temperament {{nowrap|2.27.31.49.53.(13:15:17:19)[5 & 44 & 62].}} Extending to prime 3 and tempering out 676/675 results in {{nowrap|2.3.31.49.53.(13:15:17:19)[5 & 106],}} generated by ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:12:07Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486 extends this to 2.(13:15:17:19). 

{{Adv|In fact, there are many efficient temperings available, resulting in the rank-3 temperament {{nowrap|2.27.31.49.53.(13:15:17:19)[5 & 44 & 62].}} Extending to prime 3 and tempering out 676/675 results in {{nowrap|2.3.31.49.53.(13:15:17:19)[5 & 106],}} generated by ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
{{UTBox|bz|Jaimbee|DAA520}}
In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
{{UTBox|bz|Jaimbee|DAA520}}
To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
{{UTBox|KC|Inthar|000000}}
The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

{{Navbox MOS}}

Oneirotonic

2026-11-03T05:10:59Z

Inthar: /* 5L3m3s quasi-oneirotonic */

'''Oneirotonic''' is the 5L3s [[MOS]] pattern LLsLLsLs. Its generator ranges from equalized [[8edo|3\8]] (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is [[13edo|5\13]] (461.5c). It is notable for being a compressed diatonic with one extra small step.

The basic idea of oneirotonic is sharpening the fifth beyond 5edo: the fifth becomes so sharp that two of them make a subminor/flat minor third and one more note is required to form a MOS.
== Notation ==
This article uses KISS notation, where the Celephaisian mode is 123456781. Chroma up is denoted #, chroma down as b. Alternatively, there is ground's oneirotonic notation, which preserves the diatonic order of letter names when stacking fourths (with one extra nominal): BEADGCFX, again with the Celephaisian mode as ACBDFEGXA. Note that C and B are swapped, and F and E are also swapped. Alternate generator chains are YBEADGCF and HEADGCFB from German notation.

== Structural theory ==
In the all-natural Celephaisian mode, the generators are arranged in the order 3-6-1-4-7-2-5-8.
=== Modes ===
The mode names were originally given by Cryptic Ruse, but they have disavowed them since.
{| class="wikitable"
|-
! Mode name !!Gens up !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarnathian || 0|| sLsLLsLL || style="background-color:#d66" |m || style="background-color:#d66" |m || style="background-color:#d66" |d || style="background-color:#d66" |m || style="background-color:#d66" |P || style="background-color:#d66" |m || style="background-color:#d66" |m
|-
|Hlanithian
|1
|sLLsLsLL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#66d"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#d66"|m
| style="background-color:#d66"|m
|-
| Kadathian
|2
| sLLsLLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Mnarian
|3|| LsLsLLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Ultharian
|4|| LsLLsLsL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celephaisian
|5|| LsLLsLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarnekian
|6|| LLsLsLLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Dylathian
|7|| LLsLLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}
{{UserTag|g_|Ground|7766ff|I think Celephaisian is sometimes treated as the default because it melodically resembles a mix of Aeolian and Melodic Minor, which fits the oneirotonic sound well. This is my most used mode, although I also like Ultharian, which feels like a mix of Aeolian and Dorian.}}

=== Modes of melodic Mnarian ===
The ''melodic Mnarian'' (LsLsLLLs ascending, LsLsLsLL descending) scale has an "LLL" and recreates the characteristic of diatonic modes such as Phrygian and Locrian which have LLL prominently. It's the unique binary MODMOS of oneirotonic that doesn't have consecutive s steps. The mode names of melodic Mnarian are portmanteaus of the oneirotonic mode and the diatonic mode the mode sounds most similar to.
{| class="wikitable"
|-
! Mode name !! Pattern !! 1-step !! 2-step !! 3-step !! 4-step !! 5-step !! 6-step
!7-step
|-
| Sarlocrian || sLsLsLLL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#d66" |d
| style="background-color:#d66" |m
| style="background-color:#e33" |d
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Sardorian ||sLsLLLsL
| style="background-color:#d66"|m
| style="background-color:#d66"|m
| style="background-color:#d66"|d
| style="background-color:#d66"|m
| style="background-color:#d66"|P
| style="background-color:#66d"|M
| style="background-color:#d66"|m
|-
| Mnaeolian || LsLsLsLL
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |m
|-
| Mnionian || LsLsLLLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#d66" |m
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ulphrygian || sLLLsLsL
| style="background-color:#d66" |m
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Celdorian || LsLLLsLs
| style="background-color:#66d" |M
| style="background-color:#d66" |m
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|-
| Ilarmixian || LLsLsLsL
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#66d" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |P
| style="background-color:#66d" |M
| style="background-color:#d66" |m
|-
| Dylydian || LLLsLsLs
| style="background-color:#66d" |M
| style="background-color:#66d" |M
| style="background-color:#33e" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |A
| style="background-color:#66d" |M
| style="background-color:#66d" |M
|}

== Notable tunings and tuning ranges ==
* 37edo (hardness 5/4) to 29edo (hardness 4/3): support the 2.7/5.11/5.13/5 temperament [[Ammonite]] where the generator is 13/10, the large step is 11/10, and the minor 4-step is 7/5.
* 21edo (hardness 3/2)
* 13edo (hardness 2/1)
* 31edo (hardness 5/2): [[A-Team]] tuning with an excellent 5/4. Approximates 13:17:19.
* 18edo (hardness 3/1): Minor 2-step is an excellent 7/6; 12edo whole tone. Practically optimal for 2.9.21 A-Team.
* 23edo (hardness 4/1): Supports A-Team with diminished 3-step = ~6/5.
* 28edo (hardness 5/1) and harder support 2.3.7 [[Buzzard]] which equates four perfect 3-oneirosteps with a 3/1.

=== Ground's subtypes ===
{{UTBox|g_|Ground|7766ff}}
I split oneirotonic tunings into three subtypes depending on how well they correspond to low-limit JI: Buzzard, "A-strad", and "Corvic" (which may itself be split into the rank-2 temperaments Petrtri and Ammonite).
Different ranges of oneirotonic generators may be represented by a few intervals of similar complexity. This is very different from diatonic, where every generator is approximately 3/2 or 4/3. I will focus on three of them: 13/10, 17/13, and 21/16. I ignore 9/7 because it's outside the range and 25/19 because it's used extremely rarely. 21/16 is clearly the generator of both Buzzard and A-strad, although 17/13 shows up in Slendric which is a superset of A-strad; 13/10 is clearly the generator of Corvic, although 17/13 is equated to it in the base temperament. 17/13 is close to the boundary between subtypes and does not clearly correspond to either. This splits the range into two slightly broader categories: 21/16 oneiro and 13/10 oneiro.

==== Buzzard ====
* Defining characteristics: 5edo cluster temperament, higher-complexity 7-limit approaching microtemperament.
** Approximate generator range: 11\28 to 2\5
** Approximate optimal tunings: 19\48, 21\53, 23\58
* Buzzard is an odd bit of asymmetry, given how the boundary between A-strad and Corvic is almost exactly in the middle of the oneirotonic range. This is because it removes the straddling, introducing strong concordances that upset the usual balance. Most importantly, Buzzards's subfifth at 4 generators is an accurate 3/2.
* An 8edo cluster temperament would be expected on the other side of the range. This is just non-over-one Corvic, which is tuned well over a much wider range.

==== "A-strad" ====
(straddle/dual-3 A-team)
* Defining characteristics: Straddled rough approximations of 4:5:6:7. Not as accurate as Buzzard, but with few other clear otonal chords.
** Approximate generator range: 5\13 to 11\28
** Approximate optimal tunings: 19\49, 26\67, 7\18
* Every other Mothra generator
* Basic non-straddle rank-2: 2.9.5.7/3 5&13
** Comma list: 81/80 1728/1715, which is Mothra in 2.3.5.7
* Straddled GTO string: 1200 | 2.<3.>3.5.<7.>7 || 0 4 -1 6 2 -3
* Various extensions are possible, but my usage of this tuning range doesn't depend on as many otonal chords as Corvic.

==== "Corvic" ====
(hard not to think of crows here)
* Defining characteristics: No-3 tertian chords 9:11:13:16:19, 11:13:17:20, 10:13:16, and so on. Extremely xenharmonic.
** Approximate generator range: 3\8 to 5\13 (all are somewhat close to optimal for non-over-one)
** Approximate optimal tunings (rank-3): 14,12\37, 19,16\50
* Basic rank-3: 2.5.11.13.17 13&16&21
* Extended rank-3: 2.9.5.7.11.13.17.19.23 13&16&21
** The extended subgroup is not the most accurate, but it's very low-complexity and applies reasonably to any soft oneirotonic edo. 9 and 7 have especially high error because 9/p is best close to 5\13 and 7/p is best close to 3\8. 9 is sharp and 7 is flat because 9/7 is very flat of the oneiro generator it's mapped to.
*** An alternate mapping of 9/8 is better in edos like 37 and 50, equivalent to 16/11 minus the 13/10 generator. This removes the accurate oneirotonic 9/5 found near 13edo and its accompanying chords, but improves the 9/7 and occurs very often in 5L3m3s as the acute major 1-step. The edo join should be altered to 13&16&21[-9], although this may provide unusual default generators.
*** With 7 often being flat, the oneiro generator can be interpreted as a flat 21/16, providing an often good 3.
* Being rank-3 allows the temperament to translate easily to the '''5L3m3s''' aberrismic scale. In generator-offset notation, the scale is "bicatenary" (two generator chains) and the generator is oneirotonic. All of these functional primes besides the extension's 19 and 23 are offset, and this offset can be removed from the temperament, resulting in a mostly non-over-one 2.{9:5:7:11:13:17}.19.23 (which I might also represent over-5 as 2.9/5.7/5.11/5.13/5.17/5.19.23).
* The rank-3 representation or the non-over-one rank-2 reduction could be represented with a straddle temperament, but I choose not to do that because some rank-2 tunings (Petrtri extension and Ammonite) represent the primes themselves accurately.
* May also be represented as a DR temperament based on its otonal tertian chords: GTO 1200 || +1[-1 2]+2 +4[1 -1]+3 +2[-1 2]+3 +1[4 -6]+1 | 1 1 -4 -4.
{| class="wikitable"
|+Corvic Tuning Examples in Cents (~5/4 offset)
! rowspan="2" |
| rowspan="2" |
! colspan="3" |5\13, 4\13
| rowspan="2" |
! colspan="3" |18\47, 15\47
| rowspan="2" |
! colspan="3" |13\34, 11\34
| rowspan="2" |
! colspan="3" |8\21, 7\21
| rowspan="2" |
! colspan="3" |19\50, 16\50
| rowspan="2" |
! colspan="3" |11\29, 19\58
| rowspan="2" |
! colspan="3" |14\37, 12\37
| rowspan="2" |
! colspan="3" |3\8, 5\16
| rowspan="2" |
! colspan="3" |3\8, 8\24
|-
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
!-1
!0
!1
|-
! -7
| rowspan="7" |
|0
|369
|738
| rowspan="7" |
|0
|383
|766
| rowspan="7" |
|0
|388
|776
| rowspan="7" |
|0
|400
|800
| rowspan="7" |
|24
|408
|792
| rowspan="7" |
|21
|414
|807
| rowspan="7" |
|32
|422
|811
| rowspan="7" |
|75
|450
|825
| rowspan="7" |
|50
|450
|850
|-
! -6
|462
|831
|0
|460
|843
|26
|459
|847
|35
|457
|857
|57
|480
|864
|48
|476
|869
|62
|486
|876
|65
|525
|900
|75
|500
|900
|100
|-
! -5
|923
|92
|462
|919
|102
|485
|918
|106
|494
|914
|114
|514
|936
|120
|504
|931
|124
|517
|941
|130
|519
|975
|150
|525
|950
|150
|550
|-
! -4
| class="acc1" |'''185'''
|554
| class="acc0" |'''923'''
| class="acc1" |'''179'''
|562
| class="acc0" |'''945'''
| class="acc1" |'''176'''
|565
| class="acc0" |'''953'''
| class="acc1" |'''171'''
|571
| class="acc0" |'''971'''
| class="acc1" |'''192'''
|576
| class="acc0" |'''960'''
| class="acc1" |'''186'''
|579
| class="acc0" |'''972'''
| class="acc1" |'''195'''
|584
| class="acc0" |'''973'''
| class="acc1" |'''225'''
|600
| class="acc0" |'''975'''
| class="acc1" |'''200'''
|600
| class="acc0" |'''1000'''
|-
! -3
|646
|1015
| class="acc1" |'''185'''
|638
|1021
| class="acc1" |'''204'''
|635
|1024
| class="acc1" |'''212'''
|629
|1029
| class="acc1" |'''229'''
|648
|1032
| class="acc1" |'''216'''
|641
|1034
| class="acc1" |'''228'''
|649
|1038
| class="acc1" |'''227'''
|675
|1050
| class="acc1" |'''225'''
|650
|1050
| class="acc1" |'''250'''
|-
! -2
|1108
| class="acc0" |'''277'''
|646
|1098
| class="acc0" |'''281'''
|664
|1094
| class="acc0" |'''282'''
|671
|1086
| class="acc0" |'''286'''
|686
|1104
| class="acc0" |'''288'''
|672
|1097
| class="acc0" |'''290'''
|683
|1103
| class="acc0" |'''292'''
|681
|1125
| class="acc0" |'''300'''
|675
|1100
| class="acc0" |'''300'''
|700
|-
! -1
|369
|738
|1108
|357
|740
|1123
|353
|741
|1129
|343
|743
|1143
|360
|744
|1128
|352
|745
|1138
|357
|746
|1135
|375
|750
|1125
|350
|750
|1150
|-
!0
|
|831
| class="thl" |'''0'''
| class="thl" |'''369'''
|
|817
| class="thl" |'''0'''
| class="thl" |'''383'''
|
|812
| class="thl" |'''0'''
| class="thl" |'''388'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|
|816
| class="thl" |'''0'''
| class="thl" |'''384'''
|
|807
| class="thl" |'''0'''
| class="thl" |'''393'''
|
|811
| class="thl" |'''0'''
| class="thl" |'''389'''
|
|825
| class="thl" |'''0'''
| class="thl" |'''375'''
|
|800
| class="thl" |'''0'''
| class="thl" |'''400'''
|-
!1
| rowspan="7" |
|92
|462
| class="thl" |'''831'''
| rowspan="7" |
|77
|460
| class="thl" |'''843'''
| rowspan="7" |
|71
|459
| class="thl" |'''847'''
| rowspan="7" |
|57
|457
| class="thl" |'''857'''
| rowspan="7" |
|72
|456
| class="thl" |'''840'''
| rowspan="7" |
|62
|455
| class="thl" |'''848'''
| rowspan="7" |
|65
|454
| class="thl" |'''843'''
| rowspan="7" |
|75
|450
| class="thl" |'''825'''
| rowspan="7" |
|50
|450
| class="thl" |'''850'''
|-
!2
|554
|923
| class="thl" |'''92'''
|536
|919
| class="thl" |'''102'''
|529
|918
| class="thl" |'''106'''
|514
|914
| class="thl" |'''114'''
|528
|912
| class="thl" |'''96'''
|517
|910
| class="thl" |'''103'''
|519
|908
| class="thl" |'''97'''
|525
|900
| class="thl" |'''75'''
|500
|900
| class="thl" |'''100'''
|-
!3
| class="acc0" |'''1015'''
|185
| class="thl" |'''554'''
| class="acc0" |'''996'''
|179
| class="thl" |'''562'''
| class="acc0" |'''988'''
|176
| class="thl" |'''565'''
| class="acc0" |'''971'''
|171
| class="thl" |'''571'''
| class="acc0" |'''984'''
|168
| class="thl" |'''552'''
| class="acc0" |'''972'''
|166
| class="thl" |'''559'''
| class="acc0" |'''973'''
|162
| class="thl" |'''551'''
| class="acc0" |'''975'''
|150
| class="thl" |'''525'''
| class="acc0" |'''950'''
|150
| class="thl" |'''550'''
|-
!4
|277
| class="acc0" |'''646'''
|1015
|255
| class="acc0" |'''638'''
|1021
|247
| class="acc0" |'''635'''
|1024
|229
| class="acc0" |'''629'''
|1029
|240
| class="acc0" |'''624'''
|1008
|228
| class="acc0" |'''621'''
|1014
|227
| class="acc0" |'''616'''
|1005
|225
| class="acc0" |'''600'''
|975
|200
| class="acc0" |'''600'''
|1000
|-
!5
| class="acc1" |'''738'''
|1108
|277
| class="acc1" |'''715'''
|1098
|281
| class="acc1" |'''706'''
|1094
|282
| class="acc1" |'''686'''
|1086
|286
| class="acc1" |'''696'''
|1080
|264
| class="acc1" |'''683'''
|1076
|269
| class="acc1" |'''681'''
|1070
|259
| class="acc1" |'''675'''
|1050
|225
| class="acc1" |'''650'''
|1050
|250
|-
!6
|0
|369
| class="acc1" |'''738'''
|1174
|357
| class="acc1" |'''740'''
|1165
|353
| class="acc1" |'''741'''
|1143
|343
| class="acc1" |'''743'''
|1152
|336
| class="acc1" |'''720'''
|1138
|331
| class="acc1" |'''724'''
|1135
|324
| class="acc1" |'''714'''
|1125
|300
| class="acc1" |'''675'''
|1100
|300
| class="acc1" |'''700'''
|-
!7
|462
|831
|0
|434
|817
|0
|424
|812
|0
|400
|800
|0
|408
|792
|1176
|393
|786
|1179
|389
|778
|1168
|375
|750
|1125
|350
|750
|1150
|}
{| class="wikitable"
|+Color Key
| class="thl" |
|Unison and mappings of core primes 5, 11, 13, and 17.
|-
| class="acc0" |
|Optional mappings of 7±, 19, and 23.
|-
| class="acc1" |
|Optional mappings of 3± and 9±.
|}

===== 5L3m3s quasi-oneirotonic =====
This scale may be called "sleneiro" being slentonic at m=s and oneirotonic at s=0. There are two step orders that satisfy all three monotone-MOS conditions: LmLsLmLsLms (R) and LmLsLmLsmLs (L). RA Celephaisian (sLmLsLmLsLm) is like Blackdye A Aeolian with a semitone added at the top.

{{UserTag|KC|Inthar|000000|An obvious untempered JI interpretation for sleneiro is GS(13:15:17)[11] in the 2.(13:15:17) subgroup. Tempering out the 0.7-cent comma 83521/83486 extends this to 2.(13:15:17:19). 

{{Adv|In fact, there are many efficient temperings available, resulting in the rank-3 temperament 2.27.31.49.53.(13:15:17:19)[5 & 44 & 62]. Extending to prime 3 and tempering out 676/675 results in 2.3.31.49.53.(13:15:17:19)[5 & 106], generated by ~147/128.}}}}
{| class="wikitable"
|+19\50, 16\50;
5L3m3s RA Celephaisian Highlighted;

BEADGCFX Aberrismic Notation
|-
!
! colspan="2" |-1
! colspan="2" |0
! colspan="2" |1
|-
! -7
| class="thl" |'''A+'''
| class="thl" |'''24'''
|D#
|408
|Gx-
|792
|-
! -6
| class="thl" |'''D+'''
| class="thl" |'''480'''
|G#
|864
|Cx-
|48
|-
! -5
| class="thl" |'''G+'''
| class="thl" |'''936'''
|C#
|120
|Fx-
|504
|-
! -4
| class="thl" |'''C+'''
| class="thl" |'''192'''
|F#
|576
|Xx-
|960
|-
! -3
| class="thl" |'''F+'''
| class="thl" |'''648'''
|X#
|1032
|B#-
|216
|-
! -2
| class="thl" |'''X+'''
| class="thl" |'''1104'''
| class="thl" |'''B'''
| class="thl" |'''288'''
|E#-
|672
|-
! -1
|Bb+
|360
| class="thl" |'''E'''
| class="thl" |'''744'''
|A#-
|1128
|-
!0
|Eb+
|816
| class="thl" |'''A'''
| class="thl" |'''0'''
|D#-
|384
|-
!1
|Ab+
|72
| class="thl" |'''D'''
| class="thl" |'''456'''
|G#-
|840
|-
!2
|Db+
|528
| class="thl" |'''G'''
| class="thl" |'''912'''
|C#-
|96
|-
!3
|Gb+
|984
|C
|168
|F#-
|552
|-
!4
|Cb+
|240
|F
|624
|X#-
|1008
|-
!5
|Fb+
|696
|X
|1080
|B-
|264
|-
!6
|Xb+
|1152
|Bb
|336
|E-
|720
|-
!7
|Bbb+
|408
|Eb
|792
|A-
|1176
|}

== Chords of oneirotonic ==
{{proposed}}
These chord names have been proposed by [[User:Ground|ground]] and [[User:Inthar|Inthar]].
The names have been selected to avoid overloading diatonic chord names and symbols.
=== Fifth-bounded triads ===
The prefix "tract" is used to denote compressions of diatonic chords, and symbolically, <code>>...<</code> is used to denote tract-diatonic chords.

First and second inversions of triads are denoted <code>triad₁</code> and <code>triad₂</code> in chord symbols, for example <code>>maj<₁</code> = the first inversion of the tract-major triad.
{| class="wikitable"
|+ Perfect fifth (sharp fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Supertaphric (<code>suptph</code>)
||
||0–m4d–P5d
||0–554–738
|[[File:Oneirodemossixeightofthirteen.wav|thumb]]
||0–533–733
|[[File:Oneirodemoszeroeightelevenundereighteen.wav|thumb]]
|-
!|Taphric (<code>tph</code>)
||From τάφρος "trench", because the fifth generators go down–up.
||0–P3d–P5d
||0–462–738
|[[File:Oneirodemothirteenfiveeight.wav|thumb]]
||0–467–733
|[[File:Oneirodemoszerosevenelevenundereighteen.wav|thumb]]
|-
!|Subtaphric (<code>subtph</code>)
||
||0–M2d–P5d
||0–369–738
|
||0–400–733
|[[File:Oneirodemoszerosixelevenundereighteen.wav|thumb]]
|-
!|Neutral (<code>neu</code>)
||Splits the sharp fifth in half.
||
||0–369–738
|[[File:Oneirodemothirteenffoureight.wav|thumb]]
||
|
|-
!|Suprasimic (<code>supsim</code>)
||
||0–d3d–P5d
||0–369–738
|
||0–333–733
|[[File:Oneirodemoszerofiveelevenundereighteen.wav|thumb]]
|-
!|Simic (<code>sim</code>)
||From Modern Greek σημείο "point", because the fifth generators go up–down.
||0–m2d–P5d
||0–277–738
|[[File:Oneirodemothirteenthreeeight.wav|thumb]]
||0–267–733
|[[File:Oneirodemoszerofoureleven.wav|thumb]]
|-
!|Subsimic (<code>subsim</code>)
||
||0–M1d–P5d
||0–185–738
|[[File:Oneirodemothirteentwoeight.wav|thumb]]
||0–200–733
|[[File:Oneirodemoszerothreeeleven.wav|thumb]]
|}

{| class="wikitable"
|+ Major tritone (flat fifth) bounded triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Tract-sus4 (<code>>sus4<</code>)
||
||0–P3d–M4d
||0–462–646
|[[File:Oneirodemothirteenfiveseven.wav|thumb]]
||0–467–667
|[[File:Oneirodemosseventenofeighteen.wav|thumb]]
|-
!|Tract-major (<code>>maj<</code>)
||
||0–M2d–M4d
||0–369–646
|[[File:Oneirodemothirteenfourseven.wav|thumb]]
||0–400–667
|[[File:Oneirodemossixtenofeighteen.wav|thumb]]
|-
!|Tract-neutral (<code>>neu<</code>)
||Splits the flat fifth in half.
||0–n2d–M4d
||
|
||0–333–667
|[[File:OneirodemosNEWfivesevenofeighteen.wav|thumb]]
|-
!|Tract-minor (<code>>min<</code>)
||
||0–m2d–M4d
||0–277–646
|[[File:Oneirodemonewthirteenthreeseven.wav|thumb]]
||0–267–667
|[[File:OneirodemosNEWfoursevenofeighteen.wav|thumb]]
|-
!|Tract-sus2 (<code>>sus2<</code>)
||
||0–M1d–M4d
||0–185–646
|[[File:Oneirodemothirteentwoseven.wav|thumb]]
||0–200–667
|[[File:Oneirodemosthreetenofeighteen.wav|thumb]]
|}

{{Cat|MOS patterns}}

=== Other triads ===
{| class="wikitable"
|+ Other triads
|-
!|Name (notation)
!|Description
!|In degrees (TAMNAMS)
!|13edo tuning
!Listen
!|18edo tuning
!Listen
|-
!|Grammic (<code>grm</code>)
||From "line", since the generators form a line.
||0-P3-m6
||0-462-923
|[[File:Oneirodemothirteensixth.wav|thumb]]
||0-467-933
|[[File:Oneirodemongrammic.wav|thumb]]
|}

=== Notes ===
Taphric, simic, and grammic are all antipentic terms but otherwise do not reflect specific tuning ranges. Subtaphric/suprasimic/etc. chords in grammic form can just be called inversions the same way diatonic chords are. Grammic may also be known as sensic in checkertonic.

== Jaimbee and Inthar's oneirotonic functional system ==
{{Proposed}}

Todo: convert to KISS notation

The following system has been developed by Jaimbee and Inthar. It is meant for 13edo and tunings close to 13edo or somewhat harder (like 31edo or 18edo). 18edo oneirotonic has a discordant >maj< chord and so has a more stable tonal center on minor keys.

For a DR-forward framework like this, prefer mellow timbres to bright ones to bring out the DR effect.
=== Note on symbols ===
Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats. In order:

<math>\hat{1}, \hat{2}, \hat{3}, \hat{4}, \hat{\mathrm{t}}, \hat{5}, \hat{6}, \hat{7}.</math>

When not modified, these denote the pitches of the Ilarnekian (LLsLsLLs) mode. Sharp and flat modifiers (e.g. <math>\flat\hat{3}</math>) work as in standard functional diatonic chord notation — they denote chroma (L - s) alterations from Ilarnekian.

The chord symbols used are ground's system, described above.

=== Basic chords ===
The most basic chords in this functional harmony system are:
* Tract-major triad 0-4-7\13 (<code>>maj<</code>): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1, and the DR effect benefits from added notes. Oneirotonic provides only two of these triads, so alterations are somewhat frequently used to get this triad. The tract-major triad has the following important tetrad supersets:
** 0-2-4-7\13 (<code>>majsus2<</code>): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
** 0-4-7-10\13 (<code>>dom7<</code>): A compressed dominant tetrad; approximately +1+?+1.
** 0-4-7-12\13 (<code>>maj<7</code>): Approximately +1+1+2.
* The simic triad 0-3-8\13 (<code>sim</code>): A bright and brooding if somewhat hollow-sounding minor triad. Approximately 17:20:26 or +1+2. The important supersets are:
** 0-3-8-10 (<code>sim6</code>): Approximately +1+2+1.
** 0-3-8-12 (<code>simmaj7</code>): Approximately +1+2+2.
** 0-3-8-11 (<code>simmin7</code>): Something like a minor 7th tetrad.
** 0-3-8-15 (<code>simadd9</code>)
** 0-3-8-12-15 (<code>simmaj7add9</code>): A concatenation of the minor +1+2 and major +1+1 triads.
* 0-5-9\13 (<code>>IV/I<</code>): A +1+1 triad and a compressed 2nd inversion major triad. Approximately 13:17:21.
** 0-5-7-9: Approximately +2+1+1.
** 0-5-9-12: A tract-major triad on top of a subfourth.
** 0-5-9-12-15
** 0-5-7-9-12-15-17
* 0-5-7\13 (<code>>sus4<</code>): Compressed sus4. Approximately +2+1.
* 0-4-8\13 (<code>>aug<</code>): "Submajor augmented" triad.
* 0-3-6\13 (<code>>dim<</code>): The most diminished-like triad.

=== Functional patterns ===
{{UserTag|KC|Inthar|000000|13edo oneirotonic enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("tract-major triad" or just ">maj<") and 0-277-738-923 ("simic sixth" or "sim6"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "simic", and 0-277-646-923 will be called "tract-minor 7th".

If you wish to avoid the dissonance of the fifths, just using 10\13 (e.g. [0 4 10 (12)]\13, [0 3 10 (12)]\13) works well.}}

=== Progressions ===
{{UserTag|KC|Inthar|000000|Common motions:
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{2}</math> sim6
* <math>\hat{1}</math> (>maj< or sim6) → <math>\hat{4}</math> sim6 (when ending on <math>\hat{1}</math> this sounds like diatonic V to I)
* <math>\hat{1}</math> (>maj< or sim6) → <math>\flat\hat{6}</math> sim6
* <math>\hat{1}</math> >maj< → <math>\hat{5}</math> >maj<, <math>\hat{1}</math> sim6 → <math>\hat{5}</math> (>maj< or sim6) (when ending on <math>\hat{1}</math> this is a "dominant to tonic" motion)
* <math>\hat{1}</math> >maj< → <math>\hat{3}</math> >maj<
* <math>\hat{2}</math> sim6 → <math>\flat\hat{2}</math> >maj< → <math>\hat{1}</math> >maj<
}}

=== Functional harmony ===
Like classical functional harmony, our functional harmony system is based on two tonalities:
# oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
# oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes
==== Oneiromajor (Dylathian) ====
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In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the <math>\hat{1}</math> and <math>\hat{4}</math> degrees, while simic chords appear on the degrees <math>\hat{2}, \hat{\mathrm{t}}, \hat{6}, \hat{7}.</math> For the <math>\hat{3}</math> and <math>\sharp\hat{5}</math> degrees, you get a chord of edo steps 0-3-9-11, which is the third type of DR tetrad, which could be viewed as an inversion of the tract-dominant tetrad. Alternatively, you could also play a DR chord of scale degrees 0-5-9 on the third degree, and in some contexts it may be favorable (see below).

For each of these chords, we can associate functions with them. The simplest of these relationships is between the root tract-major chord and the tract-major chord on the perfect fourth. By adding octaves on certain notes, we can recreate the familiar dominant cadence from diatonic, only now on the <math>\hat{4}</math> rather than the <math>\sharp\hat{5}.</math> The most simple of these progressions would look something like this (in ground's notation):
# B-D-F-G-F
# E-G-X-C-D
# B-D-F-G-F
Or, in 13edo steps:
# 0-2-4-7-17
# 5-7-9-12-18
#0-2-4-7-17
In this cadence, the fifth on E is so narrow that it creates a leading tone relative to the root, and by playing the octaves above E, you can create a minor tritone that wants to resolve inwards to the tract-major chord on the root. The presence of the octaves above the major third helps drive this resolution, but can be omitted. Another neat effect is that given the dominant is now on the <math>\hat{4},</math> then the <math>\hat{2}</math> simic sixth chord would be exactly halfway to the dominant, making it the mediant. It also has a much nicer simic sixth chord on it compared to the <math>\hat{3}</math> 1st inversion tract-major chord, making it more akin to how the mediant works in diatonic.

We can also relate other chords to the dominant, mediant and tonic. The relative minor is more or less exactly analogous to diatonic, being a minor third below the tonic (in the case of B Dylathian, it would be A Celephaïsian, the <math>\hat{6}</math> with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the <math>\hat{2}</math> simic chord is one semitone below the minor third of the <math>\hat{6}</math> simic chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.
# B-D-F-G-B
# `D-`E-`A-`C-C
# `A-`B-`E-`G-B
In 13edo steps:
# 0-2-4-7-13
# `2-`5-`10-`12-12
#`10-0-5-7-13
The ` denotes playing an octave lower than the root.

The <math>\hat{2}</math> (D minor) and <math>\hat{6}</math> (A minor) would probably sound the smoothest when played in a lower register than the tonic (B major) as notated, but if you want to move upwards from the root it still works. Resolving from the relative minor (A minor) to the tonic (B major) is a pretty weak but still usable resolution. Another neat resolution is moving from the <math>\hat{3}</math> (inverted tract-major) to the dominant <math>\hat{4}.</math>

If you play the 0-5-9 chord on <math>\hat{3},</math> the lowest note will be a semitone lower than the lowest in the dominant, and the highest note will be a semitone higher than the highest in the dominant. By either extending the 0-5-9 chord to 0-3-5-9, or simplifying the dominant chord to a 0-4-7 chord, you can drive this resolution very powerfully, and this could either create a chain of strong resolutions going <math>\hat{3}</math> (inverted tract-major) - <math>\hat{4}</math> - <math>\hat{1},</math> or it could help drive resolutions to the Ilarnekian mode above (in this case, E Ilarnekian).

Technically you wouldn't have to extend or simplify any of these chords, but the triad next to all the tetrads feels somewhat empty. All in all, using this technique you could probably simplify all the tetrads down to 0-4-7 and 0-3-8 for tract-major and simic, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified tract-major and simic still have a DR effect, though a bit weaker than the tetrads. The <math>\hat{6}</math> inverted tract-major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant <math>\hat{4}</math> chord. It also doesn't need any extensions with octaves to work well unlike the dominant chord, so it could be seen as a more tense version of dominant. Since it also drives the resolution up by a minor third, the same tetrad on the <math>\hat{3}</math> could be used to drive a resolution to a tract-major <math>\sharp\hat{5},</math> helping to shift the key center from B to G#. If done twice, this resolution can shift your key center up a minor third from B -> G# -> F#, which gives the progression a really jazzy feel.

The only chord we haven't covered now would be the simic <math>\hat{\mathrm{t}}</math> (namely 7-10-15-17). This chord has a much weaker relationship to the other chords, so it doesn't have any strong directionality. However, it does share some notes with a few important chords, notably the <math>\hat{1}</math> chord and the relative minor on the <math>\hat{6}.</math> A resolution to either of these will be similarly strong, that is to say, not very strong. In this case it could also be seen as a secondary mediant which is not the relative minor, about halfway between the <math>\hat{1}</math> chord and the <math>\hat{7}</math> chord an octave above it, and either of these resolutions would probably sound fine in most contexts. This gives it a role completely unlike any of the functions in traditional diatonic. It also works pretty well as a setup for the <math>\sharp\hat{5}</math> inverted tract-major, so in a progression it can help add some flair or beef to the resolution.

==== Oneiromajor (Ilarnekian) ====
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To start with the basics, Ilarnekian is just Dylathian with a flattened 6th.
In E Ilarnekian, you'd get:
E G X A C B D F E

With Ilarnekian being the second major mode (after Dylathian), we'd get the same <math>\hat{1}</math> chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant <math>\hat{4}</math> is now IV>min7<. It still can function as a dominant, though only with the added octave above the 4th, and slightly weaker than the Dylathian dominant cadence. Another interesting thing is that the <math>\hat{4}-\hat{1}</math> cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

The <math>\hat{2}</math> chord is again simic sixth, with it now driving a secondary resolution to D Ultharian instead of D Celephaïsian. The <math>\hat{3}</math> inverted tract-major chord is also still first inversion tract-major, and also still drives a pretty good resolution up to the simic sixth <math>\hat{4},</math> though admittedly weaker than Dylathian.

The <math>\hat{\mathrm{t}}</math> chord is still simic sixth, and still functions as a secondary mediant.

It gets interesting again when looking at the tract-major <math>\hat{5}</math> chord.

By playing the <math>\hat{5}</math> lower than the tonic and playing the octave above the root of the <math>\hat{5}</math> chord, you get an entirely new approach to a dominant chord. The third of the <math>\hat{5}</math> is one semitone below the tonic, and the octave above the root is one semitone above the fifth of the tonic chord. This drives a very strong inward resolution that resembles dominant in diatonic slightly more than the dominant <math>\hat{4}</math> chord in Dylathian, and a lot more than the tract-minor <math>\hat{4}</math> chord in Ilarnekian.
It would look something like this:
* E G X C
* `B `D `F G B
* E G X C

In 13edo steps:
* 0-2-4-7
* `8-`10-`12-2-8
*0-2-4-7
with ` again notating playing an octave lower than the starting chord.

Moving on, the <math>\hat{6}</math> chord would be simic sixth driving the resolution to the <math>\hat{4}</math> simic sixth, in the same way Dylathian's <math>\hat{2}</math> simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The <math>\hat{7}</math> chord would be an inverted tract-major chord, and would drive a resolution to the tonic pretty well. This comes from the fact that the 0-3-9-11 chord would have the minor third become the major second of the tonic, the root move up a semitone to the tonic, and the perfect fifth move down a semitone to become the tritone of the tonic chord. The minor sixth in the chord could be omitted to make the resolution stronger, but the chord would sound much more dissonant.

==== Oneirominor ====
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The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either <math>\flat\hat 7</math> (for its relationship to other degrees) or <math>\hat 7</math> (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order.

===== Degree 3 =====
Similar to diatonic, degree 3 serves as the "relative major".

Alternatively you can use degree 3 to set up the 5 to 1 cadence using one of the following progressions:
* <math>\flat\hat{3}</math>>maj< <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim
* <math>\flat\hat{3}</math>>maj< <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

===== Degree 5 =====
Degree 5, which has a major third on it, has the strongest tendency to go to degree 1 in oneirominor. Alternatively serves as degree 4 of the relative oneiromajor on degree 3, serving to tonicize the relative oneiromajor.

The main cadence in oneirominor is <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim or <math>\hat{5}</math>>dom7< <math>\hat{1}</math>sim because of the leading tone.

===== Degree 1 =====
The tonic.
===== Degree 4 =====
<math>\hat{4}</math>sim <math>\hat{1}</math>sim is a weaker cadence than <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution <math>\hat{4}</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim is preferable.

===== Degree 6 =====
Degree 6 is an important function in oneirominor with no analogue in diatonic. It can be used in the repeating <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> <math>\hat 1</math>sim6 -> <math>\hat 6</math>sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:
* <math>\hat 4</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat 6</math>sim or <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree 2 =====
Similar to degree 3, degree 2 can be used to set up the 5 to 1 cadence:

<math>\hat{2}</math>sim <math>\hat 4</math>sim <math>\hat{5}</math>>maj< <math>\hat{1}</math>sim

Or it can be used in conjunction with degree 4 or 6:

* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 4</math>sim
* <math>\hat 1</math>sim <math>\hat 4</math>sim <math>\hat 2</math>sim
* <math>\hat 1</math>sim <math>\hat 2</math>sim <math>\hat 6</math>sim
* <math>\hat 1</math>sim <math>\hat 6</math>sim <math>\hat 2</math>sim

===== Degree t =====
Degree t is an oneirotonic function with no analogue in diatonic. It serves several secondary roles, being related to more central functions in oneirominor, <math>\hat 6,</math> <math>\hat 4</math> and <math>\hat 2</math>:
* <math>\hat 6</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 6</math>sim
* <math>\hat 4</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 4</math>sim
* <math>\hat 2</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 2</math>sim

===== Degree 7 =====
Leading tone is the main function of <math>\hat 7</math>. It can also be related to degrees <math>\hat 2,</math> <math>\hat \mathrm{t}</math> and <math>\hat 6</math>:
* <math>\hat 2</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 2</math>sim
* <math>\hat 6</math>sim <math>\hat 7</math>sim or <math>\hat 7</math>sim <math>\hat 6</math>sim
* <math>\hat 7</math>sim <math>\hat \mathrm{t}</math>sim or <math>\hat \mathrm{t}</math>sim <math>\hat 7</math>sim
However, these are fairly weak because <math>\hat 7</math> is fairly distant from the tonic in generator space.

The 7th degree may be flattened to give it a stronger functional relationship to the tonic or other degrees; the flattened 7th degree (relative to the Celephaisian mode) provides a <math>\hat{5}</math> "dominant" for the degree <math>\flat\hat{3}</math>.

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