Oneirotonic

Oneirotonic is the 5L3s MOS pattern LLsLLsLs. Its generator ranges from equalized 3\8 (450c) to collapsed 2\5 (480c) and the generator's basic tuning (L/s = 2/1) is 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.

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.

Mode name	Gens up	Pattern	1-step	2-step	3-step	4-step	5-step	6-step	7-step
Sarnathian	0	sLsLLsLL	m	m	d	m	P	m	m
Hlanithian	1	sLLsLsLL	m	m	P	m	P	m	m
Kadathian	2	sLLsLLsL	m	m	P	m	P	M	m
Mnarian	3	LsLsLLsL	M	m	P	m	P	M	m
Ultharian	4	LsLLsLsL	M	m	P	M	P	M	m
Celephaisian	5	LsLLsLLs	M	m	P	M	P	M	M
Ilarnekian	6	LLsLsLLs	M	M	P	M	P	M	M
Dylathian	7	LLsLLsLs	M	M	P	M	A	M	M

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.

Mode name	Pattern	1-step	2-step	3-step	4-step	5-step	6-step	7-step
Sarlocrian	sLsLsLLL	m	m	d	m	d	m	m
Sardorian	sLsLLLsL	m	m	d	m	P	M	m
Mnaeolian	LsLsLsLL	M	m	P	m	P	m	m
Mnionian	LsLsLLLs	M	m	P	m	P	M	M
Ulphrygian	sLLLsLsL	m	m	P	M	P	M	m
Celdorian	LsLLLsLs	M	m	P	M	A	M	M
Ilarmixian	LLsLsLsL	M	M	P	M	P	M	m
Dylydian	LLLsLsLs	M	M	A	M	A	M	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.

Chords of oneirotonic

This page or section deals with proposed concepts. The terminology and concepts used in it are developed by one person or a small group and may lack widespread adoption.

These chord names have been proposed by ground and 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, >...< is used to denote tract-diatonic chords.

First and second inversions of triads are denoted triad₁ and triad₂ in chord symbols, for example >maj<₁ = the first inversion of the tract-major triad.

Perfect fifth (sharp fifth) bounded triads

Name (notation)	Description	In degrees (TAMNAMS)	13edo tuning	Listen	18edo tuning	Listen
Supertaphric (suptph)		0–m4d–P5d	0–554–738		0–533–733
Taphric (tph)	From τάφρος "trench", because the fifth generators go down–up.	0–P3d–P5d	0–462–738		0–467–733
Subtaphric (subtph)		0–M2d–P5d	0–369–738		0–400–733
Neutral (neu)	Splits the sharp fifth in half.		0–369–738
Suprasimic (supsim)		0–d3d–P5d	0–369–738		0–333–733
Simic (sim)	From Modern Greek σημείο "point", because the fifth generators go up–down.	0–m2d–P5d	0–277–738		0–267–733
Subsimic (subsim)		0–M1d–P5d	0–185–738		0–200–733

Major tritone (flat fifth) bounded triads

Name (notation)	Description	In degrees (TAMNAMS)	13edo tuning	Listen	18edo tuning	Listen
Tract-sus4 (>sus4<)		0–P3d–M4d	0–462–646		0–467–667
Tract-major (>maj<)		0–M2d–M4d	0–369–646		0–400–667
Tract-neutral (>neu<)	Splits the flat fifth in half.	0–n2d–M4d			0–333–667
Tract-minor (>min<)		0–m2d–M4d	0–277–646		0–267–667
Tract-sus2 (>sus2<)		0–M1d–M4d	0–185–646		0–200–667

Other triads

Other triads

Name (notation)	Description	In degrees (TAMNAMS)	13edo tuning	Listen	18edo tuning	Listen
Grammic (grm)	From "line", since the generators form a line.	0-P3-m6	0-462-923		0-467-933

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

This page or section deals with proposed concepts. The terminology and concepts used in it are developed by one person or a small group and may lack widespread adoption.

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

Todo: use Ilarnekian as default mode and indicate alterations therefrom

Degrees are indicated with Arabic numerals (or "t" for tritone/4-mosstep) with hats with the corresponding intervals' qualities placed before them; they're just intervals with hats. In order:

$\hat{1},\hat{2},\hat{3},\hat{4},\hat{\mathrm{t}},\hat{5},\hat{6},\hat{7}.$

For now, degrees are conflated with functions. This isn't a proper functional tonality notation — it doesn't specify the default key for unaltered functions — but it generalizes better to modal music. (While we could choose one of oneiromajor and oneirominor as the default tonality, there are arguments for both and we're choosing not to privilege one of them.)

When quality is not explicitly indicated, the quality is from the current mode being discussed. Degrees $\hat{2}$ (second from root), $\hat{3}$ (third from root), $\hat{\mathrm{t}}$ (tritone from root), $\hat{6}$ (sixth from root), and $\hat{7}$ (seventh from root) may be written as follows to explicitly indicate the quality of the interval from the root: $\mathrm{m}\hat{2},\mathrm{m}\hat{3},\mathrm{m}\hat{\mathrm{t}},\mathrm{m}\hat{6},\mathrm{m}\hat{7}$ for minor intervals from the root and $\mathrm{M}\hat{2},\mathrm{M}\hat{3},\mathrm{M}\hat{\mathrm{t}},\mathrm{M}\hat{6},\mathrm{M}\hat{7}$ for major intervals from the root. Degrees $\hat{1}$ (root), $\hat{4}$ (fourth from root), and $\hat{5}$ (fifth from root) may use $\mathrm{P}\hat{1},\mathrm{P}\hat{4},\mathrm{P}\hat{5}$ for perfect, $\mathrm{A}\hat{1},\mathrm{A}\hat{4},\mathrm{A}\hat{5}$ for augmented, and $\mathrm{d}\hat{1},\mathrm{d}\hat{4},\mathrm{d}\hat{5}$ for diminished.

The chord symbols used are ground's system, described in the Oneirotonic article.

Basic chords

The most basic chords in this functional harmony system are:

• Tract-major triad 0-4-7\13 (>maj<): A compressed major triad that sounds desaturated and somewhat bittersweet. Somewhat dubiously +1+1. 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 (>majsus2<): Reinforces the quasi-DR effect with an extra tone; approximately +1+1+2.
  • 0-4-7-10\13 (>dom7<): A compressed dominant tetrad; approximately +1+?+1.
  • 0-4-7-12\13 (>maj<7): Approximately +1+1+2.
• The simic triad 0-3-8\13 (sim): 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 (sim6): Approximately +1+2+1.
  • 0-3-8-12 (simmaj7): Approximately +1+2+2.
  • 0-3-8-11 (simmin7): Something like a minor 7th tetrad.
  • 0-3-8-15 (simadd9)
  • 0-3-8-12-15 (simmaj7add9): A concatenation of the minor +1+2 and major +1+1 triads.
• 0-5-9\13 (>IV/I<): 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 (>sus4<): Compressed sus4. Approximately +2+1.
• 0-4-8\13 (>aug<): "Submajor augmented" triad.
• 0-3-6\13 (>dim<): The most diminished-like triad.

Functional patterns

13edo oneiro 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".

Adding 923 and 1108 to chords works well, and for jazzy extensions one can add 185, 461, and 646 to the upper octave.

Progressions

Common motions:

• $\hat{1}$ (>maj< or sim6) → $\mathrm{M}\hat{2}$ sim6
• $\hat{1}$ (>maj< or sim6) → $\mathrm{P}\hat{4}$ sim6 (when ending on $\hat{1}$ this sounds like diatonic V to I)
• $\hat{1}$ (>maj< or sim6) → $\mathrm{m}\hat{6}$ sim6
• $\hat{1}$ >maj< → $\mathrm{P}\hat{5}$ >maj<, $\hat{1}$ sim6 → $\mathrm{P}\hat{5}$ (>maj< or sim6) (when ending on $\hat{1}$ this is a "dominant to tonic" motion)
• $\hat{1}$ >maj< → $\mathrm{M}\hat{3}$ >maj<
• $\mathrm{M}\hat{2}$ sim6 → $\mathrm{m}\hat{2}$ >maj< → $\hat{1}$ >maj<

Functional harmony

Like classical functional harmony, our functional harmony system is based on two tonalities:

1. oneiromajor, with tonic chord tract-major and the pitches of Dylathian and Ilarnekian modes
2. oneirominor, with tonic chord simic 6th and the pitches of Celephaisian and Ultharian modes

Oneiromajor (Dylathian)

In the below, interval names are in ADIN.

In Dylathian, we find tract-major chords on the $\hat{1}$ and $\hat{4}$ degrees, while simic chords appear on the degrees $\hat{2},\hat{\mathrm{t}},\hat{6},\hat{7}.$ For the $\hat{3}$ and $\hat{5}$ 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 $\hat{4}$ rather than the $\hat{5}.$ The most simple of these progressions would look something like this (in ground's notation):

1. B-D-F-G-F
2. E-G-X-C-D
3. B-D-F-G-F

Or, in 13edo steps:

1. 0-2-4-7-17
2. 5-7-9-12-18
3. 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 $\hat{4},$ then the $\hat{2}$ 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 $\hat{3}$ 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 $\hat{6}$ with the "minor" tonality). The mediant can also function as a secondary dominant for resolutions to the relative minor; the highest note in the $\hat{2}$ minor chord is one semitone below the minor third of the $\hat{6}$ minor chord. By playing the octave above certain notes, resolving between the two modes is pretty simple.

1. B-D-F-G-B
2. `D-`E-`A-`C-C
3. `A-`B-`E-`G-B

In 13edo steps:

1. 0-2-4-7-13
2. `2-`5-`10-`12-12
3. `10-0-5-7-13

The ` denotes playing an octave lower than the root.

The $\hat{2}$ (D minor) and $\hat{6}$ (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 $\hat{3}$ (inverted major) to the dominant $\hat{4}.$

If you play the 0-5-9 chord on $\hat{3},$ 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 $\hat{3}$ (inverted major) - $\hat{4}$ - $\hat{1},$ 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 major and minor, respectively. These would help since the 0-3-5-9 chord doesn't have much of a DR effect, while the simplified major and minor still have a DR effect, though a bit weaker than the tetrads. The $\hat{6}$ inverted major (9-12-18-20) chord also has some neat features, as it functions as an inversion of the dominant $\hat{4}$ 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 $\hat{3}$ could be used to drive a resolution to a major $\hat{5},$ 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 minor $\hat{\mathrm{t}}$ (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 $\hat{1}$ chord and the relative minor on the $\hat{6}.$ 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 $\hat{1}$ chord and the $\hat{7}$ 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 $\hat{5}$ inverted major, so in a progression it can help add some flair or beef to the resolution.

Oneiromajor (Ilarnekian)

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 $\hat{1}$ chord, E>maj< One of the most immediate effects we'd see, however, is that the dominant $\hat{4}$ 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 $\hat{4}-\hat{1}$ cadence is now simultaneously a minor plagal and a dominant cadence, radically different from anything in diatonic.

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

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

It gets interesting again when looking at the tract-major $\hat{5}$ chord.

By playing the $\hat{5}$ lower than the tonic and playing the octave above the root of the $\hat{5}$ chord, you get an entirely new approach to a dominant chord. The third of the $\hat{5}$ 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 $\hat{4}$ chord in Dylathian, and a lot more than the tract-minor $\hat{4}$ 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 $\hat{6}$ chord would be simic sixth driving the resolution to the $\hat{4}$ simic sixth, in the same way Dylathian's $\hat{2}$ simic sixth drives the resolution to the relative minor. It would also function as the Ilarnekian relative minor, in this case D Ultharian. The $\hat{7}$ chord would be an inverted 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

The pitches of the oneirominor tonality are usually that of the Celephaisian mode, but the 7 degree may be either $\mathrm{m}\hat{7}$ (for its relationship to other degrees) or $\mathrm{M}\hat{7}$ (mainly but not exclusively for a leading tone function).

The degrees/functions of oneirominor are listed below in generator order. The Celephaisian mode is assumed for purposes of notation.

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:

• $\hat{3}$>maj< $\hat{5}$>maj< $\hat{1}$sim
• $\hat{3}$>maj< $\hat{4}$sim $\hat{5}$>maj< $\hat{1}$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 $\hat{5}$>maj< $\hat{1}$sim or $\hat{5}$>dom7< $\hat{1}$sim because of the leading tone.

Degree 1

The tonic.

Degree 4

$\hat{4}$sim $\hat{1}$sim is a weaker cadence than $\hat{5}$>maj< $\hat{1}$sim, in fact weaker than iv -> i in diatonic because there is no descending semitone to the fifth. For a stronger resolution $\hat{4}$sim $\hat{5}$>maj< $\hat{1}$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 $\hat{1}$sim6 -> $\hat{6}$sim6 -> $\hat{1}$sim6 -> $\hat{6}$sim6 -> ... vamp. It can also be used in conjunction with other degrees that are closely related:

• $\hat{4}$sim $\hat{6}$sim or $\hat{6}$sim $\hat{4}$sim
• $\hat{2}$sim $\hat{6}$sim or $\hat{6}$sim $\hat{2}$sim

Degree 2

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

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

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

• $\hat{1}$sim $\hat{2}$sim $\hat{4}$sim
• $\hat{1}$sim $\hat{4}$sim $\hat{2}$sim
• $\hat{1}$sim $\hat{2}$sim $\hat{6}$sim
• $\hat{1}$sim $\hat{6}$sim $\hat{2}$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, $\hat{6},$ $\hat{4}$ and $\hat{2}$:

• $\hat{6}$sim $\hat{\mathrm{t}}$sim or $\hat{\mathrm{t}}$sim $\hat{6}$sim
• $\hat{4}$sim $\hat{\mathrm{t}}$sim or $\hat{\mathrm{t}}$sim $\hat{4}$sim
• $\hat{2}$sim $\hat{\mathrm{t}}$sim or $\hat{\mathrm{t}}$sim $\hat{2}$sim

Degree 7

Leading tone is the main function of $\mathrm{M}\hat{7}$. It can also be related to degrees $\hat{2},$ $\hat{\mathrm{t}}$ and $\hat{6}$:

• $\hat{2}$sim $\mathrm{M}\hat{7}$sim or $\mathrm{M}\hat{7}$sim $\hat{2}$sim
• $\hat{6}$sim $\mathrm{M}\hat{7}$sim or $\mathrm{M}\hat{7}$sim $\hat{6}$sim
• $\mathrm{M}\hat{7}$sim $\hat{\mathrm{t}}$sim or $\hat{\mathrm{t}}$sim $\mathrm{M}\hat{7}$sim

However, these are fairly weak because $\mathrm{M}\hat{7}$ 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 $\mathrm{P}\hat{5}$ "dominant" for the degree $\hat{3}$.