Xenharmonic Reference - User contributions [en]

List of xenharmonic musicians

2026-03-07T18:07:41Z

Lumithesilly: meee :3

{| class="wikitable"
|+ List
|-
! Name !! Wiki User !! Genre Tags !! Links
|-
| GroundFault Corporation || [[User:Ground]] || Progressive, maximalist, VGM-adjacent, goth
| [https://youtu.be/1bnEO8vGvbo A New Dusk on YouTube]
[https://youtu.be/rrjuGmmodn0 SOTA on YouTube]
[https://groundfco.bandcamp.com/ Bandcamp]
|-
| DotuXil || [[User:ArcusRays]] || Electronic, drum&bass || [https://youtu.be/cFpKgUD9tQI Collected Refractions on YouTube]
|-
| Brendan Byrnes || - || Rock, exotica, lo-fi, avant-pop || [https://youtu.be/I_LZjC6-Rpo Astral Bloom on YouTube]
|-
| Jumble || - || Ambient, chillwave, synthwave, nostalgic || [https://www.youtube.com/@jumblejym Jumble on YouTube]
|-
| Xotla || - || Rock, funk, electro-swing, electronic || [https://youtu.be/E36e61d8NKY The Owl & The Tortoise on YouTube]
|-
| Zhea Erose || - || Dream&bass, ambient, contemporary classical|| [https://zheaerosemusic.bandcamp.com/album/affinity Affinity on Bandcamp]
|-
| LAMPLIGHT || - || Constructed languages, electronic, pop|| [https://youtu.be/cMnuMjXeHrY Caftaphata on YouTube]
|-
| Tachy Bunker || - || Experimental, hardstyle, punk, aliencore || [https://youtu.be/MF-LeuDNGUY THE SECOND COSMOCIDE on YouTube]
|-
| Benyamind || - || Electronic, film music|| [https://www.youtube.com/@benyamind Benyamind on YouTube]
|-
| Stephen Weigel || - || Totalism, avant-garde, electronic, synthpop|| [https://www.youtube.com/@stephenweigel Stephen Weigel on YouTube]
|-
| Amano Hideya || - || Folk, solo piano || [https://www.youtube.com/@hideya Hideya on YouTube]
|-
| Sevish || - || Electronic, drum&bass, breakbeat || [https://sevish.bandcamp.com/album/big-sway Big Sway on Bandcamp]
|-
|Vector Graphics
|[[User:Vector]]
| -
|[https://www.youtube.com/playlist?list=PL5W1Um_wg1SGT3As59dXqj84c3Up_OcG0 Vector's microtonal music playlist on YouTube]
|-
|Lumi
|[[User:lumithesilly]]
| -
|[https://www.youtube.com/@ImLumiV lumi ?? on youtube]
|-

|}

37edo

2026-03-07T03:14:38Z

Lumithesilly: added steps to the thirds table

'''37edo,''' or 37 equal divisions of the octave, is the equal tuning featuring steps of (1200/37) ~= 32.4 cents, 37 of which stack to the perfect octave [[2/1]]. It is notable for having two reasonable choices for mapping prime 3 (at ~714 and ~681 cents), but mapping the rest of the 19-limit rather accurately.

== Theory ==

=== JI approximation ===
37edo's most notable feature is its status as a "dual-3" system, meaning that not only are there two tunings of 3 that can be combined to create an accurate 9/8, but those tunings of 3 are also rather accurate on their own. As a dual-3 system, it features the dual-3 diatonic scale 5L 1m 1s, resembling 38edo's diatonic but with an edostep removed from one of the small steps.{{Harmonics in ED|37|31|0}}
{| class="wikitable"
|+Thirds in 37edo
!Cents
|259
|291
|324
|356
|389
|421
|454
|-
!Quality against flat fifth
|Subminor
|Pentaminor
|'''Supraminor'''
|'''Submajor'''
|Pentamajor
|Supermajor
| rowspan="2" |
|-
!Just interpretation
|33/28
|13/11
|'''17/14'''
|'''16/13'''
|5/4
|14/11
|-
!Quality against sharp fifth
|'''Subminor'''
|Neominor
|Pentaminor
|Neutral
|Pentamajor
|Neomajor
|'''Supermajor'''
|-
!Just interpretation
|'''7/6'''
|13/11
|6/5
|16/13
|5/4
|14/11
|'''13/10, 9/7'''
|-
!2.9... interpretations
|
|
|
|11/9
|
|9/7
|
|-
!Steps
|8
|9
|10
|11
|12
|13
|14
|}
Fifth-generated thirds are bolded.

=== Chords ===
Due to 37edo's two distinct fifths, it contains two different sets of fifth-bounded triads, which might be initially understood by examining the tuning's diatonic and antidiatonic scales. The sharp fifth naturally generates arto and tendo triads representing the 2.3.5.13 subgroup, while the flat fifth naturally generates supraminor and submajor triads (note that the "submajor third" is actually the neutral third corresponding to the sharp fifth). By alternating the two fifths as in a dual-fifth system, classical major and minor triads can be generated.

=== Scales ===
As mentioned previously, 37edo supports not only the very hard mosdiatonic generated by its sharp fifth, and the soft antidiatonic generated by its flat fifth, but a "dual-3" diatonic resembling 38edo's mosdiatonic, generated by alternating the two fifths. It also has a Zarlino diatonic, where as in 15 and 22edo the three different step sizes are equidistant.

[Add groundfault scales here]

=== Regular temperaments ===
If the two versions of the third harmonic are treated as stacking to the 9th harmonic, then 37edo supports a form of "2.<3.>3.5" meantone, where two sharp fifths and two flat fifths stack to create a 5/1. Another important temperament 37edo supports using only the sharp fifth is porcupine, which it shares with 15edo and 22edo and for which it is the first edo that features a reasonable extension to the 13-limit.

== Notation ==
As an archy edo, 37edo may be notated with diatonic notation, or with KISS or diamond-mos notation using its flat antidiatonic fifth (which also has the advantage of accidentals only raising or lowering by one step). It may also be notated with a straddle-3 erac notation system, taking advantage of its straddle-3 diatonic. This has an advantage in that 5/4 is a major third, or by [[porcupine]] zarlino notation.

== Ground's notes ==
Note from [[User:ground]]: hey sorry this was copied from my notes so I'm gradually making my way through the formatting, it's kind of a lot

37edo is the tuning that I use the largest number of distinct scales in. Here are the ones I could think of:

* 5:2:1 trackdye 5L2m8s
** Step tunings: (227¢) : 162¢ : 65¢ : 32¢
** This is the quintessential [[Aberration scale]]. There are seven possible structures depending on which diatonic mode you choose to aberrate. It's basically 12edo with all the 13-limit intervals that make 37edo so strong.
* 5:3:2 blackdye 5L2m3s
** Step tunings: (227¢) : 162¢ : 97¢ : 62¢, patent val (9/8) : 10/9 : 16/15 : 81/80
** A subset of Ultrapyth[17], rather 15edo-like. It's close to the m=s Blackwood degenerate tuning, and the patent val 10/9 is a Porcupine neutral second. The 65¢ interval is possibly usable as an aberrisma, but too wide for me. I think it makes sense to use Blackwood cues here to apply it as a sort of alternate semitone, although I don't have much experience doing this. I usually just avoid it and insert fragments of the neogothic blackdye when I want an aberrisma.
** Acute Minor / Grave Major modes: The standard pental scales of 37edo. The harmony is quite nice, the semitone is familiarly sized, but the whole tones are very distorted, leading to a scale that makes it trivial to achieve a xenharmonic sound. This is one of my favorite things about 37edo.
** Grave Minor / Acute Major modes: One way to improve septal melody over the diatonic scale. I prefer the sound of the neogothic blackdye for this, but this one has the possible advantage of using the 422¢ major third in grave Aeolian and Dorian, which is more third-like than the 454¢ alternative.
* 6:2:1 blackdye 5L2m3s
** Step tunings: (227¢) : 195¢ : 65¢ : 32¢
** A subset of Ultrapyth[12], one of the two simple neogothic blackdye scales, the other being 32edo's 5:2:1. The melody is something expected from septal diasem, which makes it desirable to infuse that quality into 37edo music. The aberrisma is medium-small, which is very versatile.
** Acute Minor / Grave Major modes: The standard neogothic scales of 37edo. On top of the melodic properties, I also like neogothic minor chords, so I use this one about as much as the pental blackdye.
** Grave Minor / Acute Major modes: My preferred way to insert subminor thirds into 37edo music. Just like in the pental blackdye, no mode exists that has the inframinor sixth and diatonic fifth over the tonic, so I don't use this scale in its entirety, instead opting to mix its structures with other modes and scales.
* 7:1 diatonic 5L2s
** Step tunings: 227¢ : 32¢
** Ultrapyth[7], or Oceanfront temperament in other words. Just like with neogothic blackdye, the other Oceanfront tuning is 32edo's 6:1. This is about as hard as you can push a diatonic scale before it stops making sense, as the 454¢ major third is an effectively just 13/10, the interordinal on the boundary between major thirds and subfourths. It still has a usable 7/6 however, due to the fifth being so sharp, and I often prefer 13/10 to 9/7 anyway because it's past the peak of "majorness". Diatonic context is powerful, so as long as the instrumentation allows the comma-sized semitones to be audible, chords and melodies still make sense.
* 6:3:1 pinedye R/L 5L2m1s
** Step tunings: (227¢) : 195¢ : 97¢ : 32¢
** Unlike softer tunings like 27edo's 4:3:1, this doesn't much resemble the pental JI tuning. Instead it's closer to 25edo's 4:2:1, a compressed 12edo diatonic that uses both the flat and sharp fifth. The compressed thirds are close to 13/11 and 5/4, an excellent combination to my preference.
* 5:4:2 diasem R/L 5L2m2s
** Step tunings: (227¢) : 162¢ : 130¢ : 65¢
** This is 37edo's only tuning of diasem, and a highly distorted one at that, using the flat fifth instead of the sharp diatonic one. Like pinedye, it combines ~13/11 and ~5/4, but with no alternate fifth. I don't use this much, but it's worth mentioning because of its connection to the other scales, and the fact that it's the only concrete scale on this list to have a 130¢ step. Because the s step is 2\37, it can be split in half for a related 5:4:1 diaslen 5L2m4s.
* 6:1 archaeotonic 6L1s and 5:1 6L7s
** Step tunings: (227¢) : 195¢ : 32¢ and (195¢) : 162¢ : 32¢
** These are the scales of the whole-tone Didacus temperament. Normally I would just use archaeotonic, but 37edo's tuning is only remarkable when extended to higher limits.
* 7:5 onyx 1L6s and 5:2 pine 7L1s
** Step tunings: 227¢ : 162¢ and (227¢) : 162¢ : 65¢
** I don't use much Porcupine, but when I do, this is basically the perfect tuning. A better 6/5 than 27edo, a better 3/2 than 15edo, and a better 5/4 and 11/8 than both. Porcupine structures occasionally show up when I write chord progressions, which is always cool because I like neutral seconds.
* 7:3 smitonic 4L3s
** Step tunings: 227¢ : 97¢
** I've long been an enjoyer of the 5|1 "Vivecan" mode of smitonic. It's one of the few scales that I prefer to tune soft rather than hard, but tunings that are basic or slightly harder allow access to the very good 2.7.11 Orgone temperament. Being used to 11edo, I prefer this to the slightly harder 26edo tuning. I've been learning to accept ~11/7 as a fifth, extended from 11edo's ~14/9.
* 5:2 slentonic 5L6s
** Step tunings: (227¢) : 162¢ : 65¢
** This might be the weirdest one. I normally want Slendric for this scale structure rather than Laconic, but I've been using this to test the boundaries of my perception for drastically compressed and stretched diatonic-coded intervals. 8/7 isn't a minor third, but it might possibly be usable as one in this scale, for example.
* Mosh
* Mosh3s
* 11/8-generated temperament (low-complexity 2.11.13)
* Ammonite oneirotonic (useful for the 8edo-like chords it generates, as this is the way its two neutral seconds stack to make an octave)
* "Borcupat" (explanation needed)
* Shallowtone[16] (or [12] for a smaller ternary scale more analogous to deeptone)

My quasi-diatonic chord set in 37edo is like

* neominor [<nowiki>[7th]</nowiki>] (basic minor)
* compressed 6:7:9 (basic subminor which I don't use nearly enough)
* compressed 9:12:16:19 with stretched 9:12 (basic 47b9 ground chord)
* pental major/minor [<nowiki>[7th]</nowiki>] (basic major, alternate minor)
* pentagoth major (alternate major)
* ~10:13:15 (like major with sus quality)
* various approximations of sus4 <nowiki>[7th]</nowiki>
* ~<nowiki>[4]</nowiki>:5:6:7 (basic dominant/diminished)
* 16:19:22 (alternate diminished)
* 8:11:13 (basic superfourth/subfifth chord, tempered retroversion of 13:16:19)

Triad inversions are considered the same chord. Major and minor can be swapped (triads or tetrads retroverted), but these are situation-specific.

{{adv|37edo has a nearly perfect logarithmically stretched gentle triad, by virtue of dividing the sharp fifth into 22 equal parts, via the following mathematical coincidence:}}

{{Adv|<math>
1200 \log_2\!\left(\frac{13}{11}\cdot\frac{14}{11}\right) \cdot \frac{13}{22}
= 417.606
\approx 1200 \log_2\!\left(\frac{14}{11}\right)
= 417.508
</math>}}

{{Adv|<math>
1200 \log_2\!\left(\frac{13}{11}\cdot\frac{14}{11}\right) \cdot \frac{9}{22}
= 289.112
\approx 1200 \log_2\!\left(\frac{13}{11}\right)
= 289.210
</math>}}

{{Adv|I don’t know if this is audibly significant, but at least it’s a cool justification for specifically 37edo as a neogothic blackdye tuning.}}

{{Navbox EDO}}
{{Cat|edos}}

26edo

2026-03-07T03:12:37Z

Lumithesilly: added steps to the thirds table

{{problematic}}
'''26edo''', or 26 equal divisions of the octave, is the equal tuning featuring steps of (1200/26) ~= 46.15 cents, 26 of which stack to the perfect octave [[2/1]].

==Theory==

===JI approximation===
26edo is characterized by a flat tuning of harmonics 3, 5, and 13 and slightly sharp but accurate tunings of 7 and 11. Although its primes 3, 5, and 13 are damaged, 26edo can be used as a 13-limit temperament as it is consistent to the 13-odd-limit. Additionally, the fact that primes 3 and 13 are flat by about the same amount and 5 is flat by about double that means that intervals such as [[13/12]] and [[10/9]] are approximated well. The accurate 7 combined with the flat 5 means that [[7/5]] and [[10/7]] are both mapped to the 600¢ half octave tritone, tempering out [[50/49]]. [[16/13]] and [[11/9]] are mapped to the same interval as [[5/4]], tempering out [[65/64]], [[144/143]], and [[45/44]].

{{Harmonics in ED|26|31|0}}

===Edostep interpretations===

26edo's edostep has the following 13-limit interpretations:
* 25/24 (the difference between 5/4 and 6/5)
* 33/32 (the difference between 4/3 and 11/8)
* 36/35 (the difference between 5/4 and 9/7)
* 49/48 (the difference between 8/7 and 7/6)

===Intervals and notation===

Similar to [[19edo]], 26edo can be notated entirely with standard [[diatonic notation]], with #/b = 1\26 and x/bb = 2\26. The equivalences are Cx = Dbb, E# = Fbb, and Ex = Fb.

==Compositional theory==

{| class="wikitable"
|+Thirds in 26edo
!Quality
|Farminor
|'''Supraminor'''
|'''Submajor'''
|Farmajor
|-
!Cents
|277
|'''323.1'''
|'''369.2'''
|415.4
|-
!Just interpretation
|7/6
|'''6/5'''
|'''5/4, 16/13'''
|14/11, 9/7
|-
!Steps
|6
|'''7'''
|'''8'''
|9
|}

===Chords===

{{WIP}}

TODO:
* write about flattone

===Scales===

{{WIP}}

{{navbox EDO}}

24edo

2026-03-05T02:01:31Z

Lumithesilly: we ignore my previous change im a lil dumb

[[File:24edo.png|thumb|11- and 13-limit intervals often fall about halfway in between 12edo intervals.]]
'''24edo''', or 24 equal divisions of the octave, is the equal tuning featuring steps of (1200/24) = 50 cents, 24 of which stack to the perfect octave [[2/1]]. It is arguably one of the most common entry points into microtonality due to containing the familiar pitches of [[12edo]].

== Theory ==
24edo is rather underappreciated due to its history of being used in atonal music.

==== JI approximation ====
Although 24edo inherits its approximations of the 5-limit from 12edo, it doesn't allow one to stack more than one instance of 5/4 without excessive error accumulation. Furthermore, despite having a more accurate 7/4 than 12edo in terms of absolute error, the 7th harmonic suffers from the same problem, as well as worse problems.
{{Harmonics in ED|24|31|0}}
{| class="wikitable"
|+Thirds in 24edo
!Quality
|Inframinor
|'''Minor'''
|Neutral
|'''Major'''
|Ultramajor
|-
!Cents
|250
|'''300'''
|350
|'''400'''
|450
|-
!Just interpretation
|15/13
|'''19/16, 6/5'''
|11/9
|'''24/19, 5/4'''
|13/10
|-
!Steps
|5
|'''6'''
|7
|'''8'''
|9
|}
Diatonic thirds are bolded.

==== Chords ====
Because it contains 12edo and 8edo as subsets, 24edo has the capacity for all the same types of chords as those edos. As if that weren't enough, careful use of a set of rules known as the [[dinner party rules]] helps to add more viable chords to the list- every chord must be comprised of a chain of friends in which each note is a "friend" to every other note, no note can have an "enemy", and, there must not be any crowding except in tension chords.

Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third/ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime/inframinor second, and an infraoctave/ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third/paraminor fourth (~13/10) and an inframinor sixth/paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.

{{Navbox EDO}}
{{Cat|Edos}}

24edo

2026-03-05T02:00:59Z

Lumithesilly: added steps to the thirds table

[[File:24edo.png|thumb|11- and 13-limit intervals often fall about halfway in between 12edo intervals.]]
'''24edo''', or 24 equal divisions of the octave, is the equal tuning featuring steps of (1200/24) = 50 cents, 24 of which stack to the perfect octave [[2/1]]. It is arguably one of the most common entry points into microtonality due to containing the familiar pitches of [[12edo]].

== Theory ==
24edo is rather underappreciated due to its history of being used in atonal music.

==== JI approximation ====
Although 24edo inherits its approximations of the 5-limit from 12edo, it doesn't allow one to stack more than one instance of 5/4 without excessive error accumulation. Furthermore, despite having a more accurate 7/4 than 12edo in terms of absolute error, the 7th harmonic suffers from the same problem, as well as worse problems.
{{Harmonics in ED|24|31|0}}
{| class="wikitable"
|+Thirds in 24edo
!Quality
|Inframinor
|'''Minor'''
|Neutral
|'''Major'''
|Ultramajor
|-
!Cents
|250
|'''300'''
|350
|'''400'''
|450
|-
!Just interpretation
|15/13
|'''19/16, 6/5'''
|11/9
|'''24/19, 5/4'''
|13/10
|-
!Steps
|11
|'''12'''
|13
|'''14'''
|15
|}
Diatonic thirds are bolded.

==== Chords ====
Because it contains 12edo and 8edo as subsets, 24edo has the capacity for all the same types of chords as those edos. As if that weren't enough, careful use of a set of rules known as the [[dinner party rules]] helps to add more viable chords to the list- every chord must be comprised of a chain of friends in which each note is a "friend" to every other note, no note can have an "enemy", and, there must not be any crowding except in tension chords.

Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third/ultramajor second, a paramajor fourth (~11/8), a paraminor fifth (~16/11) and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime/inframinor second, and an infraoctave/ultramajor seventh. The most notable "frenemies"- that is, intervals that act as both "friends" and "enemies" at the same time- are a tritone, as well as a minor second, a major seventh, an ultramajor third/paraminor fourth (~13/10) and an inframinor sixth/paramajor fifth (~20/13). Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.

{{Navbox EDO}}
{{Cat|Edos}}

41edo

2026-03-05T01:59:49Z

Lumithesilly: added steps to the thirds table

'''41edo''', or 41 equal divisions of the octave, is an equal tuning with a step size of approximately 29 cents. It is known for its relatively good approximation of 11-limit just intonation.

== Theory ==

==== JI approximation ====
41edo is most accurately a 2.3.5.7.11 tuning, though it also has an acceptable if sharp 13th harmonic, notably widening the difference between the [[Collection of chords#Arto triad|arto]] (10:13:15) and [[Collection of chords#Tendo triad|tendo]] (1/10:1/13:1/15) triads such that they become simple [[Slendric]] divisions of the fifth. Because it is not a meantone system, the best diatonic to use for 5-limit harmony is the Zarlino diatonic scale (LMsLMLs), tuned in 41edo as 7-6-4-7-6-7-4. However, it also features a MOS diatonic of 7-7-3-7-7-7-3.

{{Harmonics in ED|41|31|0}}
{| class="wikitable"
|+Thirds in 41edo
!Quality
|Subminor
|'''Farminor'''
|Nearminor
|Neutral
|Nearmajor
|'''Farmajor'''
|Supermajor
|-
!Cents
|263
|'''293'''
|322
|351
|381
|'''410'''
|439
|-
!Just interpretation
|7/6
|'''13/11'''
|6/5
|11/9
|5/4
|'''14/11'''
|9/7
|-
!Steps
|9
|'''10'''
|11
|12
|13
|'''14'''
|15
|}
Thirds available in the diatonic scale generated by stacking the perfect fifth are bolded.

=== Chords ===
41edo has three different flavors of minor and major intervals as well as neutral intervals. Its subminor and supermajor intervals approximate simpler septimal ratios such as 7/4 and 9/7, while its supraminor ("nearminor") and submajor ("nearmajor") intervals approximate classical 5-limit harmony which includes ratios like 5/4 and 9/5, and its plain major and plain minor intervals approximate classic 3-limit ratios. As a result, 41edo has nine qualities of tertian, fifth-bounded triad: tendo, supermajor, novamajor, nearmajor, neutral, nearminor, novaminor, subminor. However, 41edo lacks true interordinal intervals (to reach a tuning with both neutrals and interordinals, 58edo must be used), so as for latal fourth-bounded triads, there are only four qualities.

=== Scales ===
41edo's 5-limit intervals are not found particularly early on in the chain of fifths, with 6/5 being an augmented second and 5/4 a diminished fourth. Notably, 41edo has a 17-note chromatic scale generated by the perfect fifth, 3-3-3-1-3-3-1-3-3-3-1-3-3-1-3-3-1, in which the classical (~5/4) major and classical (~6/5) minor thirds span the same number of scale steps, giving the scale familiar chord qualities.

=== Regular temperaments ===
41edo shares Schismic (and its extension Garibaldi, and thus Marvel and Hemifamity) with 29edo, Slendric (and its extension Miracle) with 31edo, Tetracot with 34edo, and Magic with 22edo. Magic is especially important here as it forms the fret layout and main string tuning for the Kite guitar.

It also contains a slightly-stretched version of equal Bohlen-Pierce tuning (where the perfect twelfth of 3/1 is split into 13 equal parts) via every fifth step. If used in a linear temperament as the generator, this temperament is called Bohpier.

== Notation ==
Since 41edo has a perfect fifth which is split exactly in half, semisharps and semiflats (as in [[Diatonic notation|neutral diatonic notation]]) can be used to notate it. A useful addition is ups and downs, which naturally reflect 41edo's structure, as 5/4 is downmajor, 81/64 is major, and 9/7 is upmajor. (In fact, "up" can be declared equivalent to "super"/"supra" and "down" equivalent to "sub".)

== Practice ==
41edo is used by the musician and conlanger Lamplight as a standard tuning for their ''Shasavic'' theory of music.

41edo is used in Kite Giedraitis's Kite Guitar, which manages the high density of notes by only having frets for every other note of 41edo, and tuning the strings in a way that allows one string to fill in the gaps of an adjacent string.

{{Navbox EDO}}
{{Cat|Edos}}

53edo

2026-03-05T01:57:24Z

Lumithesilly: forgot to bold

'''53edo''', or 53 equal divisions of the octave, is the equal tuning featuring steps of (1200/53) ~= 22.64 cents, 53 of which stack to the perfect octave [[2/1]]. 53edo is an excellent approximation to Pythagorean tuning (stacking pure 3/2 fifths). Theoretical interest in this tuning system goes back to antiquity.

== Theory ==
Unless one has a set of accidentals for the syntonic comma (see the Notation section) one is left in the unenviable position of having to label a Ptolemaic major third the same way as the Pythagorean diminished fourth, for example. Apart from that issue, 53edo is very useful for 5-limit music.

==== Edostep interpretations ====
53edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup:

* 65/64, the difference between the 13-limit tendoneutral third 16/13 and the classical major third 5/4
* 81/80 (the syntonic comma), the difference between 5/4 and the diatonic major third
* The Pythagorean comma, the difference between the Pythagorean diatonic and chromatic semitones
* 91/90, the difference between the 13-limit ultramajor third 13/10 and the septimal supermajor third 9/7
* 64/63, the difference between the diatonic major third and 9/7
* 512/507, the difference between the 13-limit neutral thirds

53edo tempers out the following commas:

* The schisma (the difference between 5/4 and the Pythagorean diminished fourth)
* The vulture comma (the difference between four 320/243 intervals and the tritave)
* The amiton (the difference between a stack of five 10/9 intervals and 27/16)
* The kleisma (the difference between a stack of three 25/24 intervals and 9/8)
* The semicomma (the difference between a stack of three 75/64 intervals and 8/5)
* 225/224 (the difference between 15/14 and 16/15)
* 385/384 (the difference between 77/64 and 6/5)
* 121/120 (the difference between 12/11 and 11/10)
* 625/624 (the difference between 25/24 and 26/25)
* 676/675 (the difference between a stack of two 15/13 intervals and the perfect fourth)

==== JI approximation ====
53edo is most usefully seen as a 2.3.5.7.13 tuning, but the 2.3.5.13 restriction is more accurate and shared with a number of its multiples, such as [[159edo]]. Because it is not a Meantone system, there are actually multiple potential diatonic scales to use for 5-limit harmony, one of which is the Zarlino diatonic scale (LMsLMLs), tuned in 53edo as 9-8-5-9-8-9-5, though this particular scale is arguably best used for Lydian or Locrian modes. There's also the Didymic diatonic scale, tuned in 53edo as 9-8-5-9-9-8-5, which is better suited for Ionian mode and Major tonality in general. However, 53edo also features a MOS diatonic of 9-9-4-9-9-9-4, which is basically the Pythagorean diatonic scale.

{{Harmonics in ED|53|31|0}}
{| class="wikitable"
|+Thirds in 53edo
!Quality
|Inframinor
|Subminor
|'''Farminor'''
|Nearminor
|Supraminor
|Submajor
|Nearmajor
|'''Farmajor'''
|Supermajor
|Ultramajor
|-
!Cents
|249
|272
|'''294'''
|317
|340
|362
|385
|'''408'''
|430
|453
|-
!Just interpretation
|15/13
|7/6, 75/64
|'''32/27'''
|6/5
|39/32
|16/13
|5/4
|'''81/64'''
|9/7, 32/25
|13/10
|-
!Steps
|11
|12
|'''13'''
|14
|15
|16
|17
|'''18'''
|19
|20
|}
Diatonic thirds are bolded.

=== Chords ===
53edo has four different flavors of minor and major intervals as well as supraminor and submajor intervals. Its inframinor and ultramajor thirds approximate 15/13 and 13/10 respectively. At the same time, 53edo's subminor and supermajor intervals approximate 7/6 and 9/7. Then there's the novaminor and novamajor thirds, which are extremely close approximations of Pythagorean minor and major thirds and can be referred to as such. There are also the pentaminor and pentamajor thirds, which are very close approximations of the Ptolemaic minor and major thirds and can also be referred to as such. Finally, the supraminor and submajor thirds approximate 39/32 and 16/13. For fourth-bounded triads, there's only really five options. The first two, which involve the approximations of 9/8 and 32/27, have a marked propensity to cause crowding, and thus are dissonant. Then there's the next two, the latal triads, which involve the approximations of 8/7 and 7/6, and which, due to their tuning are markedly less dissonant, but still dissonant. Finally, the last option, which splits the perfect fourth cleanly in half, is an ambisonance- that is, an interval that is halfway between the extremes of consonance and dissonance.

== Notation ==
This section provides some of the options for notating 53edo.

=== Pythagorean notation ===
In 53edo, the space between each of the notes that is separated by 2 steps in 12edo is instead 9 steps; notes separated by a single step in 12edo have to be distinguished from each other as the Pythagorean diatonic semitone is 4 steps while the Pythagorean chromatic semitone is 5 steps. Furthermore, the Pythagorean comma is a single step in 53edo, unlike in 12edo where it's tempered out. It is important to understand the usage of enharmonic equivalence here; unlike in systems such as 31edo where each note has an easily derivable "canonical" notation, it is important to understand the multiple faces of each of 53edo's pitches (which some might consider as a downside of using the Pythagorean system).

{| class="wikitable"
|+
!
!
|-
| colspan="2" |D
|-
|^^Ebb
|^D
|-
|vvEb
|^^D
|-
|vEb
|vvD#
|-
|Eb
|vD#
|-
|^Eb
|D#
|-
|^^Eb
|^D#
|-
|vvE
|^^D#
|-
|vE
|vvDx
|-
| colspan="2" |E
|}

==== Ups and Downs ====
Ups and downs naturally reflect 53edo's structure, as 5/4 is downmajor, 81/64 is major, and 9/7 is upmajor.

==== Syntonic-Rastmic Subchroma notation ====
Syntonic-Rastmic Subchroma notation, or SRS notation for short, uses '''synsharp''' and '''synflat''' as accidentals to cover the syntonic comma. However, while SRS notation is a 2.3.5.11 notation, only the 2.3.5 portion of the notation for 53edo is shared with multiples like 159edo.

==== Accidentals ====
53edo's accidentals, as mentioned and demonstrated previously, consist of sharps and flats, as well as either up and down accidentals, or, alternatively, synsharps and synflats and their derivatives.
{{Navbox EDO}}
{{Cat|Edos}}

31edo

2026-03-05T01:56:52Z

Lumithesilly: forgot to bold

[[File:31edo whr.png|thumb|418x418px|31edo supports [[Carlos Alpha]] and [[Miracle]], alongside supporting Meantone.]]
'''31edo''', or 31 equal divisions of the octave, is an equal tuning with a step size of approximately 39 cents. Aside from [[12edo]], it is a popular tuning of [[Meantone]] and has accurate approximations of harmonics 5 and 7.

== Theory ==

==== Edostep interpretations ====
31edo's edostep has the following interpretations in the 2...13 subgroup:

* 49/48 (the difference between 7/6 and 8/7)
* 50/49 (the difference between 7/5 and 10/7)
* 64/63 (the difference between 8/7 and 9/8)
* 36/35 (the difference between 7/6 and 6/5)
* 54/55 (the difference between 6/5 and 11/9)
* 45/44 (the difference between 5/4 and 11/9)
* 128/125 (the difference between 5/4 and 32/25)
* 65/64 (the difference between 16/13 and 5/4)

==== JI approximation ====
31edo is best understood as a 2.3.5.7.11.23 system, although it has a sharp but functional prime 13. The flatness of harmonics 9 and 11 mostly cancel out, producing a close-to-pure ~11/9 neutral interval. It has a rather functional diatonic scale, with the whole tone split into 2 and 3, with 2 steps making a chromatic semitone (or "chromatone") and 3 steps making a diatonic semitone (or "diatone").

{{Harmonics in ED|31|31|0}}
{| class="wikitable"
|+Thirds in 31edo
!Quality
|Subminor
|'''Pentaminor'''
|Neutral
|'''Pentamajor'''
|Supermajor
|-
!Cents
|271
|'''310'''
|348
|'''387'''
|426
|-
!Just interpretation
|7/6
|'''6/5'''
|11/9
|'''5/4'''
|9/7
|-
!Steps
|7
|'''8'''
|9
|'''10'''
|11
|}
Diatonic thirds are bolded.

=== Chords ===
Along with its diatonic major and minor chords which approximate 5-limit harmony, 31edo also has a narrow but functional supermajor triad, and a well-tuned subminor triad. It also supports arto and tendo chords, with its slendric chords of [0 6 18] and [0 12 18], and has a neutral triad [0 9 18] which represents both artoneutral and tendoneutral triads in the 11- and 13-limit.

=== Scales ===
31edo does not temper out 64/63, meaning that it can be used to tune [[Diasem]] while representing some simpler 5-limit intervals. 31edo's step is called a [[diesis]], and can function as an [[aberrisma]]. Due to being a prime number, 31edo has a large number of full-period MOS scales that exist in the edo. Orwell[9] ([[gramitonic]]) is one example, so is Mohajira[7] ([[mosh]]).

31edo also has a usable 12-note chromatic scale, approximating [[Golden sequences and tuning|golden]] Meantone/monocot.

=== Regular temperaments ===
Besides [[Meantone]] (for which it provides an excellent tuning and which is shared with 19edo), 31edo also supports variations of Rastmic temperament (like 24edo), Slendric (like 36edo), Miracle (like 41edo), and Orwell (like 22edo).

== Notation ==
31edo, as one of the more popular edos, has a somewhat agreed-upon notation system. This notation is simply neutral [[diatonic notation]] applied to the edo, where a half-# or half-b represents an alteration by one diesis. In this manner, all notes can be spelled in a way that does not require multiple sharps or flats.

{| class="wikitable"
|+
!Step
!Cents
!ADIN
!Neutral diatonic
!Notation
!Just intervals represented
|-
|0
|0.00
|unison
|unison
|A
|1/1
|-
|1
|38.71
|superunison
|semiaugmented unison
|At
|49/48, 50/49, 128/125
|-
|2
|77.42
|subminor second
|semidiminished second
|A#
|25/24
|-
|3
|116.13
|nearminor second
|minor second
|Bb
|16/15
|-
|4
|154.84
|neutral second
|neutral second
|Bd
|11/10, 12/11
|-
|5
|193.55
|nearmajor second
|major second
|B
|10/9, 9/8
|-
|6
|232.26
|supermajor second
|semiaugmented second
|Bt
|8/7
|-
|7
|270.97
|subminor third
|semidiminished third
|Cd
|7/6
|-
|8
|309.68
|nearminor third
|minor third
|C
|6/5
|-
|9
|348.39
|neutral third
|neutral third
|Ct
|11/9, 16/13
|-
|10
|387.10
|nearmajor third
|major third
|C#
|5/4
|-
|11
|425.81
|supermajor third
|semiaugmented third
|Db
|9/7
|-
|12
|464.52
|subfourth
|semidiminished fourth
|Dd
|21/16, 13/10
|-
|13
|503.23
|perfect fourth
|perfect fourth
|D
|4/3
|-
|14
|541.94
|neutral fourth
|semiaugmented fourth
|Dt
|11/8, 15/11
|-
|15
|580.65
|nearaugmented fourth
|augmented fourth
|D#
|7/5
|-
|16
|619.35
|neardiminished fifth
|diminished fifth
|Eb
|10/7
|-
|17
|658.06
|neutral fifth
|semidiminished fifth
|Ed
|16/11, 22/15
|-
|18
|696.77
|perfect fifth
|perfect fifth
|E
|3/2
|-
|19
|735.48
|superfifth
|semiaugmented fifth
|Et
|32/21, 20/13
|-
|20
|774.19
|subminor sixth
|semidiminished sixth
|Fd
|14/9
|-
|21
|812.90
|nearminor sixth
|minor sixth
|F
|8/5
|-
|22
|851.61
|neutral sixth
|neutral sixth
|Ft
|13/8, 18/11
|-
|23
|890.32
|nearmajor sixth
|major sixth
|F#
|5/3
|-
|24
|929.03
|supermajor sixth
|semiaugmented sixth
|Gb
|12/7
|-
|25
|967.74
|subminor seventh
|semidiminished seventh
|Gd
|7/4
|-
|26
|1,006.45
|nearminor seventh
|minor seventh
|G
|9/5, 16/9
|-
|27
|1,045.16
|neutral seventh
|neutral seventh
|Gt
|11/6, 20/11
|-
|28
|1,083.87
|nearmajor seventh
|major seventh
|G#
|15/8
|-
|29
|1,122.58
|supermajor seventh
|semiaugmented seventh
|Ab
|48/25
|-
|30
|1,161.29
|suboctave
|semidiminished octave
|Ad
|49/25, 125/64, 96/49
|-
|31
|1,200.00
|octave
|octave
|A
|2/1
|}
{{Cat|Edos}}{{Navbox EDO}}

31edo

2026-03-04T20:21:29Z

Lumithesilly: added steps to the thirds table

[[File:31edo whr.png|thumb|418x418px|31edo supports [[Carlos Alpha]] and [[Miracle]], alongside supporting Meantone.]]
'''31edo''', or 31 equal divisions of the octave, is an equal tuning with a step size of approximately 39 cents. Aside from [[12edo]], it is a popular tuning of [[Meantone]] and has accurate approximations of harmonics 5 and 7.

== Theory ==

==== Edostep interpretations ====
31edo's edostep has the following interpretations in the 2...13 subgroup:

* 49/48 (the difference between 7/6 and 8/7)
* 50/49 (the difference between 7/5 and 10/7)
* 64/63 (the difference between 8/7 and 9/8)
* 36/35 (the difference between 7/6 and 6/5)
* 54/55 (the difference between 6/5 and 11/9)
* 45/44 (the difference between 5/4 and 11/9)
* 128/125 (the difference between 5/4 and 32/25)
* 65/64 (the difference between 16/13 and 5/4)

==== JI approximation ====
31edo is best understood as a 2.3.5.7.11.23 system, although it has a sharp but functional prime 13. The flatness of harmonics 9 and 11 mostly cancel out, producing a close-to-pure ~11/9 neutral interval. It has a rather functional diatonic scale, with the whole tone split into 2 and 3, with 2 steps making a chromatic semitone (or "chromatone") and 3 steps making a diatonic semitone (or "diatone").

{{Harmonics in ED|31|31|0}}
{| class="wikitable"
|+Thirds in 31edo
!Quality
|Subminor
|'''Pentaminor'''
|Neutral
|'''Pentamajor'''
|Supermajor
|-
!Cents
|271
|'''310'''
|348
|'''387'''
|426
|-
!Just interpretation
|7/6
|'''6/5'''
|11/9
|'''5/4'''
|9/7
|-
!Steps
|7
|8
|9
|10
|11
|}
Diatonic thirds are bolded.

=== Chords ===
Along with its diatonic major and minor chords which approximate 5-limit harmony, 31edo also has a narrow but functional supermajor triad, and a well-tuned subminor triad. It also supports arto and tendo chords, with its slendric chords of [0 6 18] and [0 12 18], and has a neutral triad [0 9 18] which represents both artoneutral and tendoneutral triads in the 11- and 13-limit.

=== Scales ===
31edo does not temper out 64/63, meaning that it can be used to tune [[Diasem]] while representing some simpler 5-limit intervals. 31edo's step is called a [[diesis]], and can function as an [[aberrisma]]. Due to being a prime number, 31edo has a large number of full-period MOS scales that exist in the edo. Orwell[9] ([[gramitonic]]) is one example, so is Mohajira[7] ([[mosh]]).

31edo also has a usable 12-note chromatic scale, approximating [[Golden sequences and tuning|golden]] Meantone/monocot.

=== Regular temperaments ===
Besides [[Meantone]] (for which it provides an excellent tuning and which is shared with 19edo), 31edo also supports variations of Rastmic temperament (like 24edo), Slendric (like 36edo), Miracle (like 41edo), and Orwell (like 22edo).

== Notation ==
31edo, as one of the more popular edos, has a somewhat agreed-upon notation system. This notation is simply neutral [[diatonic notation]] applied to the edo, where a half-# or half-b represents an alteration by one diesis. In this manner, all notes can be spelled in a way that does not require multiple sharps or flats.

{| class="wikitable"
|+
!Step
!Cents
!ADIN
!Neutral diatonic
!Notation
!Just intervals represented
|-
|0
|0.00
|unison
|unison
|A
|1/1
|-
|1
|38.71
|superunison
|semiaugmented unison
|At
|49/48, 50/49, 128/125
|-
|2
|77.42
|subminor second
|semidiminished second
|A#
|25/24
|-
|3
|116.13
|nearminor second
|minor second
|Bb
|16/15
|-
|4
|154.84
|neutral second
|neutral second
|Bd
|11/10, 12/11
|-
|5
|193.55
|nearmajor second
|major second
|B
|10/9, 9/8
|-
|6
|232.26
|supermajor second
|semiaugmented second
|Bt
|8/7
|-
|7
|270.97
|subminor third
|semidiminished third
|Cd
|7/6
|-
|8
|309.68
|nearminor third
|minor third
|C
|6/5
|-
|9
|348.39
|neutral third
|neutral third
|Ct
|11/9, 16/13
|-
|10
|387.10
|nearmajor third
|major third
|C#
|5/4
|-
|11
|425.81
|supermajor third
|semiaugmented third
|Db
|9/7
|-
|12
|464.52
|subfourth
|semidiminished fourth
|Dd
|21/16, 13/10
|-
|13
|503.23
|perfect fourth
|perfect fourth
|D
|4/3
|-
|14
|541.94
|neutral fourth
|semiaugmented fourth
|Dt
|11/8, 15/11
|-
|15
|580.65
|nearaugmented fourth
|augmented fourth
|D#
|7/5
|-
|16
|619.35
|neardiminished fifth
|diminished fifth
|Eb
|10/7
|-
|17
|658.06
|neutral fifth
|semidiminished fifth
|Ed
|16/11, 22/15
|-
|18
|696.77
|perfect fifth
|perfect fifth
|E
|3/2
|-
|19
|735.48
|superfifth
|semiaugmented fifth
|Et
|32/21, 20/13
|-
|20
|774.19
|subminor sixth
|semidiminished sixth
|Fd
|14/9
|-
|21
|812.90
|nearminor sixth
|minor sixth
|F
|8/5
|-
|22
|851.61
|neutral sixth
|neutral sixth
|Ft
|13/8, 18/11
|-
|23
|890.32
|nearmajor sixth
|major sixth
|F#
|5/3
|-
|24
|929.03
|supermajor sixth
|semiaugmented sixth
|Gb
|12/7
|-
|25
|967.74
|subminor seventh
|semidiminished seventh
|Gd
|7/4
|-
|26
|1,006.45
|nearminor seventh
|minor seventh
|G
|9/5, 16/9
|-
|27
|1,045.16
|neutral seventh
|neutral seventh
|Gt
|11/6, 20/11
|-
|28
|1,083.87
|nearmajor seventh
|major seventh
|G#
|15/8
|-
|29
|1,122.58
|supermajor seventh
|semiaugmented seventh
|Ab
|48/25
|-
|30
|1,161.29
|suboctave
|semidiminished octave
|Ad
|49/25, 125/64, 96/49
|-
|31
|1,200.00
|octave
|octave
|A
|2/1
|}
{{Cat|Edos}}{{Navbox EDO}}

53edo

2026-03-02T23:51:11Z

Lumithesilly: added steps to the thirds table ! just thought this was useful and was kinda annoyed this wasn't there already

'''53edo''', or 53 equal divisions of the octave, is the equal tuning featuring steps of (1200/53) ~= 22.64 cents, 53 of which stack to the perfect octave [[2/1]]. Theoretical interest in this tuning system goes back to antiquity.

== Theory ==
Unless one has a set of accidentals for the syntonic comma (see the Notation section) one is left in the unenviable position of having to label a Ptolemaic major third the same way as the Pythagorean diminished fourth, for example. Apart from that issue, 53edo is very useful for 5-limit music.

==== Edostep interpretations ====
53edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup:

* 65/64, the difference between the 13-limit tendoneutral third 16/13 and the classical major third 5/4
* 81/80 (the syntonic comma), the difference between 5/4 and the diatonic major third
* The Pythagorean comma, the difference between the Pythagorean diatonic and chromatic semitones
* 91/90, the difference between the 13-limit ultramajor third 13/10 and the septimal supermajor third 9/7
* 64/63, the difference between the diatonic major third and 9/7
* 512/507, the difference between the 13-limit neutral thirds

53edo tempers out the following commas:

* The schisma (the difference between 5/4 and the Pythagorean diminished fourth)
* The vulture comma (the difference between four 320/243 intervals and the tritave)
* The amiton (the difference between a stack of five 10/9 intervals and 27/16)
* The kleisma (the difference between a stack of three 25/24 intervals and 9/8)
* The semicomma (the difference between a stack of three 75/64 intervals and 8/5)
* 225/224 (the difference between 15/14 and 16/15)
* 385/384 (the difference between 77/64 and 6/5)
* 121/120 (the difference between 12/11 and 11/10)
* 625/624 (the difference between 25/24 and 26/25)
* 676/675 (the difference between a stack of two 15/13 intervals and the perfect fourth)

==== JI approximation ====
53edo is most usefully seen as a 2.3.5.7.13 tuning, but the 2.3.5.13 restriction is more accurate and shared with a number of its multiples, such as [[159edo]]. Because it is not a Meantone system, there are actually multiple potential diatonic scales to use for 5-limit harmony, one of which is the Zarlino diatonic scale (LMsLMLs), tuned in 53edo as 9-8-5-9-8-9-5, though this particular scale is arguably best used for Lydian or Locrian modes. There's also the Didymic diatonic scale, tuned in 53edo as 9-8-5-9-9-8-5, which is better suited for Ionian mode and Major tonality in general. However, 53edo also features a MOS diatonic of 9-9-4-9-9-9-4, which is basically the Pythagorean diatonic scale.

{{Harmonics in ED|53|31|0}}
{| class="wikitable"
|+Thirds in 53edo
!Quality
|Inframinor
|Subminor
|'''Farminor'''
|Nearminor
|Supraminor
|Submajor
|Nearmajor
|'''Farmajor'''
|Supermajor
|Ultramajor
|-
!Cents
|249
|272
|'''294'''
|317
|340
|362
|385
|'''408'''
|430
|453
|-
!Just interpretation
|15/13
|7/6, 75/64
|'''32/27'''
|6/5
|39/32
|16/13
|5/4
|'''81/64'''
|9/7, 32/25
|13/10
|-
!Steps
|11
|12
|13
|14
|15
|16
|17
|18
|19
|20
|}
Diatonic thirds are bolded.

=== Chords ===
53edo has four different flavors of minor and major intervals as well as supraminor and submajor intervals. Its inframinor and ultramajor thirds approximate 15/13 and 13/10 respectively. At the same time, 53edo's subminor and supermajor intervals approximate 7/6 and 9/7. Then there's the novaminor and novamajor thirds, which are extremely close approximations of Pythagorean minor and major thirds and can be referred to as such. There are also the pentaminor and pentamajor thirds, which are very close approximations of the Ptolemaic minor and major thirds and can also be referred to as such. Finally, the supraminor and submajor thirds approximate 39/32 and 16/13. For fourth-bounded triads, there's only really five options. The first two, which involve the approximations of 9/8 and 32/27, have a marked propensity to cause crowding, and thus are dissonant. Then there's the next two, the latal triads, which involve the approximations of 8/7 and 7/6, and which, due to their tuning are markedly less dissonant, but still dissonant. Finally, the last option, which splits the perfect fourth cleanly in half, is an ambisonance- that is, an interval that is halfway between the extremes of consonance and dissonance.

== Notation ==
This section provides some of the options for notating 53edo.

=== Pythagorean notation ===
In 53edo, the space between each of the notes that is separated by 2 steps in 12edo is instead 9 steps; notes separated by a single step in 12edo have to be distinguished from each other as the Pythagorean diatonic semitone is 4 steps while the Pythagorean chromatic semitone is 5 steps. Furthermore, the Pythagorean comma is a single step in 53edo, unlike in 12edo where it's tempered out. It is important to understand the usage of enharmonic equivalence here; unlike in systems such as 31edo where each note has an easily derivable "canonical" notation, it is important to understand the multiple faces of each of 53edo's pitches (which some might consider as a downside of using the Pythagorean system).

{| class="wikitable"
|+
!
!
|-
| colspan="2" |D
|-
|^^Ebb
|^D
|-
|vvEb
|^^D
|-
|vEb
|vvD#
|-
|Eb
|vD#
|-
|^Eb
|D#
|-
|^^Eb
|^D#
|-
|vvE
|^^D#
|-
|vE
|vvDx
|-
| colspan="2" |E
|}

==== Ups and Downs ====
Ups and downs naturally reflect 53edo's structure, as 5/4 is downmajor, 81/64 is major, and 9/7 is upmajor.

==== Syntonic-Rastmic Subchroma notation ====
Syntonic-Rastmic Subchroma notation, or SRS notation for short, uses '''synsharp''' and '''synflat''' as accidentals to cover the syntonic comma. However, while SRS notation is a 2.3.5.11 notation, only the 2.3.5 portion of the notation for 53edo is shared with multiples like 159edo.

==== Accidentals ====
53edo's accidentals, as mentioned and demonstrated previously, consist of sharps and flats, as well as either up and down accidentals, or, alternatively, synsharps and synflats and their derivatives.
{{Cat|Edos}}

User:Lumithesilly

2026-02-14T20:29:48Z

Lumithesilly: made this page exist ?

hii, i'm lumi

i make music and post it on [https://www.youtube.com/@ImLumiV my youtube channel]

i want to help contribute to the wiki but i'm not really sure what to do