11edo: Difference between revisions

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**Imported revision 4466579 - Original comment: **
→21st century: Add Joseph Monzo's ''Monzo, 2026-0608: 11edo, 11/8 time, piano, musescore3'' (2026)
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| de = 11-EDO
: This revision was by author [[User:guest|guest]] and made on <tt>2007-05-17 16:20:26 UTC</tt>.<br>
| en = 11edo
: The original revision id was <tt>4466579</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja = 11平均律
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
}}
<h4>Original Wikitext content:</h4>
{{Infobox ET}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=11 tone equal temperament=
{{ED intro}}
== Theory ==
Compared to 12edo, the intervals of 11edo are stretched:


**Compositions**
* The "minor second" at 109.09 cents, functions melodically very much like the 100-cent minor second of 12edo.
* The "major second" at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less [[concordant]]. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from [[7/4]].
* The "minor third" at 327.27 cents, is rather sharp and encroaching upon "[[neutral]] third".
* The "major third" at 436.36 cents, is quite sharp, and closer to the [[supermajor]] third of frequency ratio [[9/7]] than the simpler third of 5/4.
* The "perfect fourth" at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the [[11/8]] superfourth than the simpler perfect fourth of 4/3.
{{Harmonics in equal|11}}


[[http://zebox.com/cgi-bin/artists/dl.cgi?danstearns_2_-_11edo.m3u+qp+m4|Over the Rivers]] by [[http://www.myspace.com/danstearns|Dan Stearns]]</pre></div>
11edo does not approximate many small prime harmonics well, only providing good approximations to 7/4 and 11/8. However, 11edo can be treated as a subset of 22edo, and take 22edo's [[6/5]], [[9/7]], and [[16/15]] via direct approximation.
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;11edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x11 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;11 tone equal temperament&lt;/h1&gt;
11edo provides the same tuning on the [[k*N subgroups|2*11 subgroup]] 2.9.15.7.11.17 as does 22edo, and on this subgroup it [[tempering out|tempers out]] the same [[comma]]s as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16:17 [[chord]] and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating [[JI]] chords.
&lt;br /&gt;
 
&lt;strong&gt;Compositions&lt;/strong&gt;&lt;br /&gt;
11edo has a good approximation of [[9/7]], hence one natural approach to harmony in 11edo is to generate chords from stacks of this interval. Incidentally, correcting the tuning of 9/7 to just tuning and stacking this interval has the beneficial side effect of also improving the tuning of the 17th harmonic to almost exactly just intonation, with an error of only [[5832/5831|0.3 cents]]. It may therefore be worth considering this JI tuning as an alternative to 11edo.
&lt;br /&gt;
 
&lt;a class="wiki_link_ext" href="http://zebox.com/cgi-bin/artists/dl.cgi?danstearns_2_-_11edo.m3u+qp+m4" rel="nofollow"&gt;Over the Rivers&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.myspace.com/danstearns" rel="nofollow"&gt;Dan Stearns&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving [[Orgone]][7] on the whites. The superfluous Ab can be made a note of [[22edo]], a tuning known as "[[elevenplus]]".
 
[[File:0-8-16-20 chord.wav|thumb|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]]
 
== Intervals and Notation ==
=== Ups and downs notation ===
11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
 
The second approach preserves the ''harmonic'' meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 11edo "on the fly".
 
The 11edo solfege in the table is derived from [[22edo Solfege|22edo solfege]].
 
{| class="wikitable center-all right-2 left-4"
! #
! [[Cent]]s
! Solfege
! Approximate Ratios*
! colspan="2" | [[Ups and downs notation|Up/down notation]] <br> with major wider <br> than minor
! colspan="2" | Up/down notation <br> with major narrower <br> than minor
! [[Smitonic]]<br>(3rd-gen)<br>notation
! [[Tútim Dennsuul Wafiil|TDW]] <br> [[Machinoid|Machine]] <br> notation
! Pseudo-Diatonic Category
!Audio
|-
| 0
| 0.00
| '''do'''
| 1/1
| P1
| A
| P1
| A
| A
| Q, P#
| Unison
|[[File:0-0 unison.mp3|frameless]]
|-
| 1
| 109.09
| '''ra'''
| [[15/14]], [[16/15]], [[17/16]], [[18/17]]
| ^1, m2
| ^A, B
| ^1, M2
| ^A, B
| A#, Bb
| Q#, Rb
| Minor second
|[[File:0-109,09 minor second (11-EDO).mp3|frameless]]
|-
| 2
| 218.18
| '''re'''
| [[8/7]], [[9/8]], [[17/15]]
| ~2, m3
| ^B, Cb
| ~2, M3
| ^B, C#
| B
| R
| Major second
|[[File:0-218,18 major second (11-EDO).mp3|frameless]]
|-
| 3
| 327.27
| '''me'''
| [[6/5]], [[11/9]], [[17/14]]
| M2, ~3
| B#, vC
| m2, ~3
| Bb, vC
| C
| R#, Sb
| Minor third
|[[File:0-327,27 minor third (11-EDO).mp3|frameless]]
|-
| 4
| 436.36
| '''mo'''
| [[9/7]], [[14/11]], [[22/17]]
| M3, v4
| C, vD
| m3, v4
| C, vD
| C#, Db
| S
| Major third/Minor fourth
|[[File:0-436,36 major third (11-EDO).mp3|frameless]]
|-
| 5
| 545.45
| '''fu'''
| [[11/8]], [[15/11]]
| P4, v5
| D, vE
| P4, v5
| D, vE
| D
| S#, Tb
| Major fourth
|[[File:0-545,45 major fourth (11-EDO).mp3|frameless]]
|-
| 6
| 654.55
| '''su'''
| [[16/11]], [[22/15]]
| ^4, P5
| ^D, E
| ^4, P5
| ^D, E
| D#, Eb
| T
| Minor fifth
|[[File:0-654,55 minor fifth (11-EDO).mp3|frameless]]
|-
| 7
| 763.64
| '''lo'''
| [[14/9]], [[11/7]], [[17/11]]
| ^5, m6
| ^E, Fb
| ^5, M6
| ^E, F#
| E
| T#, Ub
| Major fifth/Minor sixth
|[[File:0-763,64 minor sixth (11-EDO).mp3|frameless]]
|-
| 8
| 872.73
| '''la'''
| [[5/3]], [[18/11]], [[28/17]]
| ~6, m7
| vF, Gb
| ~6, M7
| vF, G#
| F
| U
| Major sixth
|[[File:0-872,73 major sixth (11-EDO).mp3|frameless]]
|-
| 9
| 981.82
| '''ta'''
| [[7/4]], [[16/9]], [[30/17]]
| M6, ~7
| F, vG
| m6, ~7
| F, vG
| F#, Gb
| U#, Pb
| Minor seventh
|[[File:0-981,82 minor seventh (11-EDO).mp3|frameless]]
|-
| 10
| 1090.91
| '''ti'''
| [[15/8]], [[17/9]], [[28/15]], [[32/17]]
| M7, v8
| G, vAv
| m7, v8
| G, vAv
| G
| P, Qb
| Major seventh
|[[File:0-1090,91 major seventh (11-EDO).mp3|frameless]]
|-
| 11
| 1200.00
| '''do'''
| 2/1
| P8
| A
| P8
| A
| A
| Q, P#
| Octave
|[[File:0-1200 octave.mp3|frameless]]
|}
<nowiki>* in 2.7.9.11.15.17 subgroup</nowiki>
 
The ups and downs notations above are heptatonic systems generated by 5ths (~3/2). Alternative notations include pentatonic 5th-generated, octatonic 5th-generated, nonatonic 5th-generated, heptatonic 3rd-generated, and hexatonic 2nd-generated.
 
'''<u>Pentatonic 5th-generated:</u>''' '''D * * E G * * A C * * D'''  ([[Sensoid]] generator = wide 3/2 = 7\11 = perfect 5thoid)
 
D - ^D/Eb - D#/vE - E - G - ^G/Ab - G#/vA - A - C - ^C/Db - C#/vD - D
 
P1 - ^1/ms3 - A1/~s3 - Ms3 - P4d - ^4d/d5d - A4d/v5d - P5d - ms7 - ~s7/d8d - Ms7/v8d - P8d (s = sub-, d = -oid)
 
pentatonic genchain of fifths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...
 
pentatonic genchain of fifths: ...ds3 - ds7 - d4d - d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1 - A5d - As3 - As7... (s = sub-, d = -oid)
 
'''<u>Octatonic 5th-generated:</u>''' '''A B * C D E * F G * H A''' ([[Sensoid]] generator = wide 3/2 = 7\11 = perfect 6th)
 
A - B - B#/Cb - C - D - E - E#/Fb - F - G - G#/Hb - H - A
 
P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9
 
octatonic genchain of sixths: ...Db - Ab - Fb - Cb - Hb - E - B - G - D - A - F - C - H - E# - B# - G# - D# - A#...
 
octatonic genchain of sixths: ...d7 - d4 - d9 - d6 - m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7 - A4 - A1 - A6 - A3...
 
'''<u>Nonatonic 5th-generated:</u> A B * C D E F G * H J A''' ([[Joanatonic]] generator = narrow 3/2 = 6\11 = perfect 6th)
 
A - B - B#/Cb - C - D - E - F - G - G#/Hb - H - J - A
 
P1 - m2 - M2/m3 - M3/m4 - M4 - P5 - P6 - m7 - M7/m8 - M8/m9 - M9 - P10
 
nonotonic genchain of sixths: ...E# - A# - F# - B# - G# - C - H - D - J - E - A - F - B - G - Cb - Hb - Db - Jb - Eb...
 
nonotonic genchain of sixths: ...M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9...
 
'''<u>Heptatonic 3rd-generated:</u> D * E F * G A * B C * D''' ([[Smitonic]] generator = 3\11 = perfect 3rd)
 
D - D#/Eb - E - F - F#/Gb - G - A - A#/Bb - B - C - C#/Db - D
 
P1 - m2 - M2 - P3 - m4 - M4 - m5 - M5 - P6 - m7 - M7 - P8
 
genchain of thirds: ...E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb...
 
genchain of thirds: ...M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6...
 
'''<u>Hexatonic 2nd-generated:</u> R * S * T * U * P Q''' '''* R''' ([[Machinoid]] generator = 2\11 = perfect 2nd)
 
R - R#/Sb - S - S#/Tb - T - T#/Ub - U - U#/Pb - P - Q - Q#/Rb - R
 
P1 - A1/d2 - P2 - m3 - M3 - m4 - M4 - m5 - M5 - P6 - A6/d7 - P7
 
genchain of seconds: ... - Qb - Rb - Sb - Tb - Ub - Pb - Q - R - S - T - U - P - Q# - R# - S# - T# - U# - P#...
 
genchain of seconds: ... - m3 - m4 - m5 - P6 - P1 - P2 - M3 - M4 - M5 - A6 - A1...
 
===Sagittal notation===
This notation is a subset of the notations for EDOs [[22edo#Sagittal notation|22]], [[44edo#Sagittal notation|44]], and [[66edo#Sagittal notation|66]].
====Evo flavor====
 
<imagemap>
File:11-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 400 0 560 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 400 106 [[22-EDO#Sagittal_notation | 22-EDO notation]]
default [[File:11-EDO_Evo_Sagittal.svg]]
</imagemap>
 
====Revo flavor====
 
<imagemap>
File:11-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 368 0 528 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 368 106 [[22-EDO#Sagittal_notation | 22-EDO notation]]
default [[File:11-EDO_Revo_Sagittal.svg]]
</imagemap>
 
== Regular temperament properties ==
=== Uniform maps ===
{{Uniform map|edo=11}}
 
=== Commas ===
11et [[tempering out|tempers out]] the following [[comma]]s. This assumes val {{val| 11 17 26 31 38 41 }}.
 
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group=note>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
| 3
| [[177147/131072]]
| {{Monzo| -17 11 }}
| 521.50
| sasawa 3rd
| Pythagorean augmented third
|-
| 5
| [[135/128]]
| {{Monzo| -7 3 1 }}
| 92.18
| Layobi
| Major chroma
|-
| 5
| [[144/125]]
| {{Monzo| 4 2 -3 }}
| 244.97
| Trigu
| University comma
|-
| 5
| [[34171875/33554432|(16 digits)]]
| {{Monzo| -25 7 6 }}
| 31.57
| Lala-tribiyo
| [[Ampersand comma]]
|-
| 5
| <abbr title="295578376007080078125/295147905179352825856">(42 digits)</abbr>
| {{Monzo| -68 18 17 }}
| 2.52
| Quinla-seyo
| [[Vavoom comma]]
|-
| 7
| <abbr title="854296875/843308032">(18 digits)</abbr>
| {{Monzo| -10 7 8 -7 }}
| 22.41
| Lasepru-aquadbiyo
| [[Blackjackisma]]
|-
| 7
| [[1029/1024]]
| {{Monzo| -10 1 0 3 }}
| 8.43
| Latrizo
| Gamelisma
|-
| 7
| [[225/224]]
| {{Monzo| -5 2 2 -1 }}
| 7.71
| Ruyoyo
| Marvel comma
|-
| 7
| [[16875/16807]]
| {{Monzo| 0 3 4 -5 }}
| 6.99
| Quinru-aquadyo
| Mirkwai comma
|-
| 7
| [[2401/2400]]
| {{Monzo| -5 -1 -2 4 }}
| 0.72
| Bizozogu
| Breedsma
|-
| 11
| [[121/120]]
| {{Monzo| -3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
| 11
| [[65536/65219]]
| {{Monzo| 16 0 0 -2 -3 }}
| 8.39
| Satrilu-aruru
| Orgonisma
|}
 
== Approximation to JI ==
{| class="wikitable"
|-
! Harmonic
! 8
!
! 9
!
! 11
!
! 14
!
! 16
|-
! JI interval from 1/1
| 1/1 = 0 cents
|
| 9/8 = 204
|
| 11/8 = 551
|
| 7/4 = 969
|
| 2/1 = 1200
|-
! Nearest 11edo interval
| 0\11 = 0¢
|
| 2\11 = 218¢
|
| 5\11 = 545
|
| 9\11 = 982
|
| 11\11 = 1200
|-
! Difference
| 0
|
| +14¢
|
| -6¢
|
| +13¢
|
| 0¢
|-
! JI interval between
|
| 9:8 = 204¢
|
| 11:9 = 347
|
| 14:11 = 418
|
| 8:7 = 231
|
|-
! Nearest 11edo interval
|
| 2\11 = 218¢
|
| 3\11 = 327
|
| 4\11 = 436
|
| 2\11 = 218
|
|-
! Difference
|
| +14¢
|
| -20¢
|
| +18¢
|
| -13¢
|
|}
 
11edo also may be considered a 2.7.9.11.15.17 subgroup temperament. See diagram:
 
[[File:11edo_approx_2-7-9-11-15-17_2ndsave.png|alt=11edo_approx_2-7-9-11-15-17_2ndsave.png|11edo_approx_2-7-9-11-15-17_2ndsave.png]]
 
== Octave stretch or compression ==
11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. Examples of slightly compressed versions of 11edo include (least to most compressed) [[ed6|28ed6]], [[ed12|39ed12]], [[zpi|30zpi]], [[equal tuning|35ed9]] and [[ed7|31ed7]].
 
To use its primes 3 or 5, extreme octave shrinking can be used, at the cost of making the octaves sound significantly weaker. [[equal tuning|37ed10]] is a very compressed version of 11edo.
 
== Scales ==
{{Main|11edo modes}}
 
=== MOS scales ===
{{Main|List of 11edo MOS scales}}
Although 11edo has one fewer interval in the octave than 12edo, in terms of [[MOS scale|moment-of-symmetry scales]], it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11 (two degrees of 11edo), 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.
 
== Instruments ==
'''11edo ukulele'''
 
[[File:11-edo-ukulele.JPG|alt=11-edo-ukulele.JPG|404x304px|11-edo-ukulele.JPG]]
 
'''Ensembles'''
 
In February 2011, [http://oddmusicuc.wordpress.com/ Oddmusic U-C], as part of its Microtonal Design Seminar, generated a 7-piece ensemble for playing music in 11edo. Instrumentation: autotuner, cümbüş, electronic keyboard, kalimba, retrofretted guitar, tuned bottles, udderbot. Recordings forthcoming.
 
'''Lumatone'''
 
[[Lumatone mapping for 11edo|Lumatone mappings for 11edo]] are available.
 
== Introductory Materials ==
* [[File:11edo_1MC.mp3|270px]] 11edo example composition by [[User:Inthar|Inthar]] (first half's in [[4L 3s]], second half is in [[3L 5s]])
 
== Music ==
{{Catrel|11edo tracks}}
=== 11 equal divisions of the octave (11edo proper) ===
==== Modern renderings ====
; {{W|Arthur Schutt}}
* [https://www.youtube.com/watch?v=GEzxtHILDr8 ''Bluin' The Black Keys''] (1926) – rendered by Francium (2024)
 
==== 20th century ====
; [[George Secor]]
* [http://xenharmony.wikispaces.com/space/showimage/11edo-improv.mp3 First Piece Ever]{{dead link}} (1970) — apparently the first piece ever written for 11edo.
 
; [[Bill Sethares]]
* [https://sethares.engr.wisc.edu/mp3s/dabo_girl.html "The Turquoise Dabo Girl"], from [https://sethares.engr.wisc.edu/xentone.html ''Xentonality''] (1997)
 
==== 21st century ====
; [[Abnormality]]
* [https://www.youtube.com/watch?v=G1rUu9qmXkE ''Scatter Brain''] (2024)
 
; [[Christopher Bailey]]
* [https://www.youtube.com/playlist?list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3 ''The Stuffed Ones''] (2004) – 4-piece suite ([http://christopherbaileymusic.com/composition-list/ details])
** [https://www.youtube.com/watch?v=NU0VvGRelUQ&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=1 "Goopy"] · [https://www.youtube.com/watch?v=4D9wDl_oxHE&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=2 "Ellie"] · [https://www.youtube.com/watch?v=53IiHdXfJwI&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=3 "Ziggy"] · [https://www.youtube.com/watch?v=4sZqpRcB-lk&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=4 "Towelbear"]
 
; [[Jacob Barton]]
* ''Hyperimprovisations Nuggetwarp'' (2009)
** [https://soundclick.com/share.cfm?id=10267904 "Piece I"] · [https://soundclick.com/share.cfm?id=10267905 "Piece II"] · [https://soundclick.com/share.cfm?id=10267906 "Piece III"]
 
; [[City of the Asleep]]
* [https://cityoftheasleep.bandcamp.com/track/she-is-my-lilac-hued-obsession "She is My Lilac-Hued Obsession"], from [https://cityoftheasleep.bandcamp.com/album/map-of-an-internal-landscape-reissue ''Map of an Internal Landscape''] (2007)
 
; [[Jason Conklin]]
* ''The City Sleeps, A Madrigal'' (2011) – [http://web.archive.org/web/20201127013549/http://micro.soonlabel.com/gene_ward_smith/Others/Conklin/Conklin-The_City_Sleeps_A_Madrigal.mp3 play] | [https://soundcloud.com/ninly/the-city-sleeps SoundCloud]
 
; [[E8 Heterotic]]
* [https://youtu.be/9tJHJEZnvFs?si=9n6I3VnejVon_iot ''Olive Flamenco''] (2019)
 
; [[Francium]]
* "Tostadosto" from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/27hl1xKswTuaQG0vIjMHhk Spotify] | [https://francium223.bandcamp.com/track/tostadosto Bandcamp] | [https://www.youtube.com/watch?v=28SOTJvT6sw YouTube]
* "Sleep Slope" from ''XenRhythms'' (2024) – [https://open.spotify.com/track/2GnUioPrMlJmMaacE6DK7i Spotify] | [https://francium223.bandcamp.com/track/sleep-slope Bandcamp] | [https://www.youtube.com/watch?v=hM0BAC_YZnQ YouTube]
 
; [[David Hamill]]
* [http://www.focalchords.com/audio/Cool_My_Head_11EDO.mp3 ''Cool My Head''] (2010)
 
; [[Andrew Heathwaite]]
* ''Orange Clips on Sausages'' (2004) – [http://web.archive.org/web/20201127012301/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+orangeclipsonsausagesin11tet.mp3 play] | [https://www.soundclick.com/music/songInfo.cfm?songID=933772 SoundClick]
* ''Blue Gel'' (2004) – [http://web.archive.org/web/20201127012646/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin11tet.mp3 play] | [https://www.soundclick.com/music/songInfo.cfm?songID=834492 SoundClick]
* ''conversation is'' (2010) – [http://web.archive.org/web/20201127012932/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+conversationis.mp3 play] | [https://www.soundclick.com/music/songInfo.cfm?songid=8839070 SoundClick]
 
; [[Hideya]]
* [https://www.youtube.com/watch?v=PcY3HrwQRRY ''Like Parker 3''] (2019)
* [https://www.youtube.com/watch?v=YawFcH4cXfs ''Like 40s music''] (2022)
 
; [[Aaron Andrew Hunt]]
* From [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal-Tempered Keyboard''] (1999–2022)
** [https://aaronandrewhunt.bandcamp.com/track/prelude-in-11et "Prelude in 11ET"]
** "Adagio in 11ET" – [https://aaronandrewhunt.bandcamp.com/track/adagio-in-11et Bandcamp] | [https://soundcloud.com/uz1kt3k/adagio-in-11et?in=uz1kt3k/sets/adagio-invention-in-11et SoundCloud]{{dead link}}
** "Invention in 11ET" – [https://aaronandrewhunt.bandcamp.com/track/invention-in-11et Bandcamp] | [https://soundcloud.com/uz1kt3k/invention-in-11et?in=uz1kt3k/sets/adagio-invention-in-11et SoundCloud]{{dead link}}
 
; [[User:Ayceman|Alexandru Ianu]]
* ''Divertimento in 11 tone Orgone'' (2021) – [[:File:Divertimento in 11 tone Orgone.pdf|sheet music]] | [https://youtu.be/8x1f5WFkF4k YouTube] – orgone in 11edo tuning
* ''Sylvian Moon Dance'' (2021) – [[:File:SylvianMoonDance.ogg|audio]] | [[:File:Sylvian_Moon_Dance.pdf|sheet music]] | [https://youtu.be/81uZbsmbet8 YouTube] – orgone in 11edo tuning
* ''Ocean of the Necrophages'' (2021) – orgone in 11edo tuning
** Piano: [[:File:Ocean of the Necrophages (4U UP).ogg|audio]] | [[:File:Ocean of the Necrophages.pdf|sheet music]] | [https://youtu.be/CWU09fXXy1s YouTube]
** Strings: [[:File:Ocean of the Necrophages (strings).ogg|audio]] | [[:File:Ocean of the Necrophages (strings).pdf|sheet music]]
 
; [[Aaron Krister Johnson]]
* [http://www.akjmusic.com/audio/black_ritual_dirge.mp3 ''Black Ritual Dirge'']{{dead link}}
 
; [[User:ks26|groundfault]]
* [https://www.youtube.com/watch?v=AEnEYk3X1as ''Ghost Bridge''] (2020)
 
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=bqIDxbc21O8 ''Micropiece in 11edo''] (2020)
* [https://www.youtube.com/watch?v=fwyM3quEzu4 ''Prelude & Fugue in 11edo, in Four Parts, for Recorder, Organ, Cello''] (2022)
* [https://www.youtube.com/watch?v=qNqDuAq6O5k ''George Secor · 11EDO improvisation (1971)''] (2022)
 
; [[Joseph Monzo]]
* [https://www.youtube.com/shorts/JMrFUKfqfeY ''Monzo, 2026-0608: 11edo, 11/8 time, piano, musescore3''] (2026)
 
; [[Mundoworld]]
* [https://www.youtube.com/watch?v=69TiqslCgeg ''Fire Memes'' (with Anthony "Pomp" Pompliano)] – Machine[6] in 11edo tuning
* [https://www.youtube.com/watch?v=MfNLxcbVzs8 ''Theory of Creation''] – Machine[6] in 11edo tuning
* "Search Party" from ''No Fun House'' (2025) – [https://open.spotify.com/track/7CMiwDuuRuFpB0skfwT2Ap Spotify] | [https://mundoworld.bandcamp.com/track/search-party Bandcamp] | [https://www.youtube.com/watch?v=hLs6MjuousI YouTube]
 
; [[User:GlitchyDarkness|No Clue Music]]
* [https://www.youtube.com/watch?v=lPKc1B6YBn4 ''Cursed Star''] (2024)
 
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=AbWxZ6yh69s "Overcoming"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
 
; [[User:Phanomium|Phanomium]]
* [https://www.youtube.com/watch?v=y939ciE9MQY ''33322''] (2024)
 
; [[X. J. Scott]]
* [https://soundclick.com/share.cfm?id=955383 ''Angkor Wat, September 1066''] (2004)
 
; [[Sevish]]
* "[[Longwayaway People]]", from ''[[Rhythm and Xen]]'' (2015)
* "[[Make a Dream]]", from ''[[Rhythm and Xen]]'' (2015)
 
; [[Jon Lyle Smith]]
* [https://archive.org/details/jls_ArchiveVol2/Jaunt_reMix2012.wav ''Jaunt''] (2012) – [http://web.archive.org/web/20201127014902/http://micro.soonlabel.com/jon-lyle-smith/Jaunt.mp3 play] | [https://www.youtube.com/watch?v=HKULte3WhuE YouTube]
* [http://archive.org/download/CounterpointIn11edo/CounterpointIn11edo.mp3 ''Counterpoint in 11EDO'']{{dead link}}
 
; [[Chris Vaisvil]]
* [https://web.archive.org/web/20201127012602/http://micro.soonlabel.com/11-ET/daily201110-gpo-jeffery-dahmer-cooks.mp3 ''Jeffrey Dahmer Cooks at 11EDO''] (2011)
* [https://web.archive.org/web/20201127015348/http://micro.soonlabel.com/11-ET/20110902_prepared_seagull_metamorphis.mp3 ''The Metamorphosis of Gregor''] (2011)
* ''Eleven Birds'' (2012) – [https://www.chrisvaisvil.com/eleven-birds/ blog] | [http://micro.soonlabel.com/11-ET/20120928-piano-11edo-eleven-birds.mp3 play]
* [https://soundcloud.com/vaisvil/the-execution-of-12-equal ''The Execution of 12 Equal'']{{dead link}}
 
; [[Randy Winchester]]
* [https://archive.org/details/jamendo-005173/10.mp3 "10. 11 / octave"], from ''[[Comets Over Flatland]]'' (2007)
 
; [[Ozan Yarman]]
* [http://www.ozanyarman.com/files/music/Icicle_Caverns.mp3 ''Icicle Caverns''] (2010) ([http://www.ozanyarman.com/files/music/icicle_caverns_score.pdf score])
 
; [[Yeah Gore]]
* [https://www.youtube.com/watch?v=FL72Z4H1IF8 ''11 TET Hernya''] (2020)
* [https://www.youtube.com/watch?v=dwel2K1Bgds ''YG_A''] (2022)
 
=== Unequal Derivatives of 11edo ===
; [[Bryan Deister]]
* ''11 Tone March'' (2023/2024)
** [https://www.youtube.com/shorts/K2QVvaRUXIQ <nowiki>[short clip]</nowiki>] (2023, with Lumatone view)
** [https://www.youtube.com/watch?v=z0lWcguNsNs <nowiki>[full version]</nowiki>] (2024, with tuning specification in video description)
 
== Videos ==
* The Stuffed Ones: ''[https://www.youtube.com/watch?v=NU0VvGRelUQ&feature=related Goopy]'', ''[https://www.youtube.com/watch?v=4D9wDl_oxHE&feature=related Ziggy]'', ''[https://www.youtube.com/watch?v=53IiHdXfJwI&feature=related Ellie]'', ''[https://www.youtube.com/watch?v=4sZqpRcB-lk&feature=related Towelbear]'' by [https://www.youtube.com/user/zipzappoozoo zipzappoozoo]
 
* [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ|Mike Battaglia]] - youtube
* [https://www.youtube.com/watch?v=4WlTPfRDPCY untitled1], computer
 
== See also ==
* [[11edo Zine]] — There is an 11edo Zine! As far as we know, 11edo is the first xenharmonic tuning system to have its own zine.
 
== Notes ==
<references group=note/>
 
[[Category:Listen]]
{{Todo|add rank 2 temperaments table}}

Latest revision as of 19:19, 10 June 2026

← 10edo 11edo 12edo →
Prime factorization 11 (prime)
Step size 109.091 ¢ 
Fifth 6\11 (654.545 ¢)
Semitones (A1:m2) -2:3 (-218.2 ¢ : 327.3 ¢)
Dual sharp fifth 7\11 (763.636 ¢)
Dual flat fifth 6\11 (654.545 ¢)
Dual major 2nd 2\11 (218.182 ¢)
(semiconvergent)
Consistency limit 3
Distinct consistency limit 3

11 equal divisions of the octave (abbreviated 11edo or 11ed2), also called 11-tone equal temperament (11tet) or 11 equal temperament (11et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 11 equal parts of about 109 ¢ each. Each step represents a frequency ratio of 21/11, or the 11th root of 2.

Theory

Compared to 12edo, the intervals of 11edo are stretched:

  • The "minor second" at 109.09 cents, functions melodically very much like the 100-cent minor second of 12edo.
  • The "major second" at 218.18 cents, works in a similar fashion to the 200-cent major second of 12edo, but as a major ninth, it may sound less concordant. Its inversion, at 981.82 cents, can function as a "bluesy" seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.
  • The "minor third" at 327.27 cents, is rather sharp and encroaching upon "neutral third".
  • The "major third" at 436.36 cents, is quite sharp, and closer to the supermajor third of frequency ratio 9/7 than the simpler third of 5/4.
  • The "perfect fourth" at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the 11/8 superfourth than the simpler perfect fourth of 4/3.
Approximation of odd harmonics in 11edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -47.4 +50.0 +13.0 +14.3 -5.9 +32.2 +2.6 +4.1 +29.8 -34.4 +26.3
Relative (%) -43.5 +45.9 +11.9 +13.1 -5.4 +29.5 +2.4 +3.8 +27.3 -31.5 +24.1
Steps
(reduced) 		17
(6) 		26
(4) 		31
(9) 		35
(2) 		38
(5) 		41
(8) 		43
(10) 		45
(1) 		47
(3) 		48
(4) 		50
(6)

11edo does not approximate many small prime harmonics well, only providing good approximations to 7/4 and 11/8. However, 11edo can be treated as a subset of 22edo, and take 22edo's 6/5, 9/7, and 16/15 via direct approximation.

11edo provides the same tuning on the 2*11 subgroup 2.9.15.7.11.17 as does 22edo, and on this subgroup it tempers out the same commas as 22. Also on this subgroup there is an approximation of the 8:9:11:14:15:16:17 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.

11edo has a good approximation of 9/7, hence one natural approach to harmony in 11edo is to generate chords from stacks of this interval. Incidentally, correcting the tuning of 9/7 to just tuning and stacking this interval has the beneficial side effect of also improving the tuning of the 17th harmonic to almost exactly just intonation, with an error of only 0.3 cents. It may therefore be worth considering this JI tuning as an alternative to 11edo.

Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving Orgone[7] on the whites. The superfluous Ab can be made a note of 22edo, a tuning known as "elevenplus".

A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.

Intervals and Notation

Ups and downs notation

11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the melodic meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

The second approach preserves the harmonic meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 11edo "on the fly".

The 11edo solfege in the table is derived from 22edo solfege.

# Cents Solfege Approximate Ratios* Up/down notation
with major wider
than minor 		Up/down notation
with major narrower
than minor 		Smitonic
(3rd-gen)
notation 		TDW
Machine
notation 		Pseudo-Diatonic Category Audio
0 0.00 do 1/1 P1 A P1 A A Q, P# Unison
1 109.09 ra 15/14, 16/15, 17/16, 18/17 ^1, m2 ^A, B ^1, M2 ^A, B A#, Bb Q#, Rb Minor second
2 218.18 re 8/7, 9/8, 17/15 ~2, m3 ^B, Cb ~2, M3 ^B, C# B R Major second
3 327.27 me 6/5, 11/9, 17/14 M2, ~3 B#, vC m2, ~3 Bb, vC C R#, Sb Minor third
4 436.36 mo 9/7, 14/11, 22/17 M3, v4 C, vD m3, v4 C, vD C#, Db S Major third/Minor fourth
5 545.45 fu 11/8, 15/11 P4, v5 D, vE P4, v5 D, vE D S#, Tb Major fourth
6 654.55 su 16/11, 22/15 ^4, P5 ^D, E ^4, P5 ^D, E D#, Eb T Minor fifth
7 763.64 lo 14/9, 11/7, 17/11 ^5, m6 ^E, Fb ^5, M6 ^E, F# E T#, Ub Major fifth/Minor sixth
8 872.73 la 5/3, 18/11, 28/17 ~6, m7 vF, Gb ~6, M7 vF, G# F U Major sixth
9 981.82 ta 7/4, 16/9, 30/17 M6, ~7 F, vG m6, ~7 F, vG F#, Gb U#, Pb Minor seventh
10 1090.91 ti 15/8, 17/9, 28/15, 32/17 M7, v8 G, vAv m7, v8 G, vAv G P, Qb Major seventh
11 1200.00 do 2/1 P8 A P8 A A Q, P# Octave

* in 2.7.9.11.15.17 subgroup

The ups and downs notations above are heptatonic systems generated by 5ths (~3/2). Alternative notations include pentatonic 5th-generated, octatonic 5th-generated, nonatonic 5th-generated, heptatonic 3rd-generated, and hexatonic 2nd-generated.

Pentatonic 5th-generated: D * * E G * * A C * * D (Sensoid generator = wide 3/2 = 7\11 = perfect 5thoid)

D - ^D/Eb - D#/vE - E - G - ^G/Ab - G#/vA - A - C - ^C/Db - C#/vD - D

P1 - ^1/ms3 - A1/~s3 - Ms3 - P4d - ^4d/d5d - A4d/v5d - P5d - ms7 - ~s7/d8d - Ms7/v8d - P8d (s = sub-, d = -oid)

pentatonic genchain of fifths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...

pentatonic genchain of fifths: ...ds3 - ds7 - d4d - d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1 - A5d - As3 - As7... (s = sub-, d = -oid)

Octatonic 5th-generated: A B * C D E * F G * H A (Sensoid generator = wide 3/2 = 7\11 = perfect 6th)

A - B - B#/Cb - C - D - E - E#/Fb - F - G - G#/Hb - H - A

P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9

octatonic genchain of sixths: ...Db - Ab - Fb - Cb - Hb - E - B - G - D - A - F - C - H - E# - B# - G# - D# - A#...

octatonic genchain of sixths: ...d7 - d4 - d9 - d6 - m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7 - A4 - A1 - A6 - A3...

Nonatonic 5th-generated: A B * C D E F G * H J A (Joanatonic generator = narrow 3/2 = 6\11 = perfect 6th)

A - B - B#/Cb - C - D - E - F - G - G#/Hb - H - J - A

P1 - m2 - M2/m3 - M3/m4 - M4 - P5 - P6 - m7 - M7/m8 - M8/m9 - M9 - P10

nonotonic genchain of sixths: ...E# - A# - F# - B# - G# - C - H - D - J - E - A - F - B - G - Cb - Hb - Db - Jb - Eb...

nonotonic genchain of sixths: ...M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9...

Heptatonic 3rd-generated: D * E F * G A * B C * D (Smitonic generator = 3\11 = perfect 3rd)

D - D#/Eb - E - F - F#/Gb - G - A - A#/Bb - B - C - C#/Db - D

P1 - m2 - M2 - P3 - m4 - M4 - m5 - M5 - P6 - m7 - M7 - P8

genchain of thirds: ...E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb...

genchain of thirds: ...M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6...

Hexatonic 2nd-generated: R * S * T * U * P Q * R (Machinoid generator = 2\11 = perfect 2nd)

R - R#/Sb - S - S#/Tb - T - T#/Ub - U - U#/Pb - P - Q - Q#/Rb - R

P1 - A1/d2 - P2 - m3 - M3 - m4 - M4 - m5 - M5 - P6 - A6/d7 - P7

genchain of seconds: ... - Qb - Rb - Sb - Tb - Ub - Pb - Q - R - S - T - U - P - Q# - R# - S# - T# - U# - P#...

genchain of seconds: ... - m3 - m4 - m5 - P6 - P1 - P2 - M3 - M4 - M5 - A6 - A1...

Sagittal notation

This notation is a subset of the notations for EDOs 22, 44, and 66.

Evo flavor

Sagittal notationPeriodic table of EDOs with sagittal notation22-EDO notation

Revo flavor

Sagittal notationPeriodic table of EDOs with sagittal notation22-EDO notation

Regular temperament properties

Uniform maps

13-limit uniform maps between 10.8 and 11.2
Min. size Max. size Wart notation Map
10.6744 10.8399 11cdeef ⟨11 17 25 30 37 40]
10.8399 10.8643 11cdf ⟨11 17 25 30 38 40]
10.8643 10.9446 11cf ⟨11 17 25 31 38 40]
10.9446 10.9823 11c ⟨11 17 25 31 38 41]
10.9823 11.0413 11 ⟨11 17 26 31 38 41]
11.0413 11.1290 11b ⟨11 18 26 31 38 41]
11.1290 11.2149 11be ⟨11 18 26 31 39 41]

Commas

11et tempers out the following commas. This assumes val ⟨11 17 26 31 38 41].

Prime
limit 		Ratio[note 1] Monzo Cents Color name Name(s)
3 177147/131072 [-17 11⟩ 521.50 sasawa 3rd Pythagorean augmented third
5 135/128 [-7 3 1⟩ 92.18 Layobi Major chroma
5 144/125 [4 2 -3⟩ 244.97 Trigu University comma
5 (16 digits) [-25 7 6⟩ 31.57 Lala-tribiyo Ampersand comma
5 (42 digits) [-68 18 17⟩ 2.52 Quinla-seyo Vavoom comma
7 (18 digits) [-10 7 8 -7⟩ 22.41 Lasepru-aquadbiyo Blackjackisma
7 1029/1024 [-10 1 0 3⟩ 8.43 Latrizo Gamelisma
7 225/224 [-5 2 2 -1⟩ 7.71 Ruyoyo Marvel comma
7 16875/16807 [0 3 4 -5⟩ 6.99 Quinru-aquadyo Mirkwai comma
7 2401/2400 [-5 -1 -2 4⟩ 0.72 Bizozogu Breedsma
11 121/120 [-3 -1 -1 0 2⟩ 14.37 Lologu Biyatisma
11 65536/65219 [16 0 0 -2 -3⟩ 8.39 Satrilu-aruru Orgonisma

Approximation to JI

Harmonic 8 9 11 14 16
JI interval from 1/1 1/1 = 0 cents 9/8 = 204 11/8 = 551 7/4 = 969 2/1 = 1200
Nearest 11edo interval 0\11 = 0¢ 2\11 = 218¢ 5\11 = 545 9\11 = 982 11\11 = 1200
Difference 0 +14¢ -6¢ +13¢ 0¢
JI interval between 9:8 = 204¢ 11:9 = 347 14:11 = 418 8:7 = 231
Nearest 11edo interval 2\11 = 218¢ 3\11 = 327 4\11 = 436 2\11 = 218
Difference +14¢ -20¢ +18¢ -13¢

11edo also may be considered a 2.7.9.11.15.17 subgroup temperament. See diagram:

11edo_approx_2-7-9-11-15-17_2ndsave.png

Octave stretch or compression

11edo has about equally bad sharp and flat mappings of primes 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight octave shrinking is advisable. Examples of slightly compressed versions of 11edo include (least to most compressed) 28ed6, 39ed12, 30zpi, 35ed9 and 31ed7.

To use its primes 3 or 5, extreme octave shrinking can be used, at the cost of making the octaves sound significantly weaker. 37ed10 is a very compressed version of 11edo.

Scales

Main article: 11edo modes

MOS scales

Main article: List of 11edo MOS scales

Although 11edo has one fewer interval in the octave than 12edo, in terms of moment-of-symmetry scales, it offers a great deal more variety. This is because 11 is a prime number, while 12 is composite. Cycles of 2\11 (two degrees of 11edo), 3\11, 4\11 and 5\11 produce scales which do not repeat at the octave until all 11 intervals have been included.

Instruments

11edo ukulele

11-edo-ukulele.JPG

Ensembles

In February 2011, Oddmusic U-C, as part of its Microtonal Design Seminar, generated a 7-piece ensemble for playing music in 11edo. Instrumentation: autotuner, cümbüş, electronic keyboard, kalimba, retrofretted guitar, tuned bottles, udderbot. Recordings forthcoming.

Lumatone

Lumatone mappings for 11edo are available.

Introductory Materials

Music

See also: Category:11edo tracks

11 equal divisions of the octave (11edo proper)

Modern renderings

Arthur Schutt

20th century

George Secor
Bill Sethares

21st century

Abnormality
Christopher Bailey
Jacob Barton
City of the Asleep
Jason Conklin
E8 Heterotic
Francium
David Hamill
Andrew Heathwaite
Hideya
Aaron Andrew Hunt
Alexandru Ianu
Aaron Krister Johnson
groundfault
Claudi Meneghin
Joseph Monzo
Mundoworld
No Clue Music
NullPointerException Music
Phanomium
X. J. Scott
Sevish
Jon Lyle Smith
Chris Vaisvil
Randy Winchester
Ozan Yarman
Yeah Gore

Unequal Derivatives of 11edo

Bryan Deister
  • 11 Tone March (2023/2024)

Videos

See also

  • 11edo Zine — There is an 11edo Zine! As far as we know, 11edo is the first xenharmonic tuning system to have its own zine.

Notes

  1. ↑ Ratios longer than 10 digits are presented by placeholders with informative hints
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