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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:genewardsmith|genewardsmith]] and made on <tt>2011-03-30 14:25:36 UTC</tt>.<br>
| en = 11edo
: The original revision id was <tt>215544438</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">[[toc|flat]]
{{ED intro}}
== 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.
{{Harmonics in equal|11}}
 
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 [[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.
 
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.
 
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"]


=11 tone equal temperament=
; [[City of the Asleep]]
11-tone equal temperament, or 11edo, divides the octave into eleven equal steps of approximately 109.09 cents.
* [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)


=Tuning=
; [[Jason Conklin]]
Compared to 12edo, the intervals of 11edo are stretched:
* ''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]
* The "minor second," at 109.09 cents, functions melodically and harmonically 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 harmonious. 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.
; [[E8 Heterotic]]
* The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."
* [https://youtu.be/9tJHJEZnvFs?si=9n6I3VnejVon_iot ''Olive Flamenco''] (2019)
* 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.
; [[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]


=Subgroup=
; [[User:GlitchyDarkness|No Clue Music]]
11edo provides the same tuning on the 2.9.15.7.11 subgroup as 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 chord and its subchords. Though the error is rather large, this does provide 11 with a variety of chords approximating JI chords.
* [https://www.youtube.com/watch?v=lPKc1B6YBn4 ''Cursed Star''] (2024)


=Intervals=
; [[NullPointerException Music]]
|| Harmonic || 8 ||  || 9 ||  || 11 ||  || 14 ||  || 16 ||
* [https://www.youtube.com/watch?v=AbWxZ6yh69s "Overcoming"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
|| 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\11edo = 0 cents ||  || 2\11 = 218 ||  || 5\11 = 545 ||  || 9\11 = 982 ||  || 11\11 = 1200 ||
|| difference || 0 ||  || +14 ||  || -6 ||  || +13 ||  || 0 ||
|| JI interval between ||  || 9:8 = 204 cents ||  || 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 ||  ||


==11 edo solfege==
; [[User:Phanomium|Phanomium]]
An 11edo solfege system can easily be applied from the [[22edo solfege]] system.
* [https://www.youtube.com/watch?v=y939ciE9MQY ''33322''] (2024)
A chromatic scale would thus be sung: **do ra re me mo fu su lo la te ti do**.


|| degrees of 11edo || cents value || solfege ||
; [[X. J. Scott]]
|| 0 || 0.00 || **do** ||
* [https://soundclick.com/share.cfm?id=955383 ''Angkor Wat, September 1066''] (2004)
|| 1 || 109.09 || **ra** ||
|| 2 || 218.18 || **re** ||
|| 3 || 327.27 || **me** ||
|| 4 || 436.36 || **mo** ||
|| 5 || 545.45 || **fu** ||
|| 6 || 654.55 || **su** ||
|| 7 || 763.64 || **lo** ||
|| 8 || 872.73 || **la** ||
|| 9 || 981.82 || **te** ||
|| 10 || 1090.91 || **ti** ||


=MOS Scales=
; [[Sevish]]
Although 11edo has one fewer interval in the octave than 12edo, in terms of [[MOSScales|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.
* "[[Longwayaway People]]", from ''[[Rhythm and Xen]]'' (2015)
* "[[Make a Dream]]", from ''[[Rhythm and Xen]]'' (2015)


2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.
; [[Jon Lyle Smith]]
3\11 generates 3 3 3 2 and 1 2 1 2 1 2 2.
* [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]
4\11 generates 4 4 3, 1 3 1 3 3, and 1 1 2 1 1 2 1 2.
* [http://archive.org/download/CounterpointIn11edo/CounterpointIn11edo.mp3 ''Counterpoint in 11EDO'']{{dead link}}
5\11 generates 5 5 1, 1 4 1 4 1, 1 1 3 1 1 3 1, and 1 1 1 2 1 1 1 2 1.


See [[11edo Modes]]
; [[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}}


=11edo Instant Ensemble=
; [[Randy Winchester]]
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.
* [https://archive.org/details/jamendo-005173/10.mp3 "10. 11 / octave"], from ''[[Comets Over Flatland]]'' (2007)


=Compositions=
; [[Ozan Yarman]]
[[http://xenharmony.wikispaces.com/space/showimage/11EDO-improv.mp3|First Piece Ever]] by George Secor, 1970. Apparently the first piece ever written for 11edo.
* [http://www.ozanyarman.com/files/music/Icicle_Caverns.mp3 ''Icicle Caverns''] (2010) ([http://www.ozanyarman.com/files/music/icicle_caverns_score.pdf score])
[[http://www.focalchords.com/audio/Cool_My_Head_11EDO.mp3|Cool My Head]] by David Hamill, 2010
Hyperimprovisations Nuggetwarp ([[http://javascript:Player%28%27../player/single_player.cfm?songid=10267904&amp;q=hi&amp;newref=1%27%29;|I]] [[http://javascript:Player%28%27../player/single_player.cfm?songid=10267905&amp;q=hi&amp;newref=1%27%29;|II]] [[http://javascript:Player%28%27../player/single_player.cfm?songid=10267906&amp;q=hi&amp;newref=1%27%29;|III]]) by Jacob Barton, 2009
She Is My Lilac-Hued Obsession on City of the Asleep, [[http://cityoftheasleep.com/music|Map of an Internal Landscape]] (2009)
[[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html|Turquoise Dabo Girl]] by [[Bill Sethares]] (spectrally bent synth ens.)
[[http://www.h-pi.com/mp3/Prelude11ET.mp3|Prelude11ET]] by [[Aaron Andrew Hunt|Aaron Hunt]] (neo-Baroque)
[[http://music.columbia.edu/%7Echris/complist.html|The Stuffed Ones]] by [[Christopher Bailey]] (keyboards concréte)
[[http://www.ozanyarman.com/files/music/Icicle_Caverns.mp3|Icicle Caverns]] by Dr. Ozan Yarman
[[http://soundclick.com/share.cfm?id=955383|Angkor Wat, September 1066]] by X. J. Scott
[[http://soundclick.com/share?songid=8839070|conversation is]] by [[Andrew Heathwaite]].
Text is a sentence borrowed from a paper by Larry Richards, set to an 11-tone row. For guitar and voice.


==Videos==
; [[Yeah Gore]]
The Stuffed Ones: [[http://www.youtube.com/watch?v=NU0VvGRelUQ&amp;feature=related|Goopy]], [[http://www.youtube.com/watch?v=4D9wDl_oxHE&amp;feature=related|Ziggy]], [[http://www.youtube.com/watch?v=53IiHdXfJwI&amp;feature=related|Ellie]], [[http://www.youtube.com/watch?v=4sZqpRcB-lk&amp;feature=related|Towelbear]] by [[http://www.youtube.com/user/zipzappoozoo|zipzappoozoo]]</pre></div>
* [https://www.youtube.com/watch?v=FL72Z4H1IF8 ''11 TET Hernya''] (2020)
<h4>Original HTML content:</h4>
* [https://www.youtube.com/watch?v=dwel2K1Bgds ''YG_A''] (2022)
<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:WikiTextTocRule:18:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;a href="#x11 tone equal temperament"&gt;11 tone equal temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Tuning"&gt;Tuning&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Subgroup"&gt;Subgroup&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#MOS Scales"&gt;MOS Scales&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt; | &lt;a href="#x11edo Instant Ensemble"&gt;11edo Instant Ensemble&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;br /&gt;
&lt;br /&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;
11-tone equal temperament, or 11edo, divides the octave into eleven equal steps of approximately 109.09 cents.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Tuning"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tuning&lt;/h1&gt;
Compared to 12edo, the intervals of 11edo are stretched:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;The &amp;quot;minor second,&amp;quot; at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.&lt;/li&gt;&lt;li&gt;The &amp;quot;major second,&amp;quot; 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 harmonious. Its inversion, at 981.82 cents, can function as a &amp;quot;bluesy&amp;quot; seventh relative to 12edo's 1000-cent interval, although it is still about 13 cents away from 7/4.&lt;/li&gt;&lt;li&gt;The &amp;quot;minor third,&amp;quot; at 327.27 cents, is rather sharp and encroaching upon &amp;quot;neutral third.&amp;quot;&lt;/li&gt;&lt;li&gt;The &amp;quot;major third,&amp;quot; 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.&lt;/li&gt;&lt;li&gt;The &amp;quot;perfect fourth,&amp;quot; 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.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Subgroup"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Subgroup&lt;/h1&gt;
11edo provides the same tuning on the 2.9.15.7.11 subgroup as 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 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;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Intervals&lt;/h1&gt;


=== 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)


&lt;table class="wiki_table"&gt;
== Videos ==
    &lt;tr&gt;
* 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]
        &lt;td&gt;Harmonic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI interval from 1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 = 0 cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8 = 204&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8 = 551&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4 = 969&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/1 = 1200&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;nearest 11edo interval&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0\11edo = 0 cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\11 = 218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\11 = 545&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9\11 = 982&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11\11 = 1200&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;difference&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI interval between&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9:8 = 204 cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11:9 = 347&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11 = 418&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8:7 = 231&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;nearest 11edo interval&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\11 = 218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3\11 = 327&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4\11 = 436&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\11 = 218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;difference&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
* [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ|Mike Battaglia]] - youtube
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Intervals-11 edo solfege"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11 edo solfege&lt;/h2&gt;
* [https://www.youtube.com/watch?v=4WlTPfRDPCY untitled1], computer
An 11edo solfege system can easily be applied from the &lt;a class="wiki_link" href="/22edo%20solfege"&gt;22edo solfege&lt;/a&gt; system.&lt;br /&gt;
A chromatic scale would thus be sung: &lt;strong&gt;do ra re me mo fu su lo la te ti do&lt;/strong&gt;.&lt;br /&gt;
&lt;br /&gt;


== 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.


&lt;table class="wiki_table"&gt;
== Notes ==
    &lt;tr&gt;
<references group=note/>
        &lt;td&gt;degrees of 11edo&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents value&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;solfege&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;do&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109.09&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;ra&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;re&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;327.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;me&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;436.36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;mo&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;545.45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;fu&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;654.55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;su&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;763.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;lo&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;872.73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;la&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;981.82&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;te&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1090.91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;ti&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[[Category:Listen]]
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="MOS Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;MOS Scales&lt;/h1&gt;
{{Todo|add rank 2 temperaments table}}
Although 11edo has one fewer interval in the octave than 12edo, in terms of &lt;a class="wiki_link" href="/MOSScales"&gt;moment-of-symmetry scales&lt;/a&gt;, 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.&lt;br /&gt;
&lt;br /&gt;
2\11 generates 2 2 2 2 3 and 2 2 2 2 2 1.&lt;br /&gt;
3\11 generates 3 3 3 2 and 1 2 1 2 1 2 2.&lt;br /&gt;
4\11 generates 4 4 3, 1 3 1 3 3, and 1 1 2 1 1 2 1 2.&lt;br /&gt;
5\11 generates 5 5 1, 1 4 1 4 1, 1 1 3 1 1 3 1, and 1 1 1 2 1 1 1 2 1.&lt;br /&gt;
&lt;br /&gt;
See &lt;a class="wiki_link" href="/11edo%20Modes"&gt;11edo Modes&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="x11edo Instant Ensemble"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11edo Instant Ensemble&lt;/h1&gt;
In February 2011, &lt;a class="wiki_link_ext" href="http://oddmusicuc.wordpress.com/" rel="nofollow"&gt;Oddmusic U-C&lt;/a&gt;, 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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Compositions&lt;/h1&gt;
&lt;a class="wiki_link_ext" href="http://xenharmony.wikispaces.com/space/showimage/11EDO-improv.mp3" rel="nofollow"&gt;First Piece Ever&lt;/a&gt; by George Secor, 1970. Apparently the first piece ever written for 11edo.&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.focalchords.com/audio/Cool_My_Head_11EDO.mp3" rel="nofollow"&gt;Cool My Head&lt;/a&gt; by David Hamill, 2010&lt;br /&gt;
Hyperimprovisations Nuggetwarp (&lt;a class="wiki_link_ext" href="http://javascript:Player%28%27../player/single_player.cfm?songid=10267904&amp;amp;q=hi&amp;amp;newref=1%27%29;" rel="nofollow"&gt;I&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://javascript:Player%28%27../player/single_player.cfm?songid=10267905&amp;amp;q=hi&amp;amp;newref=1%27%29;" rel="nofollow"&gt;II&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://javascript:Player%28%27../player/single_player.cfm?songid=10267906&amp;amp;q=hi&amp;amp;newref=1%27%29;" rel="nofollow"&gt;III&lt;/a&gt;) by Jacob Barton, 2009&lt;br /&gt;
She Is My Lilac-Hued Obsession on City of the Asleep, &lt;a class="wiki_link_ext" href="http://cityoftheasleep.com/music" rel="nofollow"&gt;Map of an Internal Landscape&lt;/a&gt; (2009)&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/dabo_girl.html" rel="nofollow"&gt;Turquoise Dabo Girl&lt;/a&gt; by &lt;a class="wiki_link" href="/Bill%20Sethares"&gt;Bill Sethares&lt;/a&gt; (spectrally bent synth ens.)&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Prelude11ET.mp3" rel="nofollow"&gt;Prelude11ET&lt;/a&gt; by &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Hunt&lt;/a&gt; (neo-Baroque)&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/complist.html" rel="nofollow"&gt;The Stuffed Ones&lt;/a&gt; by &lt;a class="wiki_link" href="/Christopher%20Bailey"&gt;Christopher Bailey&lt;/a&gt; (keyboards concréte)&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.ozanyarman.com/files/music/Icicle_Caverns.mp3" rel="nofollow"&gt;Icicle Caverns&lt;/a&gt; by Dr. Ozan Yarman&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=955383" rel="nofollow"&gt;Angkor Wat, September 1066&lt;/a&gt; by X. J. Scott &lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839070" rel="nofollow"&gt;conversation is&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;.&lt;br /&gt;
Text is a sentence borrowed from a paper by Larry Richards, set to an 11-tone row. For guitar and voice.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Compositions-Videos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Videos&lt;/h2&gt;
The Stuffed Ones: &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=NU0VvGRelUQ&amp;amp;feature=related" rel="nofollow"&gt;Goopy&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=4D9wDl_oxHE&amp;amp;feature=related" rel="nofollow"&gt;Ziggy&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=53IiHdXfJwI&amp;amp;feature=related" rel="nofollow"&gt;Ellie&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=4sZqpRcB-lk&amp;amp;feature=related" rel="nofollow"&gt;Towelbear&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.youtube.com/user/zipzappoozoo" rel="nofollow"&gt;zipzappoozoo&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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