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{{interwiki
{{interwiki
| de =  
| de = 11-EDO
| en = 11edo  
| en = 11edo  
| es =  
| es =  
| ja = 11平均律
| ja = 11平均律
}}__FORCETOC__
{{Infobox ET
| Prime factorization = 11 (prime)
| Step size = 109.091¢
| Fifth = 6\11 = 654.545¢
| Major 2nd = 1\11 = 109¢
| Minor 2nd = 3\11 = 327¢
| Augmented 1sn = -2\11 = -218¢
}}
}}
{{todo|add introduction}}
{{Infobox ET}}
{{ED intro}}
== Theory ==
Compared to 12edo, the intervals of 11edo are stretched:


==Theory==
* The "minor second" at 109.09 cents, functions melodically very much like the 100-cent minor second of 12edo.
{| class="wikitable center-all"
* 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]].
! colspan="2" | <!-- empty cell -->
* The "minor third" at 327.27 cents, is rather sharp and encroaching upon "[[neutral]] third".
! prime 2
* 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.
! prime 3
* 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.
! prime 5
{{Harmonics in equal|11}}
! prime 7
! prime 11
! prime 13
! prime 17
! prime 19
|-
! rowspan="2" | error
! absolute (¢)
| 0.0
| -47.4
| +50.0
| +13.0
| -5.9
| +32.2
| +4.1
| +29.8
|-
! [[Relative error|relative]] (%)
| 0
| -43
| +46
| +12
| -5
| +30
| +4
| +27
|-
! colspan="2" | [[nearest edomapping]]
| 11
| 6
| 4
| 9
| 5
| 8
| 1
| 3
|-
! colspan="2" | [[fifthspan]]
| 0
| +1
| -3
| -4
| -1
| +5
| +2
| -5
|}
 
11-tone equal temperament, or 11[[edo]], divides the [[octave]] into eleven equal steps of approximately 109.09 [[cent|cents]]. It is the fifth [[prime_numbers|prime]] edo, after [[2edo]], [[3edo]], [[5edo]], and [[7edo]].


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|22edo]], a tuning known as "elevenplus".
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.


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


<ul><li>The "minor second," at 109.09 cents, functions melodically and harmonically very much like the 100-cent minor second of 12edo.</li><li>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.</li><li>The "minor third," at 327.27 cents, is rather sharp and encroaching upon "neutral third."</li><li>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.</li><li>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.</li></ul>11edo provides the same tuning on the [[k*N_subgroups|2*11 subgroup]] 2.9.15.7.11 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 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.


11edo is the largest edo that patently alternates with an undivided 9/8 in a [[Well tempered nonet|wtn]].
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]]".


==Notation==
[[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.
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.


Line 87: Line 35:
The 11edo solfege in the table is derived from [[22edo Solfege|22edo solfege]].
The 11edo solfege in the table is derived from [[22edo Solfege|22edo solfege]].


{| class="wikitable center-all right-1 right-2"
{| class="wikitable center-all right-2 left-4"
! Degree
! #
! Size in <br> [[cent]]s
! [[Cent]]s
! Solfege
! Solfege
! Approximate Ratios*
! Approximate Ratios*
! Sagittal <br> notation <br>(22edo subset)
! colspan="2" | [[Ups and downs notation|Up/down notation]] <br> with major wider <br> than minor
! 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
! colspan="2" | Up/down notation <br> with major narrower <br> than minor
! [[Tútim Dennsuul Wafiil|TDW]] <br> Machine <br> notation
! [[Smitonic]]<br>(3rd-gen)<br>notation
! [[Tútim Dennsuul Wafiil|TDW]] <br> [[Machinoid|Machine]] <br> notation
! Pseudo-Diatonic Category
! Pseudo-Diatonic Category
!Audio
|-
|-
| 0
| 0
Line 102: Line 51:
| '''do'''
| '''do'''
| 1/1
| 1/1
| P1
| A
| A
| P1
| P1
| A
| A
| P1
| A
| A
| Q\P#
| Q, P#
| Unison
| Unison
|[[File:0-0 unison.mp3|frameless]]
|-
|-
| 1
| 1
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| '''ra'''
| '''ra'''
| [[15/14]], [[16/15]], [[17/16]], [[18/17]]
| [[15/14]], [[16/15]], [[17/16]], [[18/17]]
| AII\ or B!!/
| ^1, m2
| ^1, m2
| ^A, B
| ^A, B
| ^1, M2
| ^1, M2
| ^A, B
| ^A, B
| Q#\Rb
| A#, Bb
| Q#, Rb
| Minor second
| Minor second
|[[File:0-109,09 minor second (11-EDO).mp3|frameless]]
|-
|-
| 2
| 2
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| '''re'''
| '''re'''
| [[8/7]], [[9/8]], [[17/15]]
| [[8/7]], [[9/8]], [[17/15]]
| B
| ~2, m3
| ~2, m3
| ^B, Cb
| ^B, Cb
| ~2, M3
| ~2, M3
| ^B, C#
| ^B, C#
| B
| R
| R
| Major second
| Major second
|[[File:0-218,18 major second (11-EDO).mp3|frameless]]
|-
|-
| 3
| 3
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| '''me'''
| '''me'''
| [[6/5]], [[11/9]], [[17/14]]
| [[6/5]], [[11/9]], [[17/14]]
| C/I or BII\ or D\!!/
| M2, ~3
| M2, ~3
| B#, vC
| B#, vC
| m2, ~3
| m2, ~3
| Bb, vC
| Bb, vC
| R#\Sb
| C
| R#, Sb
| Minor third
| Minor third
|[[File:0-327,27 minor third (11-EDO).mp3|frameless]]
|-
|-
| 4
| 4
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| '''mo'''
| '''mo'''
| [[9/7]], [[14/11]], [[22/17]]
| [[9/7]], [[14/11]], [[22/17]]
| D\! or C/II\
| M3, v4
| M3, v4
| C, vD
| C, vD
| m3, v4
| m3, v4
| C, vD
| C, vD
| C#, Db
| S
| S
| Major third/Minor fourth
| Major third/Minor fourth
|[[File:0-436,36 major third (11-EDO).mp3|frameless]]
|-
|-
| 5
| 5
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| '''fu'''
| '''fu'''
| [[11/8]], [[15/11]]
| [[11/8]], [[15/11]]
| D/I or E\!!/
| P4, v5
| P4, v5
| D, vE
| D, vE
| P4, v5
| P4, v5
| D, vE
| D, vE
| S#\Tb
| D
| S#, Tb
| Major fourth
| Major fourth
|[[File:0-545,45 major fourth (11-EDO).mp3|frameless]]
|-
|-
| 6
| 6
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| '''su'''
| '''su'''
| [[16/11]], [[22/15]]
| [[16/11]], [[22/15]]
| E\! or D/II\
| ^4, P5
| ^4, P5
| ^D, E
| ^D, E
| ^4, P5
| ^4, P5
| ^D, E
| ^D, E
| D#, Eb
| T
| T
| Minor fifth
| Minor fifth
|[[File:0-654,55 minor fifth (11-EDO).mp3|frameless]]
|-
|-
| 7
| 7
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| '''lo'''
| '''lo'''
| [[14/9]], [[11/7]], [[17/11]]
| [[14/9]], [[11/7]], [[17/11]]
| F
| ^5, m6
| ^5, m6
| ^E, Fb
| ^E, Fb
| ^5, M6
| ^5, M6
| ^E, F#
| ^E, F#
| T#\Ub
| E
| T#, Ub
| Major fifth/Minor sixth
| Major fifth/Minor sixth
|[[File:0-763,64 minor sixth (11-EDO).mp3|frameless]]
|-
|-
| 8
| 8
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| '''la'''
| '''la'''
| [[5/3]], [[18/11]], [[28/17]]
| [[5/3]], [[18/11]], [[28/17]]
| FII\ or G!!/
| ~6, m7
| ~6, m7
| vF, Gb
| vF, Gb
| ~6, M7
| ~6, M7
| vF, G#
| vF, G#
| F
| U
| U
| Major sixth
| Major sixth
|[[File:0-872,73 major sixth (11-EDO).mp3|frameless]]
|-
|-
| 9
| 9
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| '''ta'''
| '''ta'''
| [[7/4]], [[16/9]], [[30/17]]
| [[7/4]], [[16/9]], [[30/17]]
| G
| M6, ~7
| M6, ~7
| F, vG
| F, vG
| m6, ~7
| m6, ~7
| F, vG
| F, vG
| U#\Pb
| F#, Gb
| U#, Pb
| Minor seventh
| Minor seventh
|[[File:0-981,82 minor seventh (11-EDO).mp3|frameless]]
|-
|-
| 10
| 10
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| '''ti'''
| '''ti'''
| [[15/8]], [[17/9]], [[28/15]], [[32/17]]
| [[15/8]], [[17/9]], [[28/15]], [[32/17]]
| GII\ or A!!/
| M7, v8
| M7, v8
| G, vAv
| G, vAv
| m7, v8
| m7, v8
| G, vAv
| G, vAv
| P\Qb
| G
| P, Qb
| Major seventh
| Major seventh
|[[File:0-1090,91 major seventh (11-EDO).mp3|frameless]]
|-
|-
| 11
| 11
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| '''do'''
| '''do'''
| 2/1
| 2/1
| P8
| A
| A
| P8
| P8
| A
| A
| P8
| A
| A
| Q\P#
| Q, P#
| Octave
| Octave
|[[File:0-1200 octave.mp3|frameless]]
|}
|}
*in 2.7.9.11.15.17 subgroup
<nowiki>* in 2.7.9.11.15.17 subgroup</nowiki>
 
11edo in [[Sagittal notation]]:
 
[[File:Sagittal11EDO.jpg|alt=Sagittal11EDO.jpg|Sagittal11EDO.jpg]]


These are all heptatonic notations generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, nonatonic 5th-generated, and heptatonic 3rd-generated.
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'''  (generator = wide 3/2 = 7\11 = perfect 5thoid)
'''<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
D - ^D/Eb - D#/vE - E - G - ^G/Ab - G#/vA - A - C - ^C/Db - C#/vD - D
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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)
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>Octotonic 5th-generated:</u>''' '''A B * C D E * F G * H A''' (generator = wide 3/2 = 7\11 = perfect 6th)
'''<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
A - B - B#/Cb - C - D - E - E#/Fb - F - G - G#/Hb - H - A
Line 270: Line 227:
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...
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''' (generator = narrow 3/2 = 6\11 = perfect 6th)  
'''<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
A - B - B#/Cb - C - D - E - F - G - G#/Hb - H - J - A
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nonotonic genchain of sixths: ...M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9...
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''' (generator = 3\11 = perfect 3rd)
'''<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
D - D#/Eb - E - F - F#/Gb - G - A - A#/Bb - B - C - C#/Db - D
Line 290: Line 247:
genchain of thirds: ...M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6...
genchain of thirds: ...M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6...


==Commas==
'''<u>Hexatonic 2nd-generated:</u> R * S * T * U * P Q''' '''* R''' ([[Machinoid]] generator = 2\11 = perfect 2nd)
11 EDO tempers out the following [[comma]]s. (Note: This assumes val {{val| 11 17 26 31 38 41 }}.)
 
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"
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref group=note>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cent]]s
! [[Cent]]s
! [[Color name]]
! [[Color name]]
! Name(s)
! Name(s)
|-
| 3
| [[177147/131072]]
| {{Monzo| -17 11 }}
| 521.50
| sasawa 3rd
| Pythagorean augmented third
|-
|-
| 5
| 5
Line 307: Line 309:
| 92.18
| 92.18
| Layobi
| Layobi
| Major Chroma, Major Limma, Pelogic Comma
| Major chroma
|-
| 5
| [[144/125]]
| {{Monzo| 4 2 -3 }}
| 244.97
| Trigu
| University comma
|-
|-
| 5
| 5
Line 314: Line 323:
| 31.57
| 31.57
| Lala-tribiyo
| Lala-tribiyo
| [[Ampersand]]'s Comma
| [[Ampersand comma]]
|-
|-
| 5
| 5
Line 321: Line 330:
| 2.52
| 2.52
| Quinla-seyo
| Quinla-seyo
| [[Vavoom]]
| [[Vavoom comma]]
|-
|-
| 7
| 7
Line 342: Line 351:
| 7.71
| 7.71
| Ruyoyo
| Ruyoyo
| Septimal Kleisma, Marvel Comma
| Marvel comma
|-
|-
| 7
| 7
Line 349: Line 358:
| 6.99
| 6.99
| Quinru-aquadyo
| Quinru-aquadyo
| Mirkwai
| Mirkwai comma
|-
|-
| 7
| 7
Line 372: Line 381:
| Orgonisma
| Orgonisma
|}
|}
<references/>


==JI Intervals==
== Approximation to JI ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Harmonic
! Harmonic
! | 8
! 8
! |
!  
! | 9
! 9
! |
!  
! | 11
! 11
! |
!  
! | 14
! 14
! |
!  
! | 16
! 16
|-
|-
! | JI interval from 1/1
! JI interval from 1/1
| | 1/1 = 0 cents
| 1/1 = 0 cents
| |  
|  
| | 9/8 = 204
| 9/8 = 204
| |  
|  
| | 11/8 = 551
| 11/8 = 551
| |  
|  
| | 7/4 = 969
| 7/4 = 969
| |  
|  
| | 2/1 = 1200
| 2/1 = 1200
|-
|-
! | nearest 11edo interval
! Nearest 11edo interval
| | 0\11edo = 0¢
| 0\11 = 0¢
| |  
|  
| | 2\11 = 218¢
| 2\11 = 218¢
| |  
|  
| | 5\11 = 545
| 5\11 = 545
| |  
|  
| | 9\11 = 982
| 9\11 = 982
| |  
|  
| | 11\11 = 1200
| 11\11 = 1200
|-
|-
! | difference
! Difference
| | 0
| 0
| |  
|  
| | +14¢
| +14¢
| |  
|  
| | -6¢
| -6¢
| |  
|  
| | +13¢
| +13¢
| |  
|  
| | 0¢
| 0¢
|-
|-
! | JI interval between
! JI interval between
| |  
|  
| | 9:8 = 204¢
| 9:8 = 204¢
| |  
|  
| | 11:9 = 347
| 11:9 = 347
| |  
|  
| | 14:11 = 418
| 14:11 = 418
| |  
|  
| | 8:7 = 231
| 8:7 = 231
| |  
|  
|-
|-
! | nearest 11edo interval
! Nearest 11edo interval
| |  
|  
| | 2\11 = 218¢
| 2\11 = 218¢
| |  
|  
| | 3\11 = 327
| 3\11 = 327
| |  
|  
| | 4\11 = 436
| 4\11 = 436
| |  
|  
| | 2\11 = 218
| 2\11 = 218
| |  
|  
|-
|-
! | difference
! Difference
| |  
|  
| | +14¢
| +14¢
| |  
|  
| | -20¢
| -20¢
| |  
|  
| | +18¢
| +18¢
| |  
|  
| | -13¢
| -13¢
| |  
|  
|}
|}


Line 459: Line 467:
[[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]]
[[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]]


==MOS Scales==
== Octave stretch or compression ==
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.
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]].


2\11 generates 2 2 2 2 3, a [[1L_4s|1L 4s]] scale named Machine[5]; and 2 2 2 2 2 1, a [[5L_1s|5L 1s]] scale named [[Machine|Machine]][6].
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.
[[File:Screen Shot 2020-04-23 at 11.32.40 PM.png|none|thumb|1003x1003px]]
3\11 generates 3 3 3 2; and 1 2 1 2 1 2 2, a [[4L_3s|4L 3s]] scale named [[Orgone|Orgone]][7].
[[File:Screen Shot 2020-04-23 at 11.33.13 PM.png|none|thumb|987x987px]]
4\11 generates 4 4 3; 1 3 1 3 3, a [[3L_2s|3L 2s]] scale; and 1 1 2 1 1 2 1 2, a [[3L_5s|3L 5s]] scale.
[[File:Screen Shot 2020-04-23 at 11.33.29 PM.png|none|thumb|970x970px]]
5\11 generates [[joan]] scales 5 5 1; 1 4 1 4 1, a [[2L_3s|2L 3s]] scale; 1 1 3 1 1 3 1, a [[2L_5s|2L 5s]] scale; and 1 1 1 2 1 1 1 2 1, a [[2L_7s|2L 7s]] scale.
[[File:Screen Shot 2020-04-23 at 11.33.44 PM.png|none|thumb|995x995px]]
See [[11edo_Modes|11edo Modes]]


==Pathological Modes ==
== Scales ==
2 1 1 1 2 1 1 1 1 [[2L 7s]] MOS
{{Main|11edo modes}}


3 1 1 1 1 1 1 1 1 [[1L 8s]] MOS
=== 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.


2 1 1 1 1 1 1 1 1 1 [[1L 9s]] MOS
== Instruments ==
'''11edo ukulele'''


==Instruments==
[[File:11-edo-ukulele.JPG|alt=11-edo-ukulele.JPG|404x304px|11-edo-ukulele.JPG]]
11-edo 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.
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 ==
== 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)


* [[File:11EDO-improv.mp3|link=Special:FilePath/11EDO-improv.mp3]] [http://xenharmony.wikispaces.com/space/showimage/11EDO-improv.mp3 First Piece Ever]{{Dead link}} by [[George Secor]], 1970. Apparently the first piece ever written for 11edo.
== Videos ==
* [http://www.focalchords.com/audio/Cool_My_Head_11EDO.mp3 Cool My Head] by [[David Hamill]], 2010
* 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]
* Hyperimprovisations Nuggetwarp by [[Jacob Barton]], 2009:
** [http://soundclick.com/share.cfm?id=10267904 Piece I]
** [http://soundclick.com/share.cfm?id=10267905 Piece II]
** [http://soundclick.com/share.cfm?id=10267906 Piece III]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20She%20Is%20My%20Lilac-Hued%20Obsession.mp3 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 The Turquoise Dabo Girl] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Turquoise_Dabo_Girl.mp3 play] by [[Bill Sethares]] (spectrally bent synth ens.)
* [http://www.h-pi.com/mp3/Prelude11ET.mp3 Prelude11ET] by [[Aaron Andrew Hunt]] (neo-Baroque) {{dead link}}
* [https://soundcloud.com/uz1kt3k/invention-in-11et?in=uz1kt3k/sets/adagio-invention-in-11et Invention In 11ET &#124; SoundCloud] by Aaron Andrew Hunt
* [https://soundcloud.com/uz1kt3k/adagio-in-11et?in=uz1kt3k/sets/adagio-invention-in-11et Adagio In 11ET &#124; SoundCloud] by Aaron Andrew Hunt
* [http://music.columbia.edu/%7Echris/complist.html The Stuffed Ones] by [[Christopher Bailey]] (keyboards concréte):
** [http://music.columbia.edu/%7Echris/sounds/st.goopy.mp3 goopy]
** [http://music.columbia.edu/%7Echris/sounds/st.ellie.mp3 ellie]
** [http://music.columbia.edu/%7Echris/sounds/st.ziggy.mp3 ziggy]
** [http://music.columbia.edu/%7Echris/sounds/st.towelbear.mp3 towelbear]
* [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] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+conversationis.mp3 play] by [[Andrew Heathwaite]]. Text is a sentence borrowed from a paper by Larry Richards, set to an 11-tone row. For guitar and voice.
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=933772 Orange Clips on Sausages] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+orangeclipsonsausagesin11tet.mp3 play] by Andrew Heathwaite
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=834492 Blue Gel] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin11tet.mp3 play] by Andrew Heathwaite
* [http://micro.soonlabel.com/11-ET/daily201110-gpo-jeffery-dahmer-cooks.mp3 Jeffrey Dahmer Cooks at 11edo] by [[Chris Vaisvil]]
* [http://micro.soonlabel.com/jon-lyle-smith/Jaunt.mp3 Jaunt] by [[Jon Lyle Smith]]
* [http://micro.soonlabel.com/11-ET/20110902_prepared_seagull_metamorphis.mp3 The Metamorphosis of Gregor] by Chris Vaisvil
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/10%20-%2010.%2011%20octave.mp3 Comets Over Flatland 10] by [[Randy Winchester]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Conklin/Conklin-The_City_Sleeps_A_Madrigal.mp3 The City Sleeps, A Madrigal] by [http://soundcloud.com/ninly/the-city-sleeps Jason Conklin]
* [http://archive.org/download/CounterpointIn11edo/CounterpointIn11edo.mp3 Counterpoint in 11edo] by [[Jon Lyle Smith]]
* [http://www.akjmusic.com/audio/black_ritual_dirge.mp3 Black Ritual Dirge] by [[Aaron Krister Johnson]]
* [http://chrisvaisvil.com/?p=2701 Eleven Birds] (video and music) ([http://micro.soonlabel.com/11-ET/20120928-piano-11edo-eleven-birds.mp3 audio only]) by [[Chris Vaisvil]]
* [http://soundcloud.com/vaisvil/the-execution-of-12-equal The Execution of 12 Equal] by Chris Vaisvil
* [https://www.youtube.com/watch?v=VjJgk9r_A_M Longwayaway People] by [[Sevish]]
* [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] by [[User:Ks26|ks26]]
* [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] by [[User:Ayceman|Alexandru Ianu]] ([[:File:Sylvian_Moon_Dance.pdf|sheet music]])
* [https://youtu.be/kuwv7qH4s6U Make a Dream] by Sevish (from his 2015 album "Rhythm and Xen")


==Videos==
* [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ|Mike Battaglia]] - youtube
The Stuffed Ones: <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=NU0VvGRelUQ&feature=related Goopy]''</span></span></span>, <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=4D9wDl_oxHE&feature=related Ziggy]''</span></span></span>, <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=53IiHdXfJwI&feature=related Ellie]''</span></span></span>, <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=4sZqpRcB-lk&feature=related Towelbear]''</span></span></span> by [http://www.youtube.com/user/zipzappoozoo zipzappoozoo]
* [https://www.youtube.com/watch?v=4WlTPfRDPCY untitled1], computer


<ul><li><span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]''</span></span></span>, [[Mike_Battaglia_FAQ|Mike Battaglia]] - youtube</li></ul>
== 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.


==11edo Zine==
== Notes ==
There is an 11edo Zine! As far as we know, 11edo is the first xenharmonic tuning system to have its own zine. See [[11edo_Zine|11edo Zine]].
<references group=note/>


[[Category:11edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Macrotonal]]
{{Todo|add rank 2 temperaments table}}
[[Category:Prime EDO]]
[[Category:Scale]]
[[Category:Subgroup]]
Retrieved from "https://en.xen.wiki/w/11edo"