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{{Japanese Version Page|[[20平均律|日本語]]}}
{{Interwiki
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[EDO|edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from [[5edo]]), 11, 13 & 15 (from [[10edo]]), 19 & 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.
| en = 20edo
__FORCETOC__
| de =
-----
| es = 20 EDO
| ja = 20平均律
}}
{{Infobox ET}}
{{ED intro}}


== Compositions ==
== Theory ==
20edo contains smaller edos {{EDOs| 2, 4, 5, and 10 }} and is part of the 5''n'' family of equal divisions of the octave. It fairly approximates the harmonics 7 (from [[5edo]]), 11, 13, 15 (from [[10edo]]), 19, 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20edo does a reasonably convincing approximation of harmonics 4:7:11:13:15.


* [https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo Underwater Spontaniety] (lo-fi ambient) by [https://soundcloud.com/overtoneshock Stephen Weigel]
20edo is around the point where 5edo's 3rd harmonic starts to become notably inaccurate relative to the size of the edo (that is, it is over 25 relative cents off). It thus inherits 5edo's crude [[archy]] temperament, with its particularly accurate approximation of 7/4 at 960 cents.
* [https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo God's Favorite Tuning] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo?in=overtoneshock/sets/xenharmonic-microtonal You Lied, and I'm not Mentioning your Name] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [http://www.io.com/%7Ehmiller/midi/20tet.mid Etude in 20-tone equal tuning] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3 play] by [[Herman Miller]]
* [http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 20ET — Prelude & Fugue a3] by [[Aaron Hunt]]
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=933696 We Call It Sharing Breath] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wecallitsharingbreathin20tet.mp3 play] by [[Andrew Heathwaite]]
* [http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/ The Walrus and the Carpenter] by[[Chris Vaisvil]] and Bethan Mathis
* [http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/ 20 edo Electric Guitar Improvisation] by[[Chris Vaisvil]]
* [http://chrisvaisvil.com/gobekli-tepe-20-edo-guitar-solo/ Göbekli Tepe (20 edo guitar solo)] by [[Chris Vaisvil]]
* [http://chrisvaisvil.com/a-paradigm-shift-20-edo/ A Paradigm Shift (20 edo)] by [[Chris Vaisvil]]
* [https://www.youtube.com/watch?v=8PCe5u4QsRg Composition for unconventional tempered clavier] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=zQDNqnYqCHg 5 compositions for violin and clavier in 20-EDO] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=duJHUo_ACgk Composition for cello and clavier in 20-tone equal temperament] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=u6k4lgCnHqs 5 compositions for violin and clavier in 20-tone equal temperament] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]


== Intervals ==
As 7, 11 and 15 are all flat by approximately 10 cents, their flatness cancels out when combined in composite ratios, making an 11:14:15 chord (0–7–9 steps) and its utonal inversion particularly precise. Using 9/20 as the generator and treating these as the primary major and minor triads produces [[Balzano]] nonatonic and undecatonic scales, which is probably the clearest arrangement for the black/white keys on a 20-tone keyboard.
 
Treating the generator as 11\20 creates the same scale, but the primary triads are now 13:16:19 (0–6–11 steps) and its inversion instead. The 11\20 generator is a near-optimal tuning for both [[no-threes subgroup temperaments #Mavericks|mavericks]] temperament (which has a ~[[19/13]] generator) and [[no-threes subgroup temperaments #Score|score]] temperament (which has a ~[[16/11]] generator).
 
Alternately, 20edo can be used as a tuning of the [[blackwood]] temperament, combining minor and major thirds to generate a highly symmetrical decatonic scale where every note is root to a major or minor triad and 7-limit tetrad that are heavily tempered, but in a useful way, as you can easily modulate to anywhere in the small cycle of 5ths, and build extended chords that use every note in the scale without clashing. Either of these works better than trying to force 20 into a diatonic framework.
 
20edo also possesses a [[6L 1s]] scale generated using the narrow major second of 3\20 that is probably best interpreted as the sharp extreme of [[tetracot]] temperament and a [[3L 5s]] generated by 7/20 that functions as the flat end of [[squares]].
 
Thanks to its sevenths, 20edo is an ideal tuning for its size for [[metallic harmony]].


Like [[15edo]], every note has many names. D is also C# and Eb. The major 3rd is also a perfect 4th and a dim 5th.
=== Odd harmonics ===
{{Harmonics in equal|20}}


{| class="wikitable" style="text-align:center;"
== Intervals ==
{| class="wikitable center-all right-2"
|-
|-
! Degree
! [[Degree]]
! Cents
! [[Cents]]
! Approximate Ratios
! Approximate ratios
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" |[[Ups and downs notation]]
! Nearest Harmonic
! [[2L 7s|Balzano]]<br>Notation
! [[6L 1s|Archeotonic]]<br>notation
! Nearest<br>harmonic
|-
|-
| 0
| 0
| style="text-align:right;" | 0
| 0
| 1/1
| 1/1
| unison
| unison
| P1
| P1
| D
| 1
| D
| D
| 1
| 1
|-
|-
| 1
| 1
| style="text-align:right;" | 60
| 60
| 29/28
| 29/28
| upminor 2nd
| up unison, upminor 2nd
| ^m2
| ^1, ^m2
| D^
| ^D, ^Eb
| 1#/2b
| D#
| 33
| 33
|-
|-
| 2
| 2
| style="text-align:right;" | 120
| 120
| 14/13, 15/14
|[[15/14]], 14/13
| mid 2nd
| dup unison, mid 2nd
| ~2
| ^^1, ~2
| D^^, Evv
| ^^D, vvE
| 2
| Eb
| 69
| 69
|-
|-
| 3
| 3
| style="text-align:right;" | 180
| 180
| 10/9
| 10/9
| downmajor 2nd
| downmajor 2nd
| vM2
| vM2
| Ev
| vE
| 2#/3b
| E
| 71
| 71
|-
|-
| 4
| 4
| style="text-align:right;" | 240
| 240
| 8/7, 15/13
| 8/7, 15/13
| major 2nd, minor 3rd
| major 2nd, minor 3rd
| M2, m3
| M2, m3
| E, F
| E, F
| 3
| E#
| 37
| 37
|-
|-
| 5
| 5
| style="text-align:right;" | 300
| 300
| 13/11, 19/16
| 13/11, 19/16
| upminor 3rd
| upminor 3rd
| ^m3
| ^m3
| F^
| ^F
| 3#/4b
| Fb
| 19
| 19
|-
|-
| 6
| 6
| style="text-align:right;" | 360
| 360
| 16/13, 5/4
|[[16/13]], 5/4
| mid 3rd
| mid 3rd
| ~3
| ~3
| F^^
| ^^F, vvF#
| 4
| F
| 79
| 79
|-
|-
| 7
| 7
| style="text-align:right;" | 420
| 420
| [[14/11]], [[51/40]]
|[[14/11]], [[51/40]]
| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
| F#v
| vF#
| 4#
| F#
| 41
| 41
|-
|-
| 8
| 8
| style="text-align:right;" | 480
| 480
| 25/19, 4/3
| 25/19, 4/3
| major 3rd, perfect fourth
| major 3rd, perfect fourth
| M3, P4
| M3, P4
| F#, G
| F#, G
| 5b
| Gb
| 21
| 21
|-
|-
| 9
| 9
| style="text-align:right;" | 540
| 540
| 15/11, 11/8
|[[15/11]], 11/8
| up-fourth
| up-fourth
| ^4
| ^4
| G^
| ^G
| 5
| G
| 11
| 11
|-
|-
| 10
| 10
| style="text-align:right;" | 600
| 600
| 7/5
| 7/5
| double-up fourth, double-down fifth
| mid fourth, mid fifth
| ^^4, vv5
| ~4, ~5
| G^^, Avv
| ^^G, vvA
| 5#/6b
| G#/Ab
| 91
| 91
|-
|-
| 11
| 11
| style="text-align:right;" | 660
| 660
| 22/15, 16/11
|[[22/15]], 16/11
| down-fifth
| down-fifth
| v5
| v5
| Av
| vA
| 6
| A
| 47
| 47
|-
|-
| 12
| 12
| style="text-align:right;" | 720
| 720
| 38/25, 3/2
| 38/25, 3/2
| fifth
| fifth
| P5, m6
| P5, m6
| A
| A
| 6#/7b
| A#
| 97
| 97
|-
|-
| 13
| 13
| style="text-align:right;" | 780
| 780
| 11/7, 25/16
| 11/7, 25/16
| upminor 6th
| upfifth, upminor 6th
| ^m6
| ^5, ^m6
| A^
| ^A, ^Bb
| 7
| Bb
| 25
| 25
|-
|-
| 14
| 14
| style="text-align:right;" | 840
| 840
| 13/8, 8/5
|[[13/8]], 8/5
| mid 6th
| mid 6th
| ~6
| ~6
| A^^, Bvv
| ^^A, vvB
| 7#/8b
| B
| 13
| 13
|-
|-
| 15
| 15
| style="text-align:right;" | 900
| 900
| 22/13, 32/19
| 22/13, 32/19
| downmajor 6th
| downmajor 6th
| vM6
| vM6
| Bv
| vB
| 8
| B#
| 27
| 27
|-
|-
| 16
| 16
| style="text-align:right;" | 960
| 960
| 7/4, 26/15
| 7/4, 26/15
| major 6th, minor 7th
| major 6th, minor 7th
| M6, m7
| M6, m7
| B, C
| B, C
| 8#/9b
| Cb
| 7
| 7
|-
|-
| 17
| 17
| style="text-align:right;" | 1020
| 1020
| 9/5
| 9/5
| upminor 7th
| upminor 7th
| ^m7
| ^m7
| C^
| ^C
| 9
| C
| 115
| 115
|-
|-
| 18
| 18
| style="text-align:right;" | 1080
| 1080
| 15/8, 13/7
|[[28/15]], 15/8, 13/7
| mid 7th
| mid 7th
| ~7
| ~7
| C^^, Dvv
| ^^C, vvD
| 9#
| C#
| 15
| 15
|-
|-
| 19
| 19
| style="text-align:right;" | 1140
| 1140
| 56/29
| 56/29
| downmajor 7th
| downmajor 7th
| vM7
| vM7
| Dv
| vD
| 1b
| Db
| 31
| 31
|-
|-
| 20
| 20
| style="text-align:right;" | 1200
| 1200
| 2/1
| 2/1
| octave
| octave
| P8
| P8
| D
| 1
| D
| D
| 2
| 2
|}
|}


== Chord Names ==
=== Chord names in color notation ===
20edo chord names using ups and downs:
20edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
* 0-5-12 = D F^ A = D.^m = "D upminor"
* 0-5-12 = D ^F A = D^m = "D upminor"
* 0-6-12 = D F^^ A = D.~ = "D mid"
* 0-6-12 = D ^^F A = D~ = "D mid"
* 0-7-12 = D F#v A = D.v = "D dot down" or "D downmajor"
* 0-7-12 = D vF# A = Dv = "D down" or "D downmajor"
* 0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
* 0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
* 0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
* 0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
* 0-5-12-16 = D F^ A C = Dm7(^3) = "D minor seven up-three", or D F^ A B = Dm6(^3) = "D minor six up-three"
* 0-5-12-16 = D ^F A C = D^m,7 = "D upminor add-seven", or D ^F A B = D^m,6 = "D upminor add-six"
* 0-6-12-16 = D F^^ A C = D7(~3) = "D seven mid-three", or D F^ A B = D6(~3) = "D six mid-three"
* 0-6-12-16 = D ^^F A C = D~,7 = "D mid add-seven", or D ^^F A B = D~,6 = "D mid add-six"
* 0-7-12-16 = D F#v A C = D7(v3) = "D seven down-three", or D F#v A B = D6(v3) = "D six down-three"
* 0-7-12-16 = D vF# A C = Dv,7 = "D down add-seven", or D vF# A B = Dv,6 = "D down add-six"
* 0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
* 0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
* 0-7-12-19 = D F#v A C#v = D.vM7 = "D downmajor seven"
* 0-7-12-19 = D vF# A vC# = DvM7 = "D downmajor seven"
* 0-5-12-17 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six"
* 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six"
 
For a more complete list, see [[Kite's ups and downs notation #Chords and chord Progressions]]. Because many intervals have several names, many chords do too.
 
== Notation ==
Like [[15edo]], every note has many names. D is also C# and Eb. The major third is also a perfect fourth and a diminished fifth.
 
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp4-szg}}
 
=== Kite's ups and downs notation ===
20edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4a}}
 
=== Sagittal notation ===
This notation is a superset of the notations for edos [[10edo #Sagittal notation|10]] and [[5edo #Sagittal notation|5]].
 
==== Evo and Revo flavors ====
{{Sagittal chart|}}
 
==== Evo-SZ flavor ====
{{Sagittal chart|Evo-SZ}}
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals|20}}


For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. Because many intervals have several names, many chords do too.
== Regular temperament properties ==
=== Uniform maps ===
{{Uniform map|edo=20}}


== Modes ==
=== Commas ===
20 tone equal modes:
20et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 20 32 46 56 69 74 }}.


{| class="wikitable"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
| 3 1 3 1 3 1 3 1 3 1
! [[Harmonic limit|Prime<br>limit]]
| Blackwood Major Decatonic [[5L_5s|(bi-equal decatonic]], according to the [[MOSNamingScheme|MOS naming scheme]])
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
|-
| 1 3 1 3 1 3 1 3 1 3
| 3
| Blackwood Minor Decatonic (<span style="">also bi-equal decatonic)</span>
| [[256/243]]
| {{monzo| 8 -5 }}
| 90.22
| Sawa
| Blackwood comma, Pythagorean limma
|-
|-
| 2 3 2 2 2 3 2 2 2
| 5
| Balzano Nine-tone (<span style="">[[2L_7s|fair mavila]], [[score9]])</span>
| [[16875/16384]]
| {{monzo| -14 3 4 }}
| 51.12
| Laquadyo
| Negri comma
|-
|-
| 2 2 2 2 1 2 2 2 2 2 1
| 5
| Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
| [[34171875/33554432|(16 digits)]]
| {{monzo| -25 7 6 }}
| 31.57
| Lala-tribiyo
| Ampersand comma
|-
|-
| 2 2 2 3 2 2 2 3 2
| 5
| Balzano Nine-tone inverse (also <span style="">fair mavila, score9)</span>
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| 19.55
| Sagugu
| Diaschisma
|-
|-
| 1 2 2 2 2 2 1 2 2 2 2
| 7
| Balzano Eleven-tone inverse (also score11)
| [[525/512]]
| {{monzo| -9 1 2 1 }}
| 43.41
| Lazoyoyo
| Avicennma, Avicenna's enharmonic diesis
|-
|-
| 2 3 2 3 2 3 2 3
| 7
| Octatonic ([[4L_4s|diminished]], according to the [[MOSNamingScheme|MOS naming scheme]])
| [[49/48]]
| {{monzo| -4 -1 0 2 }}
| 35.70
| Zozo
| Semaphoresma, slendro diesis
|-
|-
| 3 2 3 2 3 2 3 2
| 7
| Diminished
| [[50/49]]
| {{monzo| 1 0 2 -2 }}
| 34.98
| Biruyo
| Jubilisma, tritonic diesis
|-
|-
| 4 3 1 4 3 4 1
| 7
| Twenty-tone "Major"
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
|-
| 4 1 3 4 1 4 3
| 7
| Twenty-tone "Minor"
| [[64/63]]
| {{monzo| 6 -2 0 -1 }}
| 27.26
| Ru
| Septimal comma, Archytas' comma, Leipziger Komma
|-
|-
| 2 2 1 2 1 2 2 1 2 2 2 1
| 7
| Twelve-tone Chromatic
| <abbr title="854296875/843308032">(18 digits)</abbr>
| {{monzo| -10 7 8 -7 }}
| 22.41
| Lasepru-aquadbiyo
| [[Blackjackisma]]
|-
|-
| 2 2 2 2 1 2 2 2 2 1 2
| 7
| Zweifel Major
| [[1029/1024]]
| {{monzo| -10 1 0 3 }}
| 8.43
| Latrizo
| Gamelisma
|-
|-
| 2 1 2 2 2 2 2 1 2 2 2
| 7
| Zweifel Natural Minor
| [[225/224]]
| {{monzo| -5 2 2 -1 }}
| 7.71
| Ruyoyo
| Marvel comma, septimal kleisma
|-
|-
| 3 3 3 3 3 3 2
| 7
| Major quasi-equal Heptatonic ([[6L_1s|Grumpy heptatonic]])
| [[16875/16807]]
| {{monzo| 0 3 4 -5 }}
| 6.99
| Quinru-aquadyo
| Mirkwai comma
|-
|-
| 3 2 3 3 3 3 3
| 7
| Minor quasi-equal Heptatonic (also Grumpy heptatonic)
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
| {{monzo| 11 -10 -10 10 }}
| 5.57
| Saquinbizogu
| [[Linus comma]]
|-
|-
| 3 2 2 2 2 3 2 2 2
| 7
| Rothenberg Generalized Diatonic (also [[score9]])
| [[2401/2400]]
| {{monzo| -5 -1 -2 4 }}
| 0.72
| Bizozogu
| Breedsma
|-
|-
| 3 4 1 4 3 3 2
| 11
| Stearns Major
| [[121/120]]
| {{monzo| -3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
|-
| 7 2 7 2 2
| 13
| [[score5]] [[2L_3s|(classic pentatonic]])
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
|-
| 5 2 2 5 2 2 2
| 13
| [[score7]] ([[2L_5s|mavila, anti-diatonic]])
| [[676/675]]
| {{monzo| 2 -3 -2 0 0 2 }}
| 2.56
| Bithogu
| Island comma, parizeksma
|}
|}
<references />
== Instruments ==
* Like other members of the 5EDO family, 20-EDO lends itself well to guitar (and other fretted string instruments), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-4-4-2-0-0 (low to high), an "A" chord would be 0-0-4-4-2-0, and a "D" chord would be 2-0-0-4-4-2.
* [[Lumatone mapping for 20edo]]


== Commas ==
== Modes ==
20 EDO [[tempering out|tempers out]] the following [[Comma|commas]]. (Note: This assumes the [[val]] &lt; 20 32 46 56 69 74 |.)
20 tone equal modes:


{| class="wikitable" style="text-align:center;"
{| class="wikitable"
|-
|-
! Rational
| 3 1 3 1 3 1 3 1 3 1
! Monzo
| Blackwood Major Decatonic [[5L_5s|(pentawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
! Size (Cents)
! Name 1
! Name 2
! Name 3
|-
|-
| 256/243
| 1 3 1 3 1 3 1 3 1 3
| {{Monzo| 8 -5 }}
| Blackwood Minor Decatonic (also pentawood)
| style="text-align:right;" | 90.22
| [[Limma]]
| Pythagorean Minor 2nd
|
|-
|-
| 16875/16384
| 2 1 1 2 1 1 2 1 1 2 1 1
| {{Monzo| -14 3 4 }}
|Blackwood Major Pentadecatonic (also tri-equal pentadecatonic)
| style="text-align:right;" | 51.12
| Negri Comma
| Double Augmentation Diesis
|
|-
|-
| 9931568/9752117
|1 1 2 1 1 2 1 1 2 1 1 2
| {{Monzo| -25 7 6 }}
|Blackwood Diminished Pentadecatonic (also tri-equal pentadecatonic)
| style="text-align:right;" | 31.57
| Ampersand's Comma
|
|
|-
|-
| 2048/2025
|1 2 1 1 2 1 1 2 1 1 2 1
| {{Monzo| 11 -4 -2 }}
|Blackwood Minor Pentadecatonic (also tri-equal pentadecatonic)
| style="text-align:right;" | 19.55
|-
| Diaschisma
|2 3 2 2 2 3 2 2 2
|
| Balzano Nine-tone ([[2L_7s|balzano]], [[score9]]) <ref>[https://www.jstor.org/stable/833490?seq=1 Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach]</ref>
|
|-
|2 2 2 2 1 2 2 2 2 2 1
|Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
|-
|2 2 2 3 2 2 2 3 2
|Balzano Nine-tone inverse (also balzano, score9)
|-
|1 2 2 2 2 2 1 2 2 2 2
|Balzano Eleven-tone inverse (also score11)
|-
| 2 3 2 3 2 3 2 3
| Octatonic ([[4L_4s|tetrawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|3 2 3 2 3 2 3 2
|Diminished
|-
|2 2 1 2 2 1 2 2 1 2 2 1
|Dodecatonic
|-
|2 1 2 2 1 2 2 1 2 2 1 2
|Diminished
|-
|1 2 2 1 2 2 1 2 2 1 2 2
|Diminished
|-
|4 3 1 4 3 4 1
|Twenty-tone "Major"
|-
|4 1 3 4 1 4 3
|Twenty-tone "Minor"
|-
|-
| 525/512
|2 2 1 2 1 2 2 1 2 2 2 1
| {{Monzo| -9 1 2 1 }}
|Twelve-tone Chromatic
| style="text-align:right;" | 43.41
| Avicennma
| Avicenna's Enharmonic Diesis
|
|-
|-
| 49/48
|2 2 2 2 1 2 2 2 2 1 2
| {{Monzo| -4 -1 0 2 }}
|Zweifel Major
| style="text-align:right;" | 35.70
| Slendro Diesis
|
|
|-
|-
| 50/49
| 2 1 2 2 2 2 2 1 2 2 2
| {{Monzo| 1 0 2 -2 }}
| Zweifel Natural Minor
| style="text-align:right;" | 34.98
| Tritonic Diesis
| Jubilisma
|
|-
|-
| 686/675
|3 3 3 3 3 3 2
| {{Monzo| 1 -3 -2 3 }}
|Major quasi-equal Heptatonic ([[6L_1s|archaeotonic]])
| style="text-align:right;" | 27.99
| Senga
|
|
|-
|-
| 64/63
|3 2 3 3 3 3 3
| {{Monzo| 6 -2 0 -1 }}
|Minor quasi-equal Heptatonic (also archaeotonic)
| style="text-align:right;" | 27.26
| Septimal Comma
| Archytas' Comma
| Leipziger Komma
|-
|-
| 9859966/9733137
|2 2 1 2 1 2 1 2 1 2 1 2 1
| {{Monzo| -10 7 8 -7 }}
|Major quasi-equal Triskaidecatonic (Grumpy triskaidecatonic)
| style="text-align:right;" | 22.41
| Blackjackisma
|
|
|-
|-
| 1029/1024
|2 1 2 1 2 1 2 1 2 1 2 1 2
| {{Monzo| -10 1 0 3 }}
|Minor quasi-equal Triskaidecatonic A
| style="text-align:right;" | 8.43
| Gamelisma
|
|
|-
|-
| 225/224
|1 2 1 2 1 2 1 2 1 2 1 2 2
| {{Monzo| -5 2 2 -1 }}
|Minor quasi-equal Triskaidecatonic B
| style="text-align:right;" | 7.71
| Septimal Kleisma
| Marvel Comma
|
|-
|-
| 16875/16807
|2 1 2 1 2 1 2 1 2 1 2 2 1
| {{Monzo| 0 3 4 -5 }}
|Minor quasi-equal Triskaidecatonic C
| style="text-align:right;" | 6.99
| Mirkwai
|
|
|-
|-
| 6772805/6751042
|3 2 2 2 2 3 2 2 2
| {{Monzo| 11 -10 -10 10 }}
|Rothenberg Generalized Diatonic (also [[2L 7s|balzano]] or [[score9]])
| style="text-align:right;" | 5.57
| Linus
|
|
|-
|-
| 121/120
| 3 4 1 4 3 3 2
| {{Monzo| -3 -1 -1 0 2 }}
|Stearns Major
| style="text-align:right;" | 14.37
| Biyatisma
|
|
|-
|-
| 91/90
|7 2 7 2 2
| {{Monzo| -1 -2 -1 1 0 1 }}
|[[score5]] [[2L_3s|pentic, classic pentatonic]]
| style="text-align:right;" | 19.13
| Superleap
|
|
|-
|-
| 2401/2400
|5 2 2 5 2 2 2
| {{Monzo| -5 -1 2 4 }}
|[[score7]] ([[2L_5s|mavila, anti-diatonic]])
| style="text-align:right;" | 0.72
| Breedsma
|
|
|-
|-
| 676/675
|4 1 3 2 2 3 1 4
| {{Monzo| 2 -3 -2 0 0 2 }}
|[[polymicrotonal|8-tone 4&5edo scale]]
| style="text-align:right;" | 2.56
| Parizeksma
|
|
|}
|}
<references />
== Music ==
{{Catrel| 20edo tracks }}
; [[Ambient Esoterica]]
* [https://www.youtube.com/watch?v=xRNZJhFcoL8 ''20EDO Tablet of Union | Enochian Vision Magick''] (2025)
; [[Beheld]]
* [https://www.youtube.com/watch?v=3X5sCNzdvD4 ''Vivid vibe''] (2022)
; [[Pyotr Chernobrivets]]
* [https://www.youtube.com/watch?v=8PCe5u4QsRg ''Composition for unconventional tempered clavier''] (2013)
* [https://www.youtube.com/watch?v=zQDNqnYqCHg ''5 compositions for violin and clavier in 20-EDO''] (2016)
* [https://www.youtube.com/watch?v=duJHUo_ACgk ''Composition for cello and clavier in 20-tone equal temperament''] (2017)
* [https://www.youtube.com/watch?v=u6k4lgCnHqs ''5 compositions for violin and clavier in 20-tone equal temperament''] (2017)
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/-GTh0EyxCd0 ''20edo''] (2023)
* [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025)
* [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025)
* ''Nocturne in 20edo'' (2025)
** [https://www.youtube.com/shorts/GxElRqwqz-o Lumatone view]
** [https://www.youtube.com/watch?v=PMgYSG4-XaY Visualizer view]
* [https://www.youtube.com/shorts/peypGQ_h0ys ''another 20edo groove''] (2026)
* [https://www.youtube.com/shorts/RXi0Fq-10ME ''20edo + 25edo locked improv''] (2026)
; [[E8 Heterotic]]
* [https://www.youtube.com/watch?v=GRW1GFHFIys ''T w e n t y / T w e n t y''] (2019) – synthwave, Blackwood[10] in 20edo tuning
* [https://www.youtube.com/watch?v=zcvsvc6Hl5g "Wood"], from [https://www.youtube.com/playlist?list=PLbe8k6ZUb2FiSx8Jal1N0XjzWJM_cjgsp ''Elements''] (2019–2020) – tetracot in 20edo tuning
* [https://www.youtube.com/watch?v=KnSSdiv_rS0 ''Decade''] (2020) – synthwave
; [[Francium]]
* [https://www.youtube.com/watch?v=rkgXkQ2D3mw ''Horrible Night Of Horror''] (2023)
* [https://www.youtube.com/watch?v=26XqPsnx16w ''Madeira Preta''] (2023) – Blackwood[10] in 20edo tuning
; [[Frostburn]]
* [https://www.youtube.com/watch?v=nlF6al8MEuk ''Galloping Nightmares''] (2024) – synth metal
; [[groundfault]]
* "The Lake Reflects a Black Sky" from ''A New Dusk'' (2024) – [https://groundfco.bandcamp.com/track/the-lake-reflects-a-black-sky-29-31-20edo Bandcamp] | [https://www.youtube.com/watch?v=1bnEO8vGvbo YouTube (0:00–2:38)] – in part, the rest being in 29edo and 31edo
; [[Andrew Heathwaite]]
* ''We Call It Sharing Breath'' (2004) – [https://www.soundclick.com/music/songInfo.cfm?songID=933696 SoundClick] | [https://web.archive.org/web/20201127012147/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wecallitsharingbreathin20tet.mp3 play]
; [[Aaron Andrew Hunt]]
* [http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 ''Prelude & Fugue a3'']
; [[Mandrake]]
* [https://www.youtube.com/watch?v=ggixiKj27XQ ''Flooded Floodlights''] (2022)
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=4qWJJ7NZlLU ''Chacony & Fugue''] (2017)
* ''Canon on Twinkle Twinkle Little Star'' (2023–2024)
** [https://www.youtube.com/watch?v=6n_a9SfAjsY for organ] · [https://www.youtube.com/watch?v=UuIsIeEc-7w for baroque oboe & viola]
* [https://www.youtube.com/watch?v=5cIYrrxFN9Q ''Chacony & Fugue, in 20edo for Baroque Consort''] (2026)
; [[Herman Miller]]
* ''Etude in 20-tone equal tuning'' – [https://web.archive.org/web/20070219044535/http://www.io.com/~hmiller/midi/20tet.mid midi file] [https://web.archive.org/web/20201127014350/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3 play]
* [https://soundcloud.com/morphosyntax-1/spinning-the-web ''Spinning the Web''] (2017)
* [https://soundcloud.com/morphosyntax-1/ivari-na-taniravi ''Ivari na taniravi''] (2020)
* [https://soundcloud.com/morphosyntax-1/drifting ''Drifting''] (2020)
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=nv_VV7wZ0pE "Serenity"] from [https://youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn&si=xZwLBc6mnZ4LxN1e ''Edolian''] (2020)
* [https://www.youtube.com/watch?v=3MSEHCdd5Fg ''Tomorrow''] (2020)
* from [https://youtube.com/playlist?list=PLg1YtcJbLxnzJQVxBnHqVTv7O3297GhiU&si=yOjOgAd-Qy9JrZVF ''Lastlands OST''] (2020–2021)
** [https://www.youtube.com/watch?v=EecBtadywBk "Venture"] · [https://www.youtube.com/watch?v=6g0K7ny4csc "Impending"] · [https://www.youtube.com/watch?v=ofVPcaGOc3Y "Arrival"]
; [[Sevish]]
* "[[Enterprise]]", from ''[[Human Astronomy]]'' (2010)
; [[Tancla]]
* ''Ultraviolet'' (2021) – [https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/20-ultraviolet Bandcamp] | [https://soundcloud.com/sexytoadsandfrogsfriendcircle/20-tancla-ultraviolet?in=sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava SoundCloud]
; [[Chris Vaisvil]]
* [http://chrisvaisvil.com/a-paradigm-shift-20-edo/ ''A Paradigm Shift''] (2013)
* [http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/ ''20 edo Electric Guitar Improvisation''] (2014)
* [http://chrisvaisvil.com/gobekli-tepe-20-edo-guitar-solo/ ''Göbekli Tepe''] (2014) – for solo guitar
; [[Chris Vaisvil]] and [[Bethan Mathis]]
* [http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/ ''The Walrus and the Carpenter''] (2014)
; [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo ''Underwater Spontaniety''] (2017) – lo-fi ambient
* [https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo ''God's Favorite Tuning''] (2017) – xen-pop
* [https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo ''You Lied, and I'm not Mentioning your Name''] (2017) – xen-pop


== Books ==
== Books ==
<div class='external-image-warning' style='background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block'>
{{External Image| http://ronsword.com/images/20_tet_Coversm.jpg {{dead link}} }}
External image: http://ronsword.com/images/20_tet_Coversm.jpg<br>
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]] {{dead link}}
: <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br>
: <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small>
</div>
[[Category:IMPORTDEBUG - Change External Images]]
 
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]]


[[Category:20edo]]
[[Category:Listen]]
[[Category:books]]
[[Category:Twentuning]]
[[Category:edo]]
[[Category:Todo:add rank 2 temperaments table]]
[[Category:listen]]
[[Category:theory]]
[[Category:todo:unify_precision]]
[[Category:twentuning]]
Retrieved from "https://en.xen.wiki/w/20edo"