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| Blackwood Minor Decatonic (also bi-equal decatonic)
| Blackwood Minor Decatonic (also bi-equal decatonic)
|-
|-
| 2 3 2 2 2 3 2 2 2
| 2 1 1 2 1 1 2 1 1 2 1 1
|Blackwood Major Pentadecatonic (also tri-equal pentadecatonic)
|-
|1 1 2 1 1 2 1 1 2 1 1 2
|Blackwood Diminished Pentadecatonic (also tri-equal pentadecatonic)
|-
|1 2 1 1 2 1 1 2 1 1 2 1
|Blackwood Minor Pentadecatonic (also tri-equal pentadecatonic)
|-
|2 3 2 2 2 3 2 2 2
| Balzano Nine-tone ([[2L_7s|fair mavila]], [[score9]]) <ref>[https://www.jstor.org/stable/833490?seq=1 Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach]</ref>
| Balzano Nine-tone ([[2L_7s|fair mavila]], [[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
|2 2 2 2 1 2 2 2 2 2 1
| Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
|Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
|-
|-
| 2 2 2 3 2 2 2 3 2
|2 2 2 3 2 2 2 3 2
| Balzano Nine-tone inverse (also fair mavila, score9)
|Balzano Nine-tone inverse (also fair mavila, score9)
|-
|-
| 1 2 2 2 2 2 1 2 2 2 2
|1 2 2 2 2 2 1 2 2 2 2
| Balzano Eleven-tone inverse (also score11)
|Balzano Eleven-tone inverse (also score11)
|-
|-
| 2 3 2 3 2 3 2 3
| 2 3 2 3 2 3 2 3
| Octatonic ([[4L_4s|diminished]], according to the [[MOSNamingScheme|MOS naming scheme]])
| Octatonic ([[4L_4s|diminished]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|-
| 3 2 3 2 3 2 3 2
|3 2 3 2 3 2 3 2
| Diminished
|Diminished
|-
|2 2 1 2 2 1 2 2 1 2 2 1
|Dodecatonic
|-
|-
| 4 3 1 4 3 4 1
|2 1 2 2 1 2 2 1 2 2 1 2
| Twenty-tone "Major"
|Diminished
|-
|-
| 4 1 3 4 1 4 3
|1 2 2 1 2 2 1 2 2 1 2 2
| Twenty-tone "Minor"
|Diminished
|-
|-
| 2 2 1 2 1 2 2 1 2 2 2 1
|4 3 1 4 3 4 1
| Twelve-tone Chromatic
|Twenty-tone "Major"
|-
|-
| 2 2 2 2 1 2 2 2 2 1 2
|4 1 3 4 1 4 3
| Zweifel Major
|Twenty-tone "Minor"
|-
|2 2 1 2 1 2 2 1 2 2 2 1
|Twelve-tone Chromatic
|-
|2 2 2 2 1 2 2 2 2 1 2
|Zweifel Major
|-
|-
| 2 1 2 2 2 2 2 1 2 2 2
| 2 1 2 2 2 2 2 1 2 2 2
| Zweifel Natural Minor
| Zweifel Natural Minor
|-
|-
| 3 3 3 3 3 3 2
|3 3 3 3 3 3 2
| Major quasi-equal Heptatonic ([[6L_1s|Grumpy heptatonic]])
|Major quasi-equal Heptatonic ([[6L_1s|Grumpy heptatonic]])
|-
|-
| 3 2 3 3 3 3 3
|3 2 3 3 3 3 3
| Minor quasi-equal Heptatonic (also Grumpy heptatonic)
|Minor quasi-equal Heptatonic (also Grumpy heptatonic)
|-
|-
| 3 2 2 2 2 3 2 2 2
|2 2 1 2 1 2 1 2 1 2 1 2 1
| Rothenberg Generalized Diatonic (also [[score9]])
|Major quasi-equal Triskaidecatonic (Grumpy triskaidecatonic)
|-
|2 1 2 1 2 1 2 1 2 1 2 1 2
|Minor quasi-equal Triskaidecatonic A (also Grumpy triskaidecatonic)
|-
|1 2 1 2 1 2 1 2 1 2 1 2 2
|Minor quasi-equal Triskaidecatonic B (also Grumpy triskaidecatonic)
|-
|2 1 2 1 2 1 2 1 2 1 2 2 1
|Minor quasi-equal Triskaidecatonic C (also Grumpy triskaidecatonic)
|-
|3 2 2 2 2 3 2 2 2
|Rothenberg Generalized Diatonic (also [[score9]])
|-
|-
| 3 4 1 4 3 3 2
| 3 4 1 4 3 3 2
| Stearns Major
|Stearns Major
|-
|-
| 7 2 7 2 2
|7 2 7 2 2
| [[score5]] [[2L_3s|(classic pentatonic]])
|[[score5]] [[2L_3s|(classic pentatonic]])
|-
|-
| 5 2 2 5 2 2 2
|5 2 2 5 2 2 2
| [[score7]] ([[2L_5s|mavila, anti-diatonic]])
|[[score7]] ([[2L_5s|mavila, anti-diatonic]])
|}
|}
<references />
<references />


== Commas ==
==Commas ==
20 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 20 32 46 56 69 74 }}.)
20 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 20 32 46 56 69 74 }}.)


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[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>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
|3
| [[256/243]]
|[[256/243]]
| {{monzo| 8 -5 }}
|{{monzo| 8 -5 }}
| 90.22
|90.22
| Sawa
|Sawa
| [[Limma]], Pythagorean Minor 2nd
|[[Limma]], Pythagorean Minor 2nd
|-
|-
| 5
|5
| [[16875/16384]]
|[[16875/16384]]
| {{monzo| -14 3 4 }}
|{{monzo| -14 3 4 }}
| 51.12
| 51.12
| Laquadyo
|Laquadyo
| Negri Comma, Double Augmentation Diesis
|Negri Comma, Double Augmentation Diesis
|-
|-
| 5
| 5
| [[34171875/33554432|(16 digits)]]
|[[34171875/33554432|(16 digits)]]
| {{monzo| -25 7 6 }}
|{{monzo| -25 7 6 }}
| 31.57
|31.57
| Lala-tribiyo
|Lala-tribiyo
| [[Ampersand]], Ampersand's Comma
|[[Ampersand]], Ampersand's Comma
|-
|-
| 5
| 5
| [[2048/2025]]
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
|
| 19.55
{{monzo| 11 -4 -2 }}
| Sagugu
|19.55
| Diaschisma
|Sagugu
|Diaschisma
|-
|-
| 7
|7
| [[525/512]]
|[[525/512]]
| {{monzo| -9 1 2 1 }}
|{{monzo| -9 1 2 1 }}
| 43.41
|43.41
| Lazoyoyo
|Lazoyoyo
| Avicennma, Avicenna's Enharmonic Diesis
|Avicennma, Avicenna's Enharmonic Diesis
|-
|-
| 7
|7
| [[49/48]]
|[[49/48]]
| {{monzo| -4 -1 0 2 }}
|{{monzo| -4 -1 0 2 }}
| 35.70
|35.70
| Zozo
|Zozo
| Slendro Diesis
|Slendro Diesis
|-
|-
| 7
|7
| [[50/49]]
|[[50/49]]
| {{monzo| 1 0 2 -2 }}
|{{monzo| 1 0 2 -2 }}
| 34.98
|34.98
| Biruyo
|Biruyo
| Tritonic Diesis, Jubilisma
|Tritonic Diesis, Jubilisma
|-
|-
| 7
|7
| [[686/675]]
|[[686/675]]
| {{monzo| 1 -3 -2 3 }}
|{{monzo| 1 -3 -2 3 }}
| 27.99
|27.99
| Trizo-agugu
|Trizo-agugu
| Senga
|Senga
|-
|-
| 7
| 7
| [[64/63]]
|[[64/63]]
| {{monzo| 6 -2 0 -1 }}
|{{monzo| 6 -2 0 -1 }}
| 27.26
|27.26
| Ru
|Ru
| Septimal Comma, Archytas' Comma, Leipziger Komma
|Septimal Comma, Archytas' Comma, Leipziger Komma
|-
|-
| 7
|7
| <abbr title="854296875/843308032">(18 digits)</abbr>
|<abbr title="854296875/843308032">(18 digits)</abbr>
| {{monzo| -10 7 8 -7 }}
| {{monzo| -10 7 8 -7 }}
| 22.41
|22.41
| Lasepru-aquadbiyo
|Lasepru-aquadbiyo
| [[Blackjackisma]]
|[[Blackjackisma]]
|-
|-
| 7
|7
| [[1029/1024]]
|[[1029/1024]]
| {{monzo| -10 1 0 3 }}
|{{monzo| -10 1 0 3 }}
| 8.43
|8.43
| Latrizo
|Latrizo
| Gamelisma
|Gamelisma
|-
|-
| 7
|7
| [[225/224]]
|[[225/224]]
| {{monzo| -5 2 2 -1 }}
|{{monzo| -5 2 2 -1 }}
| 7.71
|7.71
| Ruyoyo
|Ruyoyo
| Septimal Kleisma, Marvel Comma
|Septimal Kleisma, Marvel Comma
|-
|-
| 7
|7
| [[16875/16807]]
|[[16875/16807]]
| {{monzo| 0 3 4 -5 }}
|{{monzo| 0 3 4 -5 }}
| 6.99
| 6.99
| Quinru-aquadyo
|Quinru-aquadyo
| Mirkwai
|Mirkwai
|-
|-
| 7
|7
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
| {{monzo| 11 -10 -10 10 }}
|{{monzo| 11 -10 -10 10 }}
| 5.57
|5.57
| Saquinbizogu
|Saquinbizogu
| [[Linus]]
|[[Linus]]
|-
|-
| 7
| 7
| [[2401/2400]]
|[[2401/2400]]
| {{monzo| -5 -1 -2 4 }}
|{{monzo| -5 -1 -2 4 }}
| 0.72
|0.72
| Bizozogu
|Bizozogu
| Breedsma
|Breedsma
|-
|-
| 11
|11
| [[121/120]]
|[[121/120]]
| {{monzo| -3 -1 -1 0 2 }}
|{{monzo| -3 -1 -1 0 2 }}
| 14.37
| 14.37
| Lologu
| Lologu
| Biyatisma
|Biyatisma
|-
|-
| 13
|13
| [[91/90]]
|[[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
|{{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| 19.13
| Thozogu
|Thozogu
| Superleap
|Superleap
|-
|-
| 13
|13
| [[676/675]]
|[[676/675]]
| {{monzo| 2 -3 -2 0 0 2 }}
|{{monzo| 2 -3 -2 0 0 2 }}
| 2.56
|2.56
| Bithogu
|Bithogu
| Parizeksma
|Parizeksma
|}
|}
<references/>
<references />


== Instruments ==
==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.
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.


== Books ==
==Books==
{{External Image| http://ronsword.com/images/20_tet_Coversm.jpg {{dead link}} }}
{{External Image| http://ronsword.com/images/20_tet_Coversm.jpg {{dead link}} }}
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]] {{dead link}}
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]] {{dead link}}


== Music ==
== Music==


* [https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo Underwater Spontaniety] (lo-fi ambient) by [https://soundcloud.com/overtoneshock Stephen Weigel]
*[https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo Underwater Spontaniety] (lo-fi ambient) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [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/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]
*[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://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 &amp; Fugue a3] by [[Aaron Hunt]]
*[http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 20ET — Prelude &amp; 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://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/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/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/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]]
*[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=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=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=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]
*[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]


[[Category:Theory]]
[[Category:Theory]]
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