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**Imported revision 630814365 - Original comment: fixed link to prelude and fugue in 20edo**
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="display: block; text-align: right;">[[20平均律|日本語]]</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2018-07-05 10:07:32 UTC</tt>.<br>
: The original revision id was <tt>630814365</tt>.<br>
: The revision comment was: <tt>fixed link to prelude and fugue in 20edo</tt><br>
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>
<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">&lt;span style="display: block; text-align: right;"&gt;[[20平均律|日本語]]
&lt;/span&gt;
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[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 5 edo), 11, 13 &amp; 15 (from 10 edo), 19 &amp; 27 (from 4 edo), 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.


[[toc|flat]]
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent|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 5 edo), 11, 13 &amp; 15 (from 10 edo), 19 &amp; 27 (from 4 edo), 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.
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=Compositions=  
=Compositions=
* [[https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo|Underwater Spontaniety]] (lo-fi ambient) by [[https://soundcloud.com/overtoneshock|Stephen Weigel]]
<ul><li>[https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo Underwater Spontaniety] (lo-fi ambient) by [https://soundcloud.com/overtoneshock Stephen Weigel]</li><li>[https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo God's Favorite Tuning] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]</li><li>[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]</li><li>[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|Herman Miller]]</li><li>[http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 20ET — Prelude &amp; Fugue a3] by [[Aaron_Hunt|Aaron Hunt]]</li><li>[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|Andrew Heathwaite]]</li><li>[http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/ The Walrus and the Carpenter] by[[Chris_Vaisvil| Chris Vaisvil]] and Bethan Mathis</li><li>[http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/ 20 edo Electric Guitar Improvisation] by[[Chris_Vaisvil| Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/gobekli-tepe-20-edo-guitar-solo/ Göbekli Tepe (20 edo guitar solo)] by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/a-paradigm-shift-20-edo/ A Paradigm Shift (20 edo)] by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[https://www.youtube.com/watch?v=8PCe5u4QsRg Composition for unconventional tempered clavier] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]</li><li>[https://www.youtube.com/watch?v=zQDNqnYqCHg 5 compositions for violin and clavier in 20-EDO] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]</li><li>[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]</li><li>[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]</li></ul>
* [[@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 &amp; Fugue a3]] by [[Aaron Hunt]]
* [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;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| Chris Vaisvil]] and Bethan Mathis
* [[http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/|20 edo Electric Guitar Improvisation]] by[[Chris Vaisvil| 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]]


=Properties=
=Properties=
==Intervals==  


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.
==Intervals==
||~ Degree ||~ Cents ||~ Approximate Ratios ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||~ Nearest Harmonic ||
||= 0 ||&gt; 0 ||= 1/1 ||= unison ||= P1 ||= D ||= 1 ||
||= 1 ||&gt; 60 ||= 29/28 ||= upminor 2nd ||= ^m2 ||= D^ ||= 33 ||
||= 2 ||&gt; 120 ||= 14/13, 15/14 ||= mid 2nd ||= ~2 ||= D^^, Evv ||= 69 ||
||= 3 ||&gt; 180 ||= 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||= 71 ||
||= 4 ||&gt; 240 ||= 8/7, 15/13 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= 37 ||
||= 5 ||&gt; 300 ||= 13/11, 19/16 ||= upminor 3rd ||= ^m3 ||= F^ ||= 19 ||
||= 6 ||&gt; 360 ||= 16/13, 5/4 ||= mid 3rd ||= ~3 ||= F^^ ||= 79 ||
||= 7 ||&gt; 420 ||= [[14_11|14/11]], [[51_40|51/40]] ||= downmajor 3rd ||= vM3 ||= F#v ||= 41 ||
||= 8 ||&gt; 480 ||= 25/19, 4/3 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= 21 ||
||= 9 ||&gt; 540 ||= 15/11, 11/8 ||= up-fourth ||= ^4 ||= G^ ||= 11 ||
||= 10 ||&gt; 600 ||= 7/5 ||= double-up fourth, double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= 91 ||
||= 11 ||&gt; 660 ||= 22/15, 16/11 ||= down-fifth ||= v5 ||= Av ||= 47 ||
||= 12 ||&gt; 720 ||= 38/25, 3/2 ||= fifth ||= P5, m6 ||= A ||= 97 ||
||= 13 ||&gt; 780 ||= 11/7, 25/16 ||= upminor 6th ||= ^m6 ||= A^ ||= 25 ||
||= 14 ||&gt; 840 ||= 13/8, 8/5 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= 13 ||
||= 15 ||&gt; 900 ||= 22/13, 32/19 ||= downmajor 6th ||= vM6 ||= Bv ||= 27 ||
||= 16 ||&gt; 960 ||= 7/4, 26/15 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= 7 ||
||= 17 ||&gt; 1020 ||= 9/5 ||= upminor 7th ||= ^m7 ||= C^ ||= 115 ||
||= 18 ||&gt; 1080 ||= 15/8, 13/7 ||= mid 7th ||= ~7 ||= C^^, Dvv ||= 15 ||
||= 19 ||&gt; 1140 ||= 56/29 ||= downmajor 7th ||= vM7 ||= Dv ||= 31 ||
||= 20 ||&gt; 1200 ||= 2/1 ||= octave ||= P8 ||= D ||= 2 ||


=Chord Names=  
Like [[15edo|15edo]], every note has many names. D is also C# and Eb. The major 3rd is also a perfect 4th and a dim 5th.
 
{| class="wikitable"
|-
! | Degree
! | Cents
! | Approximate Ratios
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]]
! | Nearest Harmonic
|-
| style="text-align:center;" | 0
| style="text-align:right;" | 0
| style="text-align:center;" | 1/1
| style="text-align:center;" | unison
| style="text-align:center;" | P1
| style="text-align:center;" | D
| style="text-align:center;" | 1
|-
| style="text-align:center;" | 1
| style="text-align:right;" | 60
| style="text-align:center;" | 29/28
| style="text-align:center;" | upminor 2nd
| style="text-align:center;" | ^m2
| style="text-align:center;" | D^
| style="text-align:center;" | 33
|-
| style="text-align:center;" | 2
| style="text-align:right;" | 120
| style="text-align:center;" | 14/13, 15/14
| style="text-align:center;" | mid 2nd
| style="text-align:center;" | ~2
| style="text-align:center;" | D^^, Evv
| style="text-align:center;" | 69
|-
| style="text-align:center;" | 3
| style="text-align:right;" | 180
| style="text-align:center;" | 10/9
| style="text-align:center;" | downmajor 2nd
| style="text-align:center;" | vM2
| style="text-align:center;" | Ev
| style="text-align:center;" | 71
|-
| style="text-align:center;" | 4
| style="text-align:right;" | 240
| style="text-align:center;" | 8/7, 15/13
| style="text-align:center;" | major 2nd, minor 3rd
| style="text-align:center;" | M2, m3
| style="text-align:center;" | E, F
| style="text-align:center;" | 37
|-
| style="text-align:center;" | 5
| style="text-align:right;" | 300
| style="text-align:center;" | 13/11, 19/16
| style="text-align:center;" | upminor 3rd
| style="text-align:center;" | ^m3
| style="text-align:center;" | F^
| style="text-align:center;" | 19
|-
| style="text-align:center;" | 6
| style="text-align:right;" | 360
| style="text-align:center;" | 16/13, 5/4
| style="text-align:center;" | mid 3rd
| style="text-align:center;" | ~3
| style="text-align:center;" | F^^
| style="text-align:center;" | 79
|-
| style="text-align:center;" | 7
| style="text-align:right;" | 420
| style="text-align:center;" | [[14/11|14/11]], [[51/40|51/40]]
| style="text-align:center;" | downmajor 3rd
| style="text-align:center;" | vM3
| style="text-align:center;" | F#v
| style="text-align:center;" | 41
|-
| style="text-align:center;" | 8
| style="text-align:right;" | 480
| style="text-align:center;" | 25/19, 4/3
| style="text-align:center;" | major 3rd, perfect fourth
| style="text-align:center;" | M3, P4
| style="text-align:center;" | F#, G
| style="text-align:center;" | 21
|-
| style="text-align:center;" | 9
| style="text-align:right;" | 540
| style="text-align:center;" | 15/11, 11/8
| style="text-align:center;" | up-fourth
| style="text-align:center;" | ^4
| style="text-align:center;" | G^
| style="text-align:center;" | 11
|-
| style="text-align:center;" | 10
| style="text-align:right;" | 600
| style="text-align:center;" | 7/5
| style="text-align:center;" | double-up fourth, double-down fifth
| style="text-align:center;" | ^^4, vv5
| style="text-align:center;" | G^^, Avv
| style="text-align:center;" | 91
|-
| style="text-align:center;" | 11
| style="text-align:right;" | 660
| style="text-align:center;" | 22/15, 16/11
| style="text-align:center;" | down-fifth
| style="text-align:center;" | v5
| style="text-align:center;" | Av
| style="text-align:center;" | 47
|-
| style="text-align:center;" | 12
| style="text-align:right;" | 720
| style="text-align:center;" | 38/25, 3/2
| style="text-align:center;" | fifth
| style="text-align:center;" | P5, m6
| style="text-align:center;" | A
| style="text-align:center;" | 97
|-
| style="text-align:center;" | 13
| style="text-align:right;" | 780
| style="text-align:center;" | 11/7, 25/16
| style="text-align:center;" | upminor 6th
| style="text-align:center;" | ^m6
| style="text-align:center;" | A^
| style="text-align:center;" | 25
|-
| style="text-align:center;" | 14
| style="text-align:right;" | 840
| style="text-align:center;" | 13/8, 8/5
| style="text-align:center;" | mid 6th
| style="text-align:center;" | ~6
| style="text-align:center;" | A^^, Bvv
| style="text-align:center;" | 13
|-
| style="text-align:center;" | 15
| style="text-align:right;" | 900
| style="text-align:center;" | 22/13, 32/19
| style="text-align:center;" | downmajor 6th
| style="text-align:center;" | vM6
| style="text-align:center;" | Bv
| style="text-align:center;" | 27
|-
| style="text-align:center;" | 16
| style="text-align:right;" | 960
| style="text-align:center;" | 7/4, 26/15
| style="text-align:center;" | major 6th, minor 7th
| style="text-align:center;" | M6, m7
| style="text-align:center;" | B, C
| style="text-align:center;" | 7
|-
| style="text-align:center;" | 17
| style="text-align:right;" | 1020
| style="text-align:center;" | 9/5
| style="text-align:center;" | upminor 7th
| style="text-align:center;" | ^m7
| style="text-align:center;" | C^
| style="text-align:center;" | 115
|-
| style="text-align:center;" | 18
| style="text-align:right;" | 1080
| style="text-align:center;" | 15/8, 13/7
| style="text-align:center;" | mid 7th
| style="text-align:center;" | ~7
| style="text-align:center;" | C^^, Dvv
| style="text-align:center;" | 15
|-
| style="text-align:center;" | 19
| style="text-align:right;" | 1140
| style="text-align:center;" | 56/29
| style="text-align:center;" | downmajor 7th
| style="text-align:center;" | vM7
| style="text-align:center;" | Dv
| style="text-align:center;" | 31
|-
| style="text-align:center;" | 20
| style="text-align:right;" | 1200
| style="text-align:center;" | 2/1
| style="text-align:center;" | octave
| style="text-align:center;" | P8
| style="text-align:center;" | D
| style="text-align:center;" | 2
|}
 
=Chord Names=
20edo chord names using ups and downs:
20edo chord names using ups and downs:
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 F#v A = D.v = "D dot 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 = Dm7(^3) = "D minor seven up-three", or D F^ A B = Dm6(^3) = "D minor six up-three"
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 = D7(~3) = "D seven mid-three", or D F^ A B = D6(~3) = "D six mid-three"
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 F#v A C = D7(v3) = "D seven down-three", or D F#v A B = D6(v3) = "D six down-three"
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 F#v A C#v = D.vM7 = "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 dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six"
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. Because many intervals have several names, many chords do too.


==Modes==  
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.
 
==Modes==
20 tone equal modes:
20 tone equal modes:
|| 3 1 3 1 3 1 3 1 3 1 || Blackwood Major Decatonic [[5L 5s|(bi-equal decatonic]], according to the [[MOSNamingScheme|MOS naming scheme]]) ||
|| 1 3 1 3 1 3 1 3 1 3 || Blackwood Minor Decatonic (&lt;span class="wiki_link_new"&gt;also bi-equal decatonic)&lt;/span&gt; ||
|| 2 3 2 2 2 3 2 2 2 || Balzano Nine-tone (&lt;span class="wiki_link"&gt;[[2L 7s|fair mavila]], [[score9]])&lt;/span&gt; ||
|| 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 &lt;span class="wiki_link"&gt;fair mavila, score9)&lt;/span&gt; ||
|| 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|diminished]], according to the [[MOSNamingScheme|MOS naming scheme]]) ||
|| 3 2 3 2 3 2 3 2 || Diminished ||
|| 4 3 1 4 3 4 1 || Twenty-tone "Major" ||
|| 4 1 3 4 1 4 3 || 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 || Zweifel Natural Minor ||
|| 3 3 3 3 3 3 2 || Major quasi-equal Heptatonic ([[6L 1s|Grumpy heptatonic]]) ||
|| 3 2 3 3 3 3 3 || Minor quasi-equal Heptatonic (also Grumpy heptatonic) ||
|| 3 2 2 2 2 3 2 2 2 || Rothenberg Generalized Diatonic (also [[score9]]) ||
|| 3 4 1 4 3 3 2 || Stearns Major ||
|| 7 2 7 2 2 || [[score5]] [[2L 3s|(classic pentatonic]]) ||
|| 5 2 2 5 2 2 2 || [[score7]] ([[2L 5s|mavila, anti-diatonic]]) ||
==Commas==
20 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] &lt; 20 32 46 56 69 74 |.)
||~ Rational ||~ Monzo ||~ Size (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 256/243 || | 8 -5 &gt; ||&gt; 90.22 ||= [[Limma]] ||= Pythagorean Minor 2nd ||=  ||
||= 16875/16384 || | -14 3 4 &gt; ||&gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||  ||
||= 9931568/9752117 || | -25 7 6 &gt; ||&gt; 31.57 ||= Ampersand's Comma ||=  ||=  ||
||= 2048/2025 || | 11 -4 -2 &gt; ||&gt; 19.55 ||= Diaschisma ||=  ||=  ||
||= 525/512 || | -9 1 2 1 &gt; ||&gt; 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||  ||
||= 49/48 || | -4 -1 0 2 &gt; ||&gt; 35.70 ||= Slendro Diesis ||=  ||=  ||
||= 50/49 || | 1 0 2 -2 &gt; ||&gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||=  ||
||= 686/675 || | 1 -3 -2 3 &gt; ||&gt; 27.99 ||= Senga ||=  ||=  ||
||= 64/63 || | 6 -2 0 -1 &gt; ||&gt; 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
||= 9859966/9733137 || | -10 7 8 -7 &gt; ||&gt; 22.41 ||= Blackjackisma ||=  ||=  ||
||= 1029/1024 || | -10 1 0 3 &gt; ||&gt; 8.43 ||= Gamelisma ||=  ||=  ||
||= 225/224 || | -5 2 2 -1 &gt; ||&gt; 7.71 ||= Septimal Kleisma ||= Marvel Comma ||=  ||
||= 16875/16807 || | 0 3 4 -5 &gt; ||&gt; 6.99 ||= Mirkwai ||=  ||=  ||
||= 6772805/6751042 || | 11 -10 -10 10 &gt; ||&gt; 5.57 ||= Linus ||  ||  ||
||= 121/120 || | -3 -1 -1 0 2 &gt; ||&gt; 14.37 ||= Biyatisma ||  ||  ||
||= 91/90 || | -1 -2 -1 1 0 1 &gt; ||&gt; 19.13 ||= Superleap ||  ||  ||
||= 2401/2400 || | -5 -1 2 4 &gt; ||&gt; 0.72 ||= Breedsma ||  ||  ||
||= 676/675 || | 2 -3 -2 0 0 2 &gt; ||&gt; 2.56 ||= Parizeksma ||  ||  ||
==**Books**==
[[image:http://ronsword.com/images/20_tet_Coversm.jpg width="82" height="114" link="@http://www.ronsword.com/"]]
[[@http://www.ronsword.com/|"Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more]] by [[Ron Sword]]</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;20edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="/20%E5%B9%B3%E5%9D%87%E5%BE%8B"&gt;日本語&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It contains smaller &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;s &lt;a class="wiki_link" href="/2edo"&gt;2&lt;/a&gt;, &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, and &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt; and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 &amp;amp; 15 (from 10 edo), 19 &amp;amp; 27 (from 4 edo), 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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextTocRule:14:&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:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Properties"&gt;Properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Chord Names"&gt;Chord Names&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;hr /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Compositions&lt;/h1&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo" rel="nofollow"&gt;Underwater Spontaniety&lt;/a&gt; (lo-fi ambient) by &lt;a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow"&gt;Stephen Weigel&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo" rel="nofollow" target="_blank"&gt;God's Favorite Tuning&lt;/a&gt; (xen-pop) by &lt;a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow"&gt;Stephen Weigel&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo?in=overtoneshock/sets/xenharmonic-microtonal" rel="nofollow"&gt;You Lied, and I'm not Mentioning your Name&lt;/a&gt; (xen-pop) by &lt;a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow"&gt;Stephen Weigel&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/20tet.mid" rel="nofollow"&gt;Etude in 20-tone equal tuning&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Herman%20Miller"&gt;Herman Miller&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3" rel="nofollow"&gt;20ET — Prelude &amp;amp; Fugue a3&lt;/a&gt; by &lt;a class="wiki_link" href="/Aaron%20Hunt"&gt;Aaron Hunt&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;amp;songID=933696" rel="nofollow"&gt;We Call It Sharing Breath&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wecallitsharingbreathin20tet.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/" rel="nofollow"&gt;The Walrus and the Carpenter&lt;/a&gt; by&lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt; Chris Vaisvil&lt;/a&gt; and Bethan Mathis&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/" rel="nofollow"&gt;20 edo Electric Guitar Improvisation&lt;/a&gt; by&lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt; Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/gobekli-tepe-20-edo-guitar-solo/" rel="nofollow"&gt;Göbekli Tepe (20 edo guitar solo)&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/a-paradigm-shift-20-edo/" rel="nofollow"&gt;A Paradigm Shift (20 edo)&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=8PCe5u4QsRg" rel="nofollow" target="_blank"&gt;Composition for unconventional tempered clavier&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank"&gt;Pyotr Chernobrivets&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=zQDNqnYqCHg" rel="nofollow" target="_blank"&gt;5 compositions for violin and clavier in 20-EDO&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank"&gt;Pyotr Chernobrivets&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=duJHUo_ACgk" rel="nofollow" target="_blank"&gt;Composition for cello and clavier in 20-tone equal temperament&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank"&gt;Pyotr Chernobrivets&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=u6k4lgCnHqs" rel="nofollow" target="_blank"&gt;5 compositions for violin and clavier in 20-tone equal temperament&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank"&gt;Pyotr Chernobrivets&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Properties&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Properties-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h2&gt;
&lt;br /&gt;
Like &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, every note has many names. D is also C# and Eb. The major 3rd is also a perfect 4th and a dim 5th.&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Degree&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Approximate Ratios&lt;br /&gt;
&lt;/th&gt;
        &lt;th colspan="3"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Nearest Harmonic&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;60&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;120&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14/13, 15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mid 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D^^, Evv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;69&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;180&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;71&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;240&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/7, 15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;major 2nd, minor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M2, m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E, F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;300&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/11, 19/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;360&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/13, 5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mid 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;79&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;420&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;, &lt;a class="wiki_link" href="/51_40"&gt;51/40&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#v&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;480&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;25/19, 4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;major 3rd, perfect fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M3, P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#, G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;540&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15/11, 11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;up-fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;600&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up fourth, double-down fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^4, vv5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^^, Avv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;91&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;660&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22/15, 16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;down-fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;720&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;38/25, 3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P5, m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;97&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;780&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/7, 25/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;840&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/8, 8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mid 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A^^, Bvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;900&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22/13, 32/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;960&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/4, 26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;major 6th, minor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M6, m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B, C&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1020&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;115&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1080&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15/8, 13/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mid 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^^, Dvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1140&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;56/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Chord Names&lt;/h1&gt;
|-
20edo chord names using ups and downs:&lt;br /&gt;
| | 3 1 3 1 3 1 3 1 3 1
0-4-12 = D E A = Dsus2 = &amp;quot;D sus 2&amp;quot;, or D F A = Dm = &amp;quot;D minor&amp;quot;&lt;br /&gt;
| | Blackwood Major Decatonic [[5L_5s|(bi-equal decatonic]], according to the [[MOSNamingScheme|MOS naming scheme]])
0-5-12 = D F^ A = D.^m = &amp;quot;D upminor&amp;quot;&lt;br /&gt;
|-
0-6-12 = D F^^ A = D.~ = &amp;quot;D mid&amp;quot;&lt;br /&gt;
| | 1 3 1 3 1 3 1 3 1 3
0-7-12 = D F#v A = D.v = &amp;quot;D dot down&amp;quot; or &amp;quot;D downmajor&amp;quot;&lt;br /&gt;
| | Blackwood Minor Decatonic (<span style="">also bi-equal decatonic)</span>
0-8-12 = D G A = Dsus4, or D F# A = D = &amp;quot;D&amp;quot; or &amp;quot;D major&amp;quot;&lt;br /&gt;
|-
0-4-12-16 = D F A C = Dm7 = &amp;quot;D minor seven&amp;quot;, or D F A B = Dm6 = &amp;quot;D minor six&amp;quot;&lt;br /&gt;
| | 2 3 2 2 2 3 2 2 2
0-5-12-16 = D F^ A C = Dm7(^3) = &amp;quot;D minor seven up-three&amp;quot;, or D F^ A B = Dm6(^3) = &amp;quot;D minor six up-three&amp;quot;&lt;br /&gt;
| | Balzano Nine-tone (<span style="">[[2L_7s|fair mavila]], [[score9|score9]])</span>
0-6-12-16 = D F^^ A C = D7(~3) = &amp;quot;D seven mid-three&amp;quot;, or D F^ A B = D6(~3) = &amp;quot;D six mid-three&amp;quot;&lt;br /&gt;
|-
0-7-12-16 = D F#v A C = D7(v3) = &amp;quot;D seven down-three&amp;quot;, or D F#v A B = D6(v3) = &amp;quot;D six down-three&amp;quot;&lt;br /&gt;
| | 2 2 2 2 1 2 2 2 2 2 1
0-8-12-16 = D F# A C = D7 = &amp;quot;D seven&amp;quot;, or D F# A B = D6 = &amp;quot;D six&amp;quot;&lt;br /&gt;
| | Balzano Eleven-tone, Agmon Diatonic DS4, [[score11|score11]]
0-7-12-19 = D F#v A C#v = D.vM7 = &amp;quot;D downmajor seven&amp;quot;&lt;br /&gt;
|-
0-5-12-17 = D F^ A C^ = D.^m7 = &amp;quot;D dot up minor-seven&amp;quot;, or D F^ A B^ = D.^m6 = &amp;quot;D dot up minor-six&amp;quot;&lt;br /&gt;
| | 2 2 2 3 2 2 2 3 2
For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;. Because many intervals have several names, many chords do too.&lt;br /&gt;
| | Balzano Nine-tone inverse (also <span style="">fair mavila, score9)</span>
&lt;br /&gt;
|-
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Chord Names-Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Modes&lt;/h2&gt;
| | 1 2 2 2 2 2 1 2 2 2 2
20 tone equal modes:&lt;br /&gt;
| | Balzano Eleven-tone inverse (also score11)
|-
| | 2 3 2 3 2 3 2 3
| | Octatonic ([[4L_4s|diminished]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
| | 3 2 3 2 3 2 3 2
| | Diminished
|-
| | 4 3 1 4 3 4 1
| | Twenty-tone "Major"
|-
| | 4 1 3 4 1 4 3
| | 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
| | Zweifel Natural Minor
|-
| | 3 3 3 3 3 3 2
| | Major quasi-equal Heptatonic ([[6L_1s|Grumpy heptatonic]])
|-
| | 3 2 3 3 3 3 3
| | Minor quasi-equal Heptatonic (also Grumpy heptatonic)
|-
| | 3 2 2 2 2 3 2 2 2
| | Rothenberg Generalized Diatonic (also [[score9|score9]])
|-
| | 3 4 1 4 3 3 2
| | Stearns Major
|-
| | 7 2 7 2 2
| | [[score5|score5]] [[2L_3s|(classic pentatonic]])
|-
| | 5 2 2 5 2 2 2
| | [[score7|score7]] ([[2L_5s|mavila, anti-diatonic]])
|}


==Commas==
20 EDO [[tempering_out|tempers out]] the following [[Comma|comma]]s. (Note: This assumes the [[val|val]] &lt; 20 32 46 56 69 74 |.)


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;3 1 3 1 3 1 3 1 3 1&lt;br /&gt;
! | Rational
&lt;/td&gt;
! | Monzo
        &lt;td&gt;Blackwood Major Decatonic &lt;a class="wiki_link" href="/5L%205s"&gt;(bi-equal decatonic&lt;/a&gt;, according to the &lt;a class="wiki_link" href="/MOSNamingScheme"&gt;MOS naming scheme&lt;/a&gt;)&lt;br /&gt;
! | Size (Cents)
&lt;/td&gt;
! | Name 1
    &lt;/tr&gt;
! | Name 2
    &lt;tr&gt;
! | Name 3
        &lt;td&gt;1 3 1 3 1 3 1 3 1 3&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | 256/243
        &lt;td&gt;Blackwood Minor Decatonic (&lt;span class="wiki_link_new"&gt;also bi-equal decatonic)&lt;/span&gt;&lt;br /&gt;
| | | 8 -5 &gt;
&lt;/td&gt;
| style="text-align:right;" | 90.22
    &lt;/tr&gt;
| style="text-align:center;" | [[Limma|Limma]]
    &lt;tr&gt;
| style="text-align:center;" | Pythagorean Minor 2nd
        &lt;td&gt;2 3 2 2 2 3 2 2 2&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td&gt;Balzano Nine-tone (&lt;span class="wiki_link"&gt;&lt;a class="wiki_link" href="/2L%207s"&gt;fair mavila&lt;/a&gt;, &lt;a class="wiki_link" href="/score9"&gt;score9&lt;/a&gt;)&lt;/span&gt;&lt;br /&gt;
| style="text-align:center;" | 16875/16384
&lt;/td&gt;
| | | -14 3 4 &gt;
    &lt;/tr&gt;
| style="text-align:right;" | 51.12
    &lt;tr&gt;
| style="text-align:center;" | Negri Comma
        &lt;td&gt;2 2 2 2 1 2 2 2 2 2 1&lt;br /&gt;
| style="text-align:center;" | Double Augmentation Diesis
&lt;/td&gt;
| |
        &lt;td&gt;Balzano Eleven-tone, Agmon Diatonic DS4, &lt;a class="wiki_link" href="/score11"&gt;score11&lt;/a&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | 9931568/9752117
    &lt;/tr&gt;
| | | -25 7 6 &gt;
    &lt;tr&gt;
| style="text-align:right;" | 31.57
        &lt;td&gt;2 2 2 3 2 2 2 3 2&lt;br /&gt;
| style="text-align:center;" | Ampersand's Comma
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td&gt;Balzano Nine-tone inverse (also &lt;span class="wiki_link"&gt;fair mavila, score9)&lt;/span&gt;&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
    &lt;/tr&gt;
| style="text-align:center;" | 2048/2025
    &lt;tr&gt;
| | | 11 -4 -2 &gt;
        &lt;td&gt;1 2 2 2 2 2 1 2 2 2 2&lt;br /&gt;
| style="text-align:right;" | 19.55
&lt;/td&gt;
| style="text-align:center;" | Diaschisma
        &lt;td&gt;Balzano Eleven-tone inverse (also score11)&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
| style="text-align:center;" |
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| style="text-align:center;" | 525/512
        &lt;td&gt;2 3 2 3 2 3 2 3&lt;br /&gt;
| | | -9 1 2 1 &gt;
&lt;/td&gt;
| style="text-align:right;" | 43.41
        &lt;td&gt;Octatonic (&lt;a class="wiki_link" href="/4L%204s"&gt;diminished&lt;/a&gt;, according to the &lt;a class="wiki_link" href="/MOSNamingScheme"&gt;MOS naming scheme&lt;/a&gt;)&lt;br /&gt;
| style="text-align:center;" | Avicennma
&lt;/td&gt;
| style="text-align:center;" | Avicenna's Enharmonic Diesis
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;3 2 3 2 3 2 3 2&lt;br /&gt;
| style="text-align:center;" | 49/48
&lt;/td&gt;
| | | -4 -1 0 2 &gt;
        &lt;td&gt;Diminished&lt;br /&gt;
| style="text-align:right;" | 35.70
&lt;/td&gt;
| style="text-align:center;" | Slendro Diesis
    &lt;/tr&gt;
| style="text-align:center;" |
    &lt;tr&gt;
| style="text-align:center;" |
        &lt;td&gt;4 3 1 4 3 4 1&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | 50/49
        &lt;td&gt;Twenty-tone &amp;quot;Major&amp;quot;&lt;br /&gt;
| | | 1 0 2 -2 &gt;
&lt;/td&gt;
| style="text-align:right;" | 34.98
    &lt;/tr&gt;
| style="text-align:center;" | Tritonic Diesis
    &lt;tr&gt;
| style="text-align:center;" | Jubilisma
        &lt;td&gt;4 1 3 4 1 4 3&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td&gt;Twenty-tone &amp;quot;Minor&amp;quot;&lt;br /&gt;
| style="text-align:center;" | 686/675
&lt;/td&gt;
| | | 1 -3 -2 3 &gt;
    &lt;/tr&gt;
| style="text-align:right;" | 27.99
    &lt;tr&gt;
| style="text-align:center;" | Senga
        &lt;td&gt;2 2 1 2 1 2 2 1 2 2 2 1&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td&gt;Twelve-tone Chromatic&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | 64/63
    &lt;/tr&gt;
| | | 6 -2 0 -1 &gt;
    &lt;tr&gt;
| style="text-align:right;" | 27.26
        &lt;td&gt;2 2 2 2 1 2 2 2 2 1 2&lt;br /&gt;
| style="text-align:center;" | Septimal Comma
&lt;/td&gt;
| style="text-align:center;" | Archytas' Comma
        &lt;td&gt;Zweifel Major&lt;br /&gt;
| style="text-align:center;" | Leipziger Komma
&lt;/td&gt;
|-
    &lt;/tr&gt;
| style="text-align:center;" | 9859966/9733137
    &lt;tr&gt;
| | | -10 7 8 -7 &gt;
        &lt;td&gt;2 1 2 2 2 2 2 1 2 2 2&lt;br /&gt;
| style="text-align:right;" | 22.41
&lt;/td&gt;
| style="text-align:center;" | Blackjackisma
        &lt;td&gt;Zweifel Natural Minor&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
| style="text-align:center;" |
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| style="text-align:center;" | 1029/1024
        &lt;td&gt;3 3 3 3 3 3 2&lt;br /&gt;
| | | -10 1 0 3 &gt;
&lt;/td&gt;
| style="text-align:right;" | 8.43
        &lt;td&gt;Major quasi-equal Heptatonic (&lt;a class="wiki_link" href="/6L%201s"&gt;Grumpy heptatonic&lt;/a&gt;)&lt;br /&gt;
| style="text-align:center;" | Gamelisma
&lt;/td&gt;
| style="text-align:center;" |
    &lt;/tr&gt;
| style="text-align:center;" |
    &lt;tr&gt;
|-
        &lt;td&gt;3 2 3 3 3 3 3&lt;br /&gt;
| style="text-align:center;" | 225/224
&lt;/td&gt;
| | | -5 2 2 -1 &gt;
        &lt;td&gt;Minor quasi-equal Heptatonic (also Grumpy heptatonic)&lt;br /&gt;
| style="text-align:right;" | 7.71
&lt;/td&gt;
| style="text-align:center;" | Septimal Kleisma
    &lt;/tr&gt;
| style="text-align:center;" | Marvel Comma
    &lt;tr&gt;
| style="text-align:center;" |
        &lt;td&gt;3 2 2 2 2 3 2 2 2&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | 16875/16807
        &lt;td&gt;Rothenberg Generalized Diatonic (also &lt;a class="wiki_link" href="/score9"&gt;score9&lt;/a&gt;)&lt;br /&gt;
| | | 0 3 4 -5 &gt;
&lt;/td&gt;
| style="text-align:right;" | 6.99
    &lt;/tr&gt;
| style="text-align:center;" | Mirkwai
    &lt;tr&gt;
| style="text-align:center;" |
        &lt;td&gt;3 4 1 4 3 3 2&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td&gt;Stearns Major&lt;br /&gt;
| style="text-align:center;" | 6772805/6751042
&lt;/td&gt;
| | | 11 -10 -10 10 &gt;
    &lt;/tr&gt;
| style="text-align:right;" | 5.57
    &lt;tr&gt;
| style="text-align:center;" | Linus
        &lt;td&gt;7 2 7 2 2&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;a class="wiki_link" href="/score5"&gt;score5&lt;/a&gt; &lt;a class="wiki_link" href="/2L%203s"&gt;(classic pentatonic&lt;/a&gt;)&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | 121/120
    &lt;/tr&gt;
| | | -3 -1 -1 0 2 &gt;
    &lt;tr&gt;
| style="text-align:right;" | 14.37
        &lt;td&gt;5 2 2 5 2 2 2&lt;br /&gt;
| style="text-align:center;" | Biyatisma
&lt;/td&gt;
| |
        &lt;td&gt;&lt;a class="wiki_link" href="/score7"&gt;score7&lt;/a&gt; (&lt;a class="wiki_link" href="/2L%205s"&gt;mavila, anti-diatonic&lt;/a&gt;)&lt;br /&gt;
| |
&lt;/td&gt;
|-
    &lt;/tr&gt;
| style="text-align:center;" | 91/90
&lt;/table&gt;
| | | -1 -2 -1 1 0 1 &gt;
| style="text-align:right;" | 19.13
| style="text-align:center;" | Superleap
| |
| |
|-
| style="text-align:center;" | 2401/2400
| | | -5 -1 2 4 &gt;
| style="text-align:right;" | 0.72
| style="text-align:center;" | Breedsma
| |
| |
|-
| style="text-align:center;" | 676/675
| | | 2 -3 -2 0 0 2 &gt;
| style="text-align:right;" | 2.56
| style="text-align:center;" | Parizeksma
| |
| |
|}


&lt;br /&gt;
=='''Books'''==
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Chord Names-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Commas&lt;/h2&gt;
[http://www.ronsword.com/  
20 EDO &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt; &amp;lt; 20 32 46 56 69 74 |.)&lt;br /&gt;


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&lt;table class="wiki_table"&gt;
]]
    &lt;tr&gt;
        &lt;th&gt;Rational&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Monzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Size (Cents)&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 1&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 2&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 3&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;256/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 8 -5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;90.22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Limma"&gt;Limma&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Pythagorean Minor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16875/16384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -14 3 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;51.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Negri Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Double Augmentation Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9931568/9752117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -25 7 6 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;31.57&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ampersand's Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2048/2025&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 11 -4 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;19.55&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Diaschisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;525/512&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -9 1 2 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;43.41&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Avicennma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Avicenna's Enharmonic Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;49/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -4 -1 0 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;35.70&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Slendro Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;50/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 1 0 2 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;34.98&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Tritonic Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Jubilisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;686/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 1 -3 -2 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;27.99&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Senga&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;64/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;27.26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Septimal Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Archytas' Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Leipziger Komma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9859966/9733137&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -10 7 8 -7 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;22.41&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Blackjackisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1029/1024&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -10 1 0 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;8.43&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gamelisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 2 2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;7.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Septimal Kleisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Marvel Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16875/16807&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 0 3 4 -5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;6.99&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Mirkwai&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6772805/6751042&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 11 -10 -10 10 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;5.57&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Linus&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;121/120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 -1 -1 0 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;14.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Biyatisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;91/90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -1 -2 -1 1 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;19.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Superleap&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2401/2400&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 -1 2 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.72&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Breedsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 -3 -2 0 0 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;2.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Parizeksma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron_Sword|Ron Sword]]      [[Category:20edo]]
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[[Category:edo]]
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Revision as of 00:00, 17 July 2018

日本語

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 cents each. It contains smaller edos 2, 4, 5, and 10 and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 & 15 (from 10 edo), 19 & 27 (from 4 edo), 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.

Compositions

Properties

Intervals

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.

Degree Cents Approximate Ratios ups and downs notation Nearest Harmonic
0 0 1/1 unison P1 D 1
1 60 29/28 upminor 2nd ^m2 D^ 33
2 120 14/13, 15/14 mid 2nd ~2 D^^, Evv 69
3 180 10/9 downmajor 2nd vM2 Ev 71
4 240 8/7, 15/13 major 2nd, minor 3rd M2, m3 E, F 37
5 300 13/11, 19/16 upminor 3rd ^m3 F^ 19
6 360 16/13, 5/4 mid 3rd ~3 F^^ 79
7 420 14/11, 51/40 downmajor 3rd vM3 F#v 41
8 480 25/19, 4/3 major 3rd, perfect fourth M3, P4 F#, G 21
9 540 15/11, 11/8 up-fourth ^4 G^ 11
10 600 7/5 double-up fourth, double-down fifth ^^4, vv5 G^^, Avv 91
11 660 22/15, 16/11 down-fifth v5 Av 47
12 720 38/25, 3/2 fifth P5, m6 A 97
13 780 11/7, 25/16 upminor 6th ^m6 A^ 25
14 840 13/8, 8/5 mid 6th ~6 A^^, Bvv 13
15 900 22/13, 32/19 downmajor 6th vM6 Bv 27
16 960 7/4, 26/15 major 6th, minor 7th M6, m7 B, C 7
17 1020 9/5 upminor 7th ^m7 C^ 115
18 1080 15/8, 13/7 mid 7th ~7 C^^, Dvv 15
19 1140 56/29 downmajor 7th vM7 Dv 31
20 1200 2/1 octave P8 D 2

Chord Names

20edo chord names using ups and downs:

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"

0-6-12 = D F^^ A = D.~ = "D mid"

0-7-12 = D F#v A = D.v = "D dot down" or "D downmajor"

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"

0-5-12-16 = D F^ A C = Dm7(^3) = "D minor seven up-three", or D F^ A B = Dm6(^3) = "D minor six up-three"

0-6-12-16 = D F^^ A C = D7(~3) = "D seven mid-three", or D F^ A B = D6(~3) = "D six mid-three"

0-7-12-16 = D F#v A C = D7(v3) = "D seven down-three", or D F#v A B = D6(v3) = "D six down-three"

0-8-12-16 = 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"

0-5-12-17 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six"

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs. Because many intervals have several names, many chords do too.

Modes

20 tone equal modes:

3 1 3 1 3 1 3 1 3 1 Blackwood Major Decatonic (bi-equal decatonic, according to the MOS naming scheme)
1 3 1 3 1 3 1 3 1 3 Blackwood Minor Decatonic (also bi-equal decatonic)
2 3 2 2 2 3 2 2 2 Balzano Nine-tone (fair mavila, score9)
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 fair mavila, 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 (diminished, according to the MOS naming scheme)
3 2 3 2 3 2 3 2 Diminished
4 3 1 4 3 4 1 Twenty-tone "Major"
4 1 3 4 1 4 3 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 Zweifel Natural Minor
3 3 3 3 3 3 2 Major quasi-equal Heptatonic (Grumpy heptatonic)
3 2 3 3 3 3 3 Minor quasi-equal Heptatonic (also Grumpy heptatonic)
3 2 2 2 2 3 2 2 2 Rothenberg Generalized Diatonic (also score9)
3 4 1 4 3 3 2 Stearns Major
7 2 7 2 2 score5 (classic pentatonic)
5 2 2 5 2 2 2 score7 (mavila, anti-diatonic)

Commas

20 EDO tempers out the following commas. (Note: This assumes the val < 20 32 46 56 69 74 |.)

Rational Monzo Size (Cents) Name 1 Name 2 Name 3
256/243 | 8 -5 > 90.22 Limma Pythagorean Minor 2nd
16875/16384 | -14 3 4 > 51.12 Negri Comma Double Augmentation Diesis
9931568/9752117 | -25 7 6 > 31.57 Ampersand's Comma
2048/2025 | 11 -4 -2 > 19.55 Diaschisma
525/512 | -9 1 2 1 > 43.41 Avicennma Avicenna's Enharmonic Diesis
49/48 | -4 -1 0 2 > 35.70 Slendro Diesis
50/49 | 1 0 2 -2 > 34.98 Tritonic Diesis Jubilisma
686/675 | 1 -3 -2 3 > 27.99 Senga
64/63 | 6 -2 0 -1 > 27.26 Septimal Comma Archytas' Comma Leipziger Komma
9859966/9733137 | -10 7 8 -7 > 22.41 Blackjackisma
1029/1024 | -10 1 0 3 > 8.43 Gamelisma
225/224 | -5 2 2 -1 > 7.71 Septimal Kleisma Marvel Comma
16875/16807 | 0 3 4 -5 > 6.99 Mirkwai
6772805/6751042 | 11 -10 -10 10 > 5.57 Linus
121/120 | -3 -1 -1 0 2 > 14.37 Biyatisma
91/90 | -1 -2 -1 1 0 1 > 19.13 Superleap
2401/2400 | -5 -1 2 4 > 0.72 Breedsma
676/675 | 2 -3 -2 0 0 2 > 2.56 Parizeksma

Books

[http://www.ronsword.com/

External image: http://ronsword.com/images/20_tet_Coversm.jpg

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"Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more by Ron Sword

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