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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]]
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Chord Names-Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;strong&gt;Books&lt;/strong&gt;&lt;/h2&gt;
[[Category:books]]
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[[Category:edo]]
&lt;a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank"&gt;&amp;quot;Icosaphonic Scales for Guitar&amp;quot; - Theory / Scale book with above modes and more&lt;/a&gt; by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:listen]]
[[Category:theory]]
[[Category:todo:unify_precision]]
[[Category:twentuning]]
[[Category:IMPORTDEBUG - Image in Link]]
Retrieved from "https://en.xen.wiki/w/20edo"