20edo
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- This revision was by author xenwolf and made on 2018-07-05 10:07:32 UTC.
- The original revision id was 630814365.
- The revision comment was: fixed link to prelude and fugue in 20edo
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<span style="display: block; text-align: right;">[[20平均律|日本語]] </span> 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 & 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. [[toc|flat]] ---- =Compositions= * [[https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo|Underwater Spontaniety]] (lo-fi ambient) by [[https://soundcloud.com/overtoneshock|Stephen Weigel]] * [[@https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo|God's Favorite Tuning]] (xen-pop) by [[https://soundcloud.com/overtoneshock|Stephen Weigel]] * [[https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo?in=overtoneshock/sets/xenharmonic-microtonal|You Lied, and I'm not Mentioning your Name]] (xen-pop) by [[https://soundcloud.com/overtoneshock|Stephen Weigel]] * [[http://www.io.com/%7Ehmiller/midi/20tet.mid|Etude in 20-tone equal tuning]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3|play]] by [[Herman Miller]] * [[http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3|20ET — Prelude & Fugue a3]] by [[Aaron Hunt]] * [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=933696|We Call It Sharing Breath]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wecallitsharingbreathin20tet.mp3|play]] by [[Andrew Heathwaite]] * [[http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/|The Walrus and the Carpenter]] by[[Chris Vaisvil| 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= ==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|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|14/11]], [[51_40|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 [[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== 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 (<span class="wiki_link_new">also bi-equal decatonic)</span> || || 2 3 2 2 2 3 2 2 2 || Balzano Nine-tone (<span class="wiki_link">[[2L 7s|fair mavila]], [[score9]])</span> || || 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 <span class="wiki_link">fair mavila, score9)</span> || || 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]] < 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**== [[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]]
Original HTML content:
<html><head><title>20edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/20%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
</span><br />
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 <a class="wiki_link" href="/cent">cent</a>s each. It contains smaller <a class="wiki_link" href="/edo">edo</a>s <a class="wiki_link" href="/2edo">2</a>, <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/5edo">5</a>, and <a class="wiki_link" href="/10edo">10</a> 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.<br />
<br />
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<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Compositions</h1>
<ul><li><a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo" rel="nofollow">Underwater Spontaniety</a> (lo-fi ambient) by <a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow">Stephen Weigel</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo" rel="nofollow" target="_blank">God's Favorite Tuning</a> (xen-pop) by <a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow">Stephen Weigel</a></li><li><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">You Lied, and I'm not Mentioning your Name</a> (xen-pop) by <a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow">Stephen Weigel</a></li><li><a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/20tet.mid" rel="nofollow">Etude in 20-tone equal tuning</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a></li><li><a class="wiki_link_ext" href="http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3" rel="nofollow">20ET — Prelude & Fugue a3</a> by <a class="wiki_link" href="/Aaron%20Hunt">Aaron Hunt</a></li><li><a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=933696" rel="nofollow">We Call It Sharing Breath</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wecallitsharingbreathin20tet.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/" rel="nofollow">The Walrus and the Carpenter</a> by<a class="wiki_link" href="/Chris%20Vaisvil"> Chris Vaisvil</a> and Bethan Mathis</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/" rel="nofollow">20 edo Electric Guitar Improvisation</a> by<a class="wiki_link" href="/Chris%20Vaisvil"> Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/gobekli-tepe-20-edo-guitar-solo/" rel="nofollow">Göbekli Tepe (20 edo guitar solo)</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/a-paradigm-shift-20-edo/" rel="nofollow">A Paradigm Shift (20 edo)</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=8PCe5u4QsRg" rel="nofollow" target="_blank">Composition for unconventional tempered clavier</a> by <a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank">Pyotr Chernobrivets</a></li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=zQDNqnYqCHg" rel="nofollow" target="_blank">5 compositions for violin and clavier in 20-EDO</a> by <a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank">Pyotr Chernobrivets</a></li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=duJHUo_ACgk" rel="nofollow" target="_blank">Composition for cello and clavier in 20-tone equal temperament</a> by <a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank">Pyotr Chernobrivets</a></li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=u6k4lgCnHqs" rel="nofollow" target="_blank">5 compositions for violin and clavier in 20-tone equal temperament</a> by <a class="wiki_link_ext" href="http://chernobrivets.ru/en/" rel="nofollow" target="_blank">Pyotr Chernobrivets</a></li></ul><br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Properties"></a><!-- ws:end:WikiTextHeadingRule:2 -->Properties</h1>
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Properties-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2>
<br />
Like <a class="wiki_link" href="/15edo">15edo</a>, every note has many names. D is also C# and Eb. The major 3rd is also a perfect 4th and a dim 5th.<br />
<table class="wiki_table">
<tr>
<th>Degree<br />
</th>
<th>Cents<br />
</th>
<th>Approximate Ratios<br />
</th>
<th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a><br />
</th>
<th>Nearest Harmonic<br />
</th>
</tr>
<tr>
<td style="text-align: center;">0<br />
</td>
<td style="text-align: right;">0<br />
</td>
<td style="text-align: center;">1/1<br />
</td>
<td style="text-align: center;">unison<br />
</td>
<td style="text-align: center;">P1<br />
</td>
<td style="text-align: center;">D<br />
</td>
<td style="text-align: center;">1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">1<br />
</td>
<td style="text-align: right;">60<br />
</td>
<td style="text-align: center;">29/28<br />
</td>
<td style="text-align: center;">upminor 2nd<br />
</td>
<td style="text-align: center;">^m2<br />
</td>
<td style="text-align: center;">D^<br />
</td>
<td style="text-align: center;">33<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2<br />
</td>
<td style="text-align: right;">120<br />
</td>
<td style="text-align: center;">14/13, 15/14<br />
</td>
<td style="text-align: center;">mid 2nd<br />
</td>
<td style="text-align: center;">~2<br />
</td>
<td style="text-align: center;">D^^, Evv<br />
</td>
<td style="text-align: center;">69<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3<br />
</td>
<td style="text-align: right;">180<br />
</td>
<td style="text-align: center;">10/9<br />
</td>
<td style="text-align: center;">downmajor 2nd<br />
</td>
<td style="text-align: center;">vM2<br />
</td>
<td style="text-align: center;">Ev<br />
</td>
<td style="text-align: center;">71<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4<br />
</td>
<td style="text-align: right;">240<br />
</td>
<td style="text-align: center;">8/7, 15/13<br />
</td>
<td style="text-align: center;">major 2nd, minor 3rd<br />
</td>
<td style="text-align: center;">M2, m3<br />
</td>
<td style="text-align: center;">E, F<br />
</td>
<td style="text-align: center;">37<br />
</td>
</tr>
<tr>
<td style="text-align: center;">5<br />
</td>
<td style="text-align: right;">300<br />
</td>
<td style="text-align: center;">13/11, 19/16<br />
</td>
<td style="text-align: center;">upminor 3rd<br />
</td>
<td style="text-align: center;">^m3<br />
</td>
<td style="text-align: center;">F^<br />
</td>
<td style="text-align: center;">19<br />
</td>
</tr>
<tr>
<td style="text-align: center;">6<br />
</td>
<td style="text-align: right;">360<br />
</td>
<td style="text-align: center;">16/13, 5/4<br />
</td>
<td style="text-align: center;">mid 3rd<br />
</td>
<td style="text-align: center;">~3<br />
</td>
<td style="text-align: center;">F^^<br />
</td>
<td style="text-align: center;">79<br />
</td>
</tr>
<tr>
<td style="text-align: center;">7<br />
</td>
<td style="text-align: right;">420<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/51_40">51/40</a><br />
</td>
<td style="text-align: center;">downmajor 3rd<br />
</td>
<td style="text-align: center;">vM3<br />
</td>
<td style="text-align: center;">F#v<br />
</td>
<td style="text-align: center;">41<br />
</td>
</tr>
<tr>
<td style="text-align: center;">8<br />
</td>
<td style="text-align: right;">480<br />
</td>
<td style="text-align: center;">25/19, 4/3<br />
</td>
<td style="text-align: center;">major 3rd, perfect fourth<br />
</td>
<td style="text-align: center;">M3, P4<br />
</td>
<td style="text-align: center;">F#, G<br />
</td>
<td style="text-align: center;">21<br />
</td>
</tr>
<tr>
<td style="text-align: center;">9<br />
</td>
<td style="text-align: right;">540<br />
</td>
<td style="text-align: center;">15/11, 11/8<br />
</td>
<td style="text-align: center;">up-fourth<br />
</td>
<td style="text-align: center;">^4<br />
</td>
<td style="text-align: center;">G^<br />
</td>
<td style="text-align: center;">11<br />
</td>
</tr>
<tr>
<td style="text-align: center;">10<br />
</td>
<td style="text-align: right;">600<br />
</td>
<td style="text-align: center;">7/5<br />
</td>
<td style="text-align: center;">double-up fourth, double-down fifth<br />
</td>
<td style="text-align: center;">^^4, vv5<br />
</td>
<td style="text-align: center;">G^^, Avv<br />
</td>
<td style="text-align: center;">91<br />
</td>
</tr>
<tr>
<td style="text-align: center;">11<br />
</td>
<td style="text-align: right;">660<br />
</td>
<td style="text-align: center;">22/15, 16/11<br />
</td>
<td style="text-align: center;">down-fifth<br />
</td>
<td style="text-align: center;">v5<br />
</td>
<td style="text-align: center;">Av<br />
</td>
<td style="text-align: center;">47<br />
</td>
</tr>
<tr>
<td style="text-align: center;">12<br />
</td>
<td style="text-align: right;">720<br />
</td>
<td style="text-align: center;">38/25, 3/2<br />
</td>
<td style="text-align: center;">fifth<br />
</td>
<td style="text-align: center;">P5, m6<br />
</td>
<td style="text-align: center;">A<br />
</td>
<td style="text-align: center;">97<br />
</td>
</tr>
<tr>
<td style="text-align: center;">13<br />
</td>
<td style="text-align: right;">780<br />
</td>
<td style="text-align: center;">11/7, 25/16<br />
</td>
<td style="text-align: center;">upminor 6th<br />
</td>
<td style="text-align: center;">^m6<br />
</td>
<td style="text-align: center;">A^<br />
</td>
<td style="text-align: center;">25<br />
</td>
</tr>
<tr>
<td style="text-align: center;">14<br />
</td>
<td style="text-align: right;">840<br />
</td>
<td style="text-align: center;">13/8, 8/5<br />
</td>
<td style="text-align: center;">mid 6th<br />
</td>
<td style="text-align: center;">~6<br />
</td>
<td style="text-align: center;">A^^, Bvv<br />
</td>
<td style="text-align: center;">13<br />
</td>
</tr>
<tr>
<td style="text-align: center;">15<br />
</td>
<td style="text-align: right;">900<br />
</td>
<td style="text-align: center;">22/13, 32/19<br />
</td>
<td style="text-align: center;">downmajor 6th<br />
</td>
<td style="text-align: center;">vM6<br />
</td>
<td style="text-align: center;">Bv<br />
</td>
<td style="text-align: center;">27<br />
</td>
</tr>
<tr>
<td style="text-align: center;">16<br />
</td>
<td style="text-align: right;">960<br />
</td>
<td style="text-align: center;">7/4, 26/15<br />
</td>
<td style="text-align: center;">major 6th, minor 7th<br />
</td>
<td style="text-align: center;">M6, m7<br />
</td>
<td style="text-align: center;">B, C<br />
</td>
<td style="text-align: center;">7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">17<br />
</td>
<td style="text-align: right;">1020<br />
</td>
<td style="text-align: center;">9/5<br />
</td>
<td style="text-align: center;">upminor 7th<br />
</td>
<td style="text-align: center;">^m7<br />
</td>
<td style="text-align: center;">C^<br />
</td>
<td style="text-align: center;">115<br />
</td>
</tr>
<tr>
<td style="text-align: center;">18<br />
</td>
<td style="text-align: right;">1080<br />
</td>
<td style="text-align: center;">15/8, 13/7<br />
</td>
<td style="text-align: center;">mid 7th<br />
</td>
<td style="text-align: center;">~7<br />
</td>
<td style="text-align: center;">C^^, Dvv<br />
</td>
<td style="text-align: center;">15<br />
</td>
</tr>
<tr>
<td style="text-align: center;">19<br />
</td>
<td style="text-align: right;">1140<br />
</td>
<td style="text-align: center;">56/29<br />
</td>
<td style="text-align: center;">downmajor 7th<br />
</td>
<td style="text-align: center;">vM7<br />
</td>
<td style="text-align: center;">Dv<br />
</td>
<td style="text-align: center;">31<br />
</td>
</tr>
<tr>
<td style="text-align: center;">20<br />
</td>
<td style="text-align: right;">1200<br />
</td>
<td style="text-align: center;">2/1<br />
</td>
<td style="text-align: center;">octave<br />
</td>
<td style="text-align: center;">P8<br />
</td>
<td style="text-align: center;">D<br />
</td>
<td style="text-align: center;">2<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Chord Names"></a><!-- ws:end:WikiTextHeadingRule:6 -->Chord Names</h1>
20edo chord names using ups and downs:<br />
0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"<br />
0-5-12 = D F^ A = D.^m = "D upminor"<br />
0-6-12 = D F^^ A = D.~ = "D mid"<br />
0-7-12 = D F#v A = D.v = "D dot down" or "D downmajor"<br />
0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"<br />
0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"<br />
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"<br />
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"<br />
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"<br />
0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"<br />
0-7-12-19 = D F#v A C#v = D.vM7 = "D downmajor seven"<br />
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"<br />
For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>. Because many intervals have several names, many chords do too.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Chord Names-Modes"></a><!-- ws:end:WikiTextHeadingRule:8 -->Modes</h2>
20 tone equal modes:<br />
<table class="wiki_table">
<tr>
<td>3 1 3 1 3 1 3 1 3 1<br />
</td>
<td>Blackwood Major Decatonic <a class="wiki_link" href="/5L%205s">(bi-equal decatonic</a>, according to the <a class="wiki_link" href="/MOSNamingScheme">MOS naming scheme</a>)<br />
</td>
</tr>
<tr>
<td>1 3 1 3 1 3 1 3 1 3<br />
</td>
<td>Blackwood Minor Decatonic (<span class="wiki_link_new">also bi-equal decatonic)</span><br />
</td>
</tr>
<tr>
<td>2 3 2 2 2 3 2 2 2<br />
</td>
<td>Balzano Nine-tone (<span class="wiki_link"><a class="wiki_link" href="/2L%207s">fair mavila</a>, <a class="wiki_link" href="/score9">score9</a>)</span><br />
</td>
</tr>
<tr>
<td>2 2 2 2 1 2 2 2 2 2 1<br />
</td>
<td>Balzano Eleven-tone, Agmon Diatonic DS4, <a class="wiki_link" href="/score11">score11</a><br />
</td>
</tr>
<tr>
<td>2 2 2 3 2 2 2 3 2<br />
</td>
<td>Balzano Nine-tone inverse (also <span class="wiki_link">fair mavila, score9)</span><br />
</td>
</tr>
<tr>
<td>1 2 2 2 2 2 1 2 2 2 2<br />
</td>
<td>Balzano Eleven-tone inverse (also score11)<br />
</td>
</tr>
<tr>
<td>2 3 2 3 2 3 2 3<br />
</td>
<td>Octatonic (<a class="wiki_link" href="/4L%204s">diminished</a>, according to the <a class="wiki_link" href="/MOSNamingScheme">MOS naming scheme</a>)<br />
</td>
</tr>
<tr>
<td>3 2 3 2 3 2 3 2<br />
</td>
<td>Diminished<br />
</td>
</tr>
<tr>
<td>4 3 1 4 3 4 1<br />
</td>
<td>Twenty-tone "Major"<br />
</td>
</tr>
<tr>
<td>4 1 3 4 1 4 3<br />
</td>
<td>Twenty-tone "Minor"<br />
</td>
</tr>
<tr>
<td>2 2 1 2 1 2 2 1 2 2 2 1<br />
</td>
<td>Twelve-tone Chromatic<br />
</td>
</tr>
<tr>
<td>2 2 2 2 1 2 2 2 2 1 2<br />
</td>
<td>Zweifel Major<br />
</td>
</tr>
<tr>
<td>2 1 2 2 2 2 2 1 2 2 2<br />
</td>
<td>Zweifel Natural Minor<br />
</td>
</tr>
<tr>
<td>3 3 3 3 3 3 2<br />
</td>
<td>Major quasi-equal Heptatonic (<a class="wiki_link" href="/6L%201s">Grumpy heptatonic</a>)<br />
</td>
</tr>
<tr>
<td>3 2 3 3 3 3 3<br />
</td>
<td>Minor quasi-equal Heptatonic (also Grumpy heptatonic)<br />
</td>
</tr>
<tr>
<td>3 2 2 2 2 3 2 2 2<br />
</td>
<td>Rothenberg Generalized Diatonic (also <a class="wiki_link" href="/score9">score9</a>)<br />
</td>
</tr>
<tr>
<td>3 4 1 4 3 3 2<br />
</td>
<td>Stearns Major<br />
</td>
</tr>
<tr>
<td>7 2 7 2 2<br />
</td>
<td><a class="wiki_link" href="/score5">score5</a> <a class="wiki_link" href="/2L%203s">(classic pentatonic</a>)<br />
</td>
</tr>
<tr>
<td>5 2 2 5 2 2 2<br />
</td>
<td><a class="wiki_link" href="/score7">score7</a> (<a class="wiki_link" href="/2L%205s">mavila, anti-diatonic</a>)<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Chord Names-Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h2>
20 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> < 20 32 46 56 69 74 |.)<br />
<table class="wiki_table">
<tr>
<th>Rational<br />
</th>
<th>Monzo<br />
</th>
<th>Size (Cents)<br />
</th>
<th>Name 1<br />
</th>
<th>Name 2<br />
</th>
<th>Name 3<br />
</th>
</tr>
<tr>
<td style="text-align: center;">256/243<br />
</td>
<td>| 8 -5 ><br />
</td>
<td style="text-align: right;">90.22<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/Limma">Limma</a><br />
</td>
<td style="text-align: center;">Pythagorean Minor 2nd<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">16875/16384<br />
</td>
<td>| -14 3 4 ><br />
</td>
<td style="text-align: right;">51.12<br />
</td>
<td style="text-align: center;">Negri Comma<br />
</td>
<td style="text-align: center;">Double Augmentation Diesis<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">9931568/9752117<br />
</td>
<td>| -25 7 6 ><br />
</td>
<td style="text-align: right;">31.57<br />
</td>
<td style="text-align: center;">Ampersand's Comma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">2048/2025<br />
</td>
<td>| 11 -4 -2 ><br />
</td>
<td style="text-align: right;">19.55<br />
</td>
<td style="text-align: center;">Diaschisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">525/512<br />
</td>
<td>| -9 1 2 1 ><br />
</td>
<td style="text-align: right;">43.41<br />
</td>
<td style="text-align: center;">Avicennma<br />
</td>
<td style="text-align: center;">Avicenna's Enharmonic Diesis<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">49/48<br />
</td>
<td>| -4 -1 0 2 ><br />
</td>
<td style="text-align: right;">35.70<br />
</td>
<td style="text-align: center;">Slendro Diesis<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">50/49<br />
</td>
<td>| 1 0 2 -2 ><br />
</td>
<td style="text-align: right;">34.98<br />
</td>
<td style="text-align: center;">Tritonic Diesis<br />
</td>
<td style="text-align: center;">Jubilisma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">686/675<br />
</td>
<td>| 1 -3 -2 3 ><br />
</td>
<td style="text-align: right;">27.99<br />
</td>
<td style="text-align: center;">Senga<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">64/63<br />
</td>
<td>| 6 -2 0 -1 ><br />
</td>
<td style="text-align: right;">27.26<br />
</td>
<td style="text-align: center;">Septimal Comma<br />
</td>
<td style="text-align: center;">Archytas' Comma<br />
</td>
<td style="text-align: center;">Leipziger Komma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">9859966/9733137<br />
</td>
<td>| -10 7 8 -7 ><br />
</td>
<td style="text-align: right;">22.41<br />
</td>
<td style="text-align: center;">Blackjackisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">1029/1024<br />
</td>
<td>| -10 1 0 3 ><br />
</td>
<td style="text-align: right;">8.43<br />
</td>
<td style="text-align: center;">Gamelisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">225/224<br />
</td>
<td>| -5 2 2 -1 ><br />
</td>
<td style="text-align: right;">7.71<br />
</td>
<td style="text-align: center;">Septimal Kleisma<br />
</td>
<td style="text-align: center;">Marvel Comma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">16875/16807<br />
</td>
<td>| 0 3 4 -5 ><br />
</td>
<td style="text-align: right;">6.99<br />
</td>
<td style="text-align: center;">Mirkwai<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">6772805/6751042<br />
</td>
<td>| 11 -10 -10 10 ><br />
</td>
<td style="text-align: right;">5.57<br />
</td>
<td style="text-align: center;">Linus<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">121/120<br />
</td>
<td>| -3 -1 -1 0 2 ><br />
</td>
<td style="text-align: right;">14.37<br />
</td>
<td style="text-align: center;">Biyatisma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">91/90<br />
</td>
<td>| -1 -2 -1 1 0 1 ><br />
</td>
<td style="text-align: right;">19.13<br />
</td>
<td style="text-align: center;">Superleap<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">2401/2400<br />
</td>
<td>| -5 -1 2 4 ><br />
</td>
<td style="text-align: right;">0.72<br />
</td>
<td style="text-align: center;">Breedsma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">676/675<br />
</td>
<td>| 2 -3 -2 0 0 2 ><br />
</td>
<td style="text-align: right;">2.56<br />
</td>
<td style="text-align: center;">Parizeksma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Chord Names-Books"></a><!-- ws:end:WikiTextHeadingRule:12 --><strong>Books</strong></h2>
<!-- ws:start:WikiTextRemoteImageRule:789:<a href="http://www.ronsword.com/" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="" title="" style="height: 114px; width: 82px;" /></a> --><a href="http://www.ronsword.com/" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /></a><!-- ws:end:WikiTextRemoteImageRule:789 --><br />
<a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank">"Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></body></html>