20edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 10:41:06 UTC</tt>.

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:31:21 UTC</tt>.

: The original revision id was <tt>~~602893180~~</tt>.

: The original revision id was <tt>602901152</tt>.

: The revision comment was: <tt>~~tel link removed~~</tt>

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<h4>Original Wikitext content:</h4>

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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**

||~ Degree ||~ Cents ||~ Approximate Ratios ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||~ Nearest Harmonic ||

**Ratios** ||||||= [[Ups and Downs Notation|ups and downs notation]] ||= **Nearest**

||= 0 ||> 0 ||= 1/1 ||= unison ||= P1 ||= D ||= 1 ||

**Harmonic** ||

||= 1 ||> 60 ||= 29/28 ||= upminor 2nd ||= ^m2 ||= D^ ||= 33 ||

||= 0 ||= 0 ||= 1/1 ||= unison ||= P1 ||= D ||= 1 ||

||= 2 ||> 120 ||= 14/13, 15/14 ||= mid 2nd ||= ~2 ||= D^^ / Evv ||= 69 ||

||= 1 ||= 60 ||= 29/28 ||= upminor 2nd ||= ^m2 ||= D^ ||= 33 ||

||= 3 ||> 180 ||= 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||= 71 ||

||= 2 ||= 120 ||= 14/13, 15/14 ||= mid 2nd ||= ~2 ||= D^^ / Evv ||= 69 ||

||= 4 ||> 240 ||= 8/7, 15/13 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= 37 ||

||= 3 ||= 180 ||= 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||= 71 ||

||= 5 ||> 300 ||= 13/11, 19/16 ||= upminor 3rd ||= ^m3 ||= F^ ||= 19 ||

||= 4 ||= 240 ||= 8/7, 15/13 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= 37 ||

||= 6 ||> 360 ||= 16/13, 5/4 ||= mid 3rd ||= ~3 ||= F^^ ||= 79 ||

||= 5 ||= 300 ||= 13/11, 19/16 ||= upminor 3rd ||= ^m3 ||= F^ ||= 19 ||

||= 7 ||> 420 ||= [[14_11|14/11]], [[51_40|51/40]] ||= downmajor 3rd ||= vM3 ||= F#v ||= 41 ||

||= 6 ||= 360 ||= 16/13, 5/4 ||= mid 3rd ||= ~3 ||= F^^ ||= 79 ||

||= 8 ||> 480 ||= 25/19, 4/3 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= 21 ||

||= 7 ||= 420 ||= [[~~xenharmonic/~~14_11|14/11]], [[~~xenharmonic/~~51_40|51/40]] ||= downmajor 3rd ||= vM3 ||= F#v ||= 41 ||

||= 9 ||> 540 ||= 15/11, 11/8 ||= up-fourth ||= ^4 ||= G^ ||= 11 ||

||= 8 ||= 480 ||= 25/19, 4/3 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= 21 ||

||= 10 ||> 600 ||= 7/5 ||= double-up fourth, double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= 91 ||

||= 9 ||= 540 ||= 15/11, 11/8 ||= up-fourth ||= ^4 ||= G^ ||= 11 ||

||= 11 ||> 660 ||= 22/15, 16/11 ||= down-fifth ||= v5 ||= Av ||= 47 ||

||= 10 ||= 600 ||= 7/5 ||= double-up fourth,

||= 12 ||> 720 ||= 38/25, 3/2 ||= fifth ||= P5, m6 ||= A ||= 97 ||

double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= 91 ||

||= 13 ||> 780 ||= 11/7, 25/16 ||= upminor 6th ||= ^m6 ||= A^ ||= 25 ||

||= 11 ||= 660 ||= 22/15, 16/11 ||= down-fifth ||= v5 ||= Av ||= 47 ||

||= 14 ||> 840 ||= 13/8, 8/5 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= 13 ||

||= 12 ||= 720 ||= 38/25, 3/2 ||= fifth ||= P5, m6 ||= A ||= 97 ||

||= 15 ||> 900 ||= 22/13, 32/19 ||= downmajor 6th ||= vM6 ||= Bv ||= 27 ||

||= 13 ||= 780 ||= 11/7, 25/16 ||= upminor 6th ||= ^m6 ||= A^ ||= 25 ||

||= 16 ||> 960 ||= 7/4, 26/15 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= 7 ||

||= 14 ||= 840 ||= 13/8, 8/5 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= 13 ||

||= 17 ||> 1020 ||= 9/5 ||= upminor 7th ||= ^m7 ||= C^ ||= 115 ||

||= 15 ||= 900 ||= 22/13, 32/19 ||= downmajor 6th ||= vM6 ||= Bv ||= 27 ||

||= 18 ||> 1080 ||= 15/8, 13/7 ||= mid 7th ||= ~7 ||= C^^, Dvv ||= 15 ||

||= 16 ||= 960 ||= 7/4, 26/15 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= 7 ||

||= 19 ||> 1140 ||= 56/29 ||= downmajor 7th ||= vM7 ||= Dv ||= 31 ||

||= 17 ||= 1020 ||= 9/5 ||= upminor 7th ||= ^m7 ||= C^ ||= 115 ||

||= 20 ||> 1200 ||= 2/1 ||= octave ||= P8 ||= D ||= 2 ||

||= 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:

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==Commas==

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

||~ ~~Comma~~ ||~ Monzo ||~ ~~Value~~ (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

||~ Rational ||~ Monzo ||~ Size (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

||= 256/243 ||~~<~~ | 8 -5 > ||> 90.22 ||= [[Limma]] ||= Pythagorean Minor 2nd ||= ||

||= 256/243 || | 8 -5 > ||> 90.22 ||= [[Limma]] ||= Pythagorean Minor 2nd ||= ||

||= 16875/16384 ||~~<~~ | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || ||

||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || ||

||= ||~~<~~ | -25 7 6 > ||> 31.57 ||= Ampersand's Comma ||= ||= ||

||= 9931568/9752117 || | -25 7 6 > ||> 31.57 ||= Ampersand's Comma ||= ||= ||

||= 2048/2025 ||~~<~~ | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= ||= ||

||= 2048/2025 || | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= ||= ||

||= 525/512 ||~~<~~ | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || ||

||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || ||

||= 49/48 ||~~<~~ | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= ||= ||

||= 49/48 || | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= ||= ||

||= 50/49 ||~~<~~ | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||= ||

||= 50/49 || | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||= ||

||= 686/675 ||~~<~~ | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= ||

||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= ||

||= 64/63 ||~~<~~ | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||

||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||

||= ||~~<~~ | -10 7 8 -7 > ||> 22.41 ||= Blackjackisma ||= ||= ||

||= 9859966/9733137 || | -10 7 8 -7 > ||> 22.41 ||= Blackjackisma ||= ||= ||

||= 1029/1024 ||~~<~~ | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= ||= ||

||= 1029/1024 || | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= ||= ||

||= 225/224 ||~~<~~ | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma ||= ||

||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma ||= ||

||= 16875/16807 ||~~<~~ | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= ||= ||

||= 16875/16807 || | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= ||= ||

|| || | 11 -10 -10 10/1 > ||> 5.57 ||= Linus || || ||

||= 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 || || ||

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<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"><html><head><title>20edo</title></head><body>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 &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.

<a href="#Compositions">Compositions</a> | <a href="#Properties">Properties</a> | <a href="#toc4"> </a> | <a href="#Chord Names">Chord Names</a>

<a href="#Compositions">Compositions</a> | <a href="#Properties">Properties</a> | <a href="#Chord Names">Chord Names</a>

<hr />

<hr />

<h1 id="toc0"><a name="Compositions"></a>Compositions</h1>

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<tr>

<~~td style="text-align: center;"><strong~~>Degree~~~~

<th>Degree

</td>

</th>

<~~td style="text-align: center;"><strong~~>Cents~~~~

<th>Cents

</td>

</th>

<~~td style="text-align: center;"><strong~~>Approximate~~ ~~

<th>Approximate Ratios

~~~~Ratios~~~~

</th>

</td>

<th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a>

<td colspan="3~~" style="text-align: center;~~"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a>

</th>

</td>

<th>Nearest Harmonic

<~~td style="text-align: center;"><strong~~>Nearest~~ ~~

</th>

~~~~Harmonic~~~~

</td>

</tr>

<tr>

<td style="text-align: center;">0

</td>

<td style="text-align: ~~center~~;">0

<td style="text-align: right;">0

</td>

<td style="text-align: center;">1/1

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<td style="text-align: center;">1

</td>

<td style="text-align: ~~center~~;">60

<td style="text-align: right;">60

</td>

<td style="text-align: center;">29/28

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<td style="text-align: center;">2

</td>

<td style="text-align: ~~center~~;">120

<td style="text-align: right;">120

</td>

<td style="text-align: center;">14/13, 15/14

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<td style="text-align: center;">3

</td>

<td style="text-align: ~~center~~;">180

<td style="text-align: right;">180

</td>

<td style="text-align: center;">10/9

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<td style="text-align: center;">4

</td>

<td style="text-align: ~~center~~;">240

<td style="text-align: right;">240

</td>

<td style="text-align: center;">8/7, 15/13

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<td style="text-align: center;">5

</td>

<td style="text-align: ~~center~~;">300

<td style="text-align: right;">300

</td>

<td style="text-align: center;">13/11, 19/16

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<td style="text-align: center;">6

</td>

<td style="text-align: ~~center~~;">360

<td style="text-align: right;">360

</td>

<td style="text-align: center;">16/13, 5/4

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<td style="text-align: center;">7

</td>

<td style="text-align: ~~center~~;">420

<td style="text-align: right;">420

</td>

</td>

<td style="text-align: center;">downmajor 3rd

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<td style="text-align: center;">8

</td>

<td style="text-align: ~~center~~;">480

<td style="text-align: right;">480

</td>

<td style="text-align: center;">25/19, 4/3

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<td style="text-align: center;">9

</td>

<td style="text-align: ~~center~~;">540

<td style="text-align: right;">540

</td>

<td style="text-align: center;">15/11, 11/8

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<td style="text-align: center;">10

</td>

<td style="text-align: ~~center~~;">600

<td style="text-align: right;">600

</td>

<td style="text-align: center;">7/5

</td>

<td style="text-align: center;">double-up fourth,~~ ~~

<td style="text-align: center;">double-up fourth, double-down fifth

double-down fifth

</td>

<td style="text-align: center;">^^4, vv5

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<td style="text-align: center;">11

</td>

<td style="text-align: ~~center~~;">660

<td style="text-align: right;">660

</td>

<td style="text-align: center;">22/15, 16/11

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<td style="text-align: center;">12

</td>

<td style="text-align: ~~center~~;">720

<td style="text-align: right;">720

</td>

<td style="text-align: center;">38/25, 3/2

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<td style="text-align: center;">13

</td>

<td style="text-align: ~~center~~;">780

<td style="text-align: right;">780

</td>

<td style="text-align: center;">11/7, 25/16

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<td style="text-align: center;">14

</td>

<td style="text-align: ~~center~~;">840

<td style="text-align: right;">840

</td>

<td style="text-align: center;">13/8, 8/5

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<td style="text-align: center;">15

</td>

<td style="text-align: ~~center~~;">900

<td style="text-align: right;">900

</td>

<td style="text-align: center;">22/13, 32/19

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<td style="text-align: center;">16

</td>

<td style="text-align: ~~center~~;">960

<td style="text-align: right;">960

</td>

<td style="text-align: center;">7/4, 26/15

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<td style="text-align: center;">17

</td>

<td style="text-align: ~~center~~;">1020

<td style="text-align: right;">1020

</td>

<td style="text-align: center;">9/5

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<td style="text-align: center;">18

</td>

<td style="text-align: ~~center~~;">1080

<td style="text-align: right;">1080

</td>

<td style="text-align: center;">15/8, 13/7

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<td style="text-align: center;">19

</td>

<td style="text-align: ~~center~~;">1140

<td style="text-align: right;">1140

</td>

<td style="text-align: center;">56/29

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<td style="text-align: center;">20

</td>

<td style="text-align: ~~center~~;">1200

<td style="text-align: right;">1200

</td>

<td style="text-align: center;">2/1

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</table>

<~~!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"> <~~/h1>

<h1 id="~~toc5~~"><a name="Chord Names"></a>Chord Names</h1>

<h1 id="toc4"><a name="Chord Names"></a>Chord Names</h1>

20edo chord names using ups and downs:

0-4-12 = D E A = Dsus2 = &quot;D sus 2&quot;, or D F A = Dm = &quot;D minor&quot;

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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.

<h2 id="~~toc6~~"><a name="Chord Names-Modes"></a>Modes</h2>

<h2 id="toc5"><a name="Chord Names-Modes"></a>Modes</h2>

20 tone equal modes:

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<h2 id="~~toc7~~"><a name="Chord Names-Commas"></a>Commas</h2>

<h2 id="toc6"><a name="Chord Names-Commas"></a>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> &lt; 20 32 46 56 69 74 |.)

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<tr>

<th>~~Comma~~

<th>Rational

</th>

<th>Monzo

</th>

<th>~~Value~~ (Cents)

<th>Size (Cents)

</th>

<th>Name 1

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<td style="text-align: center;">256/243

</td>

<td ~~style="text-align: left;"~~>| 8 -5 &gt;

<td>| 8 -5 &gt;

</td>

<td style="text-align: right;">90.22

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<td style="text-align: center;">16875/16384

</td>

<td ~~style="text-align: left;"~~>| -14 3 4 &gt;

<td>| -14 3 4 &gt;

</td>

<td style="text-align: right;">51.12

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</tr>

<tr>

<td style="text-align: center;">9931568/9752117

</td>

<td ~~style="text-align: left;"~~>| -25 7 6 &gt;

<td>| -25 7 6 &gt;

</td>

<td style="text-align: right;">31.57

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<td style="text-align: center;">2048/2025

</td>

<td ~~style="text-align: left;"~~>| 11 -4 -2 &gt;

<td>| 11 -4 -2 &gt;

</td>

<td style="text-align: right;">19.55

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<td style="text-align: center;">525/512

</td>

<td ~~style="text-align: left;"~~>| -9 1 2 1 &gt;

<td>| -9 1 2 1 &gt;

</td>

<td style="text-align: right;">43.41

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<td style="text-align: center;">49/48

</td>

<td ~~style="text-align: left;"~~>| -4 -1 0 2 &gt;

<td>| -4 -1 0 2 &gt;

</td>

<td style="text-align: right;">35.70

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<td style="text-align: center;">50/49

</td>

<td ~~style="text-align: left;"~~>| 1 0 2 -2 &gt;

<td>| 1 0 2 -2 &gt;

</td>

<td style="text-align: right;">34.98

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<td style="text-align: center;">686/675

</td>

<td ~~style="text-align: left;"~~>| 1 -3 -2 3 &gt;

<td>| 1 -3 -2 3 &gt;

</td>

<td style="text-align: right;">27.99

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<td style="text-align: center;">64/63

</td>

<td ~~style="text-align: left;"~~>| 6 -2 0 -1 &gt;

<td>| 6 -2 0 -1 &gt;

</td>

<td style="text-align: right;">27.26

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</tr>

<tr>

<td style="text-align: center;">9859966/9733137

</td>

<td ~~style="text-align: left;"~~>| -10 7 8 -7 &gt;

<td>| -10 7 8 -7 &gt;

</td>

<td style="text-align: right;">22.41

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<td style="text-align: center;">1029/1024

</td>

<td ~~style="text-align: left;"~~>| -10 1 0 3 &gt;

<td>| -10 1 0 3 &gt;

</td>

<td style="text-align: right;">8.43

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<td style="text-align: center;">225/224

</td>

<td ~~style="text-align: left;"~~>| -5 2 2 -1 &gt;

<td>| -5 2 2 -1 &gt;

</td>

<td style="text-align: right;">7.71

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<td style="text-align: center;">16875/16807

</td>

<td ~~style="text-align: left;"~~>| 0 3 4 -5 &gt;

<td>| 0 3 4 -5 &gt;

</td>

<td style="text-align: right;">6.99

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</tr>

<tr>

<td>

<td style="text-align: center;">6772805/6751042

</td>

<td>| 11 -10 -10 10/1 &gt;

<td>| 11 -10 -10 10 &gt;

</td>

<td style="text-align: right;">5.57

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<h2 id="~~toc8~~"><a name="Chord Names-Books"></a>Books</h2>

<h2 id="toc7"><a name="Chord Names-Books"></a>Books</h2>

<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>

<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>

<a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank">&quot;Icosaphonic Scales for Guitar&quot; - Theory / Scale book with above modes and more</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2016-12-29 10:41:06 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:31:21 UTC</tt>.<br>
-: The original revision id was <tt>602893180</tt>.<br>
+: The original revision id was <tt>602901152</tt>.<br>
-: The revision comment was: <tt>tel link removed</tt><br>
+: The revision comment was: <tt></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>
@@ Line 26: / Line 26: @@
 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**
+||~ Degree ||~ Cents ||~ Approximate Ratios ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||~ Nearest Harmonic ||
-**Ratios** ||||||= [[Ups and Downs Notation|ups and downs notation]] ||= **Nearest**
+||=  0 ||&gt;    0 ||= 1/1 ||= unison ||= P1 ||= D ||= 1 ||
-**Harmonic** ||
+||=  1 ||&gt;   60 ||= 29/28 ||= upminor 2nd ||= ^m2 ||= D^ ||= 33 ||
-||= 0 ||= 0 ||= 1/1 ||= unison ||= P1 ||= D ||= 1 ||
+||=  2 ||&gt;  120 ||= 14/13, 15/14 ||= mid 2nd ||= ~2 ||= D^^ / Evv ||= 69 ||
-||= 1 ||= 60 ||= 29/28 ||= upminor 2nd ||= ^m2 ||= D^ ||= 33 ||
+||=  3 ||&gt;  180 ||= 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||= 71 ||
-||= 2 ||= 120 ||= 14/13, 15/14 ||= mid 2nd ||= ~2 ||= D^^ / Evv ||= 69 ||
+||=  4 ||&gt;  240 ||= 8/7, 15/13 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= 37 ||
-||= 3 ||= 180 ||= 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||= 71 ||
+||=  5 ||&gt;  300 ||= 13/11, 19/16 ||= upminor 3rd ||= ^m3 ||= F^ ||= 19 ||
-||= 4 ||= 240 ||= 8/7, 15/13 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= 37 ||
+||=  6 ||&gt;  360 ||= 16/13, 5/4 ||= mid 3rd ||= ~3 ||= F^^ ||= 79 ||
-||= 5 ||= 300 ||= 13/11, 19/16 ||= upminor 3rd ||= ^m3 ||= F^ ||= 19 ||
+||=  7 ||&gt;  420 ||= [[14_11|14/11]], [[51_40|51/40]] ||= downmajor 3rd ||= vM3 ||= F#v ||= 41 ||
-||= 6 ||= 360 ||= 16/13, 5/4 ||= mid 3rd ||= ~3 ||= F^^ ||= 79 ||
+||=  8 ||&gt;  480 ||= 25/19, 4/3 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= 21 ||
-||= 7 ||= 420 ||= [[xenharmonic/14_11|14/11]], [[xenharmonic/51_40|51/40]] ||= downmajor 3rd ||= vM3 ||= F#v ||= 41 ||
+||=  9 ||&gt;  540 ||= 15/11, 11/8 ||= up-fourth ||= ^4 ||= G^ ||= 11 ||
-||= 8 ||= 480 ||= 25/19, 4/3 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= 21 ||
+||= 10 ||&gt;  600 ||= 7/5 ||= double-up fourth, double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= 91 ||
-||= 9 ||= 540 ||= 15/11, 11/8 ||= up-fourth ||= ^4 ||= G^ ||= 11 ||
+||= 11 ||&gt;  660 ||= 22/15, 16/11 ||= down-fifth ||= v5 ||= Av ||= 47 ||
-||= 10 ||= 600 ||= 7/5 ||= double-up fourth,
+||= 12 ||&gt;  720 ||= 38/25, 3/2 ||= fifth ||= P5, m6 ||= A ||= 97 ||
-double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= 91 ||
+||= 13 ||&gt;  780 ||= 11/7, 25/16 ||= upminor 6th ||= ^m6 ||= A^ ||= 25 ||
-||= 11 ||= 660 ||= 22/15, 16/11 ||= down-fifth ||= v5 ||= Av ||= 47 ||
+||= 14 ||&gt;  840 ||= 13/8, 8/5 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= 13 ||
-||= 12 ||= 720 ||= 38/25, 3/2 ||= fifth ||= P5, m6 ||= A ||= 97 ||
+||= 15 ||&gt;  900 ||= 22/13, 32/19 ||= downmajor 6th ||= vM6 ||= Bv ||= 27 ||
-||= 13 ||= 780 ||= 11/7, 25/16 ||= upminor 6th ||= ^m6 ||= A^ ||= 25 ||
+||= 16 ||&gt;  960 ||= 7/4, 26/15 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= 7 ||
-||= 14 ||= 840 ||= 13/8, 8/5 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= 13 ||
+||= 17 ||&gt; 1020 ||= 9/5 ||= upminor 7th ||= ^m7 ||= C^ ||= 115 ||
-||= 15 ||= 900 ||= 22/13, 32/19 ||= downmajor 6th ||= vM6 ||= Bv ||= 27 ||
+||= 18 ||&gt; 1080 ||= 15/8, 13/7 ||= mid 7th ||= ~7 ||= C^^, Dvv ||= 15 ||
-||= 16 ||= 960 ||= 7/4, 26/15 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= 7 ||
+||= 19 ||&gt; 1140 ||= 56/29 ||= downmajor 7th ||= vM7 ||= Dv ||= 31 ||
-||= 17 ||= 1020 ||= 9/5 ||= upminor 7th ||= ^m7 ||= C^ ||= 115 ||
+||= 20 ||&gt; 1200 ||= 2/1 ||= octave ||= P8 ||= D ||= 2 ||
-||= 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=
 edo chord names using ups and downs:
@@ Line 92: / Line 89: @@
 ==Commas==
 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] &lt; 20 32 46 56 69 74 |.)
-||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
+||~ Rational ||~ Monzo ||~ Size (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
-||= 256/243 ||&lt; | 8 -5 &gt; ||&gt; 90.22 ||= [[Limma]] ||= Pythagorean Minor 2nd ||=   ||
+||= 256/243 || | 8 -5 &gt; ||&gt; 90.22 ||= [[Limma]] ||= Pythagorean Minor 2nd ||=   ||
-||= 16875/16384 ||&lt; | -14 3 4 &gt; ||&gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||   ||
+||= 16875/16384 || | -14 3 4 &gt; ||&gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||   ||
-||=   ||&lt; | -25 7 6 &gt; ||&gt; 31.57 ||= Ampersand's Comma ||=   ||=   ||
+||= 9931568/9752117 || | -25 7 6 &gt; ||&gt; 31.57 ||= Ampersand's Comma ||=   ||=   ||
-||= 2048/2025 ||&lt; | 11 -4 -2 &gt; ||&gt; 19.55 ||= Diaschisma ||=   ||=   ||
+||= 2048/2025 || | 11 -4 -2 &gt; ||&gt; 19.55 ||= Diaschisma ||=   ||=   ||
-||= 525/512 ||&lt; | -9 1 2 1 &gt; ||&gt; 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||   ||
+||= 525/512 || | -9 1 2 1 &gt; ||&gt; 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||   ||
-||= 49/48 ||&lt; | -4 -1 0 2 &gt; ||&gt; 35.70 ||= Slendro Diesis ||=   ||=   ||
+||= 49/48 || | -4 -1 0 2 &gt; ||&gt; 35.70 ||= Slendro Diesis ||=   ||=   ||
-||= 50/49 ||&lt; | 1 0 2 -2 &gt; ||&gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||=   ||
+||= 50/49 || | 1 0 2 -2 &gt; ||&gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||=   ||
-||= 686/675 ||&lt; | 1 -3 -2 3 &gt; ||&gt; 27.99 ||= Senga ||=   ||=   ||
+||= 686/675 || | 1 -3 -2 3 &gt; ||&gt; 27.99 ||= Senga ||=   ||=   ||
-||= 64/63 ||&lt; | 6 -2 0 -1 &gt; ||&gt; 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
+||= 64/63 || | 6 -2 0 -1 &gt; ||&gt; 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
-||=   ||&lt; | -10 7 8 -7 &gt; ||&gt; 22.41 ||= Blackjackisma ||=   ||=   ||
+||= 9859966/9733137 || | -10 7 8 -7 &gt; ||&gt; 22.41 ||= Blackjackisma ||=   ||=   ||
-||= 1029/1024 ||&lt; | -10 1 0 3 &gt; ||&gt; 8.43 ||= Gamelisma ||=   ||=   ||
+||= 1029/1024 || | -10 1 0 3 &gt; ||&gt; 8.43 ||= Gamelisma ||=   ||=   ||
-||= 225/224 ||&lt; | -5 2 2 -1 &gt; ||&gt; 7.71 ||= Septimal Kleisma ||= Marvel Comma ||=   ||
+||= 225/224 || | -5 2 2 -1 &gt; ||&gt; 7.71 ||= Septimal Kleisma ||= Marvel Comma ||=   ||
-||= 16875/16807 ||&lt; | 0 3 4 -5 &gt; ||&gt; 6.99 ||= Mirkwai ||=   ||=   ||
+||= 16875/16807 || | 0 3 4 -5 &gt; ||&gt; 6.99 ||= Mirkwai ||=   ||=   ||
-||   || | 11 -10 -10 10/1 &gt; ||&gt; 5.57 ||= Linus ||   ||   ||
+||= 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 ||   ||   ||
@@ Line 118: / Line 115: @@
 <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;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:18:&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:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;a href="#Compositions"&gt;Compositions&lt;/a&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;a href="#Properties"&gt;Properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#toc4"&gt; &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Chord Names"&gt;Chord Names&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
+&lt;!-- ws:start:WikiTextTocRule:16:&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:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Properties"&gt;Properties&lt;/a&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;a href="#Chord Names"&gt;Chord Names&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;hr /&gt;
+&lt;!-- ws:end:WikiTextTocRule:25 --&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;
@@ Line 132: / Line 129: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;Degree&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;Cents&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
+         &lt;th&gt;Approximate Ratios&lt;br /&gt;
-&lt;strong&gt;Ratios&lt;/strong&gt;&lt;br /&gt;
+&lt;/th&gt;
-&lt;/td&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;td colspan="3" style="text-align: center;"&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;/td&gt;
+         &lt;th&gt;Nearest Harmonic&lt;br /&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Nearest&lt;/strong&gt;&lt;br /&gt;
+&lt;/th&gt;
-&lt;strong&gt;Harmonic&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&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: center;"&gt;0&lt;br /&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;
@@ Line 164: / Line 159: @@
          &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;60&lt;br /&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;
@@ Line 180: / Line 175: @@
          &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;120&lt;br /&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;
@@ Line 196: / Line 191: @@
          &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;180&lt;br /&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;
@@ Line 212: / Line 207: @@
          &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;240&lt;br /&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;
@@ Line 228: / Line 223: @@
          &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;300&lt;br /&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;
@@ Line 244: / Line 239: @@
          &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;360&lt;br /&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;
@@ Line 260: / Line 255: @@
          &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;420&lt;br /&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="http://xenharmonic.wikispaces.com/14_11"&gt;14/11&lt;/a&gt;, &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/51_40"&gt;51/40&lt;/a&gt;&lt;br /&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;
@@ Line 276: / Line 271: @@
          &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;480&lt;br /&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;
@@ Line 292: / Line 287: @@
          &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;540&lt;br /&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;
@@ Line 308: / Line 303: @@
          &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;600&lt;br /&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,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up fourth, double-down fifth&lt;br /&gt;
-double-down fifth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;^^4, vv5&lt;br /&gt;
@@ Line 325: / Line 319: @@
          &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;660&lt;br /&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;
@@ Line 341: / Line 335: @@
          &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;720&lt;br /&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;
@@ Line 357: / Line 351: @@
          &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;780&lt;br /&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;
@@ Line 373: / Line 367: @@
          &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;840&lt;br /&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;
@@ Line 389: / Line 383: @@
          &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;900&lt;br /&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;
@@ Line 405: / Line 399: @@
          &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;960&lt;br /&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;
@@ Line 421: / Line 415: @@
          &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1020&lt;br /&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;
@@ Line 437: / Line 431: @@
          &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1080&lt;br /&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;
@@ Line 453: / Line 447: @@
          &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1140&lt;br /&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;
@@ Line 469: / Line 463: @@
          &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1200&lt;br /&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;
@@ Line 484: / Line 478: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt; &lt;/h1&gt;
+&lt;br /&gt;
- &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Chord Names&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Chord Names&lt;/h1&gt;
 edo chord names using ups and downs:&lt;br /&gt;
 -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;
@@ Line 501: / Line 495: @@
 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;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Chord Names-Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Modes&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Chord Names-Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Modes&lt;/h2&gt;
 tone equal modes:&lt;br /&gt;
@@ Line 623: / Line 617: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Chord Names-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Commas&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Chord Names-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Commas&lt;/h2&gt;
 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;
@@ Line 629: / Line 623: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th&gt;Comma&lt;br /&gt;
+         &lt;th&gt;Rational&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;Monzo&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;Value (Cents)&lt;br /&gt;
+         &lt;th&gt;Size (Cents)&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;Name 1&lt;br /&gt;
@@ Line 645: / Line 639: @@
          &lt;td style="text-align: center;"&gt;256/243&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| 8 -5 &amp;gt;&lt;br /&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;
@@ Line 659: / Line 653: @@
          &lt;td style="text-align: center;"&gt;16875/16384&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| -14 3 4 &amp;gt;&lt;br /&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;
@@ Line 671: / Line 665: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9931568/9752117&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| -25 7 6 &amp;gt;&lt;br /&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;
@@ Line 687: / Line 681: @@
          &lt;td style="text-align: center;"&gt;2048/2025&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| 11 -4 -2 &amp;gt;&lt;br /&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;
@@ Line 701: / Line 695: @@
          &lt;td style="text-align: center;"&gt;525/512&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| -9 1 2 1 &amp;gt;&lt;br /&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;
@@ Line 715: / Line 709: @@
          &lt;td style="text-align: center;"&gt;49/48&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| -4 -1 0 2 &amp;gt;&lt;br /&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;
@@ Line 729: / Line 723: @@
          &lt;td style="text-align: center;"&gt;50/49&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| 1 0 2 -2 &amp;gt;&lt;br /&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;
@@ Line 743: / Line 737: @@
          &lt;td style="text-align: center;"&gt;686/675&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| 1 -3 -2 3 &amp;gt;&lt;br /&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;
@@ Line 757: / Line 751: @@
          &lt;td style="text-align: center;"&gt;64/63&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&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;
@@ Line 769: / Line 763: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9859966/9733137&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| -10 7 8 -7 &amp;gt;&lt;br /&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;
@@ Line 785: / Line 779: @@
          &lt;td style="text-align: center;"&gt;1029/1024&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| -10 1 0 3 &amp;gt;&lt;br /&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;
@@ Line 799: / Line 793: @@
          &lt;td style="text-align: center;"&gt;225/224&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| -5 2 2 -1 &amp;gt;&lt;br /&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;
@@ Line 813: / Line 807: @@
          &lt;td style="text-align: center;"&gt;16875/16807&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;| 0 3 4 -5 &amp;gt;&lt;br /&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;
@@ Line 825: / Line 819: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6772805/6751042&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| 11 -10 -10 10/1 &amp;gt;&lt;br /&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;
@@ Line 897: / Line 891: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Chord Names-Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;strong&gt;Books&lt;/strong&gt;&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Chord Names-Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;strong&gt;Books&lt;/strong&gt;&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:785:&amp;lt;a href=&amp;quot;http://www.ronsword.com/&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/20_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 114px; width: 82px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/" target="_blank" rel="nofollow"&gt;&lt;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;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:785 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:782:&amp;lt;a href=&amp;quot;http://www.ronsword.com/&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/20_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 114px; width: 82px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/" target="_blank" rel="nofollow"&gt;&lt;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;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:782 --&gt;&lt;br /&gt;
 &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>