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:<br>

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 03:02:25 UTC</tt>.<br>

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 05:21:17 UTC</tt>.<br>

: The original revision id was <tt>~~602811484~~</tt>.<br>

: The original revision id was <tt>602813162</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>

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=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|~~up/down~~ notation]] ||= **Nearest**

**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 ||

||= 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 ||

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||= 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:

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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.<br />

<br />

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

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

<hr />

<hr />

<br />

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

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<h1 id="toc2"><a name="Properties"></a>Properties</h1>

<h2 id="toc3"><a name="Properties-Intervals"></a>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 />

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<strong>Ratios</strong><br />

</td>

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

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

</td>

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

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</td>

</td>

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</table>

<h2 id="toc4"> </h2>

<h1 id="toc4"> </h1>

<h2 id="~~toc5~~"><a name="~~Properties~~-Modes"></a>Modes</h2>

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

20edo chord names using ups and downs:<br />

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

0-5-12 = D F^ A = D.^m = &quot;D upminor&quot;<br />

0-6-12 = D F^^ A = D.~ = &quot;D mid&quot;<br />

0-7-12 = D F#v A = D.v = &quot;D dot down&quot; or &quot;D downmajor&quot;<br />

0-8-12 = D G A = Dsus4, or D F# A = D = &quot;D&quot; or &quot;D major&quot;<br />

0-4-12-16 = D F A C = Dm7 = &quot;D minor seven&quot;, or D F A B = Dm6 = &quot;D minor six&quot;<br />

0-5-12-16 = D F^ A C = Dm7(^3) = &quot;D minor seven up-three&quot;, or D F^ A B = Dm6(^3) = &quot;D minor six up-three&quot;<br />

0-6-12-16 = D F^^ A C = D7(~3) = &quot;D seven mid-three&quot;, or D F^ A B = D6(~3) = &quot;D six mid-three&quot;<br />

0-7-12-16 = D F#v A C = D7(v3) = &quot;D seven down-three&quot;, or D F#v A B = D6(v3) = &quot;D six down-three&quot;<br />

0-8-12-16 = D F# A C = D7 = &quot;D seven&quot;, or D F# A B = D6 = &quot;D six&quot;<br />

0-7-12-19 = D F#v A C#v = D.vM7 = &quot;D downmajor seven&quot;<br />

0-5-12-17 = D F^ A C^ = D.^m7 = &quot;D dot up minor-seven&quot;, or D F^ A B^ = D.^m6 = &quot;D dot up minor-six&quot;<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 />

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

20 tone equal modes:<br />

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<br />

<h2 id="~~toc6~~"><a name="~~Properties~~-Commas"></a>Commas</h2>

<h2 id="toc7"><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; <a class="wiki_link" href="http://tel.wikispaces.com/20%2032%2046%2056%2069%2074">20 32 46 56 69 74</a>/1 |.)<br />

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<br />

<h2 id="~~toc7~~"><a name="~~Properties~~-Books"></a><strong>Books</strong></h2>

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

<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><br />

<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>

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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:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 03:02:25 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 05:21:17 UTC</tt>.<br>
-: The original revision id was <tt>602811484</tt>.<br>
+: The original revision id was <tt>602813162</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>
@@ Line 24: / Line 24: @@
 =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|up/down notation]] ||= **Nearest**
+**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 ||
+||= 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 ||
@@ Line 49: / Line 51: @@
 ||= 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:
+-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
+-5-12 = D F^ A = D.^m = "D upminor"
+-6-12 = D F^^ A = D.~ = "D mid"
+-7-12 = D F#v A = D.v = "D dot down" or "D downmajor"
+-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
+-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
+-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"
+-6-12-16 = D F^^ A C = D7(~3) = "D seven mid-three", or D F^ A B = D6(~3) = "D six mid-three"
+-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"
+-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
+-7-12-19 = D F#v A C#v = D.vM7 = "D downmajor seven"
+-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==
 tone equal modes:
@@ Line 100: / Line 118: @@
 <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: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;!-- 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: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:end:WikiTextTocRule:25 --&gt;&lt;hr /&gt;
+&lt;!-- ws:end:WikiTextTocRule:28 --&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 108: / Line 126: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Properties&lt;/h1&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Properties-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&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;
@@ Line 119: / Line 139: @@
 &lt;strong&gt;Ratios&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;up/down 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;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Nearest&lt;/strong&gt;&lt;br /&gt;
@@ Line 168: / Line 188: @@
          &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 style="text-align: center;"&gt;D^^ / Evv&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;69&lt;br /&gt;
@@ Line 464: / Line 484: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt; &lt;/h2&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;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Properties-Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Modes&lt;/h2&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;
+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;
+-5-12 = D F^ A = D.^m = &amp;quot;D upminor&amp;quot;&lt;br /&gt;
+-6-12 = D F^^ A = D.~ = &amp;quot;D mid&amp;quot;&lt;br /&gt;
+-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;
+-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;
+-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;
+-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;
+-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;
+-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;
+-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;
+-7-12-19 = D F#v A C#v = D.vM7 = &amp;quot;D downmajor seven&amp;quot;&lt;br /&gt;
+-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;
+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;
 tone equal modes:&lt;br /&gt;
@@ Line 587: / Line 623: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Properties-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Commas&lt;/h2&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;
 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; &lt;a class="wiki_link" href="http://tel.wikispaces.com/20%2032%2046%2056%2069%2074"&gt;20 32 46 56 69 74&lt;/a&gt;/1 |.)&lt;br /&gt;
@@ Line 861: / Line 897: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Properties-Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;strong&gt;Books&lt;/strong&gt;&lt;/h2&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: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;!-- 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;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>