13edo: Difference between revisions

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Wikispaces>xenwolf
**Imported revision 164990969 - Original comment: **
Wikispaces>jdfreivald
**Imported revision 233314848 - Original comment: Added comma table.**
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2010-09-23 16:43:04 UTC</tt>.<br>
: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 19:42:29 UTC</tt>.<br>
: The original revision id was <tt>164990969</tt>.<br>
: The original revision id was <tt>233314848</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>Added comma table.</tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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>
<h4>Original Wikitext content:</h4>
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[[http://www.h-pi.com/midi/13ET.mid|Two-Part Invention in 13ET]] by [[Aaron Andrew Hunt]]
[[http://www.h-pi.com/midi/13ET.mid|Two-Part Invention in 13ET]] by [[Aaron Andrew Hunt]]
[[http://www.h-pi.com/midi/Prelude13ET.mid|Prelude in 13ET]] by [[Aaron Andrew Hunt]]
[[http://www.h-pi.com/midi/Prelude13ET.mid|Prelude in 13ET]] by [[Aaron Andrew Hunt]]
[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=835265|Spikey Hair in 13tET]] by [[Andrew Heathwaite]]</pre></div>
[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=835265|Spikey Hair in 13tET]] by [[Andrew Heathwaite]]
 
==Commas==
13 EDO tempers out the following commas. (Note: This assumes the val &lt; 13 21 30 36 45 48 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
|| 2109375/2097152 || | -21 3 7 &gt; || 10.06 || Semicomma || Fokker Comma ||  ||
|| 1029/1000 || | -3 1 -3 3 &gt; || 49.49 || Keega ||  ||  ||
|| 525/512 || | -9 1 2 1 &gt; || 43.41 || Avicennma || Avicenna's Enharmonic Diesis ||  ||
|| 64/63 || | 6 -2 0 -1 &gt; || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||
|| 64827/64000 || | -9 3 -3 4 &gt; || 22.23 || Squalentine ||  ||  ||
|| 3125/3087 || | -2 5 -3 &gt; || 21.18 || Gariboh ||  ||  ||
|| 3136/3125 || | 6 -5 2 &gt; || 6.08 || Hemimean ||  ||  ||
|| 121/120 || | -3 -1 -1 2 &gt; || 14.37 || Biyatisma ||  ||  ||
|| 441/440 || | -3 2 -1 2 -1 &gt; || 3.93 || Werckisma ||  ||  ||</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;13edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x13 tone equal temperament / 13edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;13 tone equal temperament / 13edo&lt;/h1&gt;
<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;13edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x13 tone equal temperament / 13edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;13 tone equal temperament / 13edo&lt;/h1&gt;
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13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp;amp; major sixth are xenharmonic (not similar to anything available in 12edo). Due to the prime character of the number 13, 13edo can form several xenharmonic &lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry scales&lt;/a&gt;. The diagram below shows five &amp;quot;families&amp;quot; of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, &amp;amp; 6\13, respectively.&lt;br /&gt;
13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp;amp; major sixth are xenharmonic (not similar to anything available in 12edo). Due to the prime character of the number 13, 13edo can form several xenharmonic &lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry scales&lt;/a&gt;. The diagram below shows five &amp;quot;families&amp;quot; of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, &amp;amp; 6\13, respectively.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:2:&amp;lt;img src=&amp;quot;/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:146:&amp;lt;img src=&amp;quot;/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:146 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:3:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/13edo%20horograms.pdf?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@13edo horograms.pdf&amp;quot; title=&amp;quot;File: 13edo horograms.pdf&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="13edo horograms.pdf" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');" class="filename" title="13edo horograms.pdf"&gt;13edo horograms.pdf&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/13edo%20horograms.pdf"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;242 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:3 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:147:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/13edo%20horograms.pdf?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@13edo horograms.pdf&amp;quot; title=&amp;quot;File: 13edo horograms.pdf&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="13edo horograms.pdf" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');" class="filename" title="13edo horograms.pdf"&gt;13edo horograms.pdf&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/13edo%20horograms.pdf"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;242 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:147 --&gt;&lt;br /&gt;
~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson&lt;br /&gt;
~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;a class="wiki_link_ext" href="http://www.h-pi.com/midi/13ET.mid" rel="nofollow"&gt;Two-Part Invention in 13ET&lt;/a&gt; by &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Andrew Hunt&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.h-pi.com/midi/13ET.mid" rel="nofollow"&gt;Two-Part Invention in 13ET&lt;/a&gt; by &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Andrew Hunt&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.h-pi.com/midi/Prelude13ET.mid" rel="nofollow"&gt;Prelude in 13ET&lt;/a&gt; by &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Andrew Hunt&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.h-pi.com/midi/Prelude13ET.mid" rel="nofollow"&gt;Prelude in 13ET&lt;/a&gt; by &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Andrew Hunt&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;amp;songID=835265" rel="nofollow"&gt;Spikey Hair in 13tET&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;amp;songID=835265" rel="nofollow"&gt;Spikey Hair in 13tET&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x13 tone equal temperament / 13edo-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Commas&lt;/h2&gt;
13 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 13 21 30 36 45 48 |.)&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Comma&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;
        &lt;th&gt;Name 1&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 2&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 3&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2109375/2097152&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -21 3 7 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10.06&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Semicomma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Fokker Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1029/1000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 1 -3 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;49.49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Keega&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;525/512&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -9 1 2 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;43.41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Avicennma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Avicenna's Enharmonic Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27.26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Septimal Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Archytas' Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Leipziger Komma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64827/64000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -9 3 -3 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22.23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Squalentine&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3125/3087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -2 5 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gariboh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3136/3125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 -5 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6.08&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemimean&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 -1 -1 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Biyatisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 2 -1 2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Werckisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 19:42, 31 May 2011

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author jdfreivald and made on 2011-05-31 19:42:29 UTC.
The original revision id was 233314848.
The revision comment was: Added comma table.

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

Original Wikitext content:

=13 tone equal temperament / 13edo= 

13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third & major sixth are xenharmonic (not similar to anything available in 12edo). Due to the prime character of the number 13, 13edo can form several xenharmonic [[MOSScales|moment of symmetry scales]]. The diagram below shows five "families" of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, & 6\13, respectively.

[[image:13edo_horograms.jpg]]
[[file:13edo horograms.pdf]]
~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson

**Compositions**

[[http://www.microtonalmusic.net/audio/slowdance13edo.mp3|Slow Dance]] by [[http://danielthompson.blogspot.com/|Daniel Thompson]]
[[http://www.io.com/%7Ehmiller/midi/triskaidekaphobia.mid|Triskaidekaphobia]] by [[http://www.io.com/%7Ehmiller/music/|Herman Miller]]
[[http://home.snafu.de/djwolf/ChangeOfRegime.pdf|Change of Regime: Prelude, Invention & Air to a Ground in 13tet]] by [[Daniel Wolf]]
[[http://www.h-pi.com/midi/13ET.mid|Two-Part Invention in 13ET]] by [[Aaron Andrew Hunt]]
[[http://www.h-pi.com/midi/Prelude13ET.mid|Prelude in 13ET]] by [[Aaron Andrew Hunt]]
[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=835265|Spikey Hair in 13tET]] by [[Andrew Heathwaite]]

==Commas== 
13 EDO tempers out the following commas. (Note: This assumes the val < 13 21 30 36 45 48 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
|| 2109375/2097152 || | -21 3 7 > || 10.06 || Semicomma || Fokker Comma ||   ||
|| 1029/1000 || | -3 1 -3 3 > || 49.49 || Keega ||   ||   ||
|| 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || Avicenna's Enharmonic Diesis ||   ||
|| 64/63 || | 6 -2 0 -1 > || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||
|| 64827/64000 || | -9 3 -3 4 > || 22.23 || Squalentine ||   ||   ||
|| 3125/3087 || | -2 5 -3 > || 21.18 || Gariboh ||   ||   ||
|| 3136/3125 || | 6 -5 2 > || 6.08 || Hemimean ||   ||   ||
|| 121/120 || | -3 -1 -1 2 > || 14.37 || Biyatisma ||   ||   ||
|| 441/440 || | -3 2 -1 2 -1 > || 3.93 || Werckisma ||   ||   ||

Original HTML content:

<html><head><title>13edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x13 tone equal temperament / 13edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->13 tone equal temperament / 13edo</h1>
 <br />
13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo). Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:146:&lt;img src=&quot;/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /><!-- ws:end:WikiTextLocalImageRule:146 --><br />
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~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br />
<br />
<strong>Compositions</strong><br />
<br />
<a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br />
<a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/triskaidekaphobia.mid" rel="nofollow">Triskaidekaphobia</a> by <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/music/" rel="nofollow">Herman Miller</a><br />
<a class="wiki_link_ext" href="http://home.snafu.de/djwolf/ChangeOfRegime.pdf" rel="nofollow">Change of Regime: Prelude, Invention &amp; Air to a Ground in 13tet</a> by <a class="wiki_link" href="/Daniel%20Wolf">Daniel Wolf</a><br />
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/13ET.mid" rel="nofollow">Two-Part Invention in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/Prelude13ET.mid" rel="nofollow">Prelude in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=835265" rel="nofollow">Spikey Hair in 13tET</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a><br />
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x13 tone equal temperament / 13edo-Commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas</h2>
 13 EDO tempers out the following commas. (Note: This assumes the val &lt; 13 21 30 36 45 48 |.)<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>Value (Cents)<br />
</th>
        <th>Name 1<br />
</th>
        <th>Name 2<br />
</th>
        <th>Name 3<br />
</th>
    </tr>
    <tr>
        <td>2109375/2097152<br />
</td>
        <td>| -21 3 7 &gt;<br />
</td>
        <td>10.06<br />
</td>
        <td>Semicomma<br />
</td>
        <td>Fokker Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1029/1000<br />
</td>
        <td>| -3 1 -3 3 &gt;<br />
</td>
        <td>49.49<br />
</td>
        <td>Keega<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>525/512<br />
</td>
        <td>| -9 1 2 1 &gt;<br />
</td>
        <td>43.41<br />
</td>
        <td>Avicennma<br />
</td>
        <td>Avicenna's Enharmonic Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>64/63<br />
</td>
        <td>| 6 -2 0 -1 &gt;<br />
</td>
        <td>27.26<br />
</td>
        <td>Septimal Comma<br />
</td>
        <td>Archytas' Comma<br />
</td>
        <td>Leipziger Komma<br />
</td>
    </tr>
    <tr>
        <td>64827/64000<br />
</td>
        <td>| -9 3 -3 4 &gt;<br />
</td>
        <td>22.23<br />
</td>
        <td>Squalentine<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3125/3087<br />
</td>
        <td>| -2 5 -3 &gt;<br />
</td>
        <td>21.18<br />
</td>
        <td>Gariboh<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3136/3125<br />
</td>
        <td>| 6 -5 2 &gt;<br />
</td>
        <td>6.08<br />
</td>
        <td>Hemimean<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>121/120<br />
</td>
        <td>| -3 -1 -1 2 &gt;<br />
</td>
        <td>14.37<br />
</td>
        <td>Biyatisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>441/440<br />
</td>
        <td>| -3 2 -1 2 -1 &gt;<br />
</td>
        <td>3.93<br />
</td>
        <td>Werckisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

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