13edo
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=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:<h1> --><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 & 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 "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.<br />
<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 & 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&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:<h2> --><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 < 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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><br />
</td>
<td>3.93<br />
</td>
<td>Werckisma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>