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
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<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>
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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 & 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 />
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~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br />
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<strong>Compositions</strong><br />
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<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 Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/Prelude13ET.mid" rel="nofollow">Prelude in 13ET</a> by Aaron Andrew Hunt</body></html>