13edo: Difference between revisions
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Wikispaces>hstraub **Imported revision 21205365 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 104020717 - Original comment: ** |
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<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: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-19 14:06:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>104020717</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | ||
<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;white-space: pre-wrap ! important" class="old-revision-html">=13 tone equal temperament= | <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;white-space: pre-wrap ! important" class="old-revision-html">=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]] | |||
~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson | |||
**Compositions** | **Compositions** | ||
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[[http://www.h-pi.com/midi/Prelude13ET.mid|Prelude in 13ET]] by Aaron Andrew Hunt</pre></div> | [[http://www.h-pi.com/midi/Prelude13ET.mid|Prelude in 13ET]] by Aaron Andrew Hunt</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"><html><head><title>13edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x13 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->13 tone equal temperament</h1> | <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>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 /> | <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:2:&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:2 --><br /> | |||
~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br /> | |||
<br /> | |||
<strong>Compositions</strong><br /> | <strong>Compositions</strong><br /> | ||
<br /> | <br /> | ||
Revision as of 14:06, 19 November 2009
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2009-11-19 14:06:49 UTC.
- The original revision id was 104020717.
- The revision comment was:
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]] ~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
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 /> <!-- ws:start:WikiTextLocalImageRule:2:<img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="" title="" /> --><img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /><!-- ws:end:WikiTextLocalImageRule:2 --><br /> ~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 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>