13edo: Difference between revisions
Wikispaces>igliashon **Imported revision 506177532 - Original comment: ** |
Wikispaces>igliashon **Imported revision 506177642 - 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:igliashon|igliashon]] and made on <tt>2014-05-03 07: | : This revision was by author [[User:igliashon|igliashon]] and made on <tt>2014-05-03 07:28:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>506177642</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> | ||
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=//Best approximates 2.5.9.11.13.17.19.21//= | =//Best approximates 2.5.9.11.13.17.19.21//= | ||
=13edo | =13edo: 13 equal divisions of the octave= | ||
13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth [[prime numbers|prime]] edo, following [[11edo]] and coming before [[17edo]]. The steps less than 600¢ are narrower than their nearest 12edo approximation, while those greater than 600¢ are wider. This allows for some neat ear-bending tricks, whereby melodic gestures reminiscent of 12edo can quickly arrive at an unfamiliar place. | 13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth [[prime numbers|prime]] edo, following [[11edo]] and coming before [[17edo]]. The steps less than 600¢ are narrower than their nearest 12edo approximation, while those greater than 600¢ are wider. This allows for some neat ear-bending tricks, whereby melodic gestures reminiscent of 12edo can quickly arrive at an unfamiliar place. | ||
As a temperament of 21-odd-limit Just Intonation, 13edo has excellent approximations to the 11th and 21st harmonics, and reasonable approximations to the 5th, 9th, 13th, 17th, and 19th harmonics. For most purposes it does not offer acceptable approximations to the 3rd, 7th, or 15th. The lack of reasonable approximation to the 3rd harmonic makes 13edo unsuitable for common-practice music, but its good approximations to ratios of 11, 13, and 21 make it a very xenharmonic tuning, as these identities are not remotely represented in 12edo. Despite its reputation for dissonance, it is an excellent rank-1 temperament on the 2.5.9.11.13.17.19.21 subgroup, and has a substantial repertoire of complex consonances for its small size. | As a temperament of 21-odd-limit Just Intonation, 13edo has excellent approximations to the 11th and 21st harmonics, and reasonable approximations to the 5th, 9th, 13th, 17th, and 19th harmonics. For most purposes it does not offer acceptable approximations to the 3rd, 7th, or 15th. The lack of reasonable approximation to the 3rd harmonic makes 13edo unsuitable for common-practice music, but its good approximations to ratios of 11, 13, and 21 make it a very xenharmonic tuning, as these identities are not remotely represented in 12edo. Despite its reputation for dissonance, it is an excellent rank-1 temperament on the 2.5.9.11.13.17.19.21 subgroup, and has a substantial repertoire of complex consonances for its small size. | ||
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Other approaches explored by specific composers and theorists are outlined further down, in the context of more complete tonal systems. | Other approaches explored by specific composers and theorists are outlined further down, in the context of more complete tonal systems. | ||
Play the 4:5:9 chord: | Play the 4:5:9 chord: | ||
[[media type="file" key="13 edo 459 chord.wav" width="300" height="50"]] | [[media type="file" key="13 edo 459 chord.wav" width="300" height="50"]] | ||
Play the 4:5:9:11 chord: | Play the 4:5:9:11 chord: | ||
[[media type="file" key="13 edo 45911 chord.wav" width="300" height="50"]] | [[media type="file" key="13 edo 45911 chord.wav" width="300" height="50"]] | ||
Play the 4:5:9:13 chord: | Play the 4:5:9:13 chord: | ||
[[media type="file" key="13 edo 45913 chord.wav" width="300" height="50"]] | [[media type="file" key="13 edo 45913 chord.wav" width="300" height="50"]] | ||
Play the 4:5:9:21 chord: | Play the 4:5:9:21 chord: | ||
[[media type="file" key="13 edo 45921 chord.wav" width="300" height="50"]] | [[media type="file" key="13 edo 45921 chord.wav" width="300" height="50"]] | ||
=Notational and Compositional Approaches to 13edo= | =Notational and Compositional Approaches to 13edo= | ||
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[[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Margo-Schulter-For_Claudi-2014-02-17-13edo.mp3|For Claudi]] by [[http://soonlabel.com/xenharmonic/archives/1788|Margo Schulter]]</pre></div> | [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Margo-Schulter-For_Claudi-2014-02-17-13edo.mp3|For Claudi]] by [[http://soonlabel.com/xenharmonic/archives/1788|Margo Schulter]]</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:WikiTextTocRule: | <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:WikiTextTocRule:39:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><a href="#Best approximates 2.5.9.11.13.17.19.21">Best approximates 2.5.9.11.13.17.19.21</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#x13edo: 13 equal divisions of the octave">13edo: 13 equal divisions of the octave</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Notational and Compositional Approaches to 13edo">Notational and Compositional Approaches to 13edo</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/23473422?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;23473422&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player-beta.js"> | ||
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<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc0"><a name="Best approximates 2.5.9.11.13.17.19.21"></a><!-- ws:end:WikiTextHeadingRule:9 --><em>Best approximates 2.5.9.11.13.17.19.21</em></h1> | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc0"><a name="Best approximates 2.5.9.11.13.17.19.21"></a><!-- ws:end:WikiTextHeadingRule:9 --><em>Best approximates 2.5.9.11.13.17.19.21</em></h1> | ||
<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc1"><a name="x13edo | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc1"><a name="x13edo: 13 equal divisions of the octave"></a><!-- ws:end:WikiTextHeadingRule:11 -->13edo: 13 equal divisions of the octave</h1> | ||
13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/11edo">11edo</a> and coming before <a class="wiki_link" href="/17edo">17edo</a>. The steps less than 600¢ are narrower than their nearest 12edo approximation, while those greater than 600¢ are wider. This allows for some neat ear-bending tricks, whereby melodic gestures reminiscent of 12edo can quickly arrive at an unfamiliar place.<br /> | 13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/11edo">11edo</a> and coming before <a class="wiki_link" href="/17edo">17edo</a>. The steps less than 600¢ are narrower than their nearest 12edo approximation, while those greater than 600¢ are wider. This allows for some neat ear-bending tricks, whereby melodic gestures reminiscent of 12edo can quickly arrive at an unfamiliar place.<br /> | ||
<br /> | <br /> | ||
As a temperament of 21-odd-limit Just Intonation, 13edo has excellent approximations to the 11th and 21st harmonics, and reasonable approximations to the 5th, 9th, 13th, 17th, and 19th harmonics. For most purposes it does not offer acceptable approximations to the 3rd, 7th, or 15th. The lack of reasonable approximation to the 3rd harmonic makes 13edo unsuitable for common-practice music, but its good approximations to ratios of 11, 13, and 21 make it a very xenharmonic tuning, as these identities are not remotely represented in 12edo. Despite its reputation for dissonance, it is an excellent rank-1 temperament on the 2.5.9.11.13.17.19.21 subgroup, and has a substantial repertoire of complex consonances for its small size.<br /> | |||
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<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:1095:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/13ed2-001.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@13ed2-001.svg&quot; title=&quot;File: 13ed2-001.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="13ed2-001.svg" /></a><div><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');" class="filename" title="13ed2-001.svg">13ed2-001.svg</a><br /><ul><li><a href="/file/detail/13ed2-001.svg">Details</a></li><li><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg">Download</a></li><li style="color: #666">15 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:1095 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:13 -->Scales in 13edo</h1> | ||
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 <u><a class="wiki_link" href="/degree">degree</a>s of</u> 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | 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 <u><a class="wiki_link" href="/degree">degree</a>s of</u> 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | ||
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~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson<br /> | ~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson<br /> | ||
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Another neat facet of 13-EDO is the fact that any 12-EDO scale can be &quot;turned into&quot; a 13-EDO scale by either adding an extra semitone, or turning an existent semitone into a whole-tone. Because of this, melody in 13-EDO can be quite mind-bending and uncanny, and phrases that begin in a familiar way quickly lead to something totally unexpected.<br /> | Another neat facet of 13-EDO is the fact that any 12-EDO scale can be &quot;turned into&quot; a 13-EDO scale by either adding an extra semitone, or turning an existent semitone into a whole-tone. Because of this, melody in 13-EDO can be quite mind-bending and uncanny, and phrases that begin in a familiar way quickly lead to something totally unexpected.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc3"><a name="Harmony in 13edo"></a><!-- ws:end:WikiTextHeadingRule:15 -->Harmony in 13edo</h1> | ||
Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a &quot;stack of 3rds&quot; the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (<u><a class="wiki_link" href="/13edo#top">degree</a>s</u> 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the <a class="wiki_link" href="/k%2AN%20subgroups">2*13 subgroup</a> 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et.<br /> | Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a &quot;stack of 3rds&quot; the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (<u><a class="wiki_link" href="/13edo#top">degree</a>s</u> 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the <a class="wiki_link" href="/k%2AN%20subgroups">2*13 subgroup</a> 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et.<br /> | ||
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Other approaches explored by specific composers and theorists are outlined further down, in the context of more complete tonal systems.<br /> | Other approaches explored by specific composers and theorists are outlined further down, in the context of more complete tonal systems.<br /> | ||
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Play the 4:5:9 chord: <br /> | Play the 4:5:9 chord:<br /> | ||
<!-- ws:start:WikiTextMediaRule:3:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20459%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 459 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+459+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:3 --><br /> | <!-- ws:start:WikiTextMediaRule:3:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20459%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 459 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+459+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:3 --><br /> | ||
Play the 4:5:9:11 chord: <br /> | Play the 4:5:9:11 chord:<br /> | ||
<!-- ws:start:WikiTextMediaRule:4:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045911%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45911 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45911+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:4 --><br /> | <!-- ws:start:WikiTextMediaRule:4:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045911%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45911 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45911+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:4 --><br /> | ||
Play the 4:5:9:13 chord: <br /> | Play the 4:5:9:13 chord:<br /> | ||
<!-- ws:start:WikiTextMediaRule:5:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045913%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45913 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45913+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:5 --><br /> | <!-- ws:start:WikiTextMediaRule:5:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045913%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45913 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45913+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:5 --><br /> | ||
Play the 4:5:9:21 chord: <br /> | Play the 4:5:9:21 chord:<br /> | ||
<!-- ws:start:WikiTextMediaRule:6:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045921%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45921 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45921+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:6 --><br /> | <!-- ws:start:WikiTextMediaRule:6:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045921%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45921 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45921+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:6 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc4"><a name="Notational and Compositional Approaches to 13edo"></a><!-- ws:end:WikiTextHeadingRule:17 -->Notational and Compositional Approaches to 13edo</h1> | ||
13edo has drawn the attention of numerous composers and theorists, some of whom have devoted some effort to provide a notation and an outline of a compositional approach to it. Some of these are included in the following tables:<br /> | 13edo has drawn the attention of numerous composers and theorists, some of whom have devoted some effort to provide a notation and an outline of a compositional approach to it. Some of these are included in the following tables:<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:19:&lt;h3&gt; --><h3 id="toc5"><a name="Notational and Compositional Approaches to 13edo--7-nominal notations:"></a><!-- ws:end:WikiTextHeadingRule:19 -->7-nominal notations:</h3> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:21:&lt;h3&gt; --><h3 id="toc6"><a name="Notational and Compositional Approaches to 13edo--8-nominal notations:"></a><!-- ws:end:WikiTextHeadingRule:21 -->8-nominal notations:</h3> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:23:&lt;h2&gt; --><h2 id="toc7"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods"></a><!-- ws:end:WikiTextHeadingRule:23 -->The Cryptic Ruse Methods</h2> | ||
13edo offers two main candidates for diatonic-like scales: the 6L1s heptatonic MOS generated by 2\13, and the 5L3s octatonic MOS. Both of these scales are Rothenberg proper, and bear a slightly-twisted resemblance to the 12edo diatonic scale. Specifically, the 6L1s scale resembles the 12edo diatonic with one of its semitones replaced with a whole-tone, while the 5L3s scale resembles the 12edo diatonic with an extra semitone inserted between two adjacent whole-tones.<br /> | 13edo offers two main candidates for diatonic-like scales: the 6L1s heptatonic MOS generated by 2\13, and the 5L3s octatonic MOS. Both of these scales are Rothenberg proper, and bear a slightly-twisted resemblance to the 12edo diatonic scale. Specifically, the 6L1s scale resembles the 12edo diatonic with one of its semitones replaced with a whole-tone, while the 5L3s scale resembles the 12edo diatonic with an extra semitone inserted between two adjacent whole-tones.<br /> | ||
<br /> | <br /> | ||
<span style="background-color: #ffffff;">To facilitate discussion of these scales, Cryptic Ruse has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands.</span><br /> | <span style="background-color: #ffffff;">To facilitate discussion of these scales, Cryptic Ruse has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands.</span><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:25:&lt;h3&gt; --><h3 id="toc8"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in The Archaeotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:25 -->Modes and Harmony in The Archaeotonic Scale</h3> | ||
A 7-nominal notaiton is proposed, using the letters A-G. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &quot;C&quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | A 7-nominal notaiton is proposed, using the letters A-G. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &quot;C&quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1088:&lt;img src=&quot;/file/view/Archeotonic.png/252639498/Archeotonic.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Archeotonic.png/252639498/Archeotonic.png" alt="Archeotonic.png" title="Archeotonic.png" /><!-- ws:end:WikiTextLocalImageRule:1088 --><br /> | ||
Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.<br /> | Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.<br /> | ||
<br /> | <br /> | ||
There may be other concordant harmonies possible in this scale that do not represent segments of the overtone series; further exploration is pending.<br /> | There may be other concordant harmonies possible in this scale that do not represent segments of the overtone series; further exploration is pending.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:27:&lt;h3&gt; --><h3 id="toc9"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in the Oneirotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:27 -->Modes and Harmony in the Oneirotonic Scale</h3> | ||
Here an 8-nominal notation is proposed, using letters A-H. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &quot;C&quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | Here an 8-nominal notation is proposed, using letters A-H. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &quot;C&quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | ||
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There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.<br /> | There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:29:&lt;h2&gt; --><h2 id="toc10"><a name="Notational and Compositional Approaches to 13edo-The Kentaku (aka William Lynch) Method"></a><!-- ws:end:WikiTextHeadingRule:29 -->The Kentaku (aka William Lynch) Method</h2> | ||
<span style="font-size: 13px; line-height: 1.5;">Normally, 13 edo can be notated by adding an accidental between E and F. For some reading the same staff with the same letters but in different places can be mind boggling and lead to confusion. That's why some have recommended different options. </span><br /> | <span style="font-size: 13px; line-height: 1.5;">Normally, 13 edo can be notated by adding an accidental between E and F. For some reading the same staff with the same letters but in different places can be mind boggling and lead to confusion. That's why some have recommended different options. </span><br /> | ||
<br /> | <br /> | ||
<span style="font-size: 13px; line-height: 1.5;">13 edo may be better suited to be notated by using the 8 notes of the MOS father[8] as the naturals. In order to not become confused,</span><br /> | <span style="font-size: 13px; line-height: 1.5;">13 edo may be better suited to be notated by using the 8 notes of the MOS father[8] as the naturals. In order to not become confused,</span><br /> | ||
a new set of letters may benefit by giving 13 edo a fresh perspective. William Lynch proposes using the letters JKLMNOPQ as the notes of Father[8] with J being an 11/8 from a normal C, in order to give it a more personal identify rather than hearing it as C. The remaining letters of 13 edo are notated with sharps and flats like 12 edo. The whole alphabet is written J-J#-K-K#-L-M-M#-N-N#-O-P-P#-Q-J . There are no accidentals between LM, OP, and QJ.<br /> | a new set of letters may benefit by giving 13 edo a fresh perspective. William Lynch proposes using the letters JKLMNOPQ as the notes of Father[8] with J being an 11/8 from a normal C, in order to give it a more personal identify rather than hearing it as C. The remaining letters of 13 edo are notated with sharps and flats like 12 edo. The whole alphabet is written J-J#-K-K#-L-M-M#-N-N#-O-P-P#-Q-J . There are no accidentals between LM, OP, and QJ.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1090:&lt;img src=&quot;/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG" alt="13 edo alphabet.PNG" title="13 edo alphabet.PNG" /><!-- ws:end:WikiTextLocalImageRule:1090 --><br /> | ||
Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.<br /> | Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.<br /> | ||
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13 EDO Chromatic Scale in Octatonic Notation:<br /> | 13 EDO Chromatic Scale in Octatonic Notation:<br /> | ||
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Also, this approach allows for a circle of fourths to be produced:<br /> | Also, this approach allows for a circle of fourths to be produced:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1093:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG" alt="13 ET circle of fourths.PNG" title="13 ET circle of fourths.PNG" /><!-- ws:end:WikiTextLocalImageRule:1093 --><br /> | ||
Listen to Ryonian on J (F#) <!-- ws:start:WikiTextMediaRule:7:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo Ryo mode.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:7 --><br /> | Listen to Ryonian on J (F#) <!-- ws:start:WikiTextMediaRule:7:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo Ryo mode.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:7 --><br /> | ||
Listen to Dylathian on J: (F#) <!-- ws:start:WikiTextMediaRule:8:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 8 tone mode 1.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:8 --><br /> | Listen to Dylathian on J: (F#) <!-- ws:start:WikiTextMediaRule:8:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 8 tone mode 1.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:8 --><br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kentaku%27s%20Approach%20to%2013EDO">More on William Lynch's 13 EDO octatonic approach</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kentaku%27s%20Approach%20to%2013EDO">More on William Lynch's 13 EDO octatonic approach</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc11"><a name="Mapping to Standard Keyboards"></a><!-- ws:end:WikiTextHeadingRule:31 -->Mapping to Standard Keyboards</h1> | ||
The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use.<br /> | The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use.<br /> | ||
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| Line 1,197: | Line 1,195: | ||
The archeotonic tonality is much simpler to deal with, you just leave out a tone and remember which one. Although, for diatonic use it may be more convenient to put the missing tone between E/F or B/C to keep it on the white keys, with the remaining small step where it looks like it should be.<br /> | The archeotonic tonality is much simpler to deal with, you just leave out a tone and remember which one. Although, for diatonic use it may be more convenient to put the missing tone between E/F or B/C to keep it on the white keys, with the remaining small step where it looks like it should be.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:33:&lt;h1&gt; --><h1 id="toc12"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:33 -->Commas</h1> | ||
13 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 val &lt; 13 21 30 36 45 48 |.)<br /> | 13 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 val &lt; 13 21 30 36 45 48 |.)<br /> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:35:&lt;h1&gt; --><h1 id="toc13"><a name="Animism"></a><!-- ws:end:WikiTextHeadingRule:35 -->Animism</h1> | ||
The animist comma, 105/104, appears whenever 3*5*7=13... 13edo does not approximate 3 and 7 individually (26edo does), but 13edo has 21/16 (=3*7) and is also an animist temperament. In 13 edo, the 5th harmonic is tuned so flatly that 5/4 = 16/13, leading to some interesting identities. So two scales stand out through this construction<br /> | The animist comma, 105/104, appears whenever 3*5*7=13... 13edo does not approximate 3 and 7 individually (26edo does), but 13edo has 21/16 (=3*7) and is also an animist temperament. In 13 edo, the 5th harmonic is tuned so flatly that 5/4 = 16/13, leading to some interesting identities. So two scales stand out through this construction<br /> | ||
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0 1 3 4 5 8 9 10 12 13 nonatonic<br /> | 0 1 3 4 5 8 9 10 12 13 nonatonic<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><h1 id="toc14"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:37 --><strong>Compositions</strong></h1> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a></span> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a></span> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3" rel="nofollow">Prelude in 13ET</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3" rel="nofollow">Prelude in 13ET</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | ||