37edo: Difference between revisions
Wikispaces>akjmicro **Imported revision 288879209 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 288886795 - 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>2011-12-31 01:56:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288886795</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">37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. Using its best (and sharp) fifth, | <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">37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th [[prime numbers|prime]] edo, following [[31edo]] and coming before [[41edo]]. | ||
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[porcupine]] temperament. Using its alternative flat fifth, it tempers out 16875/16384, making it a [[negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[gorgo]]/[[laconic]]). | |||
37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS. | 37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS. | ||
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== Music in 37edo == | ==Music in 37edo== | ||
[[http://www.akjmusic.com/audio/toccata_bianca_37edo.mp3|Toccata Bianca 37edo]] by [[http://www.akjmusic.com|Aaron Krister Johnson]] | [[http://www.akjmusic.com/audio/toccata_bianca_37edo.mp3|Toccata Bianca 37edo]] by [[http://www.akjmusic.com|Aaron Krister Johnson]]</pre></div> | ||
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<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>37edo</title></head><body>37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. Using its best (and sharp) fifth, | <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>37edo</title></head><body>37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/31edo">31edo</a> and coming before <a class="wiki_link" href="/41edo">41edo</a>.<br /> | ||
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Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of <a class="wiki_link" href="/porcupine">porcupine</a> temperament. Using its alternative flat fifth, it tempers out 16875/16384, making it a <a class="wiki_link" href="/negri">negri</a> tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth (<a class="wiki_link" href="/gorgo">gorgo</a>/<a class="wiki_link" href="/laconic">laconic</a>).<br /> | |||
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37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.<br /> | 37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.<br /> | ||
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<!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Subgroups">Subgroups</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#The Two Fifths">The Two Fifths</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Subgroups">Subgroups</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#The Two Fifths">The Two Fifths</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Linear temperaments-Music in 37edo"></a><!-- ws:end:WikiTextHeadingRule:10 --> Music in 37edo </h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Linear temperaments-Music in 37edo"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music in 37edo</h2> | ||
<a class="wiki_link_ext" href="http://www.akjmusic.com/audio/toccata_bianca_37edo.mp3" rel="nofollow">Toccata Bianca 37edo</a> by <a class="wiki_link_ext" href="http://www.akjmusic.com" rel="nofollow">Aaron Krister Johnson</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://www.akjmusic.com/audio/toccata_bianca_37edo.mp3" rel="nofollow">Toccata Bianca 37edo</a> by <a class="wiki_link_ext" href="http://www.akjmusic.com" rel="nofollow">Aaron Krister Johnson</a></body></html></pre></div> | ||