37edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 321892370 - Original comment: ** |
Wikispaces>phylingual **Imported revision 339321122 - 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:phylingual|phylingual]] and made on <tt>2012-05-24 20:25:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>339321122</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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<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 [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/31edo|31edo]] and coming before [[xenharmonic/41edo|41edo]]. | <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 [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/31edo|31edo]] and coming before [[xenharmonic/41edo|41edo]]. | ||
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[xenharmonic/porcupine|porcupine]] temperament. Using its alternative flat fifth, it tempers out 16875/16384, making it a [[xenharmonic/negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[xenharmonic/gorgo|gorgo]]/[[xenharmonic/laconic|laconic]]). | Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[xenharmonic/porcupine|porcupine]] temperament. (It is the optimal patent val for [[Porcupine family#Porcupinefish|porcupinefish]], which is about as accurate as "13-limit porcupine" will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a [[xenharmonic/negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[xenharmonic/gorgo|gorgo]]/[[xenharmonic/laconic|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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<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="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo">31edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo">41edo</a>.<br /> | <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="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo">31edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/porcupine">porcupine</a> temperament. Using its alternative flat fifth, it tempers out 16875/16384, making it a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/gorgo">gorgo</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/laconic">laconic</a>).<br /> | Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porcupine">porcupine</a> temperament. (It is the optimal patent val for <a class="wiki_link" href="/Porcupine%20family#Porcupinefish">porcupinefish</a>, which is about as accurate as &quot;13-limit porcupine&quot; will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/gorgo">gorgo</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 /> | ||