37edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 285079696 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 285125514 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-12-12 13:36:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>285125514</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, it tempers out 250/243, making it a variant of [[ | <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, it 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. | |||
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[[37ED4]] | [[37ED4]] | ||
[[square root of 13 over 10|The Square Root of 13/10]]</pre></div> | [[square root of 13 over 10|The Square Root of 13/10]] | ||
=Linear temperaments= | |||
||~ Generator ||~ "Sharp 3/2" temperaments ||~ "Flat 3/2" temperaments (37b val) || | |||
|| 1\37 || || || | |||
|| 2\37 || [[Sycamore family|Sycamore]] || || | |||
|| 3\37 || [[Passion]] || || | |||
|| 4\37 || [[Twothirdtonic]] || [[Negri]] || | |||
|| 5\37 || [[Porcupine]]/[[The Biosphere#Oceanfront-Oceanfront%20Children-Porcupinefish|porcupinefish]] || || | |||
|| 6\37 |||| [[Chromatic pairs#Roulette|Roulette]] || | |||
|| 7\37 || [[Semaja]] || [[Gorgo]]/[[Laconic]] || | |||
|| 8\37 || || || | |||
|| 9\37 || || || | |||
|| 10\37 || || || | |||
|| 11\37 || [[Beatles]] || || | |||
|| 12\37 || [[Würschmidt]] (out-of-tune) || || | |||
|| 13\37 || || || | |||
|| 14\37 || [[Ammonite]] || || | |||
|| 15\37 || **Not** [[superpyth]] || || | |||
|| 16\37 || || **Not** [[mavila]] (this is "undecimation") || | |||
|| 17\37 || [[Emka]] || || | |||
|| 18\37 || || ||</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>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, it tempers out 250/243, making it a variant of <a class="wiki_link" href="/ | <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, it 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 /> | ||
< | |||
<br /> | <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: | <!-- ws:start:WikiTextTocRule:10:&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:10 --><!-- ws:start:WikiTextTocRule:11: --><a href="#Subgroups">Subgroups</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#The Two Fifths">The Two Fifths</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:16 --><hr /> | ||
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<a class="wiki_link" href="/37ED4">37ED4</a><br /> | <a class="wiki_link" href="/37ED4">37ED4</a><br /> | ||
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<a class="wiki_link" href="/square%20root%20of%2013%20over%2010">The Square Root of 13/10</a></body></html></pre></div> | <a class="wiki_link" href="/square%20root%20of%2013%20over%2010">The Square Root of 13/10</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:8 -->Linear temperaments</h1> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Generator<br /> | |||
</th> | |||
<th>&quot;Sharp 3/2&quot; temperaments<br /> | |||
</th> | |||
<th>&quot;Flat 3/2&quot; temperaments (37b val)<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>1\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Sycamore%20family">Sycamore</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Passion">Passion</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Twothirdtonic">Twothirdtonic</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Negri">Negri</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Porcupine">Porcupine</a>/<a class="wiki_link" href="/The%20Biosphere#Oceanfront-Oceanfront%20Children-Porcupinefish">porcupinefish</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6\37<br /> | |||
</td> | |||
<td colspan="2"><a class="wiki_link" href="/Chromatic%20pairs#Roulette">Roulette</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Semaja">Semaja</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Gorgo">Gorgo</a>/<a class="wiki_link" href="/Laconic">Laconic</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Beatles">Beatles</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/W%C3%BCrschmidt">Würschmidt</a> (out-of-tune)<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Ammonite">Ammonite</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15\37<br /> | |||
</td> | |||
<td><strong>Not</strong> <a class="wiki_link" href="/superpyth">superpyth</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><strong>Not</strong> <a class="wiki_link" href="/mavila">mavila</a> (this is &quot;undecimation&quot;)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17\37<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Emka">Emka</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> |