Schismatic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 163991491 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 164134009 - 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:genewardsmith|genewardsmith]] and made on <tt>2010-09-20 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-20 22:14:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>164134009</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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Map: [<1 0 15 -59|, <0 1 -8 39|] | Map: [<1 0 15 -59|, <0 1 -8 39|] | ||
Edos: 171, 1079, 1250, 1421</pre></div> | Edos: 171, 1079, 1250, 1421 | ||
===Grackle=== | |||
Commas: 126/125, 32805/32768 | |||
7-limit minimax | |||
Eigenmonzos: 2, 7/6 | |||
9-limit minimax | |||
Eigenmonzos: 2, 9/7 | |||
Map: [<1 0 15 -44|, <0 1 -8 -26|] | |||
Edos: 77, 89</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>Schismatic family</title></head><body>The 5-limit parent comma for the schismatic family is the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymus comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. Its <a class="wiki_link" href="/monzo">monzo</a> is |-15 8 1&gt;, and flipping that yields &lt;&lt;1 -8 -15|| for the <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768. <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>Schismatic family</title></head><body>The 5-limit parent comma for the schismatic family is the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymus comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. Its <a class="wiki_link" href="/monzo">monzo</a> is |-15 8 1&gt;, and flipping that yields &lt;&lt;1 -8 -15|| for the <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768. <br /> | ||
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<br /> | <br /> | ||
Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]<br /> | Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]<br /> | ||
Edos: 171, 1079, 1250, 1421</body></html></pre></div> | Edos: 171, 1079, 1250, 1421<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Grackle"></a><!-- ws:end:WikiTextHeadingRule:6 -->Grackle</h3> | |||
Commas: 126/125, 32805/32768<br /> | |||
<br /> | |||
7-limit minimax<br /> | |||
Eigenmonzos: 2, 7/6<br /> | |||
<br /> | |||
9-limit minimax<br /> | |||
Eigenmonzos: 2, 9/7<br /> | |||
<br /> | |||
Map: [&lt;1 0 15 -44|, &lt;0 1 -8 -26|]<br /> | |||
Edos: 77, 89</body></html></pre></div> | |||