Schismatic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 239340937 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 239768967 - 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>2011- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-02 16:18:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>239768967</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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Wedgie: <<4 -32 -15 -60 -35 55|| | Wedgie: <<4 -32 -15 -60 -35 55|| | ||
[[edo|Edos]]: [[171edo|171]], [[643edo|643]] | [[edo|Edos]]: [[171edo|171]], [[643edo|643]] | ||
Badness: 0.0112</pre></div> | Badness: 0.0112 | ||
=Sextilififths= | |||
Commas: 32768/32805, 235298/234375 | |||
POTE generator: ~21/20 = 83.053 | |||
Map: [<1 2 -1 -1|, <0 -6 48 55|] | |||
EDOs: 29, 101, 130, 289, 419 | |||
Badness: 0.1088 | |||
==11-limit== | |||
Commas: 441/440, 4000/3993, 235298/234375 | |||
POTE generator: ~21/20 = 83.049 | |||
Map: [<1 2 -1 -1 0|, <0 -6 48 55 50|] | |||
EDOs: 29, 130, 289 | |||
Badness: 0.0455 | |||
==13-limit== | |||
Commas: 363/363, 441/440, 676/675, 10985/10976 | |||
POTE generator: ~21/20 = 83.049 | |||
Map: [<1 2 -1 -1 0 1|, <0 -6 48 55 50 39|] | |||
EDOs: 29, 130, 289 | |||
Badness: 0.0253</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><!-- 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>Schismatic family</title></head><body><!-- ws:start:WikiTextTocRule:36:&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:36 --><!-- ws:start:WikiTextTocRule:37: --><a href="#Five limit">Five limit</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Guiron">Guiron</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: --> | <a href="#Pontiac">Pontiac</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Grackle">Grackle</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Bischismic">Bischismic</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Term">Term</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Sesquiquartififths">Sesquiquartififths</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Sextilififths">Sextilififths</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:55 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit</h1> | ||
The 5-limit parent comma for the schismatic family is the <a class="wiki_link" href="/schisma">schisma</a> of 32805/32768, which is the amount by which the Pythagorean comma exceeds the <a class="wiki_link" href="/Didymus%20comma">Didymus comma</a> (<a class="wiki_link" href="/81_80">81/80</a>), 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 /> | The 5-limit parent comma for the schismatic family is the <a class="wiki_link" href="/schisma">schisma</a> of 32805/32768, which is the amount by which the Pythagorean comma exceeds the <a class="wiki_link" href="/Didymus%20comma">Didymus comma</a> (<a class="wiki_link" href="/81_80">81/80</a>), 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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Wedgie: &lt;&lt;4 -32 -15 -60 -35 55||<br /> | Wedgie: &lt;&lt;4 -32 -15 -60 -35 55||<br /> | ||
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/643edo">643</a><br /> | <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/643edo">643</a><br /> | ||
Badness: 0.0112</body></html></pre></div> | Badness: 0.0112<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Sextilififths"></a><!-- ws:end:WikiTextHeadingRule:30 -->Sextilififths</h1> | |||
Commas: 32768/32805, 235298/234375<br /> | |||
<br /> | |||
POTE generator: ~21/20 = 83.053<br /> | |||
<br /> | |||
Map: [&lt;1 2 -1 -1|, &lt;0 -6 48 55|]<br /> | |||
EDOs: 29, 101, 130, 289, 419<br /> | |||
Badness: 0.1088<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Sextilififths-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | |||
Commas: 441/440, 4000/3993, 235298/234375<br /> | |||
<br /> | |||
POTE generator: ~21/20 = 83.049<br /> | |||
<br /> | |||
Map: [&lt;1 2 -1 -1 0|, &lt;0 -6 48 55 50|]<br /> | |||
EDOs: 29, 130, 289<br /> | |||
Badness: 0.0455<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Sextilififths-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | |||
Commas: 363/363, 441/440, 676/675, 10985/10976<br /> | |||
<br /> | |||
POTE generator: ~21/20 = 83.049<br /> | |||
<br /> | |||
Map: [&lt;1 2 -1 -1 0 1|, &lt;0 -6 48 55 50 39|]<br /> | |||
EDOs: 29, 130, 289<br /> | |||
Badness: 0.0253</body></html></pre></div> | |||