Schismatic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 279276974 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 289387361 - 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> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-03 19:18:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>289387361</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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EDOs: 17, 26, 43, 60, 77, 94, 171 | EDOs: 17, 26, 43, 60, 77, 94, 171 | ||
Badness: 0.0307 | Badness: 0.0307 | ||
</pre></div> | |||
=Quanharuk= | |||
Commas: 16875/16807, 32805/32768 | |||
POTE generator: ~56/45 = 380.355 | |||
Map: [<1 0 15 12|, <0 5 -40 -29|] | |||
Wedgie: <<5 -40 -29 -75 -60 45|| | |||
EDOs: 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd | |||
Badness: 0.0720 | |||
==11-limit== | |||
Commas: 540/539, 1375/1372, 32805/32768 | |||
POTE generator: ~56/45 = 380.352 | |||
Map: [<1 0 15 12 -7|, <0 5 -40 -29 33|] | |||
EDOs: 41, 142, 183, 224, 631d, 855d, 1079d | |||
Badness: 0.0315</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:52:&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:52 --><!-- ws:start:WikiTextTocRule:53: --><a href="#Five limit">Five limit</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Guiron">Guiron</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Pogo">Pogo</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Pontiac">Pontiac</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Grackle">Grackle</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Bischismic">Bischismic</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Term">Term</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Sesquiquartififths">Sesquiquartififths</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#Sextilififths">Sextilififths</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#Tsaharuk">Tsaharuk</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Quanharuk">Quanharuk</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:79 --><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;5 -40 24 -75 24 168||<br /> | Wedgie: &lt;&lt;5 -40 24 -75 24 168||<br /> | ||
EDOs: 17, 26, 43, 60, 77, 94, 171<br /> | EDOs: 17, 26, 43, 60, 77, 94, 171<br /> | ||
Badness: 0.0307</body></html></pre></div> | Badness: 0.0307<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Quanharuk"></a><!-- ws:end:WikiTextHeadingRule:48 -->Quanharuk</h1> | |||
Commas: 16875/16807, 32805/32768<br /> | |||
<br /> | |||
POTE generator: ~56/45 = 380.355<br /> | |||
<br /> | |||
Map: [&lt;1 0 15 12|, &lt;0 5 -40 -29|]<br /> | |||
Wedgie: &lt;&lt;5 -40 -29 -75 -60 45||<br /> | |||
EDOs: 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd<br /> | |||
Badness: 0.0720<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Quanharuk-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2> | |||
Commas: 540/539, 1375/1372, 32805/32768<br /> | |||
<br /> | |||
POTE generator: ~56/45 = 380.352<br /> | |||
<br /> | |||
Map: [&lt;1 0 15 12 -7|, &lt;0 5 -40 -29 33|]<br /> | |||
EDOs: 41, 142, 183, 224, 631d, 855d, 1079d<br /> | |||
Badness: 0.0315</body></html></pre></div> | |||