Porcupine family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 323721440 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 325704998 - 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>2012-04- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-26 16:18:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>325704998</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: 22, 80c, 102cd, 124cd | EDOs: 22, 80c, 102cd, 124cd | ||
Badness: 0.0684 | Badness: 0.0684 | ||
===Music=== | ===Music=== | ||
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EDOs: 29, 37, 66 | EDOs: 29, 37, 66 | ||
Badness: 0.0272 | Badness: 0.0272 | ||
=Ceratitid= | |||
Commas: 250/243, 1728/1715 | |||
POTE generator: ~36/35 = 54.384 | |||
Map: [<1 2 3 3|, <0 -9 -15 -4|] | |||
Wedgie: <<9 15 4 3 -19 -33|| | |||
EDOs: 22 | |||
Badness: 0.115 | |||
==11-limit== | |||
Commas: 55/54, 100/99, 5324/5145 | |||
POTE generator: ~36/35 = 54.376 | |||
Map: [<1 2 3 3 4|, <0 -9 -15 -4 -12|] | |||
EDOs: 22 | |||
Badness: 0.0513 | |||
==13-limit== | |||
Commas: 55/54, 65/63, 100/99, 352/343 | |||
POTE generator: ~36/35 = 54.665 | |||
Map: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|] | |||
EDOs: 22 | |||
Badness: 0.0447 | |||
=Porky= | =Porky= | ||
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Badness: 0.0302</pre></div> | Badness: 0.0302</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>Porcupine 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>Porcupine family</title></head><body><!-- ws:start:WikiTextTocRule:54:&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:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Porcupine">Porcupine</a><!-- 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: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --> | <a href="#Ceratitid">Ceratitid</a><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Coendou">Coendou</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:82 --><hr /> | ||
The 5-limit parent comma for the porcupine family is 250/243, the maximal <a class="wiki_link" href="/diesis">diesis</a> or porcupine comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. This tells us the <a class="wiki_link" href="/generator">generator</a> is a minor whole tone, the <a class="wiki_link" href="/10_9">10/9</a> interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.<br /> | The 5-limit parent comma for the porcupine family is 250/243, the maximal <a class="wiki_link" href="/diesis">diesis</a> or porcupine comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. This tells us the <a class="wiki_link" href="/generator">generator</a> is a minor whole tone, the <a class="wiki_link" href="/10_9">10/9</a> interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.<br /> | ||
<br /> | <br /> | ||
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EDOs: 22, 80c, 102cd, 124cd<br /> | EDOs: 22, 80c, 102cd, 124cd<br /> | ||
Badness: 0.0684<br /> | Badness: 0.0684<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Hedgehog-Hedgepig-Music"></a><!-- ws:end:WikiTextHeadingRule:24 -->Music</h3> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Hedgehog-Hedgepig-Music"></a><!-- ws:end:WikiTextHeadingRule:24 -->Music</h3> | ||
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Badness: 0.0272<br /> | Badness: 0.0272<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Ceratitid"></a><!-- ws:end:WikiTextHeadingRule:38 -->Ceratitid</h1> | ||
Commas: 250/243, 1728/1715<br /> | |||
<br /> | |||
POTE generator: ~36/35 = 54.384<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]<br /> | |||
Wedgie: &lt;&lt;9 15 4 3 -19 -33||<br /> | |||
EDOs: 22<br /> | |||
Badness: 0.115<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Ceratitid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> | |||
Commas: 55/54, 100/99, 5324/5145<br /> | |||
<br /> | |||
POTE generator: ~36/35 = 54.376<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]<br /> | |||
EDOs: 22<br /> | |||
Badness: 0.0513<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Ceratitid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2> | |||
Commas: 55/54, 65/63, 100/99, 352/343<br /> | |||
<br /> | |||
POTE generator: ~36/35 = 54.665<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]<br /> | |||
EDOs: 22<br /> | |||
Badness: 0.0447<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:44 -->Porky</h1> | |||
Commas: 225/224, 250/243<br /> | Commas: 225/224, 250/243<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0544<br /> | Badness: 0.0544<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | ||
Commas: 55/54, 100/99, 225/224<br /> | Commas: 55/54, 100/99, 225/224<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0273<br /> | Badness: 0.0273<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Coendou"></a><!-- ws:end:WikiTextHeadingRule:48 -->Coendou</h1> | ||
Commas: 250/243, 525/512<br /> | Commas: 250/243, 525/512<br /> | ||
<br /> | <br /> | ||
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Badness: 0.1183<br /> | Badness: 0.1183<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Coendou-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2> | ||
Commas: 55/54, 100/99, 525/512<br /> | Commas: 55/54, 100/99, 525/512<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0497<br /> | Badness: 0.0497<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Coendou-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | ||
Commas: 55/54, 65/64, 100/99, 105/104<br /> | Commas: 55/54, 65/64, 100/99, 105/104<br /> | ||
<br /> | <br /> | ||