Porcupine family: Difference between revisions
Wikispaces>xenwolf **Imported revision 247581183 - Original comment: inclusion test with link in the heading** |
Wikispaces>genewardsmith **Imported revision 247732115 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 15:08:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>247732115</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
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Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|] | Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|] | ||
EDOs: 14, 15, 29, 44, 73, 160 | EDOs: 14, 15, 29, 44, 73, 160 | ||
=Ammonite= | |||
Commas: 250/243, 686/675 | |||
POTE generator: ~9/7 = 454.448 | |||
Map: [<1 5 8 10|, <0 -9 -15 -19|] | |||
Wedgie: <<9 15 19 3 5 2|| | |||
EDOs: 29, 37, 66 | |||
Badness: 0.1077 | |||
==11-limit== | |||
Commas: 55/54, 100/99, 686/675 | |||
POTE generator: ~9/7 = 454.512 | |||
Map: [<1 5 8 10 8|, <0 -9 -15 -19 -12|] | |||
EDOs: 29, 37, 66 | |||
Badness: 0.0457 | |||
==13-limit== | |||
Commas: 55/54, 91/90, 100/99, 169/168 | |||
POTE generator: ~13/10 = 454.429 | |||
Map: [<1 5 8 10 8 9|, <0 -9 -15 -19 -12 -14|] | |||
EDOs: 29, 37, 66 | |||
Badness: 0.0272 | |||
=Porky= | =Porky= | ||
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</pre></div> | </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:27:&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:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><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: 14, 15, 29, 44, 73, 160<br /> | EDOs: 14, 15, 29, 44, 73, 160<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:17 -->Ammonite</h1> | ||
Commas: 250/243, 686/675<br /> | |||
<br /> | |||
POTE generator: ~9/7 = 454.448<br /> | |||
<br /> | |||
Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]<br /> | |||
Wedgie: &lt;&lt;9 15 19 3 5 2||<br /> | |||
EDOs: 29, 37, 66<br /> | |||
Badness: 0.1077<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:19:&lt;h2&gt; --><h2 id="toc9"><a name="Ammonite-11-limit"></a><!-- ws:end:WikiTextHeadingRule:19 -->11-limit</h2> | |||
Commas: 55/54, 100/99, 686/675<br /> | |||
<br /> | |||
POTE generator: ~9/7 = 454.512<br /> | |||
<br /> | |||
Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]<br /> | |||
EDOs: 29, 37, 66<br /> | |||
Badness: 0.0457<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:21:&lt;h2&gt; --><h2 id="toc10"><a name="Ammonite-13-limit"></a><!-- ws:end:WikiTextHeadingRule:21 -->13-limit</h2> | |||
Commas: 55/54, 91/90, 100/99, 169/168<br /> | |||
<br /> | |||
POTE generator: ~13/10 = 454.429<br /> | |||
<br /> | |||
Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]<br /> | |||
EDOs: 29, 37, 66<br /> | |||
Badness: 0.0272<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc11"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:23 -->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:25:&lt;h2&gt; --><h2 id="toc12"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:25 -->11-limit</h2> | ||
Commas: 55/54, 100/99, 225/224<br /> | Commas: 55/54, 100/99, 225/224<br /> | ||
<br /> | <br /> | ||