Porcupine family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 299586828 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 299875542 - 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>2012-02-08 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-08 16:31:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>299875542</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 2 3 5 4|, <0 -3 -5 -16 -4|] | Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|] | ||
EDOs: 7, 8, 15, 22, 29, 51, 73 | EDOs: 7, 8, 15, 22, 29, 51, 73 | ||
Badness: 0.0273</pre></div> | Badness: 0.0273 | ||
=Coendou= | |||
Commas: 250/243, 525/512 | |||
POTE generator: ~10/9 = 166.041 | |||
Map: [<1 2 3 1|, <0 -3 -5 13|] | |||
Wedgie: <<3 5 -13 1 -29 -44|| | |||
EDOs: 7, 29, 65c, 94cd | |||
Badness: 0.1183 | |||
==11-limit== | |||
Commas: 55/54, 100/99, 525/512 | |||
POTE generator: ~10/9 = 165.981 | |||
Map: [<1 2 3 1 4|, <0 -3 -5 13 -4|] | |||
EDOs: 7, 29, 65ce, 94cde | |||
Badness: 0.0497 | |||
==13-limit== | |||
Commas: 55/54, 65/64, 100/99, 105/104 | |||
POTE generator: ~10/9 = 165.974 | |||
Map: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|] | |||
EDOs: 7, 29, 65cef, 94cdef | |||
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: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: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Hedgehog">Hedgehog</a><!-- 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="#Nautilus">Nautilus</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="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Coendou">Coendou</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 --><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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Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]<br /> | Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]<br /> | ||
EDOs: 7, 8, 15, 22, 29, 51, 73<br /> | EDOs: 7, 8, 15, 22, 29, 51, 73<br /> | ||
Badness: 0.0273</body></html></pre></div> | Badness: 0.0273<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Coendou"></a><!-- ws:end:WikiTextHeadingRule:30 -->Coendou</h1> | |||
Commas: 250/243, 525/512<br /> | |||
<br /> | |||
POTE generator: ~10/9 = 166.041<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]<br /> | |||
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||<br /> | |||
EDOs: 7, 29, 65c, 94cd<br /> | |||
Badness: 0.1183<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Coendou-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | |||
Commas: 55/54, 100/99, 525/512<br /> | |||
<br /> | |||
POTE generator: ~10/9 = 165.981<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]<br /> | |||
EDOs: 7, 29, 65ce, 94cde<br /> | |||
Badness: 0.0497<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Coendou-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | |||
Commas: 55/54, 65/64, 100/99, 105/104<br /> | |||
<br /> | |||
POTE generator: ~10/9 = 165.974<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]<br /> | |||
EDOs: 7, 29, 65cef, 94cdef<br /> | |||
Badness: 0.0302</body></html></pre></div> | |||