Porcupine family: Difference between revisions

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**Imported revision 319879020 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 319906058 - 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>2012-04-12 12:55:41 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-12 13:55:28 UTC</tt>.<br>
: The original revision id was <tt>319879020</tt>.<br>
: The original revision id was <tt>319906058</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: 7, 15, 22f, 37f
EDOs: 7, 15, 22f, 37f
Badness: 0.0213
Badness: 0.0213
==Porkpie==
Commas: 55/54, 64/63, 65/63, 100/99
POTE generator: ~10/9 = 163.688
Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]
EDOs: 7, 15f, 22
Badness: 0.0260


=Hystrix=  
=Hystrix=  
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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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:42:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Coendou"&gt;Coendou&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:44:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Coendou"&gt;Coendou&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;
&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;hr /&gt;
&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;hr /&gt;
The 5-limit parent comma for the porcupine family is 250/243, the maximal &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; or porcupine comma. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |1 -5 3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 5 1|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. This tells us the &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; is a minor whole tone, the &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; 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.&lt;br /&gt;
The 5-limit parent comma for the porcupine family is 250/243, the maximal &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; or porcupine comma. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |1 -5 3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 5 1|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. This tells us the &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; is a minor whole tone, the &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0213&lt;br /&gt;
Badness: 0.0213&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Hystrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hystrix&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Porcupine-Porkpie"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Porkpie&lt;/h2&gt;
Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 163.688&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 2 4 3|, &amp;lt;0 -3 -5 6 -4 5|]&lt;br /&gt;
EDOs: 7, 15f, 22&lt;br /&gt;
Badness: 0.0260&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Hystrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Hystrix&lt;/h1&gt;
  Hystrix, with wedgie &amp;lt;&amp;lt;3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;. They can try the even sharper fifth of hystrix in &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; and see how that suits.&lt;br /&gt;
  Hystrix, with wedgie &amp;lt;&amp;lt;3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;. They can try the even sharper fifth of hystrix in &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; and see how that suits.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 10d, 12, 13d, 15&lt;br /&gt;
EDOs: 10d, 12, 13d, 15&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Hedgehog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Hedgehog&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Hedgehog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Hedgehog&lt;/h1&gt;
  Hedgehog, with wedgie &amp;lt;&amp;lt;6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &amp;lt;146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.&lt;br /&gt;
  Hedgehog, with wedgie &amp;lt;&amp;lt;6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &amp;lt;146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0440&lt;br /&gt;
Badness: 0.0440&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h2&gt;
  Commas: 50/49, 55/54, 99/98&lt;br /&gt;
  Commas: 50/49, 55/54, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0231&lt;br /&gt;
Badness: 0.0231&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Hedgehog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Hedgehog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
Commas: 50/49, 55/54, 65/63, 99/98&lt;br /&gt;
Commas: 50/49, 55/54, 65/63, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0215&lt;br /&gt;
Badness: 0.0215&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Hedgehog-Hedgepig"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Hedgepig&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Hedgehog-Hedgepig"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Hedgepig&lt;/h2&gt;
  Commas: 50/49, 245/243, 385/384&lt;br /&gt;
  Commas: 50/49, 245/243, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0684&lt;br /&gt;
Badness: 0.0684&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Hedgehog-Hedgepig-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Music&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Hedgehog-Hedgepig-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Music&lt;/h3&gt;
  &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow"&gt;Phobos Light&lt;/a&gt; by Chris Vaisvil in Hedgehog[14] &lt;a class="wiki_link" href="/hedgehog14"&gt;tuned&lt;/a&gt; to 22edo.&lt;br /&gt;
  &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow"&gt;Phobos Light&lt;/a&gt; by Chris Vaisvil in Hedgehog[14] &lt;a class="wiki_link" href="/hedgehog14"&gt;tuned&lt;/a&gt; to 22edo.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Nautilus&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Nautilus&lt;/h1&gt;
  Commas: 49/48, 250/243&lt;br /&gt;
  Commas: 49/48, 250/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 10, 15, 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/102edo"&gt;102cd&lt;/a&gt;&lt;br /&gt;
EDOs: 10, 15, 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/102edo"&gt;102cd&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
  Commas: 49/48, 55/54, 245/242&lt;br /&gt;
  Commas: 49/48, 55/54, 245/242&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde&lt;br /&gt;
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
  Commas: 49/48, 55/54, 91/90, 100/99&lt;br /&gt;
  Commas: 49/48, 55/54, 91/90, 100/99&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow"&gt;Nautilus Reverie&lt;/a&gt; by &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Calvin Jones-Coolidge&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow"&gt;Nautilus Reverie&lt;/a&gt; by &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Calvin Jones-Coolidge&lt;/a&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Ammonite&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Ammonite&lt;/h1&gt;
  Commas: 250/243, 686/675&lt;br /&gt;
  Commas: 250/243, 686/675&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 331: Line 349:
Badness: 0.1077&lt;br /&gt;
Badness: 0.1077&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Ammonite-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Ammonite-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
  Commas: 55/54, 100/99, 686/675&lt;br /&gt;
  Commas: 55/54, 100/99, 686/675&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 340: Line 358:
Badness: 0.0457&lt;br /&gt;
Badness: 0.0457&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
  Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
  Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 349: Line 367:
Badness: 0.0272&lt;br /&gt;
Badness: 0.0272&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Porky&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Porky&lt;/h1&gt;
  Commas: 225/224, 250/243&lt;br /&gt;
  Commas: 225/224, 250/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 359: Line 377:
Badness: 0.0544&lt;br /&gt;
Badness: 0.0544&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h2&gt;
  Commas: 55/54, 100/99, 225/224&lt;br /&gt;
  Commas: 55/54, 100/99, 225/224&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 368: Line 386:
Badness: 0.0273&lt;br /&gt;
Badness: 0.0273&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Coendou"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Coendou&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Coendou"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Coendou&lt;/h1&gt;
  Commas: 250/243, 525/512&lt;br /&gt;
  Commas: 250/243, 525/512&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 378: Line 396:
Badness: 0.1183&lt;br /&gt;
Badness: 0.1183&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Coendou-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Coendou-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
  Commas: 55/54, 100/99, 525/512&lt;br /&gt;
  Commas: 55/54, 100/99, 525/512&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 387: Line 405:
Badness: 0.0497&lt;br /&gt;
Badness: 0.0497&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Coendou-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Coendou-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
  Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
  Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;

Revision as of 13:55, 12 April 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-04-12 13:55:28 UTC.
The original revision id was 319906058.
The revision comment was:

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Original Wikitext content:

[[toc|flat]]
----
The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10_9|10/9]] 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.

[[POTE tuning|POTE generator]]: 163.950

Map: [<1 2 3|, <0 -3 -5|]

EDOs: [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]

==Seven limit children== 
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[64_63|64/63]], the [[Archyta's comma]], for [[Porcupine family#Porcupine|porcupine]], [[36_35|36/35]], the [[septimal quarter tone]], for [[Porcupine family#Hystrix|hystrix]], [[50_49|50/49]], the [[jubilisma]], for [[Porcupine family#Hedgehog|hedgehog]], and [[49_48|49/48]], the [[slendro diesis]], for [[Porcupine family#Nautilus|nautilus]].

=Porcupine= 
[[Porcupine]], with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to [[7_4|7/4]]. For this to work you need a small minor tone such as [[22edo]] provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.

Commas: 250/243, 64/63

[[POTE tuning|POTE generator]]: ~10/9 = 162.880

Map: [<1 2 3 2|, <0 -3 -5 6|]
EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]

==11-limit== 
Commas: 55/54, 64/63, 100/99

POTE generator: ~10/9 = 162.747

Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|]
EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]]
Badness: 0.0217

==13-limit==
Commas: 40/39, 55/54, 64/63, 66/65

POTE generator: ~10/9 = 162.708

Map: [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|]
EDOs: 7, 15, 22f, 37f
Badness: 0.0213

==Porkpie==
Commas: 55/54, 64/63, 65/63, 100/99

POTE generator: ~10/9 = 163.688

Map: [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|]
EDOs: 7, 15f, 22
Badness: 0.0260

=Hystrix= 
Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.

Commas: 36/35, 160/147

[[POTE tuning|POTE generator]]: 158.868

Map: [<1 2 3 3|, <0 -3 -5 -1|]

EDOs: 10d, 12, 13d, 15

=Hedgehog= 
Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.

Commas: 50/49, 245/243

[[POTE tuning|POTE generator]]: ~9/7 = 435.648

Map: [<2 1 1 2|, <0 3 5 5|]
Wedgie: <<6 10 10 2 -1 -5||
EDOs: 22, [[146edo|146]]
Badness: 0.0440

==11-limit== 
Commas: 50/49, 55/54, 99/98

POTE generator: ~9/7 = 435.386

Map: [<2 1 1 2 4|, <0 3 5 5 4|]
EDOs: 14c, 22, 58ce, 80ce, 102cde
Badness: 0.0231

==13-limit==
Commas: 50/49, 55/54, 65/63, 99/98

POTE generator: ~9/7 = 435.861

Map: [<2 1 1 2 4 3|, <0 3 5 5 4 6|]
EDOs: 14cf, 22
Badness: 0.0215

==Hedgepig== 
Commas: 50/49, 245/243, 385/384

POTE generator: ~9/7 = 435.425

Map: [<2 1 1 2 12|, <0 3 5 5 -7|]
EDOs: 22, 80c, 102cd, 124cd
Badness: 0.0684

===Music=== 
[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.

=Nautilus= 
Commas: 49/48, 250/243

Pote generator: ~21/20 = 82.505

Map: [<1 2 3 3|, <0 -6 -10 -3|]
Wedgie: <<6 10 3 2 -12 -21||
EDOs: 10, 15, 19, [[29edo|29]], [[102edo|102cd]]

==11-limit== 
Commas: 49/48, 55/54, 245/242

POTE generator: ~21/20 = 82.504

Map: [<1 2 3 3 4|, <0 -6 -10 -3 -8|]
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde

==13-limit== 
Commas: 49/48, 55/54, 91/90, 100/99

POTE generator: ~21/20 = 62.530

Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|]
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde

[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3|Nautilus Reverie]] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]]
=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= 
Commas: 225/224, 250/243

POTE generator: ~10/9 = 164.412

Map: [<1 2 3 5|, <0 -3 -5 -16|]
Wedgie: <<3 5 16 1 17 23||
EDOS: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0544

==11-limit== 
Commas: 55/54, 100/99, 225/224

POTE generator: ~10/9 = 164.552

Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|]
EDOs: 7, 8, 15, 22, 29, 51, 73
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

Original HTML content:

<html><head><title>Porcupine family</title></head><body><!-- ws:start:WikiTextTocRule:44:&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:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- 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="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- 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:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Nautilus">Nautilus</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: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Coendou">Coendou</a><!-- 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 --><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 />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br />
<br />
Map: [&lt;1 2 3|, &lt;0 -3 -5|]<br />
<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/95edo">95c</a>, <a class="wiki_link" href="/117edo">117bc</a>, <a class="wiki_link" href="/139edo">139bc</a>, <a class="wiki_link" href="/161edo">161bc</a>, <a class="wiki_link" href="/183edo">183bc</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2>
 The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. That means <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Archyta%27s%20comma">Archyta's comma</a>, for <a class="wiki_link" href="/Porcupine%20family#Porcupine">porcupine</a>, <a class="wiki_link" href="/36_35">36/35</a>, the <a class="wiki_link" href="/septimal%20quarter%20tone">septimal quarter tone</a>, for <a class="wiki_link" href="/Porcupine%20family#Hystrix">hystrix</a>, <a class="wiki_link" href="/50_49">50/49</a>, the <a class="wiki_link" href="/jubilisma">jubilisma</a>, for <a class="wiki_link" href="/Porcupine%20family#Hedgehog">hedgehog</a>, and <a class="wiki_link" href="/49_48">49/48</a>, the <a class="wiki_link" href="/slendro%20diesis">slendro diesis</a>, for <a class="wiki_link" href="/Porcupine%20family#Nautilus">nautilus</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h1>
 <a class="wiki_link" href="/Porcupine">Porcupine</a>, with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to <a class="wiki_link" href="/7_4">7/4</a>. For this to work you need a small minor tone such as <a class="wiki_link" href="/22edo">22edo</a> provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.<br />
<br />
Commas: 250/243, 64/63<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br />
<br />
Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]<br />
EDOs: 22, <a class="wiki_link" href="/59edo">59</a>, <a class="wiki_link" href="/81edo">81bd</a>, <a class="wiki_link" href="/140edo">140bd</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
 Commas: 55/54, 64/63, 100/99<br />
<br />
POTE generator: ~10/9 = 162.747<br />
<br />
Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]<br />
EDOs: <a class="wiki_link" href="/7edo">7</a>, 15, 22, <a class="wiki_link" href="/37edo">37</a>, <a class="wiki_link" href="/59edo">59</a><br />
Badness: 0.0217<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Porcupine-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
Commas: 40/39, 55/54, 64/63, 66/65<br />
<br />
POTE generator: ~10/9 = 162.708<br />
<br />
Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]<br />
EDOs: 7, 15, 22f, 37f<br />
Badness: 0.0213<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Porcupine-Porkpie"></a><!-- ws:end:WikiTextHeadingRule:8 -->Porkpie</h2>
Commas: 55/54, 64/63, 65/63, 100/99<br />
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POTE generator: ~10/9 = 163.688<br />
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Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]<br />
EDOs: 7, 15f, 22<br />
Badness: 0.0260<br />
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Hystrix"></a><!-- ws:end:WikiTextHeadingRule:10 -->Hystrix</h1>
 Hystrix, with wedgie &lt;&lt;3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried <a class="wiki_link" href="/15edo">15edo</a>. They can try the even sharper fifth of hystrix in <a class="wiki_link" href="/68edo">68edo</a> and see how that suits.<br />
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Commas: 36/35, 160/147<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.868<br />
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Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]<br />
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EDOs: 10d, 12, 13d, 15<br />
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:12 -->Hedgehog</h1>
 Hedgehog, with wedgie &lt;&lt;6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.<br />
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Commas: 50/49, 245/243<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 435.648<br />
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Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]<br />
Wedgie: &lt;&lt;6 10 10 2 -1 -5||<br />
EDOs: 22, <a class="wiki_link" href="/146edo">146</a><br />
Badness: 0.0440<br />
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Hedgehog-11-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->11-limit</h2>
 Commas: 50/49, 55/54, 99/98<br />
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POTE generator: ~9/7 = 435.386<br />
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Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]<br />
EDOs: 14c, 22, 58ce, 80ce, 102cde<br />
Badness: 0.0231<br />
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Hedgehog-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2>
Commas: 50/49, 55/54, 65/63, 99/98<br />
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POTE generator: ~9/7 = 435.861<br />
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Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]<br />
EDOs: 14cf, 22<br />
Badness: 0.0215<br />
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Hedgehog-Hedgepig"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hedgepig</h2>
 Commas: 50/49, 245/243, 385/384<br />
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POTE generator: ~9/7 = 435.425<br />
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Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]<br />
EDOs: 22, 80c, 102cd, 124cd<br />
Badness: 0.0684<br />
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Hedgehog-Hedgepig-Music"></a><!-- ws:end:WikiTextHeadingRule:20 -->Music</h3>
 <a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow">Phobos Light</a> by Chris Vaisvil in Hedgehog[14] <a class="wiki_link" href="/hedgehog14">tuned</a> to 22edo.<br />
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:22 -->Nautilus</h1>
 Commas: 49/48, 250/243<br />
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Pote generator: ~21/20 = 82.505<br />
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Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]<br />
Wedgie: &lt;&lt;6 10 3 2 -12 -21||<br />
EDOs: 10, 15, 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/102edo">102cd</a><br />
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2>
 Commas: 49/48, 55/54, 245/242<br />
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POTE generator: ~21/20 = 82.504<br />
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Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]<br />
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde<br />
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<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2>
 Commas: 49/48, 55/54, 91/90, 100/99<br />
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POTE generator: ~21/20 = 62.530<br />
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Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]<br />
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde<br />
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<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow">Nautilus Reverie</a> by <a class="wiki_link" href="/IgliashonJones">Igliashon Calvin Jones-Coolidge</a><br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:28 -->Ammonite</h1>
 Commas: 250/243, 686/675<br />
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POTE generator: ~9/7 = 454.448<br />
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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 />
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<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Ammonite-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2>
 Commas: 55/54, 100/99, 686/675<br />
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POTE generator: ~9/7 = 454.512<br />
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Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]<br />
EDOs: 29, 37, 66<br />
Badness: 0.0457<br />
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<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Ammonite-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2>
 Commas: 55/54, 91/90, 100/99, 169/168<br />
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POTE generator: ~13/10 = 454.429<br />
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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 />
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<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:34 -->Porky</h1>
 Commas: 225/224, 250/243<br />
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POTE generator: ~10/9 = 164.412<br />
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Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]<br />
Wedgie: &lt;&lt;3 5 16 1 17 23||<br />
EDOS: 7, 8, 15, 22, 29, 51, 73<br />
Badness: 0.0544<br />
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<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2>
 Commas: 55/54, 100/99, 225/224<br />
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POTE generator: ~10/9 = 164.552<br />
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Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]<br />
EDOs: 7, 8, 15, 22, 29, 51, 73<br />
Badness: 0.0273<br />
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<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Coendou"></a><!-- ws:end:WikiTextHeadingRule:38 -->Coendou</h1>
 Commas: 250/243, 525/512<br />
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POTE generator: ~10/9 = 166.041<br />
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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 />
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<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Coendou-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2>
 Commas: 55/54, 100/99, 525/512<br />
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POTE generator: ~10/9 = 165.981<br />
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Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]<br />
EDOs: 7, 29, 65ce, 94cde<br />
Badness: 0.0497<br />
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<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Coendou-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2>
 Commas: 55/54, 65/64, 100/99, 105/104<br />
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POTE generator: ~10/9 = 165.974<br />
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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>