Porcupine family: Difference between revisions
Wikispaces>guest **Imported revision 216818554 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 220115936 - 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>2011-04-13 22:57:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>220115936</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">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 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. | <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;white-space: pre-wrap ! important" class="old-revision-html">[[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 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 | [[POTE tuning|POTE generator]]: 163.950 | ||
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The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus. | The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus. | ||
=Porcupine= | =Porcupine= | ||
Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 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. | Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 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. | ||
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Map: [<2 1 1 2|, <0 3 5 5|] | Map: [<2 1 1 2|, <0 3 5 5|] | ||
Wedgie: <<6 10 10 2 -1 -5|| | |||
EDOs: 22, 146 | |||
EDOs: | =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: 14, 15, 29, 44, 73, 160 | |||
==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: 14, 15, 29, 44, 73, 160 | |||
==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: 14, 15, 29, 44, 73, 160</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>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 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.<br /> | <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:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
<!-- ws:end:WikiTextTocRule:25 --><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 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.<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> | ||
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The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h1> | |||
Porcupine, with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. 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 /> | Porcupine, with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. 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 /> | <br /> | ||
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<br /> | <br /> | ||
Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]<br /> | Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]<br /> | ||
Wedgie: &lt;&lt;6 10 10 2 -1 -5||<br /> | |||
EDOs: 22, 146<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nautilus</h1> | |||
Commas: 49/48, 250/243<br /> | |||
<br /> | |||
Pote generator: ~21/20 = 82.505<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]<br /> | |||
Wedgie: &lt;&lt;6 10 3 2 -12 -21||<br /> | |||
EDOs: 14, 15, 29, 44, 73, 160<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> | |||
Commas: 49/48, 55/54, 245/242<br /> | |||
<br /> | |||
POTE generator: ~21/20 = 82.504<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]<br /> | |||
EDOs: 14, 15, 29, 44, 73, 160<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2> | |||
Commas: 49/48, 55/54, 91/90, 100/99<br /> | |||
<br /> | |||
POTE generator: ~21/20 = 62.530<br /> | |||
<br /> | <br /> | ||
EDOs: | Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]<br /> | ||
EDOs: 14, 15, 29, 44, 73, 160</body></html></pre></div> |