Magic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 278347320 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 287077970 - 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>2011- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-17 14:42:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>287077970</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: 19, 22, 31f, 34ef, 41ef | EDOs: 19, 22, 31f, 34ef, 41ef | ||
Badness: 0.0255 | Badness: 0.0255 | ||
=Hocus= | |||
Commas: 225/224, 243/242, 245/242 | |||
POTE generator: ~14/11 = 409.910 | |||
Map: [<1 5 3 11 12|, <0 -10 -2 -24 -25|] | |||
EDOs: 38d, 41, 120cd, 161cd, 202cd | |||
Badness: 0.0385 | |||
==13-limit== | |||
Commas: 105/104, 196/195, 243/242, 245/242 | |||
POTE generator: ~14/11 = 410.004 | |||
Map: [<1 5 3 11 12 16|, <0 -10 -2 -24 -25 -36|] | |||
EDOs: 41, 79d, 120cd | |||
Badness: 0.0303 | |||
=Muggles= | =Muggles= | ||
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Badness: 0.0827</pre></div> | Badness: 0.0827</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>Magic 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>Magic family</title></head><body><!-- ws:start:WikiTextTocRule:26:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#Five limit magic">Five limit magic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 2em;"><a href="#Five limit magic-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 1em;"><a href="#Magic">Magic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#Magic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#Magic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 3em;"><a href="#Magic-13-limit-Sorcery">Sorcery</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 3em;"><a href="#Magic-13-limit-Necromancy">Necromancy</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Magic-Telepathy">Telepathy</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 3em;"><a href="#Magic-Telepathy-13-limit telepathy">13-limit telepathy</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 1em;"><a href="#Hocus">Hocus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 2em;"><a href="#Hocus-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 1em;"><a href="#Muggles">Muggles</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 1em;"><a href="#Astrology">Astrology</a></div> | ||
<!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --></div> | |||
<!-- ws:end:WikiTextTocRule:40 --><br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit magic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit magic</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit magic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit magic</h1> | ||
The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of sense sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of sense sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | ||
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Badness: 0.0255<br /> | Badness: 0.0255<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Muggles"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Hocus"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hocus</h1> | ||
Commas: 225/224, 243/242, 245/242<br /> | |||
<br /> | |||
POTE generator: ~14/11 = 409.910<br /> | |||
<br /> | |||
Map: [&lt;1 5 3 11 12|, &lt;0 -10 -2 -24 -25|]<br /> | |||
EDOs: 38d, 41, 120cd, 161cd, 202cd<br /> | |||
Badness: 0.0385<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Hocus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> | |||
Commas: 105/104, 196/195, 243/242, 245/242<br /> | |||
<br /> | |||
POTE generator: ~14/11 = 410.004<br /> | |||
<br /> | |||
Map: [&lt;1 5 3 11 12 16|, &lt;0 -10 -2 -24 -25 -36|]<br /> | |||
EDOs: 41, 79d, 120cd<br /> | |||
Badness: 0.0303<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Muggles"></a><!-- ws:end:WikiTextHeadingRule:22 -->Muggles</h1> | |||
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.<br /> | Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.<br /> | ||
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EDOs: 19, 73bcd, 92bcd<br /> | EDOs: 19, 73bcd, 92bcd<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Astrology"></a><!-- ws:end:WikiTextHeadingRule:24 -->Astrology</h1> | ||
Commas: 50/49, 3125/3072<br /> | Commas: 50/49, 3125/3072<br /> | ||
<br /> | <br /> | ||