Pythagorean family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 304282212 - Original comment: Reverted to Dec 29, 2011 12:16 pm** |
Wikispaces>genewardsmith **Imported revision 332273242 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-09 01:49:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>332273242</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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EDOs: 12, 24, 36, 72ce | EDOs: 12, 24, 36, 72ce | ||
Badness: 0.0345 | Badness: 0.0345 | ||
===13-limit=== | |||
Commas: 56/55, 66/65, 81/80, 105/104 | |||
POTE generator: ~36/35 = 37.232 | |||
Map: [<12 19 28 0 8 11|, <0 0 0 1 1 1|] | |||
EDOs: 12f, 24, 36f, 60cf | |||
Badness: 0.0284 | |||
=Omicronbeta temperament= | =Omicronbeta temperament= | ||
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Map: [<24 38 0 123 83 33|, <0 0 1 -1 0 1|] | Map: [<24 38 0 123 83 33|, <0 0 1 -1 0 1|] | ||
EDOs: 24, 48f, 72, 168df, 240df | EDOs: 24, 48f, 72, 168df, 240df | ||
Badness: 0.0269 | Badness: 0.0269</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>Pythagorean 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>Pythagorean family</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Compton temperament">Compton temperament</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Catler temperament">Catler temperament</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- 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="#Omicronbeta temperament">Omicronbeta temperament</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Hours">Hours</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><br /> | ||
The Pythagorean family tempers out the Pythagorean comma, 531441/524288 = |-19 12&gt;, and hence the fifths form a closed 12-note circle of fifths, identical to <a class="wiki_link" href="/12edo">12edo</a>. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.<br /> | The Pythagorean family tempers out the Pythagorean comma, 531441/524288 = |-19 12&gt;, and hence the fifths form a closed 12-note circle of fifths, identical to <a class="wiki_link" href="/12edo">12edo</a>. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0345<br /> | Badness: 0.0345<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Catler temperament-Catcall-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h3> | ||
Commas: 56/55, 66/65, 81/80, 105/104<br /> | |||
<br /> | |||
POTE generator: ~36/35 = 37.232<br /> | |||
<br /> | |||
Map: [&lt;12 19 28 0 8 11|, &lt;0 0 0 1 1 1|]<br /> | |||
EDOs: 12f, 24, 36f, 60cf<br /> | |||
Badness: 0.0284<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Omicronbeta temperament"></a><!-- ws:end:WikiTextHeadingRule:18 -->Omicronbeta temperament</h1> | |||
Commas: 225/224, 243/242, 441/440, 4375/4356<br /> | Commas: 225/224, 243/242, 441/440, 4375/4356<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0300<br /> | Badness: 0.0300<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Hours"></a><!-- ws:end:WikiTextHeadingRule:20 -->Hours</h1> | ||
Commas: 19683/19600, 33075/32768<br /> | Commas: 19683/19600, 33075/32768<br /> | ||
<br /> | <br /> | ||
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Badness: 0.1161<br /> | Badness: 0.1161<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Hours-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | ||
Commas: 243/242, 385/384, 9801/9800<br /> | Commas: 243/242, 385/384, 9801/9800<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0362<br /> | Badness: 0.0362<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Hours-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2> | ||
Commas: 243/242, 351/350, 364/363, 385/384<br /> | Commas: 243/242, 351/350, 364/363, 385/384<br /> | ||
<br /> | <br /> | ||