Kleismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 213971398 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213972140 - 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>2011-03-25 11: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-25 11:12:38 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213972140</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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Commas: 15625/15552, 179200/177147 | Commas: 15625/15552, 179200/177147 | ||
=Hemikleismic= | |||
Commas: 4000/3969, 6144/6125 | Commas: 4000/3969, 6144/6125 | ||
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EDOs: 53, 121 | EDOs: 53, 121 | ||
=Clyde= | |||
[[Comma|Commas]]: 245/243, 3136/3125 | [[Comma|Commas]]: 245/243, 3136/3125 | ||
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[[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]] | [[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]] | ||
=Tritikleismic= | |||
Commas: 15625/15552, 1029/1024 | Commas: 15625/15552, 1029/1024 | ||
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Badness: 0.0563 | Badness: 0.0563 | ||
==11-limit== | |||
Commas: 385/384, 441/440, 4000/3993 | Commas: 385/384, 441/440, 4000/3993 | ||
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Badness: 0.0193 | Badness: 0.0193 | ||
==13-limit== | |||
Commas: 325/324, 364/363, 441/440, 625/624 | Commas: 325/324, 364/363, 441/440, 625/624 | ||
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Badness: 0.0157 | Badness: 0.0157 | ||
=Quadritikleismic= | |||
Commas: 15625/15552, 2401/2400 | Commas: 15625/15552, 2401/2400 | ||
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Badness: 0.0392 | Badness: 0.0392 | ||
==11-limit== | |||
Commas: 385/384, 1375/1372, 6250/6237 | Commas: 385/384, 1375/1372, 6250/6237 | ||
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Badness: 0.0234 | Badness: 0.0234 | ||
==13-limit== | |||
Commas: 325/324, 385/384, 625/624, 1573/1568 | Commas: 325/324, 385/384, 625/624, 1573/1568 | ||
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Badness: 0.0187</pre></div> | Badness: 0.0187</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>Kleismic family</title></head><body><!-- ws:start:WikiTextTocRule:38:&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:38 --><!-- ws:start:WikiTextTocRule:39: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Countercata">Countercata</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: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- 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: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <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>Kleismic family</title></head><body><!-- ws:start:WikiTextTocRule:38:&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:38 --><!-- ws:start:WikiTextTocRule:39: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Countercata">Countercata</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: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Tritikleismic">Tritikleismic</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: --> | <a href="#Quadritikleismic">Quadritikleismic</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | ||
<!-- ws:end:WikiTextTocRule:58 --><br /> | <!-- ws:end:WikiTextTocRule:58 --><br /> | ||
The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br /> | The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br /> | ||
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Commas: 15625/15552, 179200/177147<br /> | Commas: 15625/15552, 179200/177147<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt; | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:22 -->Hemikleismic</h1> | ||
Commas: 4000/3969, 6144/6125<br /> | Commas: 4000/3969, 6144/6125<br /> | ||
<br /> | <br /> | ||
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EDOs: 53, 121<br /> | EDOs: 53, 121<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt; | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:24 -->Clyde</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/155edo">155</a><br /> | <a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/155edo">155</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt; | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:26 -->Tritikleismic</h1> | ||
Commas: 15625/15552, 1029/1024<br /> | Commas: 15625/15552, 1029/1024<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0563<br /> | Badness: 0.0563<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt; | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2> | ||
Commas: 385/384, 441/440, 4000/3993<br /> | Commas: 385/384, 441/440, 4000/3993<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0193<br /> | Badness: 0.0193<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt; | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h2> | ||
Commas: 325/324, 364/363, 441/440, 625/624<br /> | Commas: 325/324, 364/363, 441/440, 625/624<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0157<br /> | Badness: 0.0157<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt; | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:32 -->Quadritikleismic</h1> | ||
Commas: 15625/15552, 2401/2400<br /> | Commas: 15625/15552, 2401/2400<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0392<br /> | Badness: 0.0392<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt; | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | ||
Commas: 385/384, 1375/1372, 6250/6237<br /> | Commas: 385/384, 1375/1372, 6250/6237<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0234<br /> | Badness: 0.0234<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt; | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->13-limit</h2> | ||
Commas: 325/324, 385/384, 625/624, 1573/1568<br /> | Commas: 325/324, 385/384, 625/624, 1573/1568<br /> | ||
<br /> | <br /> | ||