Kleismic family: Difference between revisions
Wikispaces>spt3125 **Imported revision 479287936 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 488400996 - 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>2014-02-10 01:43:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>488400996</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: 15, 34d, 49, 132bcd | EDOs: 15, 34d, 49, 132bcd | ||
Badness: 0.0949 | Badness: 0.0949 | ||
==11-limit== | |||
Commas: 64/63, 100/99, 1331/1323 | |||
POTE generator: ~6/5 = 318.282 | |||
Map: [<1 0 1 6 4|, <0 6 5 -12 -2|] | |||
EDOs: 15, 34d, 49 | |||
Badness: 0.0369 | |||
=Catakleismic= | =Catakleismic= | ||
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[[http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3|A Fight for Phi]] by Vito Sicurella</pre></div> | [[http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3|A Fight for Phi]] by Vito Sicurella</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: | <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:104:&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:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 1em;"><a href="#Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 1em;"><a href="#Keemun">Keemun</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#Keemun-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Keemun-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 3em;"><a href="#Keemun-13-limit-Kema">Kema</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 3em;"><a href="#Keemun-13-limit-Kumbaya">Kumbaya</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Keemun-Qeema">Qeema</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 3em;"><a href="#Keemun-Qeema-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 2em;"><a href="#Keemun-Darjeeling">Darjeeling</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 3em;"><a href="#Keemun-Darjeeling-13-limit Darjeeling">13-limit Darjeeling</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 1em;"><a href="#Catalan">Catalan</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Catalan-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 1em;"><a href="#Catakleismic">Catakleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 2em;"><a href="#Catakleismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Catakleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 1em;"><a href="#Cataclysmic">Cataclysmic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 2em;"><a href="#Cataclysmic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 1em;"><a href="#Catalytic">Catalytic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Catalytic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Countercata">Countercata</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Countercata-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Countercata-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 1em;"><a href="#Metakleismic">Metakleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 2em;"><a href="#Metakleismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 2em;"><a href="#Metakleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 1em;"><a href="#Hemikleismic">Hemikleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 2em;"><a href="#Hemikleismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 2em;"><a href="#Hemikleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 1em;"><a href="#Clyde">Clyde</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 2em;"><a href="#Clyde-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Clyde-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Bikleismic">Bikleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Bikleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 1em;"><a href="#Tritikleismic">Tritikleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Tritikleismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Tritikleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 1em;"><a href="#Quadritikleismic">Quadritikleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 2em;"><a href="#Quadritikleismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Quadritikleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 1em;"><a href="#Kleiboh">Kleiboh</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 2em;"><a href="#Kleiboh-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Kleiboh-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 1em;"><a href="#Novemkleismic">Novemkleismic</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Novemkleismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 2em;"><a href="#Novemkleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 1em;"><a href="#Sqrtphi">Sqrtphi</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Sqrtphi-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 2em;"><a href="#Sqrtphi-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 2em;"><a href="#Sqrtphi-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Sqrtphi-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 2em;"><a href="#Sqrtphi-Scales">Scales</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 2em;"><a href="#Sqrtphi-Music">Music</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --></div> | ||
<!-- ws:end:WikiTextTocRule:157 -->The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the <strong>kleismic family</strong> 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. This 5-limit temperament (virtually a microtemperament) is commonly called <strong>Hanson</strong>, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are 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 /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br /> | ||
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Badness: 0.0949<br /> | Badness: 0.0949<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Catalan-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | ||
Commas: 64/63, 100/99, 1331/1323<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 318.282<br /> | |||
<br /> | |||
Map: [&lt;1 0 1 6 4|, &lt;0 6 5 -12 -2|]<br /> | |||
EDOs: 15, 34d, 49<br /> | |||
Badness: 0.0369<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Catakleismic"></a><!-- ws:end:WikiTextHeadingRule:24 -->Catakleismic</h1> | |||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Catakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384, 4375/4374<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384, 4375/4374<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0218<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0218<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Catakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 169/168, 225/224, 325/324, 540/539<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 169/168, 225/224, 325/324, 540/539<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0169<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0169<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Cataclysmic"></a><!-- ws:end:WikiTextHeadingRule:30 -->Cataclysmic</h1> | ||
Commas: 99/98, 176/175, 2200/2187<br /> | Commas: 99/98, 176/175, 2200/2187<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0400<br /> | Badness: 0.0400<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Cataclysmic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2> | ||
Commas: 99/98, 169/168, 176/175, 275/273<br /> | Commas: 99/98, 169/168, 176/175, 275/273<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0226<br /> | Badness: 0.0226<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Catalytic"></a><!-- ws:end:WikiTextHeadingRule:34 -->Catalytic</h1> | ||
Commas: 225/224, 441/440, 4375/4374<br /> | Commas: 225/224, 441/440, 4375/4374<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0304<br /> | Badness: 0.0304<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Catalytic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->13-limit</h2> | ||
Commas: 169/168 225/224 325/324 1716/1715<br /> | Commas: 169/168 225/224 325/324 1716/1715<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0223<br /> | Badness: 0.0223<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Countercata"></a><!-- ws:end:WikiTextHeadingRule:38 -->Countercata</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0521<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0521<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Countercata-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 2200/2187, 3388/3375<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 2200/2187, 3388/3375<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0398<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0398<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Countercata-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 385/384, 625/624<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 385/384, 625/624<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0202<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Metakleismic"></a><!-- ws:end:WikiTextHeadingRule:44 -->Metakleismic</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 179200/177147<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 179200/177147<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.1635<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.1635<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Metakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 896/891, 2200/2187, 14700/14641<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 896/891, 2200/2187, 14700/14641<br /> | ||
<br /> | <br /> | ||
| Line 757: | Line 776: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0486<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0486<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Metakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 364/363, 625/624<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 364/363, 625/624<br /> | ||
<br /> | <br /> | ||
| Line 766: | Line 785: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0244<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0244<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:50 -->Hemikleismic</h1> | ||
Commas: 4000/3969, 6144/6125<br /> | Commas: 4000/3969, 6144/6125<br /> | ||
<br /> | <br /> | ||
| Line 775: | Line 794: | ||
Badness: 0.0521<br /> | Badness: 0.0521<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Hemikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->11-limit</h2> | ||
Commas: 121/120, 176/175, 4000/3969<br /> | Commas: 121/120, 176/175, 4000/3969<br /> | ||
<br /> | <br /> | ||
| Line 784: | Line 803: | ||
Badness: 0.0380<br /> | Badness: 0.0380<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Hemikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->13-limit</h2> | ||
Commas: 121/120, 176/175, 275/273, 325/324<br /> | Commas: 121/120, 176/175, 275/273, 325/324<br /> | ||
<br /> | <br /> | ||
| Line 793: | Line 812: | ||
Badness: 0.0260<br /> | Badness: 0.0260<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc28"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:56 -->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 /> | ||
| Line 809: | Line 828: | ||
Badness: 0.0473<br /> | Badness: 0.0473<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Clyde-11-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->11-limit</h2> | ||
Commas: 245/243, 3136/3125, 385/384<br /> | Commas: 245/243, 3136/3125, 385/384<br /> | ||
<br /> | <br /> | ||
| Line 818: | Line 837: | ||
Badness: 0.0474<br /> | Badness: 0.0474<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Clyde-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h2> | ||
Commas: 196/195, 245/243, 385/384, 625/624<br /> | Commas: 196/195, 245/243, 385/384, 625/624<br /> | ||
<br /> | <br /> | ||
| Line 827: | Line 846: | ||
Badness: 0.0268<br /> | Badness: 0.0268<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Bikleismic"></a><!-- ws:end:WikiTextHeadingRule:62 -->Bikleismic</h1> | ||
Commas: 225/224, 243/242, 4375/4356<br /> | Commas: 225/224, 243/242, 4375/4356<br /> | ||
<br /> | <br /> | ||
| Line 836: | Line 855: | ||
Badness: 0.0293<br /> | Badness: 0.0293<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Bikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2> | ||
Commas: 169/168, 225/224, 243/242, 325/324<br /> | Commas: 169/168, 225/224, 243/242, 325/324<br /> | ||
<br /> | <br /> | ||
| Line 845: | Line 864: | ||
Badness: 0.0218<br /> | Badness: 0.0218<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:66 -->Tritikleismic</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 1029/1024<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 1029/1024<br /> | ||
<br /> | <br /> | ||
| Line 855: | Line 874: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0563<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0563<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 4000/3993<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 864: | Line 883: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0193<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0193<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 364/363, 441/440, 625/624<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 364/363, 441/440, 625/624<br /> | ||
<br /> | <br /> | ||
| Line 873: | Line 892: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0157<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0157<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h1&gt; --><h1 id="toc36"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:72 -->Quadritikleismic</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 2401/2400<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 2401/2400<br /> | ||
<br /> | <br /> | ||
| Line 883: | Line 902: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0392<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0392<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->11-limit</h2> | ||
Commas: 385/384, 1375/1372, 6250/6237<br /> | Commas: 385/384, 1375/1372, 6250/6237<br /> | ||
<br /> | <br /> | ||
| Line 892: | Line 911: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0234<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0234<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->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 /> | ||
| Line 901: | Line 920: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0187<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0187<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h1&gt; --><h1 id="toc39"><a name="Kleiboh"></a><!-- ws:end:WikiTextHeadingRule:78 -->Kleiboh</h1> | ||
Commas: 1728/1715, 3125/3087<br /> | Commas: 1728/1715, 3125/3087<br /> | ||
<br /> | <br /> | ||
| Line 911: | Line 930: | ||
Badness: 0.0765<br /> | Badness: 0.0765<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Kleiboh-11-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->11-limit</h2> | ||
Commas: 176/175, 540/539, 3125/3087<br /> | Commas: 176/175, 540/539, 3125/3087<br /> | ||
<br /> | <br /> | ||
| Line 920: | Line 939: | ||
Badness: 0.0528<br /> | Badness: 0.0528<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Kleiboh-13-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->13-limit</h2> | ||
Commas: 176/175, 275/273, 325/324, 540/539<br /> | Commas: 176/175, 275/273, 325/324, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 929: | Line 948: | ||
Badness: 0.0311<br /> | Badness: 0.0311<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h1&gt; --><h1 id="toc42"><a name="Novemkleismic"></a><!-- ws:end:WikiTextHeadingRule:84 -->Novemkleismic</h1> | ||
Commas: 15625/15552, 40353607/40310784<br /> | Commas: 15625/15552, 40353607/40310784<br /> | ||
<br /> | <br /> | ||
| Line 939: | Line 958: | ||
Badness: 0.1934<br /> | Badness: 0.1934<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:86:&lt;h2&gt; --><h2 id="toc43"><a name="Novemkleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:86 -->11-limit</h2> | ||
Commas: 1375/1372, 4000/3993, 15625/15552<br /> | Commas: 1375/1372, 4000/3993, 15625/15552<br /> | ||
<br /> | <br /> | ||
| Line 948: | Line 967: | ||
Badness: 0.05172<br /> | Badness: 0.05172<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Novemkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->13-limit</h2> | ||
Commas: 325/324, 625/624, 1375/1372, 4000/3993<br /> | Commas: 325/324, 625/624, 1375/1372, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 957: | Line 976: | ||
Badness: 0.0391<br /> | Badness: 0.0391<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:90:&lt;h1&gt; --><h1 id="toc45"><a name="Sqrtphi"></a><!-- ws:end:WikiTextHeadingRule:90 -->Sqrtphi</h1> | ||
Commas: 15625/15552, 16875/16807<br /> | Commas: 15625/15552, 16875/16807<br /> | ||
<br /> | <br /> | ||
| Line 968: | Line 987: | ||
Badness: 0.0704<br /> | Badness: 0.0704<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Sqrtphi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:92 -->11-limit</h2> | ||
Commas: 540/539, 1375/1372, 4375/4356<br /> | Commas: 540/539, 1375/1372, 4375/4356<br /> | ||
<br /> | <br /> | ||
| Line 977: | Line 996: | ||
Badness: 0.0255<br /> | Badness: 0.0255<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Sqrtphi-13-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->13-limit</h2> | ||
Commas: 325/324, 364/363, 625/624, 1375/1372<br /> | Commas: 325/324, 364/363, 625/624, 1375/1372<br /> | ||
<br /> | <br /> | ||
| Line 986: | Line 1,005: | ||
Badness: 0.0200<br /> | Badness: 0.0200<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Sqrtphi-17-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->17-limit</h2> | ||
Commas: 325/324, 364/363, 375/374, 540/539, 595/594<br /> | Commas: 325/324, 364/363, 375/374, 540/539, 595/594<br /> | ||
<br /> | <br /> | ||
| Line 995: | Line 1,014: | ||
Badness: 0.0130<br /> | Badness: 0.0130<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:98:&lt;h2&gt; --><h2 id="toc49"><a name="Sqrtphi-19-limit"></a><!-- ws:end:WikiTextHeadingRule:98 -->19-limit</h2> | ||
Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594<br /> | Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594<br /> | ||
<br /> | <br /> | ||
| Line 1,004: | Line 1,023: | ||
Badness: 0.0147<br /> | Badness: 0.0147<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Sqrtphi-Scales"></a><!-- ws:end:WikiTextHeadingRule:100 -->Scales</h2> | ||
<a class="wiki_link" href="/sqrtphi17">sqrtphi17</a><br /> | <a class="wiki_link" href="/sqrtphi17">sqrtphi17</a><br /> | ||
<a class="wiki_link" href="/sqrtphi23">sqrtphi23</a><br /> | <a class="wiki_link" href="/sqrtphi23">sqrtphi23</a><br /> | ||
<a class="wiki_link" href="/sqrtphi49">sqrtphi49</a><br /> | <a class="wiki_link" href="/sqrtphi49">sqrtphi49</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:102:&lt;h2&gt; --><h2 id="toc51"><a name="Sqrtphi-Music"></a><!-- ws:end:WikiTextHeadingRule:102 -->Music</h2> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3" rel="nofollow">Prelude for Piano in Square root of Phi Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3" rel="nofollow">Prelude for Piano in Square root of Phi Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3" rel="nofollow">A Fight for Phi</a> by Vito Sicurella</body></html></pre></div> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3" rel="nofollow">A Fight for Phi</a> by Vito Sicurella</body></html></pre></div> | ||