Kleismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 292546906 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 300189938 - 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>2012-02-09 13:02:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>300189938</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: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]] | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]] | ||
[[Badness]]: 0.0187 | [[Badness]]: 0.0187 | ||
=Novemkleismic= | |||
Commas: 15625/15552, 40353607/40310784 | |||
POTE generator: ~6/5 = 317.005 | |||
Map: [<9 0 9 11|, <0 6 5 6|] | |||
Wedgie: <<54 45 54 -54 -66 -1|| | |||
EDOs: 72, 261, 333, 405, 477c, 882c | |||
Badness: 0.1934 | |||
==11-limit== | |||
Commas: 1375/1372, 4000/3993, 15625/15552 | |||
POTE generator: ~6/5 = 317.010 | |||
Map: [<9 0 9 11 24|, <0 6 5 6 3|] | |||
EDOs: 72, 261, 333, 405, 882c | |||
Badness: 0.05172 | |||
==13-limit== | |||
Commas: 325/324, 625/624, 1375/1372, 4000/3993 | |||
POTE generator: ~6/5 = 317.086 | |||
Map: [<9 0 9 11 24 0|, <0 6 5 6 3 14|] | |||
EDOs: 72, 261, 333, 738cf, 1071bcf | |||
Badness: 0.0391 | |||
=Sqrtphi= | =Sqrtphi= | ||
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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:82:&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:82 --><!-- ws:start:WikiTextTocRule:83: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#Cataclysmic">Cataclysmic</a><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#Catalytic">Catalytic</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --> | <a href="#Countercata">Countercata</a><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | <a href="#Bikleismic">Bikleismic</a><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --> | <a href="#Quadritikleismic">Quadritikleismic</a><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --> | <a href="#Novemkleismic">Novemkleismic</a><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --> | <a href="#Sqrtphi">Sqrtphi</a><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><br /> | ||
<br /> | <br /> | ||
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 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 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 <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 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 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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<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:62:&lt;h1&gt; --><h1 id="toc31"><a name="Sqrtphi"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Novemkleismic"></a><!-- ws:end:WikiTextHeadingRule:62 -->Novemkleismic</h1> | ||
Commas: 15625/15552, 40353607/40310784<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 317.005<br /> | |||
<br /> | |||
Map: [&lt;9 0 9 11|, &lt;0 6 5 6|]<br /> | |||
Wedgie: &lt;&lt;54 45 54 -54 -66 -1||<br /> | |||
EDOs: 72, 261, 333, 405, 477c, 882c<br /> | |||
Badness: 0.1934<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Novemkleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->11-limit</h2> | |||
Commas: 1375/1372, 4000/3993, 15625/15552<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 317.010<br /> | |||
<br /> | |||
Map: [&lt;9 0 9 11 24|, &lt;0 6 5 6 3|]<br /> | |||
EDOs: 72, 261, 333, 405, 882c<br /> | |||
Badness: 0.05172<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Novemkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->13-limit</h2> | |||
Commas: 325/324, 625/624, 1375/1372, 4000/3993<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 317.086<br /> | |||
<br /> | |||
Map: [&lt;9 0 9 11 24 0|, &lt;0 6 5 6 3 14|]<br /> | |||
EDOs: 72, 261, 333, 738cf, 1071bcf<br /> | |||
Badness: 0.0391<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Sqrtphi"></a><!-- ws:end:WikiTextHeadingRule:68 -->Sqrtphi</h1> | |||
Commas: 15625/15552, 16875/16807<br /> | Commas: 15625/15552, 16875/16807<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0704<br /> | Badness: 0.0704<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Sqrtphi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->11-limit</h2> | ||
Commas: 540/539, 1375/1372, 4375/4356<br /> | Commas: 540/539, 1375/1372, 4375/4356<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0255<br /> | Badness: 0.0255<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Sqrtphi-13-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->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 /> | ||
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Badness: 0.0200<br /> | Badness: 0.0200<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Sqrtphi-17-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->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 /> | ||
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Badness: 0.0130<br /> | Badness: 0.0130<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Sqrtphi-19-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->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 /> | ||
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Badness: 0.0147<br /> | Badness: 0.0147<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Sqrtphi-Scales"></a><!-- ws:end:WikiTextHeadingRule:78 -->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:80:&lt;h2&gt; --><h2 id="toc40"><a name="Sqrtphi-Music"></a><!-- ws:end:WikiTextHeadingRule:80 -->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> | ||