Kleismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 282280830 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 282453024 - 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>2011-12-05 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-05 12:47:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>282453024</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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Map: [<1 0 1 4 2|, <0 12 10 -9 11|] | Map: [<1 0 1 4 2|, <0 12 10 -9 11|] | ||
EDOs: 15, 38, 53, 68 | EDOs: 15, 38, 53, 68, 121e | ||
Badness: 0.0380 | Badness: 0.0380 | ||
==13-limit== | |||
Commas: 121/120, 176/175, 275/273, 325/324 | |||
POTE generator: ~11/10 = 158.655 | |||
Map: [<1 0 1 4 2 0|, <0 12 10 -9 11 28|] | |||
EDOs: 15, 53, 121e | |||
Badness: 0.0260 | |||
=Clyde= | =Clyde= | ||
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[[http://www.facebook.com/l.php?u=http%3A%2F%2Fmicro.soonlabel.com%2Fsqrt_phi%2Fdaily20111123a-sqrt-phi-17.mp3&h=nAQHnhy1hAQGVMAVjTXfyUlmvUHZQ1fvxDGsx2IIg9xdZYQ|Prelude for Piano in Square root of Phi Tuning]] by [[Chris Vaisvil]]</pre></div> | [[http://www.facebook.com/l.php?u=http%3A%2F%2Fmicro.soonlabel.com%2Fsqrt_phi%2Fdaily20111123a-sqrt-phi-17.mp3&h=nAQHnhy1hAQGVMAVjTXfyUlmvUHZQ1fvxDGsx2IIg9xdZYQ|Prelude for Piano in Square root of Phi Tuning]] by [[Chris Vaisvil]]</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:66:&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:66 --><!-- ws:start:WikiTextTocRule:67: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --> | <a href="#Cataclysmic">Cataclysmic</a><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#Countercata">Countercata</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --> | <a href="#Quadritikleismic">Quadritikleismic</a><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#Sqrtphi">Sqrtphi</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><br /> | ||
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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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<br /> | <br /> | ||
Map: [&lt;1 0 1 4 2|, &lt;0 12 10 -9 11|]<br /> | Map: [&lt;1 0 1 4 2|, &lt;0 12 10 -9 11|]<br /> | ||
EDOs: 15, 38, 53, 68<br /> | EDOs: 15, 38, 53, 68, 121e<br /> | ||
Badness: 0.0380<br /> | Badness: 0.0380<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Hemikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | ||
Commas: 121/120, 176/175, 275/273, 325/324<br /> | |||
<br /> | |||
POTE generator: ~11/10 = 158.655<br /> | |||
<br /> | |||
Map: [&lt;1 0 1 4 2 0|, &lt;0 12 10 -9 11 28|]<br /> | |||
EDOs: 15, 53, 121e<br /> | |||
Badness: 0.0260<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:36 -->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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Badness: 0.0473<br /> | Badness: 0.0473<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Clyde-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> | ||
Commas: 245/243, 3136/3125, 385/384<br /> | Commas: 245/243, 3136/3125, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0474<br /> | Badness: 0.0474<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:40 -->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 /> | ||
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<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:42:&lt;h2&gt; --><h2 id="toc21"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->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 /> | ||
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<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:44:&lt;h2&gt; --><h2 id="toc22"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->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 /> | ||
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<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:46:&lt;h1&gt; --><h1 id="toc23"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:46 -->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 /> | ||
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<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:48:&lt;h2&gt; --><h2 id="toc24"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->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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<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:50:&lt;h2&gt; --><h2 id="toc25"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->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 /> | ||
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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: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Sqrtphi"></a><!-- ws:end:WikiTextHeadingRule:52 -->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:54:&lt;h2&gt; --><h2 id="toc27"><a name="Sqrtphi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->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:56:&lt;h2&gt; --><h2 id="toc28"><a name="Sqrtphi-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->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:58:&lt;h2&gt; --><h2 id="toc29"><a name="Sqrtphi-17-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->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:60:&lt;h2&gt; --><h2 id="toc30"><a name="Sqrtphi-19-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->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:62:&lt;h2&gt; --><h2 id="toc31"><a name="Sqrtphi-Scales"></a><!-- ws:end:WikiTextHeadingRule:62 -->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:64:&lt;h2&gt; --><h2 id="toc32"><a name="Sqrtphi-Music"></a><!-- ws:end:WikiTextHeadingRule:64 -->Music</h2> | ||
<a class="wiki_link_ext" href="http://www.facebook.com/l.php?u=http%3A%2F%2Fmicro.soonlabel.com%2Fsqrt_phi%2Fdaily20111123a-sqrt-phi-17.mp3&amp;h=nAQHnhy1hAQGVMAVjTXfyUlmvUHZQ1fvxDGsx2IIg9xdZYQ" rel="nofollow">Prelude for Piano in Square root of Phi Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://www.facebook.com/l.php?u=http%3A%2F%2Fmicro.soonlabel.com%2Fsqrt_phi%2Fdaily20111123a-sqrt-phi-17.mp3&amp;h=nAQHnhy1hAQGVMAVjTXfyUlmvUHZQ1fvxDGsx2IIg9xdZYQ" rel="nofollow">Prelude for Piano in Square root of Phi Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></body></html></pre></div> | ||