Kleismic family: Difference between revisions
Wikispaces>xenwolf **Imported revision 238259987 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 239796939 - 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>2011-07-03 00:45:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>239796939</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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==13-limit== | ==13-limit== | ||
Commas: | Commas: 325/324, 364/363, 625/624, 1375/1372 | ||
POTE generator: ~14/11 = 416.585 | |||
Map: [<1 12 11 16 17 28|, <0 -30 -25 -38 -39 -70|] | |||
EDOs: 72, 121, 193 | |||
Badness: 0.0200 | |||
==17-limit== | ==17-limit== | ||
Commas: | Commas: 325/324, 364/363, 375/374, 540/539, 595/594 | ||
POTE generator: ~14/11 = 416.585 | |||
Map: [<1 12 11 16 17 28 27|, <0 -30 -25 -38 -39 -70 -66|] | |||
EDOs: 72, 121, 193 | |||
Badness: 0.0130 | |||
==19-limit== | |||
Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594 | |||
POTE generator: ~14/11 = 416.580 | |||
Map: [<1 12 11 16 17 28 27 -2|, <0 -30 -25 -38 -39 -70 -66 18|] | |||
EDOs: 72, 121, 193 | |||
Badness: 0.0147 | |||
</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:52:&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:52 --><!-- ws:start:WikiTextTocRule:53: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Countercata">Countercata</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Tritikleismic">Tritikleismic</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="#Quadritikleismic">Quadritikleismic</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="#Sqrtphi">Sqrtphi</a><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:79 --><br /> | ||
<br /> | <br /> | ||
The <a class="wiki_link" href="/5-limit">5-limit</a> 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. This 5-limit temperament is commonly called hanson, 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 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. This 5-limit temperament is commonly called hanson, 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 /> | ||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Sqrtphi-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Sqrtphi-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2> | ||
Commas: | Commas: 325/324, 364/363, 625/624, 1375/1372<br /> | ||
<br /> | |||
POTE generator: ~14/11 = 416.585<br /> | |||
<br /> | |||
Map: [&lt;1 12 11 16 17 28|, &lt;0 -30 -25 -38 -39 -70|]<br /> | |||
EDOs: 72, 121, 193<br /> | |||
Badness: 0.0200<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Sqrtphi-17-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->17-limit</h2> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Sqrtphi-17-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->17-limit</h2> | ||
Commas: | Commas: 325/324, 364/363, 375/374, 540/539, 595/594<br /> | ||
<br /> | |||
POTE generator: ~14/11 = 416.585<br /> | |||
<br /> | |||
Map: [&lt;1 12 11 16 17 28 27|, &lt;0 -30 -25 -38 -39 -70 -66|]<br /> | |||
EDOs: 72, 121, 193<br /> | |||
Badness: 0.0130<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Sqrtphi-19-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->19-limit</h2> | |||
Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594<br /> | |||
<br /> | |||
POTE generator: ~14/11 = 416.580<br /> | |||
<br /> | |||
Map: [&lt;1 12 11 16 17 28 27 -2|, &lt;0 -30 -25 -38 -39 -70 -66 18|]<br /> | |||
EDOs: 72, 121, 193<br /> | |||
Badness: 0.0147</body></html></pre></div> | |||