Kleismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 213987220 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213990166 - 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 11:57:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213990166</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, 19, 34, 87, 121, 208 | EDOs: 15, 19, 34, 87, 121, 208 | ||
Badness: 0.0486 | Badness: 0.0486 | ||
==13-limit== | |||
Commas: 325/324, 352/351, 364/363, 625/624 | |||
POTE generator: ~6/5 = 317.311 | |||
Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|] | |||
EDOs: 15, 19, 34, 87, 121, 208 | |||
Badness: 0.0244 | |||
=Hemikleismic= | =Hemikleismic= | ||
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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: | <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:42:&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:42 --><!-- ws:start:WikiTextTocRule:43: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Countercata">Countercata</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Quadritikleismic">Quadritikleismic</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:64 --><br /> | ||
<br /> | <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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Badness: 0.0486<br /> | Badness: 0.0486<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Metakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2> | ||
Commas: 325/324, 352/351, 364/363, 625/624<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 317.311<br /> | |||
<br /> | |||
Map: [&lt;1 0 1 -12 -5 0|, &lt;0 6 5 56 32 14|]<br /> | |||
EDOs: 15, 19, 34, 87, 121, 208<br /> | |||
Badness: 0.0244<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:26 -->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: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:28 -->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: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:30 -->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: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->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: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->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: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:36 -->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: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->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: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->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 /> | ||