Kleismic family: Difference between revisions
Wikispaces>xenwolf **Imported revision 235943316 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 237416209 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-06-18 02:43:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>237416209</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> | ||
| Line 212: | Line 212: | ||
Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|] | Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|] | ||
EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]] | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]] | ||
[[Badness]]: 0.0187</pre></div> | [[Badness]]: 0.0187 | ||
=Sqrtphi= | |||
Commas: 15625/15552, 16875/16807 | |||
[[POTE tuning|POTE generator]]: ~125/98 = 416.603 cents | |||
Sqrt(phi) = 416.545 cents | |||
Map: [<1 12 11 16|, <0 -30 -25 -38|] | |||
EDOs: 49, 72, 193, 265 | |||
Badness: 0.0704 | |||
==11-limit== | |||
Commas: 540/539, 1375/1372, 4375/4356 | |||
POTE generator: ~14/11 = 416.604 | |||
Map: [<1 12 11 16 17|, <0 -30 -25 -38 -39|] | |||
EDOs: 49, 72, 193, 265 | |||
Badness: 0.0255 | |||
==13-limit== | |||
Commas: 351/350, 540/539, 975/968, 1375/1372 | |||
==17-limit== | |||
Commas: 351/350, 540/539, 561/560, 2028/2023, 5355/5324 </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:50:&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:50 --><!-- ws:start:WikiTextTocRule:51: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Countercata">Countercata</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="#Metakleismic">Metakleismic</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: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Quadritikleismic">Quadritikleismic</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Sqrtphi">Sqrtphi</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:76 --><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 /> | ||
| Line 420: | Line 446: | ||
Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]<br /> | Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]<br /> | ||
EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a><br /> | EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a><br /> | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0187</body></html></pre></div> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0187<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Sqrtphi"></a><!-- ws:end:WikiTextHeadingRule:42 -->Sqrtphi</h1> | |||
Commas: 15625/15552, 16875/16807<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~125/98 = 416.603 cents<br /> | |||
<br /> | |||
Sqrt(phi) = 416.545 cents<br /> | |||
<br /> | |||
Map: [&lt;1 12 11 16|, &lt;0 -30 -25 -38|]<br /> | |||
EDOs: 49, 72, 193, 265<br /> | |||
Badness: 0.0704<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Sqrtphi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->11-limit</h2> | |||
Commas: 540/539, 1375/1372, 4375/4356<br /> | |||
<br /> | |||
POTE generator: ~14/11 = 416.604<br /> | |||
<br /> | |||
Map: [&lt;1 12 11 16 17|, &lt;0 -30 -25 -38 -39|]<br /> | |||
EDOs: 49, 72, 193, 265<br /> | |||
Badness: 0.0255<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> | |||
Commas: 351/350, 540/539, 975/968, 1375/1372<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> | |||
Commas: 351/350, 540/539, 561/560, 2028/2023, 5355/5324</body></html></pre></div> | |||