Kleismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 204731744 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213970350 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-25 11:08:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213970350</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<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 [[19edo]] is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]]. | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<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 [[19edo]] is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]]. | |||
[[POTE tuning|POTE generator]]: 317.007 | [[POTE tuning|POTE generator]]: 317.007 | ||
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Map: [<1 0 1|, <0 6 5|] | Map: [<1 0 1|, <0 6 5|] | ||
=Seven limit children= | |||
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator. | The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator. | ||
=Keemun= | |||
[[Comma|Commas]]: 49/48, 126/125 | [[Comma|Commas]]: 49/48, 126/125 | ||
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Badness: 0.0274 | Badness: 0.0274 | ||
==11-limit== | |||
Commas: 49/48, 56/55, 100/99 | Commas: 49/48, 56/55, 100/99 | ||
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Badness: 0.0274 | Badness: 0.0274 | ||
==13-limit== | |||
Commas: 49/48, 56/55, 78/77, 100/99 | Commas: 49/48, 56/55, 78/77, 100/99 | ||
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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>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 /> | <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:36:&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:36 --><!-- ws:start:WikiTextTocRule:37: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | ||
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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 /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br /> | ||
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Map: [&lt;1 0 1|, &lt;0 6 5|]<br /> | Map: [&lt;1 0 1|, &lt;0 6 5|]<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt; | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1> | ||
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Keemun"></a><!-- ws:end:WikiTextHeadingRule:2 -->Keemun</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 49/48, 126/125<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 49/48, 126/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0274<br /> | Badness: 0.0274<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Keemun-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | ||
Commas: 49/48, 56/55, 100/99<br /> | Commas: 49/48, 56/55, 100/99<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0274<br /> | Badness: 0.0274<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt; | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Keemun-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | ||
Commas: 49/48, 56/55, 78/77, 100/99<br /> | Commas: 49/48, 56/55, 78/77, 100/99<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0297<br /> | Badness: 0.0297<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name=" | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Keemun-Catakleismic"></a><!-- ws:end:WikiTextHeadingRule:8 -->Catakleismic</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 225: | Line 229: | ||
Badness: 0.0215<br /> | Badness: 0.0215<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name=" | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Keemun-Catakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h3> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384, 4375/4374<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384, 4375/4374<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0218<br /> | Badness: 0.0218<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name=" | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Keemun-Catakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h3> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 169/168, 225/224, 325/324, 540/539<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 169/168, 225/224, 325/324, 540/539<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0169<br /> | Badness: 0.0169<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name=" | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Keemun-Countercata"></a><!-- ws:end:WikiTextHeadingRule:14 -->Countercata</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br /> | ||
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Badness: 0.0521<br /> | Badness: 0.0521<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name=" | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Keemun-Countercata-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h3> | ||
Commas: 385/384, 2200/2187, 3388/3375<br /> | Commas: 385/384, 2200/2187, 3388/3375<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0398<br /> | Badness: 0.0398<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name=" | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Keemun-Countercata-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h3> | ||
Commas: 325/324, 352/351, 385/384, 625/624<br /> | Commas: 325/324, 352/351, 385/384, 625/624<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0202<br /> | Badness: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name=" | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Keemun-Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Hemikleismic</h2> | ||
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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name=" | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Keemun-Clyde"></a><!-- ws:end:WikiTextHeadingRule:22 -->Clyde</h2> | ||
<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:24:&lt;h2&gt; --><h2 id="toc12"><a name=" | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Keemun-Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:24 -->Tritikleismic</h2> | ||
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:26:&lt;h3&gt; --><h3 id="toc13"><a name=" | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Keemun-Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h3> | ||
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:28:&lt;h3&gt; --><h3 id="toc14"><a name=" | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Keemun-Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h3> | ||
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:30:&lt;h2&gt; --><h2 id="toc15"><a name=" | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Keemun-Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:30 -->Quadritikleismic</h2> | ||
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:32:&lt;h3&gt; --><h3 id="toc16"><a name=" | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Keemun-Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h3> | ||
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:34:&lt;h3&gt; --><h3 id="toc17"><a name=" | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Keemun-Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h3> | ||
Commas: 325/324, 385/384, 625/624, 1573/1568<br /> | Commas: 325/324, 385/384, 625/624, 1573/1568<br /> | ||
<br /> | <br /> | ||