Starling temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 327964144 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 327998318 - 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>2012-05-01 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-01 12:03:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>327998318</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: 27e, 31f, 58f, 116cef | EDOs: 27e, 31f, 58f, 116cef | ||
Badness: 0.0276 | Badness: 0.0276 | ||
==Maneh== | |||
Commas: 66/65, 105/104, 126/125, 540/539 | |||
POTE generator: ~6/5 = 309.804 | |||
Map: [<1 9 9 8 22 23|, <0 -10 -9 -7 -25 -26|] | |||
EDOs: 31 | |||
Badness: 0.0299 | |||
==Myno== | ==Myno== | ||
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Badness: 0.0289</pre></div> | Badness: 0.0289</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>Starling temperaments</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>Starling temperaments</title></head><body><!-- ws:start:WikiTextTocRule:98:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 1em;"><a href="#Starling comma">Starling comma</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 1em;"><a href="#Myna temperament">Myna temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 1em;"><a href="#x5-limit">5-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#x5-limit-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#x5-limit-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 2em;"><a href="#x5-limit-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#x5-limit-Minah">Minah</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#x5-limit-Maneh">Maneh</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#x5-limit-Myno">Myno</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#x5-limit-Coleto">Coleto</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 1em;"><a href="#Sensi temperament">Sensi temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensor">Sensor</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensor-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensis">Sensis</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensis-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensus">Sensus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensus-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 1em;"><a href="#Valentine temperament">Valentine temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Valentine temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Dwynwen">Dwynwen</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Lupercalia">Lupercalia</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Valentino">Valentino</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 1em;"><a href="#Alicorn temperament">Alicorn temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-Camahueto">Camahueto</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 3em;"><a href="#Alicorn temperament-Camahueto-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 1em;"><a href="#Casablanca temperament">Casablanca temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Casablanca temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 2em;"><a href="#Casablanca temperament-Marrakesh">Marrakesh</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 3em;"><a href="#Casablanca temperament-Marrakesh-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 3em;"><a href="#Casablanca temperament-Marrakesh-Murakuc">Murakuc</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 1em;"><a href="#Nusecond temperament">Nusecond temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 2em;"><a href="#Nusecond temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 2em;"><a href="#Nusecond temperament-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 1em;"><a href="#Thuja">Thuja</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Thuja-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 2em;"><a href="#Thuja-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 1em;"><a href="#Cypress">Cypress</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Cypress-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Cypress-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Cypress-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 1em;"><a href="#Bisemidim">Bisemidim</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 2em;"><a href="#Bisemidim-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Bisemidim-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 1em;"><a href="#Kumonga">Kumonga</a></div> | ||
<!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 2em;"><a href="#Kumonga-7-limit">7-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Kumonga-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Kumonga-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --></div> | ||
<!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Starling comma"></a><!-- ws:end:WikiTextHeadingRule:0 -->Starling comma</h1> | |||
This page discusses some of the temperaments tempering out <a class="wiki_link" href="/126_125">126/125</a>, the <a class="wiki_link" href="/starling%20comma">starling comma</a> or <a class="wiki_link" href="/septimal%20semicomma">septimal semicomma</a>. Since (6/5)^3 = 126/125 * 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the <a class="wiki_link" href="/starling%20tetrad">starling tetrad</a>, the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before <a class="wiki_link" href="/12edo">12edo</a> established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.<br /> | This page discusses some of the temperaments tempering out <a class="wiki_link" href="/126_125">126/125</a>, the <a class="wiki_link" href="/starling%20comma">starling comma</a> or <a class="wiki_link" href="/septimal%20semicomma">septimal semicomma</a>. Since (6/5)^3 = 126/125 * 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the <a class="wiki_link" href="/starling%20tetrad">starling tetrad</a>, the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before <a class="wiki_link" href="/12edo">12edo</a> established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.<br /> | ||
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Badness: 0.0276<br /> | Badness: 0.0276<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x5-limit-Myno"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x5-limit-Maneh"></a><!-- ws:end:WikiTextHeadingRule:14 -->Maneh</h2> | ||
Commas: 66/65, 105/104, 126/125, 540/539<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 309.804<br /> | |||
<br /> | |||
Map: [&lt;1 9 9 8 22 23|, &lt;0 -10 -9 -7 -25 -26|]<br /> | |||
EDOs: 31<br /> | |||
Badness: 0.0299<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x5-limit-Myno"></a><!-- ws:end:WikiTextHeadingRule:16 -->Myno</h2> | |||
Commas: 99/98, 126/125, 385/384<br /> | Commas: 99/98, 126/125, 385/384<br /> | ||
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Badness: 0.0334<br /> | Badness: 0.0334<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x5-limit-Coleto"></a><!-- ws:end:WikiTextHeadingRule:18 -->Coleto</h2> | ||
Commas: 56/55, 100/99, 1728/1715<br /> | Commas: 56/55, 100/99, 1728/1715<br /> | ||
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<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3" rel="nofollow">Myna Music</a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3" rel="nofollow">Myna Music</a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Sensi temperament"></a><!-- ws:end:WikiTextHeadingRule:20 -->Sensi temperament</h1> | ||
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. <a class="wiki_link" href="/46edo">46edo</a> is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.<br /> | Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. <a class="wiki_link" href="/46edo">46edo</a> is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.<br /> | ||
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Badness: 0.0256<br /> | Badness: 0.0256<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Sensi temperament-Sensor"></a><!-- ws:end:WikiTextHeadingRule:22 -->Sensor</h2> | ||
Commas: 126/125, 245/243, 385/384<br /> | Commas: 126/125, 245/243, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0379<br /> | Badness: 0.0379<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Sensi temperament-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h3> | ||
Commas: 91/90, 126/125, 169/168, 385/384<br /> | Commas: 91/90, 126/125, 169/168, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0256<br /> | Badness: 0.0256<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Sensi temperament-Sensis"></a><!-- ws:end:WikiTextHeadingRule:26 -->Sensis</h2> | ||
Commas: 56/55, 100/99, 245/243<br /> | Commas: 56/55, 100/99, 245/243<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0287<br /> | Badness: 0.0287<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Sensi temperament-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h3> | ||
Commas: 56/55, 78/77, 91/90, 100/99<br /> | Commas: 56/55, 78/77, 91/90, 100/99<br /> | ||
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Badness: 0.0200<br /> | Badness: 0.0200<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Sensi temperament-Sensus"></a><!-- ws:end:WikiTextHeadingRule:30 -->Sensus</h2> | ||
Commas: 126/125, 176/175, 245/243<br /> | Commas: 126/125, 176/175, 245/243<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0295<br /> | Badness: 0.0295<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Sensi temperament-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h3> | ||
Commas: 91/90, 126/125, 169/168, 352/351<br /> | Commas: 91/90, 126/125, 169/168, 352/351<br /> | ||
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Badness: 0.0208<br /> | Badness: 0.0208<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Valentine temperament"></a><!-- ws:end:WikiTextHeadingRule:34 -->Valentine temperament</h1> | ||
Valentine tempers out 1029/1024 and 6144/6125 as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3*7/5. In this respect it resembles miracle, with a generator of 3*5/7, and casablanca, with a generator of 5*7/3. These three generators are the simplest in terms of the relationship of tetrads in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">lattice of 7-limit tetrads</a>. Valentine can also be described as the 31&amp;46 temperament, and <a class="wiki_link" href="/77edo">77edo</a>, <a class="wiki_link" href="/108edo">108edo</a> or <a class="wiki_link" href="/185edo">185edo</a> make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)^(1/9) as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as &lt;&lt;9 5 -3 7 ... ||, tempering out 121/120 and 441/440; 46et has a valentine generator 3/46 which is only 0.0117 cents sharp of the minimax generator, (11/7)^(1/10).<br /> | Valentine tempers out 1029/1024 and 6144/6125 as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3*7/5. In this respect it resembles miracle, with a generator of 3*5/7, and casablanca, with a generator of 5*7/3. These three generators are the simplest in terms of the relationship of tetrads in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">lattice of 7-limit tetrads</a>. Valentine can also be described as the 31&amp;46 temperament, and <a class="wiki_link" href="/77edo">77edo</a>, <a class="wiki_link" href="/108edo">108edo</a> or <a class="wiki_link" href="/185edo">185edo</a> make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)^(1/9) as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as &lt;&lt;9 5 -3 7 ... ||, tempering out 121/120 and 441/440; 46et has a valentine generator 3/46 which is only 0.0117 cents sharp of the minimax generator, (11/7)^(1/10).<br /> | ||
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| Line 729: | Line 748: | ||
Badness: 0.0311<br /> | Badness: 0.0311<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Valentine temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br /> | ||
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See also: <a class="wiki_link" href="/Chords%20of%20valentine">Chords of valentine</a><br /> | See also: <a class="wiki_link" href="/Chords%20of%20valentine">Chords of valentine</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Valentine temperament-Dwynwen"></a><!-- ws:end:WikiTextHeadingRule:38 -->Dwynwen</h2> | ||
Commas: 91/90, 121/120, 126/125, 176/175<br /> | Commas: 91/90, 121/120, 126/125, 176/175<br /> | ||
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| Line 757: | Line 776: | ||
Badness: 0.0235<br /> | Badness: 0.0235<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Valentine temperament-Lupercalia"></a><!-- ws:end:WikiTextHeadingRule:40 -->Lupercalia</h2> | ||
Commas: 66/65, 105/104, 121/120, 126/125<br /> | Commas: 66/65, 105/104, 121/120, 126/125<br /> | ||
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| Line 766: | Line 785: | ||
Badness: 0.0213<br /> | Badness: 0.0213<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Valentine temperament-Valentino"></a><!-- ws:end:WikiTextHeadingRule:42 -->Valentino</h2> | ||
Commas: 121/120, 126/125, 176/175, 196/195<br /> | Commas: 121/120, 126/125, 176/175, 196/195<br /> | ||
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| Line 775: | Line 794: | ||
Badness: 0.0207<br /> | Badness: 0.0207<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Alicorn temperament"></a><!-- ws:end:WikiTextHeadingRule:44 -->Alicorn temperament</h1> | ||
Commas: 126/125, 10976/10935<br /> | Commas: 126/125, 10976/10935<br /> | ||
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Badness: 0.0409<br /> | Badness: 0.0409<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Alicorn temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | ||
Commas: 126/125, 540/539, 896/891<br /> | Commas: 126/125, 540/539, 896/891<br /> | ||
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| Line 794: | Line 813: | ||
Badness: 0.0392<br /> | Badness: 0.0392<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Alicorn temperament-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | ||
Commas: 126/125, 144/143, 196/195, 676/675<br /> | Commas: 126/125, 144/143, 196/195, 676/675<br /> | ||
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| Line 804: | Line 823: | ||
Badness: 0.0237<br /> | Badness: 0.0237<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Alicorn temperament-Camahueto"></a><!-- ws:end:WikiTextHeadingRule:50 -->Camahueto</h2> | ||
Commas: 126/125, 10976/10935, 385/384<br /> | Commas: 126/125, 10976/10935, 385/384<br /> | ||
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| Line 813: | Line 832: | ||
Badness: 0.0659<br /> | Badness: 0.0659<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="Alicorn temperament-Camahueto-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h3> | ||
Commas: 126/125, 196/195, 385/384, 676/675<br /> | Commas: 126/125, 196/195, 385/384, 676/675<br /> | ||
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<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Casablanca temperament"></a><!-- ws:end:WikiTextHeadingRule:54 -->Casablanca temperament</h1> | ||
Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, &lt;&lt;19 14 4 -22 -47 -30||, or as 31&amp;73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.<br /> | Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, &lt;&lt;19 14 4 -22 -47 -30||, or as 31&amp;73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.<br /> | ||
<br /> | <br /> | ||
| Line 836: | Line 855: | ||
Badness: 0.1012<br /> | Badness: 0.1012<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Casablanca temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> | ||
Commas: 126/125, 385/384, 2420/2401<br /> | Commas: 126/125, 385/384, 2420/2401<br /> | ||
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Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Casablanca temperament-Marrakesh"></a><!-- ws:end:WikiTextHeadingRule:58 -->Marrakesh</h2> | ||
Commas: 126/125, 176/175, 14641/14580<br /> | Commas: 126/125, 176/175, 14641/14580<br /> | ||
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Badness: 0.0405<br /> | Badness: 0.0405<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h3&gt; --><h3 id="toc30"><a name="Casablanca temperament-Marrakesh-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h3> | ||
126/125, 176/175, 196/195, 17303/17280<br /> | 126/125, 176/175, 196/195, 17303/17280<br /> | ||
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| Line 863: | Line 882: | ||
Badness: 0.0408<br /> | Badness: 0.0408<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h3&gt; --><h3 id="toc31"><a name="Casablanca temperament-Marrakesh-Murakuc"></a><!-- ws:end:WikiTextHeadingRule:62 -->Murakuc</h3> | ||
Commas: 126/125, 144/143, 176/175, 1540/1521<br /> | Commas: 126/125, 144/143, 176/175, 1540/1521<br /> | ||
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| Line 872: | Line 891: | ||
Badness: 0.0414<br /> | Badness: 0.0414<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Nusecond temperament"></a><!-- ws:end:WikiTextHeadingRule:64 -->Nusecond temperament</h1> | ||
Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70, or in terms of its wedgie as &lt;&lt;11 13 17 -5 -4 3||. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. <a class="wiki_link" href="/31edo">31edo</a> can be used as a tuning, or <a class="wiki_link" href="/132edo">132edo</a> with a val which is the sum of the <a class="wiki_link" href="/Patent%20val">patent vals</a> for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.<br /> | Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70, or in terms of its wedgie as &lt;&lt;11 13 17 -5 -4 3||. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. <a class="wiki_link" href="/31edo">31edo</a> can be used as a tuning, or <a class="wiki_link" href="/132edo">132edo</a> with a val which is the sum of the <a class="wiki_link" href="/Patent%20val">patent vals</a> for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.<br /> | ||
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| Line 892: | Line 911: | ||
Badness: 0.0504<br /> | Badness: 0.0504<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Nusecond temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 99/98, 121/120, 126/125<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 99/98, 121/120, 126/125<br /> | ||
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| Line 909: | Line 928: | ||
Badness: 0.0256<br /> | Badness: 0.0256<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Nusecond temperament-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->13-limit</h2> | ||
Commas: 66/65 99/98 121/120 126/125<br /> | Commas: 66/65 99/98 121/120 126/125<br /> | ||
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| Line 918: | Line 937: | ||
Badness: 0.0233<br /> | Badness: 0.0233<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Thuja"></a><!-- ws:end:WikiTextHeadingRule:70 -->Thuja</h1> | ||
Commas: 126/125, 65536/64827<br /> | Commas: 126/125, 65536/64827<br /> | ||
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| Line 928: | Line 947: | ||
Badness: 0.0884<br /> | Badness: 0.0884<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Thuja-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2> | ||
Commas: 126/125, 176/175, 1344/1331<br /> | Commas: 126/125, 176/175, 1344/1331<br /> | ||
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| Line 937: | Line 956: | ||
Badness: 0.0331<br /> | Badness: 0.0331<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Thuja-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2> | ||
Commas: 126/125, 144/143, 176/175, 364/363<br /> | Commas: 126/125, 144/143, 176/175, 364/363<br /> | ||
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| Line 946: | Line 965: | ||
Badness: 0.0228<br /> | Badness: 0.0228<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h1&gt; --><h1 id="toc38"><a name="Cypress"></a><!-- ws:end:WikiTextHeadingRule:76 -->Cypress</h1> | ||
Comma: 258280326/244140625<br /> | Comma: 258280326/244140625<br /> | ||
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| Line 955: | Line 974: | ||
Badness: 0.8166<br /> | Badness: 0.8166<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Cypress-7-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->7-limit</h2> | ||
Commas: 126/125, 19683/19208<br /> | Commas: 126/125, 19683/19208<br /> | ||
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| Line 965: | Line 984: | ||
Badness: 0.0998<br /> | Badness: 0.0998<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Cypress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->11-limit</h2> | ||
Commas: 99/98, 126/125, 243/242 <br /> | Commas: 99/98, 126/125, 243/242 <br /> | ||
<br /> | <br /> | ||
| Line 974: | Line 993: | ||
Badness: 0.0427<br /> | Badness: 0.0427<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Cypress-13-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->13-limit</h2> | ||
Commas: 66/65, 99/98. 126/125, 243/242 <br /> | Commas: 66/65, 99/98. 126/125, 243/242 <br /> | ||
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| Line 983: | Line 1,002: | ||
Badness: 0.0378<br /> | Badness: 0.0378<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h1&gt; --><h1 id="toc42"><a name="Bisemidim"></a><!-- ws:end:WikiTextHeadingRule:84 -->Bisemidim</h1> | ||
Commas: 126/125, 118098/117649<br /> | Commas: 126/125, 118098/117649<br /> | ||
<br /> | <br /> | ||
| Line 993: | Line 1,012: | ||
Badness: 0.0978<br /> | Badness: 0.0978<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:86:&lt;h2&gt; --><h2 id="toc43"><a name="Bisemidim-11-limit"></a><!-- ws:end:WikiTextHeadingRule:86 -->11-limit</h2> | ||
Commas: 126/125, 540/539, 1344/1331<br /> | Commas: 126/125, 540/539, 1344/1331<br /> | ||
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| Line 1,002: | Line 1,021: | ||
Badness: 0.0412<br /> | Badness: 0.0412<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Bisemidim-13-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->13-limit</h2> | ||
Commas: 126/125, 144/143, 196/195, 364/363<br /> | Commas: 126/125, 144/143, 196/195, 364/363<br /> | ||
<br /> | <br /> | ||
| Line 1,011: | Line 1,030: | ||
Badness: 0.0239<br /> | Badness: 0.0239<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:90:&lt;h1&gt; --><h1 id="toc45"><a name="Kumonga"></a><!-- ws:end:WikiTextHeadingRule:90 -->Kumonga</h1> | ||
Comma: 1289945088/1220703125<br /> | Comma: 1289945088/1220703125<br /> | ||
<br /> | <br /> | ||
| Line 1,020: | Line 1,039: | ||
Badness: 0.7296<br /> | Badness: 0.7296<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Kumonga-7-limit"></a><!-- ws:end:WikiTextHeadingRule:92 -->7-limit</h2> | ||
Commas: 126/125, 12288/12005<br /> | Commas: 126/125, 12288/12005<br /> | ||
<br /> | <br /> | ||
| Line 1,030: | Line 1,049: | ||
Badness: 0.0875<br /> | Badness: 0.0875<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Kumonga-11-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->11-limit</h2> | ||
Commas: 126/125, 176/175, 864/847<br /> | Commas: 126/125, 176/175, 864/847<br /> | ||
<br /> | <br /> | ||
| Line 1,039: | Line 1,058: | ||
Badness: 0.0433<br /> | Badness: 0.0433<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Kumonga-13-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->13-limit</h2> | ||
Commas: 78/77, 126/125, 144/143, 176/175<br /> | Commas: 78/77, 126/125, 144/143, 176/175<br /> | ||
<br /> | <br /> | ||