Starling temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 326242790 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 326388136 - 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>2012-04- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-28 11:41:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>326388136</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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In addition to 126/125, myna tempers out 1728/1715, the orwell comma, and 2401/2400, the breedsma. It can also be described as the 27&31 temperament, or in terms of its wedgie <<10 9 7 -9 -17 -9||. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6^(1/10) as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits. | In addition to 126/125, myna tempers out 1728/1715, the orwell comma, and 2401/2400, the breedsma. It can also be described as the 27&31 temperament, or in terms of its wedgie <<10 9 7 -9 -17 -9||. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6^(1/10) as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits. | ||
=5-limit= | |||
Comma: 10077696/9765625 | |||
POTE generator: ~6/5 = 310.140 | |||
Map: [<1 9 9|, <0 -10 -9|] | |||
EDOs: 27, 31, 58, 89, 325c | |||
Badness: 0.2500 | |||
==7-limit== | |||
[[Comma|Commas]]: 126/125, 1728/1715 | [[Comma|Commas]]: 126/125, 1728/1715 | ||
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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:86:&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:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 1em;"><a href="#Starling comma">Starling comma</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 1em;"><a href="#Myna temperament">Myna temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 1em;"><a href="#x5-limit">5-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#x5-limit-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#x5-limit-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 2em;"><a href="#x5-limit-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#x5-limit-Minah">Minah</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#x5-limit-Myno">Myno</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 2em;"><a href="#x5-limit-Coleto">Coleto</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 1em;"><a href="#Sensi temperament">Sensi temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensor">Sensor</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensor-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensis">Sensis</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensis-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensus">Sensus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensus-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 1em;"><a href="#Valentine temperament">Valentine temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 2em;"><a href="#Valentine temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Dwynwen">Dwynwen</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Lupercalia">Lupercalia</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Valentino">Valentino</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 1em;"><a href="#Alicorn temperament">Alicorn temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-Camahueto">Camahueto</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 3em;"><a href="#Alicorn temperament-Camahueto-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 1em;"><a href="#Casablanca temperament">Casablanca temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Casablanca temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 2em;"><a href="#Casablanca temperament-Marrakesh">Marrakesh</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 3em;"><a href="#Casablanca temperament-Marrakesh-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 3em;"><a href="#Casablanca temperament-Marrakesh-Murakuc">Murakuc</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Nusecond temperament">Nusecond temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Nusecond temperament-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 2em;"><a href="#Nusecond temperament-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 1em;"><a href="#Thuja">Thuja</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Thuja-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Thuja-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Bisemidim">Bisemidim</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Bisemidim-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Bisemidim-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 1em;"><a href="#Kumonga">Kumonga</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 2em;"><a href="#Kumonga-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 2em;"><a href="#Kumonga-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --></div> | |||
<!-- ws:end:WikiTextTocRule:130 --><!-- 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 /> | ||
<br /> | <br /> | ||
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In addition to 126/125, myna tempers out 1728/1715, the orwell comma, and 2401/2400, the breedsma. It can also be described as the 27&amp;31 temperament, or in terms of its wedgie &lt;&lt;10 9 7 -9 -17 -9||. It has 6/5 as a generator, and <a class="wiki_link" href="/58edo">58edo</a> can be used as a tuning, with <a class="wiki_link" href="/89edo">89edo</a> being a better one, and fans of round amounts in cents may like <a class="wiki_link" href="/120edo">120edo</a>. It is also possible to tune myna with pure fifths by taking 6^(1/10) as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.<br /> | In addition to 126/125, myna tempers out 1728/1715, the orwell comma, and 2401/2400, the breedsma. It can also be described as the 27&amp;31 temperament, or in terms of its wedgie &lt;&lt;10 9 7 -9 -17 -9||. It has 6/5 as a generator, and <a class="wiki_link" href="/58edo">58edo</a> can be used as a tuning, with <a class="wiki_link" href="/89edo">89edo</a> being a better one, and fans of round amounts in cents may like <a class="wiki_link" href="/120edo">120edo</a>. It is also possible to tune myna with pure fifths by taking 6^(1/10) as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->5-limit</h1> | |||
Comma: 10077696/9765625<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 310.140<br /> | |||
<br /> | |||
Map: [&lt;1 9 9|, &lt;0 -10 -9|]<br /> | |||
EDOs: 27, 31, 58, 89, 325c<br /> | |||
Badness: 0.2500<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x5-limit-7-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->7-limit</h2> | |||
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 1728/1715<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 126/125, 1728/1715<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0270<br /> | Badness: 0.0270<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x5-limit-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h2> | ||
Commas: 126/125, 176/175, 243/242<br /> | Commas: 126/125, 176/175, 243/242<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0168<br /> | Badness: 0.0168<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5-limit-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h2> | ||
Commas: 126/125, 144/143, 176/175, 196/195<br /> | Commas: 126/125, 144/143, 176/175, 196/195<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0171<br /> | Badness: 0.0171<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x5-limit-Minah"></a><!-- ws:end:WikiTextHeadingRule:12 -->Minah</h2> | ||
Commas: 78/77, 91/90, 126/125, 176/175<br /> | Commas: 78/77, 91/90, 126/125, 176/175<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0276<br /> | Badness: 0.0276<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x5-limit-Myno"></a><!-- ws:end:WikiTextHeadingRule:14 -->Myno</h2> | ||
Commas: 99/98, 126/125, 385/384<br /> | Commas: 99/98, 126/125, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0334<br /> | Badness: 0.0334<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x5-limit-Coleto"></a><!-- ws:end:WikiTextHeadingRule:16 -->Coleto</h2> | ||
Commas: 56/55, 100/99, 1728/1715<br /> | Commas: 56/55, 100/99, 1728/1715<br /> | ||
<br /> | <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:18:&lt;h1&gt; --><h1 id="toc9"><a name="Sensi temperament"></a><!-- ws:end:WikiTextHeadingRule:18 -->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 /> | ||
<br /> | <br /> | ||
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Badness: 0.0256<br /> | Badness: 0.0256<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Sensi temperament-Sensor"></a><!-- ws:end:WikiTextHeadingRule:20 -->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:22:&lt;h3&gt; --><h3 id="toc11"><a name="Sensi temperament-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->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:24:&lt;h2&gt; --><h2 id="toc12"><a name="Sensi temperament-Sensis"></a><!-- ws:end:WikiTextHeadingRule:24 -->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:26:&lt;h3&gt; --><h3 id="toc13"><a name="Sensi temperament-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Sensi temperament-Sensus"></a><!-- ws:end:WikiTextHeadingRule:28 -->Sensus</h2> | ||
Commas: 126/125, 176/175, 245/243<br /> | Commas: 126/125, 176/175, 245/243<br /> | ||
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Badness: 0.0295<br /> | Badness: 0.0295<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Sensi temperament-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Valentine temperament"></a><!-- ws:end:WikiTextHeadingRule:32 -->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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Badness: 0.0311<br /> | Badness: 0.0311<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Valentine temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Valentine temperament-Dwynwen"></a><!-- ws:end:WikiTextHeadingRule:36 -->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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Badness: 0.0235<br /> | Badness: 0.0235<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Valentine temperament-Lupercalia"></a><!-- ws:end:WikiTextHeadingRule:38 -->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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Badness: 0.0213<br /> | Badness: 0.0213<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Valentine temperament-Valentino"></a><!-- ws:end:WikiTextHeadingRule:40 -->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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Badness: 0.0207<br /> | Badness: 0.0207<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Alicorn temperament"></a><!-- ws:end:WikiTextHeadingRule:42 -->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:44:&lt;h2&gt; --><h2 id="toc22"><a name="Alicorn temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->11-limit</h2> | ||
Commas: 126/125, 540/539, 896/891<br /> | Commas: 126/125, 540/539, 896/891<br /> | ||
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Badness: 0.0392<br /> | Badness: 0.0392<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Alicorn temperament-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->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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Badness: 0.0237<br /> | Badness: 0.0237<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Alicorn temperament-Camahueto"></a><!-- ws:end:WikiTextHeadingRule:48 -->Camahueto</h2> | ||
Commas: 126/125, 10976/10935, 385/384<br /> | Commas: 126/125, 10976/10935, 385/384<br /> | ||
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Badness: 0.0659<br /> | Badness: 0.0659<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h3&gt; --><h3 id="toc25"><a name="Alicorn temperament-Camahueto-13-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->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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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Casablanca temperament"></a><!-- ws:end:WikiTextHeadingRule:52 -->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 /> | ||
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| Line 763: | Line 785: | ||
Badness: 0.1012<br /> | Badness: 0.1012<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Casablanca temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2> | ||
Commas: 126/125, 385/384, 2420/2401<br /> | Commas: 126/125, 385/384, 2420/2401<br /> | ||
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| Line 772: | Line 794: | ||
Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Casablanca temperament-Marrakesh"></a><!-- ws:end:WikiTextHeadingRule:56 -->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:58:&lt;h3&gt; --><h3 id="toc29"><a name="Casablanca temperament-Marrakesh-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->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 790: | Line 812: | ||
Badness: 0.0408<br /> | Badness: 0.0408<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h3&gt; --><h3 id="toc30"><a name="Casablanca temperament-Marrakesh-Murakuc"></a><!-- ws:end:WikiTextHeadingRule:60 -->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 799: | Line 821: | ||
Badness: 0.0414<br /> | Badness: 0.0414<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Nusecond temperament"></a><!-- ws:end:WikiTextHeadingRule:62 -->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 819: | Line 841: | ||
Badness: 0.0504<br /> | Badness: 0.0504<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Nusecond temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->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 836: | Line 858: | ||
Badness: 0.0256<br /> | Badness: 0.0256<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Nusecond temperament-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->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 845: | Line 867: | ||
Badness: 0.0233<br /> | Badness: 0.0233<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Thuja"></a><!-- ws:end:WikiTextHeadingRule:68 -->Thuja</h1> | ||
Commas: 126/125, 65536/64827<br /> | Commas: 126/125, 65536/64827<br /> | ||
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| Line 855: | Line 877: | ||
Badness: 0.0884<br /> | Badness: 0.0884<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Thuja-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->11-limit</h2> | ||
Commas: 126/125, 176/175, 1344/1331<br /> | Commas: 126/125, 176/175, 1344/1331<br /> | ||
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| Line 864: | Line 886: | ||
Badness: 0.0331<br /> | Badness: 0.0331<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Thuja-13-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->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 873: | Line 895: | ||
Badness: 0.0228<br /> | Badness: 0.0228<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h1&gt; --><h1 id="toc37"><a name="Bisemidim"></a><!-- ws:end:WikiTextHeadingRule:74 -->Bisemidim</h1> | ||
Commas: 126/125, 118098/117649<br /> | Commas: 126/125, 118098/117649<br /> | ||
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| Line 883: | Line 905: | ||
Badness: 0.0978<br /> | Badness: 0.0978<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Bisemidim-11-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->11-limit</h2> | ||
Commas: 126/125, 540/539, 1344/1331<br /> | Commas: 126/125, 540/539, 1344/1331<br /> | ||
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| Line 892: | Line 914: | ||
Badness: 0.0412<br /> | Badness: 0.0412<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Bisemidim-13-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->13-limit</h2> | ||
Commas: 126/125, 144/143, 196/195, 364/363<br /> | Commas: 126/125, 144/143, 196/195, 364/363<br /> | ||
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| Line 901: | Line 923: | ||
Badness: 0.0239<br /> | Badness: 0.0239<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h1&gt; --><h1 id="toc40"><a name="Kumonga"></a><!-- ws:end:WikiTextHeadingRule:80 -->Kumonga</h1> | ||
Commas: 126/125, 12288/12005<br /> | Commas: 126/125, 12288/12005<br /> | ||
<br /> | <br /> | ||
| Line 911: | Line 933: | ||
Badness: 0.0875<br /> | Badness: 0.0875<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Kumonga-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2> | ||
Commas: 126/125, 176/175, 864/847<br /> | Commas: 126/125, 176/175, 864/847<br /> | ||
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Badness: 0.0433<br /> | Badness: 0.0433<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Kumonga-13-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->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 /> | ||