Meantone family: Difference between revisions
Wikispaces>xenwolf **Imported revision 235941682 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 240715343 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-10 14:17:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240715343</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: [[12edo|12]], [[19edo|19]], [[31edo|31]], [[267edo|267]], [[298edo|298]] | EDOs: [[12edo|12]], [[19edo|19]], [[31edo|31]], [[267edo|267]], [[298edo|298]] | ||
[[Badness]]: 0.0180 | [[Badness]]: 0.0180 | ||
===Grosstone=== | |||
Commas: 81/80, 99/98, 126/125, 144/143 | |||
POTE generator: ~3/2 = 697.264 | |||
Map: [<1 0 -4 -13 -25 29|, <0 1 4 10 18 -16|] | |||
EDOs: 12, 31, 43, 74 | |||
Badness: 0.0259 | |||
==Meanpop== | ==Meanpop== | ||
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[[Badness]]: 0.0255</pre></div> | [[Badness]]: 0.0255</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>Meantone family</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Meantone family</title></head><body><!-- ws:start:WikiTextTocRule:50:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Septimal meantone">Septimal meantone</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Flattone">Flattone</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Dominant">Dominant</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Sharptone">Sharptone</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Injera">Injera</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Godzilla">Godzilla</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Mohajira">Mohajira</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Mothra">Mothra</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Squares">Squares</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Liese">Liese</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#Squares">Squares</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:76 --><br /> | ||
The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0180<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0180<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Grosstone"></a><!-- ws:end:WikiTextHeadingRule:8 -->Grosstone</h3> | ||
Commas: 81/80, 99/98, 126/125, 144/143<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 697.264<br /> | |||
<br /> | |||
Map: [&lt;1 0 -4 -13 -25 29|, &lt;0 1 4 10 18 -16|]<br /> | |||
EDOs: 12, 31, 43, 74<br /> | |||
Badness: 0.0259<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Septimal meantone-Meanpop"></a><!-- ws:end:WikiTextHeadingRule:10 -->Meanpop</h2> | |||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 126/125, 385/384<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 126/125, 385/384<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Septimal meantone-Meanpop-13-limit Meanpop"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit Meanpop</h3> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 105/104, 144/143, 196/195<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 105/104, 144/143, 196/195<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0209<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0209<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Septimal meantone-Meanenneadecal"></a><!-- ws:end:WikiTextHeadingRule:14 -->Meanenneadecal</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 81/80<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 81/80<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0214<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0214<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Septimal meantone-Meanenneadecal-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h3> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 78/77, 81/80<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 78/77, 81/80<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0212<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0212<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Flattone"></a><!-- ws:end:WikiTextHeadingRule:18 -->Flattone</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 525/512<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 525/512<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0386<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0386<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Dominant"></a><!-- ws:end:WikiTextHeadingRule:20 -->Dominant</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 64/63<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 64/63<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0207<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0207<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Sharptone"></a><!-- ws:end:WikiTextHeadingRule:22 -->Sharptone</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 21/20, 28/27<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 21/20, 28/27<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0248<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0248<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Injera"></a><!-- ws:end:WikiTextHeadingRule:24 -->Injera</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 50/49, 81/80<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 50/49, 81/80<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0311<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0311<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Godzilla"></a><!-- ws:end:WikiTextHeadingRule:26 -->Godzilla</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 81/80<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 81/80<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0267<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0267<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Godzilla-Music"></a><!-- ws:end:WikiTextHeadingRule:28 -->Music</h2> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3" rel="nofollow">Godzilla Example</a> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3" rel="nofollow">Godzilla Example</a> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</a><br /> | ||
<a class="wiki_link_ext" href="http://tinyurl.com/4uyumk9" rel="nofollow">&quot;Change is on the Wind&quot;</a> in Godzilla[9] by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | <a class="wiki_link_ext" href="http://tinyurl.com/4uyumk9" rel="nofollow">&quot;Change is on the Wind&quot;</a> in Godzilla[9] by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Mohajira"></a><!-- ws:end:WikiTextHeadingRule:30 -->Mohajira</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 6144/6125<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 6144/6125<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0557<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0557<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Mohajira-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 121/120, 176/175<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 121/120, 176/175<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0261<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0261<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Mothra"></a><!-- ws:end:WikiTextHeadingRule:34 -->Mothra</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 1029/1024<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 1029/1024<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0371<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0371<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Mothra-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 99/98, 385/384<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 99/98, 385/384<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0256<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0256<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Squares"></a><!-- ws:end:WikiTextHeadingRule:38 -->Squares</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 2401/2400<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 2401/2400<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3" rel="nofollow">Square 8</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3" rel="nofollow">Square 8</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Squares-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 385/384, 1375/1372<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 385/384, 1375/1372<br /> | ||
<br /> | <br /> | ||
| Line 596: | Line 614: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Liese"></a><!-- ws:end:WikiTextHeadingRule:42 -->Liese</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 686/675<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 686/675<br /> | ||
<br /> | <br /> | ||
| Line 614: | Line 632: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0467<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0467<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Squares"></a><!-- ws:end:WikiTextHeadingRule:44 -->Squares</h1> | ||
Commas: 81/80, 2401/2400<br /> | Commas: 81/80, 2401/2400<br /> | ||
<br /> | <br /> | ||
| Line 624: | Line 642: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0460<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0460<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Squares-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 121/120<br /> | Commas: 81/80, 99/98, 121/120<br /> | ||
<br /> | <br /> | ||
| Line 633: | Line 651: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0216<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0216<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Squares-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | ||
Commas: 81/80, 99/98, 121/120, 66/65<br /> | Commas: 81/80, 99/98, 121/120, 66/65<br /> | ||
<br /> | <br /> | ||