Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 288694700 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 288702914 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-28 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-28 22:39:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288702914</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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Generators: 2, 11/9 | Generators: 2, 11/9 | ||
EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]],[[31edo| 31d]] | EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]],[[31edo| 31d]] | ||
=Migration= | |||
Commas: 81/80, 121/120, 126/125 | |||
POTE generator: ~11/9 = 348.182 | |||
Map: [<1 1 0 -3 2|, <0 2 8 20 5|] | |||
EDOs: 31, 100de, 131bde, 162bde | |||
Badness: 0.0255 | |||
=Orphic= | =Orphic= | ||
| Line 560: | Line 569: | ||
Badness: 0.0364</pre></div> | Badness: 0.0364</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:102:&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:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 1em;"><a href="#Septimal meantone">Septimal meantone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens">Unidecimal meantone aka Huygens</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone">Tridecimal meantone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone">Grosstone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Meanpop">Meanpop</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Meanpop-13-limit Meanpop">13-limit Meanpop</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Meanpop-Meanplop">Meanplop</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Meanenneadecal">Meanenneadecal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Meanenneadecal-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 1em;"><a href="#Flattone">Flattone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Flattone-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 2em;"><a href="#Flattone-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 1em;"><a href="#Dominant">Dominant</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Dominant-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 2em;"><a href="#Dominant-Domineering">Domineering</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 1em;"><a href="#Sharptone">Sharptone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 1em;"><a href="#Injera">Injera</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 2em;"><a href="#Injera-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Injera-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 1em;"><a href="#Godzilla">Godzilla</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 2em;"><a href="#Godzilla-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Godzilla-Semafour">Semafour</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Godzilla-Music">Music</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 1em;"><a href="#Mohajira">Mohajira</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 2em;"><a href="#Mohajira-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 2em;"><a href="#Mohajira-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 1em;"><a href="#Maqamic">Maqamic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 2em;"><a href="#Maqamic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 1em;"><a href="#Migration">Migration</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 1em;"><a href="#Orphic">Orphic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 2em;"><a href="#Orphic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Orphic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Mothra">Mothra</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Mothra-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Mothra-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Mothra-Mosura">Mosura</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 3em;"><a href="#Mothra-Mosura-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 1em;"><a href="#Squares">Squares</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 2em;"><a href="#Squares-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Squares-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 1em;"><a href="#Cuboctahedra">Cuboctahedra</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 2em;"><a href="#Cuboctahedra-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 1em;"><a href="#Liese">Liese</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Liese-Liesel">Liesel</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Liese-Elisa">Elisa</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 1em;"><a href="#Jerome">Jerome</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Jerome-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Jerome-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 2em;"><a href="#Jerome-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 1em;"><a href="#Undevigintone">Undevigintone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --></div> | ||
<!-- ws:end:WikiTextTocRule:154 -->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 /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.239<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.239<br /> | ||
| Line 947: | Line 957: | ||
EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10c</a>, <a class="wiki_link" href="/17edo">17c</a>, <a class="wiki_link" href="/24edo">24d</a>,<a class="wiki_link" href="/31edo"> 31d</a><br /> | EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10c</a>, <a class="wiki_link" href="/17edo">17c</a>, <a class="wiki_link" href="/24edo">24d</a>,<a class="wiki_link" href="/31edo"> 31d</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Orphic"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Migration"></a><!-- ws:end:WikiTextHeadingRule:58 -->Migration</h1> | ||
Commas: 81/80, 121/120, 126/125<br /> | |||
<br /> | |||
POTE generator: ~11/9 = 348.182<br /> | |||
<br /> | |||
Map: [&lt;1 1 0 -3 2|, &lt;0 2 8 20 5|]<br /> | |||
EDOs: 31, 100de, 131bde, 162bde<br /> | |||
Badness: 0.0255<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Orphic"></a><!-- ws:end:WikiTextHeadingRule:60 -->Orphic</h1> | |||
Commas: 81/80, 5898240/5764801<br /> | Commas: 81/80, 5898240/5764801<br /> | ||
<br /> | <br /> | ||
| Line 957: | Line 976: | ||
Badness: 0.2588<br /> | Badness: 0.2588<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Orphic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 73728/73205<br /> | Commas: 81/80, 99/98, 73728/73205<br /> | ||
<br /> | <br /> | ||
| Line 966: | Line 985: | ||
Badness: 0.1015<br /> | Badness: 0.1015<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Orphic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2> | ||
Commas: 81/80, 99/98, 144/143, 2200/2197<br /> | Commas: 81/80, 99/98, 144/143, 2200/2197<br /> | ||
<br /> | <br /> | ||
| Line 975: | Line 994: | ||
Badness: 0.0535<br /> | Badness: 0.0535<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Mothra"></a><!-- ws:end:WikiTextHeadingRule:66 -->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 /> | ||
| Line 994: | Line 1,013: | ||
<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:68:&lt;h2&gt; --><h2 id="toc34"><a name="Mothra-11-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->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 /> | ||
| Line 1,003: | Line 1,022: | ||
<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:70:&lt;h2&gt; --><h2 id="toc35"><a name="Mothra-13-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->13-limit</h2> | ||
Commas: 81/80, 99/98, 105/104, 144/143<br /> | Commas: 81/80, 99/98, 105/104, 144/143<br /> | ||
<br /> | <br /> | ||
| Line 1,012: | Line 1,031: | ||
Badness: 0.0240<br /> | Badness: 0.0240<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Mothra-Mosura"></a><!-- ws:end:WikiTextHeadingRule:72 -->Mosura</h2> | ||
Commas: 81/80, 176/175, 1029/1024<br /> | Commas: 81/80, 176/175, 1029/1024<br /> | ||
<br /> | <br /> | ||
| Line 1,021: | Line 1,040: | ||
Badness: 0.0313<br /> | Badness: 0.0313<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h3&gt; --><h3 id="toc37"><a name="Mothra-Mosura-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h3> | ||
Commas: 81/80, 144/143, 176/175, 1029/1024<br /> | Commas: 81/80, 144/143, 176/175, 1029/1024<br /> | ||
<br /> | <br /> | ||
| Line 1,030: | Line 1,049: | ||
Badness: 0.0369<br /> | Badness: 0.0369<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h1&gt; --><h1 id="toc38"><a name="Squares"></a><!-- ws:end:WikiTextHeadingRule:76 -->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 /> | ||
| Line 1,052: | Line 1,071: | ||
<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:78:&lt;h2&gt; --><h2 id="toc39"><a name="Squares-11-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 121/120<br /> | Commas: 81/80, 99/98, 121/120<br /> | ||
<br /> | <br /> | ||
| Line 1,061: | Line 1,080: | ||
<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:80:&lt;h2&gt; --><h2 id="toc40"><a name="Squares-13-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->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 /> | ||
| Line 1,070: | Line 1,089: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0255<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0255<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h1&gt; --><h1 id="toc41"><a name="Cuboctahedra"></a><!-- ws:end:WikiTextHeadingRule:82 -->Cuboctahedra</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Cuboctahedra-11-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->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 /> | ||
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| Line 1,080: | Line 1,099: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:86:&lt;h1&gt; --><h1 id="toc43"><a name="Liese"></a><!-- ws:end:WikiTextHeadingRule:86 -->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 /> | ||
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| Line 1,098: | Line 1,117: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0467<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0467<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Liese-Liesel"></a><!-- ws:end:WikiTextHeadingRule:88 -->Liesel</h2> | ||
Commas: 56/55, 81/80, 540/539<br /> | Commas: 56/55, 81/80, 540/539<br /> | ||
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| Line 1,107: | Line 1,126: | ||
Badness: 0.0407<br /> | Badness: 0.0407<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Liese-Elisa"></a><!-- ws:end:WikiTextHeadingRule:90 -->Elisa</h2> | ||
Commas: 77/75, 81/80, 99/98<br /> | Commas: 77/75, 81/80, 99/98<br /> | ||
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| Line 1,116: | Line 1,135: | ||
Badness: 0.0416<br /> | Badness: 0.0416<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:92:&lt;h1&gt; --><h1 id="toc46"><a name="Jerome"></a><!-- ws:end:WikiTextHeadingRule:92 -->Jerome</h1> | ||
Jerome is related to <a class="wiki_link" href="/20ed5">Hieronymus' tuning</a>; the Hieronymus generator is 5^(1/20), or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size.<br /> | Jerome is related to <a class="wiki_link" href="/20ed5">Hieronymus' tuning</a>; the Hieronymus generator is 5^(1/20), or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size.<br /> | ||
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| Line 1,128: | Line 1,147: | ||
Badness: 0.1087<br /> | Badness: 0.1087<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Jerome-11-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 864/847<br /> | Commas: 81/80, 99/98, 864/847<br /> | ||
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| Line 1,137: | Line 1,156: | ||
Badness: 0.0479<br /> | Badness: 0.0479<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Jerome-13-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->13-limit</h2> | ||
Commas: 77/78, 81/80, 99/98, 144/143<br /> | Commas: 77/78, 81/80, 99/98, 144/143<br /> | ||
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| Line 1,146: | Line 1,165: | ||
Badness: 0.0293<br /> | Badness: 0.0293<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:98:&lt;h2&gt; --><h2 id="toc49"><a name="Jerome-17-limit"></a><!-- ws:end:WikiTextHeadingRule:98 -->17-limit</h2> | ||
Commas: 78/77, 81/80, 99/98, 144/143, 189/187<br /> | Commas: 78/77, 81/80, 99/98, 144/143, 189/187<br /> | ||
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| Line 1,155: | Line 1,174: | ||
Badness: 0.0209<br /> | Badness: 0.0209<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:100:&lt;h1&gt; --><h1 id="toc50"><a name="Undevigintone"></a><!-- ws:end:WikiTextHeadingRule:100 -->Undevigintone</h1> | ||
Commas: 49/48, 81/80, 126/125<br /> | Commas: 49/48, 81/80, 126/125<br /> | ||
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