Marvel temperaments: Difference between revisions
Wikispaces>phylingual **Imported revision 353613468 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 379862454 - 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>2012-11-06 18:22:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>379862454</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: 10, 19e, 29, 77cde | EDOs: 10, 19e, 29, 77cde | ||
Badness: 0.0353 | Badness: 0.0353 | ||
==13-limit== | |||
Commas: 49/48, 55/54, 65/64, 91/90 | |||
POTE generator: ~15/14 = 124.545 | |||
Map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|] | |||
EDOs: 10, 19e, 29, 77cdef | |||
Badness: 0.0216 | |||
=Wizard= | =Wizard= | ||
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Badness: 0.0735</pre></div> | Badness: 0.0735</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>Marvel 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>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:114:&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:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 1em;"><a href="#Negri">Negri</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Negri-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Negri-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Negril">Negril</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Negril-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 1em;"><a href="#Negric">Negric</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 2em;"><a href="#Negric-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 1em;"><a href="#Negroni">Negroni</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Negroni-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Wizard">Wizard</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Wizard-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Wizard-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Wizard-Lizard">Lizard</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 2em;"><a href="#Wizard-Gizzard">Gizzard</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 2em;"><a href="#Wizard-Mage">Mage</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 1em;"><a href="#Triton">Triton</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Triton-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Tritonic">Tritonic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Tritonic-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Tritonic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Tritonic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Tritonic-Tritoni">Tritoni</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 1em;"><a href="#Merman">Merman</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 2em;"><a href="#Merman-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Merman-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Merman-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 1em;"><a href="#Septimin">Septimin</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Septimin-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Septimin-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Septimin-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 1em;"><a href="#Slender">Slender</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Slender-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Slender-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 1em;"><a href="#Marvo">Marvo</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 2em;"><a href="#Marvo-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Marvo-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 1em;"><a href="#Marvolo">Marvolo</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 2em;"><a href="#Marvolo-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Marvolo-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 1em;"><a href="#Amavil">Amavil</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 2em;"><a href="#Amavil-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Amavil-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 1em;"><a href="#Enneaportent">Enneaportent</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 2em;"><a href="#Enneaportent-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 2em;"><a href="#Enneaportent-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 1em;"><a href="#Submajor">Submajor</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 2em;"><a href="#Submajor-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 2em;"><a href="#Submajor-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 2em;"><a href="#Submajor-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Submajor-Interpental">Interpental</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 3em;"><a href="#Submajor-Interpental-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 1em;"><a href="#Alphorn">Alphorn</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 2em;"><a href="#Alphorn-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --></div> | ||
<!-- ws:end:WikiTextTocRule:172 -->This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =<a class="wiki_link" href="/225_224"> 225/224</a>, the <a class="wiki_link" href="/marvel%20comma">marvel comma</a> or <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.<br /> | |||
<br /> | <br /> | ||
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.<br /> | Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.<br /> | ||
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Badness: 0.0353<br /> | Badness: 0.0353<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Negroni-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2> | ||
Commas: 49/48, 55/54, 65/64, 91/90<br /> | |||
<br /> | |||
POTE generator: ~15/14 = 124.545<br /> | |||
<br /> | |||
Map: [&lt;1 2 2 3 5 4|, &lt;0 -4 3 -2 -15 -3|]<br /> | |||
EDOs: 10, 19e, 29, 77cdef<br /> | |||
Badness: 0.0216<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:18 -->Wizard</h1> | |||
Comma: 2197265625/2147483648<br /> | Comma: 2197265625/2147483648<br /> | ||
<br /> | <br /> | ||
| Line 660: | Line 679: | ||
Badness: 0.3864<br /> | Badness: 0.3864<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Wizard-7-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->7-limit</h2> | ||
Commas: 225/224, 118098/117649<br /> | Commas: 225/224, 118098/117649<br /> | ||
<br /> | <br /> | ||
| Line 670: | Line 689: | ||
Badness: 0.0408<br /> | Badness: 0.0408<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 4000/3993<br /> | Commas: 225/224, 385/384, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 679: | Line 698: | ||
Badness: 0.0185<br /> | Badness: 0.0185<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Wizard-Lizard"></a><!-- ws:end:WikiTextHeadingRule:24 -->Lizard</h2> | ||
Commas: 225/224, 351/350, 364/363, 385/384<br /> | Commas: 225/224, 351/350, 364/363, 385/384<br /> | ||
<br /> | <br /> | ||
| Line 688: | Line 707: | ||
Badness: 0.0218<br /> | Badness: 0.0218<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Wizard-Lizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->17-limit</h3> | ||
Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br /> | Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br /> | ||
<br /> | <br /> | ||
| Line 697: | Line 716: | ||
Badness: 0.0145<br /> | Badness: 0.0145<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Wizard-Lizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->19-limit</h3> | ||
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br /> | Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br /> | ||
<br /> | <br /> | ||
| Line 706: | Line 725: | ||
Badness: 0.0157<br /> | Badness: 0.0157<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Wizard-Gizzard"></a><!-- ws:end:WikiTextHeadingRule:30 -->Gizzard</h2> | ||
Commas: 225/224, 385/384, 325/324, 1573/1568<br /> | Commas: 225/224, 385/384, 325/324, 1573/1568<br /> | ||
<br /> | <br /> | ||
| Line 715: | Line 734: | ||
Badness: 0.0203<br /> | Badness: 0.0203<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Wizard-Gizzard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->17-limit</h3> | ||
Commas: 225/224, 289/288, 325/324, 375/374, 385/384<br /> | Commas: 225/224, 289/288, 325/324, 375/374, 385/384<br /> | ||
<br /> | <br /> | ||
| Line 724: | Line 743: | ||
Badness: 0.0136<br /> | Badness: 0.0136<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Wizard-Gizzard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->19-limit</h3> | ||
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399<br /> | Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399<br /> | ||
<br /> | <br /> | ||
| Line 733: | Line 752: | ||
Badness: 0.0148<br /> | Badness: 0.0148<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Wizard-Mage"></a><!-- ws:end:WikiTextHeadingRule:36 -->Mage</h2> | ||
Commas: 99/98, 176/175, 1331/1296<br /> | Commas: 99/98, 176/175, 1331/1296<br /> | ||
<br /> | <br /> | ||
| Line 742: | Line 761: | ||
Badness: 0.0578<br /> | Badness: 0.0578<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:38 -->Triton</h1> | ||
Commas: 225/224, 1029/1000<br /> | Commas: 225/224, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 752: | Line 771: | ||
Badness: 0.0592<br /> | Badness: 0.0592<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Triton-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> | ||
Commas: 45/44, 56/55, 1029/1000<br /> | Commas: 45/44, 56/55, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 761: | Line 780: | ||
Badness: 0.0457<br /> | Badness: 0.0457<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:42 -->Tritonic</h1> | ||
Comnma: 553584375/536870912<br /> | Comnma: 553584375/536870912<br /> | ||
<br /> | <br /> | ||
| Line 770: | Line 789: | ||
Badness: 0.3785<br /> | Badness: 0.3785<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Tritonic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->7-limit</h2> | ||
Commas: 225/224, 50421/50000<br /> | Commas: 225/224, 50421/50000<br /> | ||
<br /> | <br /> | ||
| Line 779: | Line 798: | ||
EDOs: <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/91edo">91</a>, <a class="wiki_link" href="/122edo">122</a>, 213bcd<br /> | EDOs: <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/91edo">91</a>, <a class="wiki_link" href="/122edo">122</a>, 213bcd<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | ||
Commas: 121/120, 225/224, 441/440<br /> | Commas: 121/120, 225/224, 441/440<br /> | ||
<br /> | <br /> | ||
| Line 788: | Line 807: | ||
Badness: 0.0237<br /> | Badness: 0.0237<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Tritonic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | ||
Commas: 105/104, 121/120, 196/195, 275/273<br /> | Commas: 105/104, 121/120, 196/195, 275/273<br /> | ||
<br /> | <br /> | ||
| Line 797: | Line 816: | ||
Badness: 0.0230<br /> | Badness: 0.0230<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Tritonic-Tritoni"></a><!-- ws:end:WikiTextHeadingRule:50 -->Tritoni</h2> | ||
Commas: 225/224, 385/384, 27783/27500<br /> | Commas: 225/224, 385/384, 27783/27500<br /> | ||
<br /> | <br /> | ||
| Line 806: | Line 825: | ||
Badness: 0.0455<br /> | Badness: 0.0455<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Merman"></a><!-- ws:end:WikiTextHeadingRule:52 -->Merman</h1> | ||
Comma: 1121008359375/1099511627776<br /> | Comma: 1121008359375/1099511627776<br /> | ||
<br /> | <br /> | ||
| Line 815: | Line 834: | ||
Badness: 0.4538<br /> | Badness: 0.4538<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Merman-7-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->7-limit</h2> | ||
Commas: 225/224, 2500000/2470629<br /> | Commas: 225/224, 2500000/2470629<br /> | ||
<br /> | <br /> | ||
| Line 825: | Line 844: | ||
Badness: 0.0551<br /> | Badness: 0.0551<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Merman-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> | ||
Commas: 225/224, 441/440, 1344/1331<br /> | Commas: 225/224, 441/440, 1344/1331<br /> | ||
<br /> | <br /> | ||
| Line 834: | Line 853: | ||
Badness: 0.0364<br /> | Badness: 0.0364<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Merman-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2> | ||
Commas: 144/143, 225/224, 364/363, 441/440<br /> | Commas: 144/143, 225/224, 364/363, 441/440<br /> | ||
<br /> | <br /> | ||
| Line 842: | Line 861: | ||
EDOs: 41, 84, 125e, 209ef, 293ef<br /> | EDOs: 41, 84, 125e, 209ef, 293ef<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:60 -->Septimin</h1> | ||
Comma: 35595703125/34359738368<br /> | Comma: 35595703125/34359738368<br /> | ||
<br /> | <br /> | ||
| Line 851: | Line 870: | ||
Badness: 0.6709<br /> | Badness: 0.6709<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Septimin-7-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->7-limit</h2> | ||
Commas: 225/224, 84035/82944<br /> | Commas: 225/224, 84035/82944<br /> | ||
<br /> | <br /> | ||
| Line 860: | Line 879: | ||
EDOs: 9, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br /> | EDOs: 9, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 2401/2376<br /> | Commas: 225/224, 385/384, 2401/2376<br /> | ||
<br /> | <br /> | ||
| Line 868: | Line 887: | ||
EDOs: 9, 32, 41, 91, 223cdef<br /> | EDOs: 9, 32, 41, 91, 223cdef<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->13-limit</h2> | ||
Commas: 105/104, 144/143, 196/195, 245/242<br /> | Commas: 105/104, 144/143, 196/195, 245/242<br /> | ||
<br /> | <br /> | ||
| Line 876: | Line 895: | ||
EDOs: 9, 41, 91<br /> | EDOs: 9, 41, 91<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:68 -->Slender</h1> | ||
Commas: 225/225, 589824/588245<br /> | Commas: 225/225, 589824/588245<br /> | ||
<br /> | <br /> | ||
| Line 886: | Line 905: | ||
Badness: 0.0569<br /> | Badness: 0.0569<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 1331/1323<br /> | Commas: 225/224, 385/384, 1331/1323<br /> | ||
<br /> | <br /> | ||
| Line 895: | Line 914: | ||
Badness: 25.342<br /> | Badness: 25.342<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->13-limit</h2> | ||
Commas: 225/224, 275/273, 385/384, 1331/1323<br /> | Commas: 225/224, 275/273, 385/384, 1331/1323<br /> | ||
<br /> | <br /> | ||
| Line 904: | Line 923: | ||
Badness: 25.913<br /> | Badness: 25.913<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h1&gt; --><h1 id="toc37"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:74 -->Marvo</h1> | ||
Commas: 225/224, 78125000/78121827<br /> | Commas: 225/224, 78125000/78121827<br /> | ||
<br /> | <br /> | ||
| Line 913: | Line 932: | ||
EDOs: 65, 72<br /> | EDOs: 65, 72<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->11-limit</h2> | ||
Commas: 225/224, 243/242, 4000/3993<br /> | Commas: 225/224, 243/242, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 921: | Line 940: | ||
EDOs: 65, 72, 281, 497<br /> | EDOs: 65, 72, 281, 497<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Marvo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->13-limit</h2> | ||
Commas: 243/242, 225/224, 351/350, 1625/1617<br /> | Commas: 243/242, 225/224, 351/350, 1625/1617<br /> | ||
<br /> | <br /> | ||
| Line 930: | Line 949: | ||
Badness: 0.0269<br /> | Badness: 0.0269<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h1&gt; --><h1 id="toc40"><a name="Marvolo"></a><!-- ws:end:WikiTextHeadingRule:80 -->Marvolo</h1> | ||
Commas: 225/224, 156250000/155649627<br /> | Commas: 225/224, 156250000/155649627<br /> | ||
<br /> | <br /> | ||
| Line 940: | Line 959: | ||
Badness: 0.0833<br /> | Badness: 0.0833<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Marvolo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2> | ||
Commas: 225/224, 441/440, 4000/3993<br /> | Commas: 225/224, 441/440, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 949: | Line 968: | ||
Badness: 0.0290<br /> | Badness: 0.0290<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Marvolo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->13-limit</h2> | ||
Commas: 169/168, 225/224, 364/363, 441/440<br /> | Commas: 169/168, 225/224, 364/363, 441/440<br /> | ||
<br /> | <br /> | ||
| Line 958: | Line 977: | ||
Badness: 0.0215<br /> | Badness: 0.0215<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:86:&lt;h1&gt; --><h1 id="toc43"><a name="Amavil"></a><!-- ws:end:WikiTextHeadingRule:86 -->Amavil</h1> | ||
Commas: 225/224, 17496/16807<br /> | Commas: 225/224, 17496/16807<br /> | ||
<br /> | <br /> | ||
| Line 968: | Line 987: | ||
Badness: 0.1096<br /> | Badness: 0.1096<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Amavil-11-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->11-limit</h2> | ||
Commas: 99/98, 176/175, 864/847<br /> | Commas: 99/98, 176/175, 864/847<br /> | ||
<br /> | <br /> | ||
| Line 977: | Line 996: | ||
Badness: 0.0426<br /> | Badness: 0.0426<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Amavil-13-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->13-limit</h2> | ||
Commas: 78/77, 99/98, 144/143, 176/175<br /> | Commas: 78/77, 99/98, 144/143, 176/175<br /> | ||
<br /> | <br /> | ||
| Line 986: | Line 1,005: | ||
Badness: 0.0258<br /> | Badness: 0.0258<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:92:&lt;h1&gt; --><h1 id="toc46"><a name="Enneaportent"></a><!-- ws:end:WikiTextHeadingRule:92 -->Enneaportent</h1> | ||
Commas: 225/224, 40353607/40310784<br /> | Commas: 225/224, 40353607/40310784<br /> | ||
<br /> | <br /> | ||
| Line 996: | Line 1,015: | ||
Badness: 0.0937<br /> | Badness: 0.0937<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Enneaportent-11-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 12005/11979<br /> | Commas: 225/224, 385/384, 12005/11979<br /> | ||
<br /> | <br /> | ||
| Line 1,005: | Line 1,024: | ||
Badness: 0.0304<br /> | Badness: 0.0304<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Enneaportent-13-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->13-limit</h2> | ||
Commas: 169/168 225/224 364/363 1716/1715<br /> | Commas: 169/168 225/224 364/363 1716/1715<br /> | ||
<br /> | <br /> | ||
| Line 1,014: | Line 1,033: | ||
Badness: 0.0223<br /> | Badness: 0.0223<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:98:&lt;h1&gt; --><h1 id="toc49"><a name="Submajor"></a><!-- ws:end:WikiTextHeadingRule:98 -->Submajor</h1> | ||
Comma: 69198046875/68719476736<br /> | Comma: 69198046875/68719476736<br /> | ||
<br /> | <br /> | ||
| Line 1,023: | Line 1,042: | ||
Badness: 0.1302<br /> | Badness: 0.1302<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Submajor-7-limit"></a><!-- ws:end:WikiTextHeadingRule:100 -->7-limit</h2> | ||
Commas: 225/224, 51200/50421<br /> | Commas: 225/224, 51200/50421<br /> | ||
<br /> | <br /> | ||
| Line 1,033: | Line 1,052: | ||
Badness: 0.0605<br /> | Badness: 0.0605<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:102:&lt;h2&gt; --><h2 id="toc51"><a name="Submajor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:102 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 6655/6561<br /> | Commas: 225/224, 385/384, 6655/6561<br /> | ||
<br /> | <br /> | ||
| Line 1,042: | Line 1,061: | ||
Badness: 0.0506<br /> | Badness: 0.0506<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:104:&lt;h2&gt; --><h2 id="toc52"><a name="Submajor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:104 -->13-limit</h2> | ||
Commas: 169/168, 225/224, 275/273, 385/384<br /> | Commas: 169/168, 225/224, 275/273, 385/384<br /> | ||
<br /> | <br /> | ||
| Line 1,051: | Line 1,070: | ||
Badness: 0.0277<br /> | Badness: 0.0277<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:106:&lt;h2&gt; --><h2 id="toc53"><a name="Submajor-Interpental"></a><!-- ws:end:WikiTextHeadingRule:106 -->Interpental</h2> | ||
Commas: 99/98, 176/175, 51200/50421<br /> | Commas: 99/98, 176/175, 51200/50421<br /> | ||
<br /> | <br /> | ||
| Line 1,060: | Line 1,079: | ||
Badness: 0.0518<br /> | Badness: 0.0518<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:108:&lt;h3&gt; --><h3 id="toc54"><a name="Submajor-Interpental-13-limit"></a><!-- ws:end:WikiTextHeadingRule:108 -->13-limit</h3> | ||
Commas: 99/98, 169/168, 176/175, 640/637<br /> | Commas: 99/98, 169/168, 176/175, 640/637<br /> | ||
<br /> | <br /> | ||
| Line 1,069: | Line 1,088: | ||
Badness: 0.0297<br /> | Badness: 0.0297<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:110:&lt;h1&gt; --><h1 id="toc55"><a name="Alphorn"></a><!-- ws:end:WikiTextHeadingRule:110 -->Alphorn</h1> | ||
Commas: 225/224, 5764801/5668704<br /> | Commas: 225/224, 5764801/5668704<br /> | ||
<br /> | <br /> | ||
| Line 1,079: | Line 1,098: | ||
Badness: 0.1293<br /> | Badness: 0.1293<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:112:&lt;h2&gt; --><h2 id="toc56"><a name="Alphorn-11-limit"></a><!-- ws:end:WikiTextHeadingRule:112 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 12250/11979<br /> | Commas: 225/224, 385/384, 12250/11979<br /> | ||
<br /> | <br /> | ||