Marvel temperaments: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>phylingual **Imported revision 353613468 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 379862454 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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> | ||
| Line 81: | Line 81: | ||
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= | ||
| Line 519: | Line 528: | ||
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 /> | ||
| Line 651: | Line 661: | ||
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 /> | ||
Revision as of 18:22, 6 November 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-11-06 18:22:18 UTC.
- The original revision id was 379862454.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[toc]] This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[225_224| 225/224]], the [[marvel comma]] or [[septimal kleisma]]. 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. 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. =Negri= [[Comma]]s: 49/48, 225/224 [[POTE tuning|POTE temperament]]: ~15/14 = 125.608 [[Map]]: [<1 2 2 3|, <0 -4 3 -2|] [[Wedgie]]: <<4 -3 2 -14 -8 13|| EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]] ==11-limit== Commas: 45/44, 49/48, 56/55 [[POTE tuning|POTE generator]]: ~15/14 = 126.474 Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|] EDOs: 9, 10, 19 [[Badness]]: 0.0262 ==13-limit== Commas: 45/44, 49/48, 56/55, 78/77 [[POTE tuning|POTE generator]]: ~14/13 = 126.431 Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|] EDOs: 9, 10, 19 =Negril= Commas: 49/48, 100/99, 225/224 POTE generator: ~15/14 = 124.767 Map: [<1 2 2 3 2|, <0 -4 3 -2 14|] EDOs: 19, [[29edo|29]], [[48edo|48df]], [[77edo|77cdf]] Badness: 0.0387 ==13-limit== Commas: 49/48, 65/64, 91/90, 875/858 POTE generator: ~15/14 = 124.716 Map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|] EDOs: 9, 10, 19, 29, 48, 77 Badness: 0.0244 =Negric= Commas: 33/32, 49/48, 77/75 POTE generator: ~15/14 = 127.039 Map: [<1 2 2 3 3|, <0 -4 3 -2 4|] EDOs: 9, 19, [[85edo|85]] Badness: 0.0306 ==13-limit== Commas: 33/32, 49/48, 65/64, 91/90 POTE generator: ~15/14 = 127.039 Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|] EDOs: 9, 19, 85 Badness: 0.0202 =Negroni= Commas: 49/48, 55/54, 225/224 POTE generator: ~15/14 = 124.539 Map: [<1 2 2 3 5|, <0 -4 3 -2 -15|] EDOs: 10, 19e, 29, 77cde 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= Comma: 2197265625/2147483648 POTE generator: ~5/4 = 383.212 Map: [<2 1 5|, <0 6 -1|] EDOs: 22, 50, 72, 166, 238c, 310c, 548bc Badness: 0.3864 ==7-limit== Commas: 225/224, 118098/117649 [[POTE tuning|POTE temperament]]: 383.256 Map: [<2 1 5 2|, <0 6 -1 10|] Wedgie: <<12 -2 20 -31 -2 52|| EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238c]], [[310edo|310c]], [[382edo|382c]] Badness: 0.0408 ==11-limit== Commas: 225/224, 385/384, 4000/3993 [[POTE tuning|POTE temperament]]: 383.232 Map: [<2 1 5 2 8|, <0 6 -1 10 -3|] EDOs: 22, 50, 72, 94, [[166edo|166]], [[238edo|238c]], [[310edo|310c]] Badness: 0.0185 ==Lizard== Commas: 225/224, 351/350, 364/363, 385/384 [[POTE tuning|POTE temperament]]: 383.389 Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|] EDOs: 22, 50, 72, 122, 194df Badness: 0.0218 ===17-limit=== Commas: 221/220, 273/272, 289/288, 351/350, 375/374 [[POTE tuning|POTE temperament]]: 383.381 Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|] EDOs: 22, 50, 72, 122g, 194dfg Badness: 0.0145 ===19-limit=== Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342 [[POTE tuning|POTE generator]]: ~5/4 = 383.477 Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|] EDOs: 22h, 50, 72, [[122edo|122g]], [[194edo|194dfg]] Badness: 0.0157 ==Gizzard== Commas: 225/224, 385/384, 325/324, 1573/1568 POTE generator: ~5/4 = 383.170 Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|] EDOs: [[22edo|22]], [[26edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238cf]] Badness: 0.0203 ===17-limit=== Commas: 225/224, 289/288, 325/324, 375/374, 385/384 POTE generator: ~5/4 = 383.175 Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|] EDOs: 22f, 72, 94, [[166edo|166g]], [[238edo|238cfg]] Badness: 0.0136 ===19-limit=== Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399 POTE generator: ~5/4 = 383.138 Map: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|] EDOs: 22f, 72, 94, 166g Badness: 0.0148 ==Mage== Commas: 99/98, 176/175, 1331/1296 POTE generator: ~55/48 = 216.876 Map: [<2 1 5 2 4|, <0 6 -1 10 8|] EDOs: 22, 72e, 94e Badness: 0.0578 =Triton= Commas: 225/224, 1029/1000 [[POTE tuning|POTE temperament]]: ~7/5 = 568.865 Map: [<1 0 6 7|, <0 3 -7 -8|] Wedgie: <<3 -7 -8 -18 -21 1|| EDOs: 17d, 19, 78bd, 97bd Badness: 0.0592 ==11-limit== Commas: 45/44, 56/55, 1029/1000 POTE generator: ~7/5 = 569.144 Map: [<1 0 6 7 4|, <0 3 -7 -8 -1|] EDOs: 19, 59bde, 78bde, 97bde Badness: 0.0457 =Tritonic= Comnma: 553584375/536870912 POTE generator: ~45/32 = 580.219 Map: [<1 4 -3|, <0 -5 11|] EDOs: 29, 31, 60, 91 Badness: 0.3785 ==7-limit== Commas: 225/224, 50421/50000 [[POTE tuning|POTE temperament]]: 580.286 Map: [<1 4 -3 -3|, <0 -5 11 12|] Wedgie: <<5 -11 -12 -29 -33 3|| EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], 213bcd ==11-limit== Commas: 121/120, 225/224, 441/440 [[POTE tuning|POTE generator]]: ~7/5 = 580.267 Map: [<1 4 -3 -3 2|, <0 -5 11 12 3|] EDOs: 29, 31, 60e Badness: 0.0237 ==13-limit== Commas: 105/104, 121/120, 196/195, 275/273 POTE generator: ~7/5 = 580.108 Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|] EDOs: 29, 31, 60e, 151cde Badness: 0.0230 ==Tritoni== Commas: 225/224, 385/384, 27783/27500 POTE generator: ~7/5 = 580.389 Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|] EDOs: 31, 91, 122 Badness: 0.0455 =Merman= Comma: 1121008359375/1099511627776 POTE generator: ~45/32 = 585.634 Map: [<1 5 -5|, <0 -7 15|] EDOs: 41, 84, 125, 209, 334c, 543bc Badness: 0.4538 ==7-limit== Commas: 225/224, 2500000/2470629 POTE generator: ~7/5 = 585.585 Map: [<1 5 -5 -5|, <0 -7 15 16|] Wedgie: <<7 -15 -16 -40 -45 5|| EDOs: 41, 84, 125 Badness: 0.0551 ==11-limit== Commas: 225/224, 441/440, 1344/1331 POTE generator: ~7/5 = 585.606 Map: [<1 5 -5 -5 2|, <0 -7 15 16 3]] EDOs: 41, 84, 125e Badness: 0.0364 ==13-limit== Commas: 144/143, 225/224, 364/363, 441/440 POTE generator: ~7/5 = 585.657 Map: [<1 5 -5 -5 2 12|, <0 -7 15 16 3 -17|] EDOs: 41, 84, 125e, 209ef, 293ef =Septimin= Comma: 35595703125/34359738368 POTE generator: ~75/64 = 263.658 Map: [<1 4 1|, <0 -11 6|] EDOs: 9, 32, 41, 91, 132, 223c, 355bc Badness: 0.6709 ==7-limit== Commas: 225/224, 84035/82944 [[POTE tuning|POTE temperament]]: 263.632 Map: [<1 4 1 5|, <0 -11 6 -10|] Wedgie: <<11 -6 10 -35 -15 40|| EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]] ==11-limit== Commas: 225/224, 385/384, 2401/2376 [[POTE tuning|POTE temperament]]: 263.634 Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|] EDOs: 9, 32, 41, 91, 223cdef ==13-limit== Commas: 105/104, 144/143, 196/195, 245/242 [[POTE tuning|POTE temperament]]: 263.700 Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|] EDOs: 9, 41, 91 =Slender= Commas: 225/225, 589824/588245 [[POTE tuning|POTE temperament]]: ~49/48 = 38.413 Map: [<1 2 2 3|, <0 -13 10 -6|] Wedgie: <<13 -10 6 -46 -27 42|| EDOs: 31, 94, 125 Badness: 0.0569 ==11-limit== Commas: 225/224, 385/384, 1331/1323 [[POTE tuning|POTE temperament]]: ~49/48 = 38.387 Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|] EDOs: 31, 63, 94, 125 Badness: 25.342 ==13-limit== Commas: 225/224, 275/273, 385/384, 1331/1323 POTE generator: ~49/48 = 38.314 Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|] EDOs: 31, 63, 94 Badness: 25.913 =Marvo= Commas: 225/224, 78125000/78121827 [[POTE tuning|POTE temperament]]: ~27/20 = 516.694 Map: [<1 5 12 29|, <0 -6 -17 -46|] Wedgie: <<6, 17, 46, 13, 56 59|| EDOs: 65, 72 ==11-limit== Commas: 225/224, 243/242, 4000/3993 [[POTE tuning|POTE temperament]]: ~27/20 = 516.699 Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|] EDOs: 65, 72, 281, 497 ==13-limit== Commas: 243/242, 225/224, 351/350, 1625/1617 POTE generator: ~27/20 = 516.730 Map: [<1 5 12 29 12 39|, <0 -6 -17 -46 -15 -62|] EDOs: 72, 137, 209, 281f, 490bcf Badness: 0.0269 =Marvolo= Commas: 225/224, 156250000/155649627 POTE generator: ~21/20 = 83.348 Map: [<1 2 1 1|, <0 -6 19 26|] Wedgie: <<6 -19 -26 -44 -58 -7|| EDOs: 29, 43, 72, 619bcd, 691bcd Badness: 0.0833 ==11-limit== Commas: 225/224, 441/440, 4000/3993 POTE generator: ~21/20 = 83.340 Map: [<1 2 1 1 2|, <0 -6 19 26 21|] EDOs: 29, 43, 72 Badness: 0.0290 ==13-limit== Commas: 169/168, 225/224, 364/363, 441/440 POTE generator: ~21/20 = 83.330 Map: [<1 2 1 1 2 3|, <0 -6 19 26 21 10|] EDOs: 29, 43, 72 Badness: 0.0215 =Amavil= Commas: 225/224, 17496/16807 POTE generator: ~48/35 = 529.979 Map: [<1 6 1 9|, <0 -10 3 -14|] Wedgie: <<10 -3 14 -28 -6 41|| EDOs: 9, 34d, 43, 77d Badness: 0.1096 ==11-limit== Commas: 99/98, 176/175, 864/847 POTE generator: ~15/11 = 529.974 Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|] EDOs: 9, 34d, 43, 77de Badness: 0.0426 ==13-limit== Commas: 78/77, 99/98, 144/143, 176/175 POTE generator: ~15/11 = 529.951 Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|] EDOs: 9, 34d, 43, 77de Badness: 0.0258 =Enneaportent= Commas: 225/224, 40353607/40310784 POTE generator: ~5/4 = 383.165 Map: [<9 0 28 11|, <0 2 -1 2|] Wedgie: <<18 -9 18 -56 -22 67|| EDOs: 9, 54, 63, 72, 495bcd Badness: 0.0937 ==11-limit== Commas: 225/224, 385/384, 12005/11979 POTE generator: ~5/4 = 383.146 Map: [<9 0 28 11 24|, <0 2 -1 2 1|] EDOs: 9, 54, 63, 72, 423cd, 495bcd Badness: 0.0304 ==13-limit== Commas: 169/168 225/224 364/363 1716/1715 POTE generator: ~5/4 = 383.047 Map: [<9 0 28 11 24 19|, <0 2 -1 2 1 2|] EDOs: 9, 54, 63, 72, 279cf Badness: 0.0223 =Submajor= Comma: 69198046875/68719476736 POTE generator: ~10125/8192 = 362.321 Map: [<1 4 -1|, <0 -8 11|] EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc Badness: 0.1302 ==7-limit== Commas: 225/224, 51200/50421 POTE generator: ~49/40 = 362.255 Map: [<1 4 -1 1|, <0 -8 11 6|] Wedgie: <<8 -11 -6 -36 -32 17|| EDOs: 10, 33, 43, 53 Badness: 0.0605 ==11-limit== Commas: 225/224, 385/384, 6655/6561 POTE generator: ~27/22 = 362.101 Map: [<1 4 -1 1 11|, <0 -8 11 6 -25|] EDOs: 10, 53, 116, 169de, 285cde Badness: 0.0506 ==13-limit== Commas: 169/168, 225/224, 275/273, 385/384 POTE generator: ~16/13 = 362.105 Map: [<1 4 -1 1 11 4|, <0 -8 11 6 -25 -1|] EDOs: 10, 53, 116, 169de, 285cdef Badness: 0.0277 ==Interpental== Commas: 99/98, 176/175, 51200/50421 POTE generator: ~49/40 = 362.418 Map: [<1 4 -1 1 -5|, <0 -8 11 6 28|] EDOs: 43, 53, 96, 149d Badness: 0.0518 ===13-limit=== Commas: 99/98, 169/168, 176/175, 640/637 POTE generator: ~16/13 = 362.402 Map: [<1 4 -1 1 -5 4|, <0 -8 11 6 28 -1|] EDOs: 43, 53, 96, 149d Badness: 0.0297 =Alphorn= Commas: 225/224, 5764801/5668704 POTE generator: ~48/35 = 556.221 Map: [<1 9 0 13|, <0 -16 5 -22|] Wedgie: <<16 -5 22 -45 -10 65|| EDOs: 28d, 41, 151cd, 192cd, 233cd Badness: 0.1293 ==11-limit== Commas: 225/224, 385/384, 12250/11979 POTE generator: ~11/8 = 556.144 Map: [<1 9 0 13 3|, <0 -16 5 -22 1|] EDOs: 41, 315cde Badness: 0.0735
Original HTML content:
<html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:114:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><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:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Negri-11-limit">11-limit</a></div> <!-- 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:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Negril">Negril</a></div> <!-- 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:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 1em;"><a href="#Negric">Negric</a></div> <!-- 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:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 1em;"><a href="#Negroni">Negroni</a></div> <!-- 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:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Wizard">Wizard</a></div> <!-- 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:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Wizard-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Wizard-Lizard">Lizard</a></div> <!-- 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:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-19-limit">19-limit</a></div> <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 2em;"><a href="#Wizard-Gizzard">Gizzard</a></div> <!-- 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:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-19-limit">19-limit</a></div> <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 2em;"><a href="#Wizard-Mage">Mage</a></div> <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 1em;"><a href="#Triton">Triton</a></div> <!-- 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:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Tritonic">Tritonic</a></div> <!-- 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:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Tritonic-11-limit">11-limit</a></div> <!-- 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:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Tritonic-Tritoni">Tritoni</a></div> <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 1em;"><a href="#Merman">Merman</a></div> <!-- 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:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Merman-11-limit">11-limit</a></div> <!-- 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:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 1em;"><a href="#Septimin">Septimin</a></div> <!-- 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:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Septimin-11-limit">11-limit</a></div> <!-- 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:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 1em;"><a href="#Slender">Slender</a></div> <!-- 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:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Slender-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 1em;"><a href="#Marvo">Marvo</a></div> <!-- 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:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Marvo-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 1em;"><a href="#Marvolo">Marvolo</a></div> <!-- 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:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Marvolo-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 1em;"><a href="#Amavil">Amavil</a></div> <!-- 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:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Amavil-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 1em;"><a href="#Enneaportent">Enneaportent</a></div> <!-- 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:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 1em;"><a href="#Submajor">Submajor</a></div> <!-- 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:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 2em;"><a href="#Submajor-11-limit">11-limit</a></div> <!-- 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:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Submajor-Interpental">Interpental</a></div> <!-- 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:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 1em;"><a href="#Alphorn">Alphorn</a></div> <!-- 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:171 --><!-- ws:start:WikiTextTocRule:172: --></div> <!-- ws:end:WikiTextTocRule:172 -->This page discusses some of the temperaments tempering out |-5 2 2 -1> =<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 /> 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 /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1> <a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 225/224<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~15/14 = 125.608<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 2 2 3|, <0 -4 3 -2|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<4 -3 2 -14 -8 13||<br /> EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/86edo">86</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> Commas: 45/44, 49/48, 56/55<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 126.474<br /> <br /> Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]<br /> EDOs: 9, 10, 19<br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0262<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> Commas: 45/44, 49/48, 56/55, 78/77<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~14/13 = 126.431<br /> <br /> Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]<br /> EDOs: 9, 10, 19<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Negril"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negril</h1> Commas: 49/48, 100/99, 225/224<br /> <br /> POTE generator: ~15/14 = 124.767<br /> <br /> Map: [<1 2 2 3 2|, <0 -4 3 -2 14|]<br /> EDOs: 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/48edo">48df</a>, <a class="wiki_link" href="/77edo">77cdf</a><br /> Badness: 0.0387<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Negril-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> Commas: 49/48, 65/64, 91/90, 875/858<br /> <br /> POTE generator: ~15/14 = 124.716<br /> <br /> Map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]<br /> EDOs: 9, 10, 19, 29, 48, 77<br /> Badness: 0.0244<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Negric"></a><!-- ws:end:WikiTextHeadingRule:10 -->Negric</h1> Commas: 33/32, 49/48, 77/75<br /> <br /> POTE generator: ~15/14 = 127.039<br /> <br /> Map: [<1 2 2 3 3|, <0 -4 3 -2 4|]<br /> EDOs: 9, 19, <a class="wiki_link" href="/85edo">85</a><br /> Badness: 0.0306<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> Commas: 33/32, 49/48, 65/64, 91/90<br /> <br /> POTE generator: ~15/14 = 127.039<br /> <br /> Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]<br /> EDOs: 9, 19, 85<br /> Badness: 0.0202<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Negroni"></a><!-- ws:end:WikiTextHeadingRule:14 -->Negroni</h1> Commas: 49/48, 55/54, 225/224<br /> <br /> POTE generator: ~15/14 = 124.539<br /> <br /> Map: [<1 2 2 3 5|, <0 -4 3 -2 -15|]<br /> EDOs: 10, 19e, 29, 77cde<br /> Badness: 0.0353<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><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: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|]<br /> EDOs: 10, 19e, 29, 77cdef<br /> Badness: 0.0216<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:18 -->Wizard</h1> Comma: 2197265625/2147483648<br /> <br /> POTE generator: ~5/4 = 383.212<br /> <br /> Map: [<2 1 5|, <0 6 -1|]<br /> EDOs: 22, 50, 72, 166, 238c, 310c, 548bc<br /> Badness: 0.3864<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Wizard-7-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->7-limit</h2> Commas: 225/224, 118098/117649<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.256<br /> <br /> Map: [<2 1 5 2|, <0 6 -1 10|]<br /> Wedgie: <<12 -2 20 -31 -2 52||<br /> EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238c</a>, <a class="wiki_link" href="/310edo">310c</a>, <a class="wiki_link" href="/382edo">382c</a><br /> Badness: 0.0408<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> Commas: 225/224, 385/384, 4000/3993<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.232<br /> <br /> Map: [<2 1 5 2 8|, <0 6 -1 10 -3|]<br /> EDOs: 22, 50, 72, 94, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238c</a>, <a class="wiki_link" href="/310edo">310c</a><br /> Badness: 0.0185<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Wizard-Lizard"></a><!-- ws:end:WikiTextHeadingRule:24 -->Lizard</h2> Commas: 225/224, 351/350, 364/363, 385/384<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.389<br /> <br /> Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|]<br /> EDOs: 22, 50, 72, 122, 194df<br /> Badness: 0.0218<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h3> --><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 /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.381<br /> <br /> Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|]<br /> EDOs: 22, 50, 72, 122g, 194dfg<br /> Badness: 0.0145<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h3> --><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 /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~5/4 = 383.477<br /> <br /> Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|]<br /> EDOs: 22h, 50, 72, <a class="wiki_link" href="/122edo">122g</a>, <a class="wiki_link" href="/194edo">194dfg</a><br /> Badness: 0.0157<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h2> --><h2 id="toc15"><a name="Wizard-Gizzard"></a><!-- ws:end:WikiTextHeadingRule:30 -->Gizzard</h2> Commas: 225/224, 385/384, 325/324, 1573/1568<br /> <br /> POTE generator: ~5/4 = 383.170<br /> <br /> Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|]<br /> EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/26edo">72</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238cf</a><br /> Badness: 0.0203<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h3> --><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 /> <br /> POTE generator: ~5/4 = 383.175<br /> <br /> Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|]<br /> EDOs: 22f, 72, 94, <a class="wiki_link" href="/166edo">166g</a>, <a class="wiki_link" href="/238edo">238cfg</a><br /> Badness: 0.0136<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h3> --><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 /> <br /> POTE generator: ~5/4 = 383.138<br /> <br /> Map: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|]<br /> EDOs: 22f, 72, 94, 166g<br /> Badness: 0.0148<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="Wizard-Mage"></a><!-- ws:end:WikiTextHeadingRule:36 -->Mage</h2> Commas: 99/98, 176/175, 1331/1296<br /> <br /> POTE generator: ~55/48 = 216.876<br /> <br /> Map: [<2 1 5 2 4|, <0 6 -1 10 8|]<br /> EDOs: 22, 72e, 94e<br /> Badness: 0.0578<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h1> --><h1 id="toc19"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:38 -->Triton</h1> Commas: 225/224, 1029/1000<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~7/5 = 568.865<br /> <br /> Map: [<1 0 6 7|, <0 3 -7 -8|]<br /> Wedgie: <<3 -7 -8 -18 -21 1||<br /> EDOs: 17d, 19, 78bd, 97bd<br /> Badness: 0.0592<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="Triton-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> Commas: 45/44, 56/55, 1029/1000<br /> <br /> POTE generator: ~7/5 = 569.144<br /> <br /> Map: [<1 0 6 7 4|, <0 3 -7 -8 -1|]<br /> EDOs: 19, 59bde, 78bde, 97bde<br /> Badness: 0.0457<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:42 -->Tritonic</h1> Comnma: 553584375/536870912<br /> <br /> POTE generator: ~45/32 = 580.219<br /> <br /> Map: [<1 4 -3|, <0 -5 11|]<br /> EDOs: 29, 31, 60, 91<br /> Badness: 0.3785<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="Tritonic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->7-limit</h2> Commas: 225/224, 50421/50000<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.286<br /> <br /> Map: [<1 4 -3 -3|, <0 -5 11 12|]<br /> Wedgie: <<5 -11 -12 -29 -33 3||<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 /> <!-- ws:start:WikiTextHeadingRule:46:<h2> --><h2 id="toc23"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> Commas: 121/120, 225/224, 441/440<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/5 = 580.267<br /> <br /> Map: [<1 4 -3 -3 2|, <0 -5 11 12 3|]<br /> EDOs: 29, 31, 60e<br /> Badness: 0.0237<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h2> --><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 /> <br /> POTE generator: ~7/5 = 580.108<br /> <br /> Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|]<br /> EDOs: 29, 31, 60e, 151cde<br /> Badness: 0.0230<br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h2> --><h2 id="toc25"><a name="Tritonic-Tritoni"></a><!-- ws:end:WikiTextHeadingRule:50 -->Tritoni</h2> Commas: 225/224, 385/384, 27783/27500<br /> <br /> POTE generator: ~7/5 = 580.389<br /> <br /> Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]<br /> EDOs: 31, 91, 122<br /> Badness: 0.0455<br /> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h1> --><h1 id="toc26"><a name="Merman"></a><!-- ws:end:WikiTextHeadingRule:52 -->Merman</h1> Comma: 1121008359375/1099511627776<br /> <br /> POTE generator: ~45/32 = 585.634<br /> <br /> Map: [<1 5 -5|, <0 -7 15|]<br /> EDOs: 41, 84, 125, 209, 334c, 543bc<br /> Badness: 0.4538<br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h2> --><h2 id="toc27"><a name="Merman-7-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->7-limit</h2> Commas: 225/224, 2500000/2470629<br /> <br /> POTE generator: ~7/5 = 585.585<br /> <br /> Map: [<1 5 -5 -5|, <0 -7 15 16|]<br /> Wedgie: <<7 -15 -16 -40 -45 5||<br /> EDOs: 41, 84, 125<br /> Badness: 0.0551<br /> <br /> <!-- ws:start:WikiTextHeadingRule:56:<h2> --><h2 id="toc28"><a name="Merman-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> Commas: 225/224, 441/440, 1344/1331<br /> <br /> POTE generator: ~7/5 = 585.606<br /> <br /> Map: [<1 5 -5 -5 2|, <0 -7 15 16 3]]<br /> EDOs: 41, 84, 125e<br /> Badness: 0.0364<br /> <br /> <!-- ws:start:WikiTextHeadingRule:58:<h2> --><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 /> <br /> POTE generator: ~7/5 = 585.657<br /> <br /> Map: [<1 5 -5 -5 2 12|, <0 -7 15 16 3 -17|]<br /> EDOs: 41, 84, 125e, 209ef, 293ef<br /> <br /> <!-- ws:start:WikiTextHeadingRule:60:<h1> --><h1 id="toc30"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:60 -->Septimin</h1> Comma: 35595703125/34359738368<br /> <br /> POTE generator: ~75/64 = 263.658<br /> <br /> Map: [<1 4 1|, <0 -11 6|]<br /> EDOs: 9, 32, 41, 91, 132, 223c, 355bc<br /> Badness: 0.6709<br /> <br /> <!-- ws:start:WikiTextHeadingRule:62:<h2> --><h2 id="toc31"><a name="Septimin-7-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->7-limit</h2> Commas: 225/224, 84035/82944<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.632<br /> <br /> Map: [<1 4 1 5|, <0 -11 6 -10|]<br /> Wedgie: <<11 -6 10 -35 -15 40||<br /> EDOs: 9, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:64:<h2> --><h2 id="toc32"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->11-limit</h2> Commas: 225/224, 385/384, 2401/2376<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.634<br /> <br /> Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|]<br /> EDOs: 9, 32, 41, 91, 223cdef<br /> <br /> <!-- ws:start:WikiTextHeadingRule:66:<h2> --><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 /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.700<br /> <br /> Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|]<br /> EDOs: 9, 41, 91<br /> <br /> <!-- ws:start:WikiTextHeadingRule:68:<h1> --><h1 id="toc34"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:68 -->Slender</h1> Commas: 225/225, 589824/588245<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.413<br /> <br /> Map: [<1 2 2 3|, <0 -13 10 -6|]<br /> Wedgie: <<13 -10 6 -46 -27 42||<br /> EDOs: 31, 94, 125<br /> Badness: 0.0569<br /> <br /> <!-- ws:start:WikiTextHeadingRule:70:<h2> --><h2 id="toc35"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->11-limit</h2> Commas: 225/224, 385/384, 1331/1323<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.387<br /> <br /> Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|]<br /> EDOs: 31, 63, 94, 125<br /> Badness: 25.342<br /> <br /> <!-- ws:start:WikiTextHeadingRule:72:<h2> --><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 /> <br /> POTE generator: ~49/48 = 38.314<br /> <br /> Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|]<br /> EDOs: 31, 63, 94<br /> Badness: 25.913<br /> <br /> <!-- ws:start:WikiTextHeadingRule:74:<h1> --><h1 id="toc37"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:74 -->Marvo</h1> Commas: 225/224, 78125000/78121827<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~27/20 = 516.694<br /> <br /> Map: [<1 5 12 29|, <0 -6 -17 -46|]<br /> Wedgie: <<6, 17, 46, 13, 56 59||<br /> EDOs: 65, 72<br /> <br /> <!-- ws:start:WikiTextHeadingRule:76:<h2> --><h2 id="toc38"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->11-limit</h2> Commas: 225/224, 243/242, 4000/3993<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~27/20 = 516.699<br /> <br /> Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|]<br /> EDOs: 65, 72, 281, 497<br /> <br /> <!-- ws:start:WikiTextHeadingRule:78:<h2> --><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 /> <br /> POTE generator: ~27/20 = 516.730<br /> <br /> Map: [<1 5 12 29 12 39|, <0 -6 -17 -46 -15 -62|]<br /> EDOs: 72, 137, 209, 281f, 490bcf<br /> Badness: 0.0269<br /> <br /> <!-- ws:start:WikiTextHeadingRule:80:<h1> --><h1 id="toc40"><a name="Marvolo"></a><!-- ws:end:WikiTextHeadingRule:80 -->Marvolo</h1> Commas: 225/224, 156250000/155649627<br /> <br /> POTE generator: ~21/20 = 83.348<br /> <br /> Map: [<1 2 1 1|, <0 -6 19 26|]<br /> Wedgie: <<6 -19 -26 -44 -58 -7||<br /> EDOs: 29, 43, 72, 619bcd, 691bcd<br /> Badness: 0.0833<br /> <br /> <!-- ws:start:WikiTextHeadingRule:82:<h2> --><h2 id="toc41"><a name="Marvolo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2> Commas: 225/224, 441/440, 4000/3993<br /> <br /> POTE generator: ~21/20 = 83.340<br /> <br /> Map: [<1 2 1 1 2|, <0 -6 19 26 21|]<br /> EDOs: 29, 43, 72<br /> Badness: 0.0290<br /> <br /> <!-- ws:start:WikiTextHeadingRule:84:<h2> --><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 /> <br /> POTE generator: ~21/20 = 83.330<br /> <br /> Map: [<1 2 1 1 2 3|, <0 -6 19 26 21 10|]<br /> EDOs: 29, 43, 72<br /> Badness: 0.0215<br /> <br /> <!-- ws:start:WikiTextHeadingRule:86:<h1> --><h1 id="toc43"><a name="Amavil"></a><!-- ws:end:WikiTextHeadingRule:86 -->Amavil</h1> Commas: 225/224, 17496/16807<br /> <br /> POTE generator: ~48/35 = 529.979<br /> <br /> Map: [<1 6 1 9|, <0 -10 3 -14|]<br /> Wedgie: <<10 -3 14 -28 -6 41||<br /> EDOs: 9, 34d, 43, 77d<br /> Badness: 0.1096<br /> <br /> <!-- ws:start:WikiTextHeadingRule:88:<h2> --><h2 id="toc44"><a name="Amavil-11-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->11-limit</h2> Commas: 99/98, 176/175, 864/847<br /> <br /> POTE generator: ~15/11 = 529.974<br /> <br /> Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|]<br /> EDOs: 9, 34d, 43, 77de<br /> Badness: 0.0426<br /> <br /> <!-- ws:start:WikiTextHeadingRule:90:<h2> --><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 /> <br /> POTE generator: ~15/11 = 529.951<br /> <br /> Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|]<br /> EDOs: 9, 34d, 43, 77de<br /> Badness: 0.0258<br /> <br /> <!-- ws:start:WikiTextHeadingRule:92:<h1> --><h1 id="toc46"><a name="Enneaportent"></a><!-- ws:end:WikiTextHeadingRule:92 -->Enneaportent</h1> Commas: 225/224, 40353607/40310784<br /> <br /> POTE generator: ~5/4 = 383.165<br /> <br /> Map: [<9 0 28 11|, <0 2 -1 2|]<br /> Wedgie: <<18 -9 18 -56 -22 67||<br /> EDOs: 9, 54, 63, 72, 495bcd<br /> Badness: 0.0937<br /> <br /> <!-- ws:start:WikiTextHeadingRule:94:<h2> --><h2 id="toc47"><a name="Enneaportent-11-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->11-limit</h2> Commas: 225/224, 385/384, 12005/11979<br /> <br /> POTE generator: ~5/4 = 383.146<br /> <br /> Map: [<9 0 28 11 24|, <0 2 -1 2 1|]<br /> EDOs: 9, 54, 63, 72, 423cd, 495bcd<br /> Badness: 0.0304<br /> <br /> <!-- ws:start:WikiTextHeadingRule:96:<h2> --><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 /> <br /> POTE generator: ~5/4 = 383.047<br /> <br /> Map: [<9 0 28 11 24 19|, <0 2 -1 2 1 2|]<br /> EDOs: 9, 54, 63, 72, 279cf<br /> Badness: 0.0223<br /> <br /> <!-- ws:start:WikiTextHeadingRule:98:<h1> --><h1 id="toc49"><a name="Submajor"></a><!-- ws:end:WikiTextHeadingRule:98 -->Submajor</h1> Comma: 69198046875/68719476736<br /> <br /> POTE generator: ~10125/8192 = 362.321<br /> <br /> Map: [<1 4 -1|, <0 -8 11|]<br /> EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc<br /> Badness: 0.1302<br /> <br /> <!-- ws:start:WikiTextHeadingRule:100:<h2> --><h2 id="toc50"><a name="Submajor-7-limit"></a><!-- ws:end:WikiTextHeadingRule:100 -->7-limit</h2> Commas: 225/224, 51200/50421<br /> <br /> POTE generator: ~49/40 = 362.255<br /> <br /> Map: [<1 4 -1 1|, <0 -8 11 6|]<br /> Wedgie: <<8 -11 -6 -36 -32 17||<br /> EDOs: 10, 33, 43, 53<br /> Badness: 0.0605<br /> <br /> <!-- ws:start:WikiTextHeadingRule:102:<h2> --><h2 id="toc51"><a name="Submajor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:102 -->11-limit</h2> Commas: 225/224, 385/384, 6655/6561<br /> <br /> POTE generator: ~27/22 = 362.101<br /> <br /> Map: [<1 4 -1 1 11|, <0 -8 11 6 -25|]<br /> EDOs: 10, 53, 116, 169de, 285cde<br /> Badness: 0.0506<br /> <br /> <!-- ws:start:WikiTextHeadingRule:104:<h2> --><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 /> <br /> POTE generator: ~16/13 = 362.105<br /> <br /> Map: [<1 4 -1 1 11 4|, <0 -8 11 6 -25 -1|]<br /> EDOs: 10, 53, 116, 169de, 285cdef<br /> Badness: 0.0277<br /> <br /> <!-- ws:start:WikiTextHeadingRule:106:<h2> --><h2 id="toc53"><a name="Submajor-Interpental"></a><!-- ws:end:WikiTextHeadingRule:106 -->Interpental</h2> Commas: 99/98, 176/175, 51200/50421<br /> <br /> POTE generator: ~49/40 = 362.418<br /> <br /> Map: [<1 4 -1 1 -5|, <0 -8 11 6 28|]<br /> EDOs: 43, 53, 96, 149d<br /> Badness: 0.0518<br /> <br /> <!-- ws:start:WikiTextHeadingRule:108:<h3> --><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 /> <br /> POTE generator: ~16/13 = 362.402<br /> <br /> Map: [<1 4 -1 1 -5 4|, <0 -8 11 6 28 -1|]<br /> EDOs: 43, 53, 96, 149d<br /> Badness: 0.0297<br /> <br /> <!-- ws:start:WikiTextHeadingRule:110:<h1> --><h1 id="toc55"><a name="Alphorn"></a><!-- ws:end:WikiTextHeadingRule:110 -->Alphorn</h1> Commas: 225/224, 5764801/5668704<br /> <br /> POTE generator: ~48/35 = 556.221<br /> <br /> Map: [<1 9 0 13|, <0 -16 5 -22|]<br /> Wedgie: <<16 -5 22 -45 -10 65||<br /> EDOs: 28d, 41, 151cd, 192cd, 233cd<br /> Badness: 0.1293<br /> <br /> <!-- ws:start:WikiTextHeadingRule:112:<h2> --><h2 id="toc56"><a name="Alphorn-11-limit"></a><!-- ws:end:WikiTextHeadingRule:112 -->11-limit</h2> Commas: 225/224, 385/384, 12250/11979<br /> <br /> POTE generator: ~11/8 = 556.144<br /> <br /> Map: [<1 9 0 13 3|, <0 -16 5 -22 1|]<br /> EDOs: 41, 315cde<br /> Badness: 0.0735</body></html>