Diaschismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 332699968 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 336795458 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-17 17:04:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>336795458</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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Badness: 0.0283 | Badness: 0.0283 | ||
==13-limit== | ===13-limit=== | ||
Commas: 50/49, 55/54, 64/63, 65/63 | Commas: 50/49, 55/54, 64/63, 65/63 | ||
| Line 94: | Line 94: | ||
EDOs: 10, 22, 54f, 76bdf | EDOs: 10, 22, 54f, 76bdf | ||
Badness: 0.0252 | Badness: 0.0252 | ||
==Pajaric== | |||
Commas: 45/44, 50/49, 56/55 | |||
POTE generator: ~3/2 = 705.524 | |||
Map: [<2 0 11 12 7|, <0 1 -2 -2 0|] | |||
EDOs: 10, 12, 22e, 34de | |||
Badness: 0.0238 | |||
===13-limit=== | |||
Commas: 40/39, 45/44, 50/49, 56/55 | |||
POTE generator: ~3/2 = 707.442 | |||
Map: [<2 0 11 12 7 17|, <0 1 -2 -2 0 -3|] | |||
EDOs: 10, 12f, 22ef, 34def | |||
Badness: 0.0205 | |||
==Pajaro== | ==Pajaro== | ||
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EDOs: 24 | EDOs: 24 | ||
Badness: 0.0457 | Badness: 0.0457 | ||
</pre></div> | </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>Diaschismic family</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Diaschismic family</title></head><body><!-- ws:start:WikiTextTocRule:86:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 1em;"><a href="#Srutal">Srutal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Srutal-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#Srutal-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 1em;"><a href="#Pajara">Pajara</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 2em;"><a href="#Pajara-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#Pajara-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Pajara-Pajarous">Pajarous</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 3em;"><a href="#Pajara-Pajarous-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 2em;"><a href="#Pajara-Pajaric">Pajaric</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 3em;"><a href="#Pajara-Pajaric-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 2em;"><a href="#Pajara-Pajaro">Pajaro</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Pajara-Hemipaj">Hemipaj</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 1em;"><a href="#Diaschismic">Diaschismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 2em;"><a href="#Diaschismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Diaschismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#Diaschismic-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 1em;"><a href="#Keen">Keen</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Keen-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 1em;"><a href="#Bidia">Bidia</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#Bidia-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Bidia-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 1em;"><a href="#Echidna">Echidna</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 2em;"><a href="#Echidna-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Echidna-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 2em;"><a href="#Echidna-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 1em;"><a href="#Echidnic">Echidnic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Echidnic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 2em;"><a href="#Echidnic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 1em;"><a href="#Shrutar">Shrutar</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Shrutar-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 2em;"><a href="#Shrutar-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Shrutar-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 2em;"><a href="#Shrutar-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 1em;"><a href="#Sruti">Sruti</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Sruti-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Sruti-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Anguirus">Anguirus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Anguirus-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Anguirus-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 1em;"><a href="#Shru">Shru</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 2em;"><a href="#Shru-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 2em;"><a href="#Shru-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --></div> | |||
<!-- ws:end:WikiTextTocRule:130 -->The 5-limit parent comma for the <strong>diaschismic family</strong> is 2048/2025, the <a class="wiki_link" href="/diaschisma">diaschisma</a>. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or <strong>srutal</strong>, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. <a class="wiki_link" href="/34edo">34edo</a> is a good tuning choice, with <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/56edo">56edo</a>, <a class="wiki_link" href="/58edo">58edo</a> or <a class="wiki_link" href="/80edo">80edo</a> being other possibilities. Both <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/22edo">22edo</a> support it, and retuning them to a MOS of diaschismic gives two scale possibilities.<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 704.898<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 704.898<br /> | ||
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Badness: 0.0283<br /> | Badness: 0.0283<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt; | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Pajara-Pajarous-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h3> | ||
Commas: 50/49, 55/54, 64/63, 65/63<br /> | Commas: 50/49, 55/54, 64/63, 65/63<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0252<br /> | Badness: 0.0252<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Pajara-Pajaro"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Pajara-Pajaric"></a><!-- ws:end:WikiTextHeadingRule:18 -->Pajaric</h2> | ||
Commas: 45/44, 50/49, 56/55<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 705.524<br /> | |||
<br /> | |||
Map: [&lt;2 0 11 12 7|, &lt;0 1 -2 -2 0|]<br /> | |||
EDOs: 10, 12, 22e, 34de<br /> | |||
Badness: 0.0238<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Pajara-Pajaric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h3> | |||
Commas: 40/39, 45/44, 50/49, 56/55<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 707.442<br /> | |||
<br /> | |||
Map: [&lt;2 0 11 12 7 17|, &lt;0 1 -2 -2 0 -3|]<br /> | |||
EDOs: 10, 12f, 22ef, 34def<br /> | |||
Badness: 0.0205<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Pajara-Pajaro"></a><!-- ws:end:WikiTextHeadingRule:22 -->Pajaro</h2> | |||
Commas: 40/39, 50/49, 55/54, 64/63<br /> | Commas: 40/39, 50/49, 55/54, 64/63<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0274<br /> | Badness: 0.0274<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Pajara-Hemipaj"></a><!-- ws:end:WikiTextHeadingRule:24 -->Hemipaj</h2> | ||
Commas: 50/49, 64/63, 121/120 <br /> | Commas: 50/49, 64/63, 121/120 <br /> | ||
<br /> | <br /> | ||
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Badness: 0.0389<br /> | Badness: 0.0389<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Diaschismic"></a><!-- ws:end:WikiTextHeadingRule:26 -->Diaschismic</h1> | ||
A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&amp;58. However described, diaschismic has wedgie &lt;&lt;2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. <a class="wiki_link" href="/58edo">58et</a> provides an excellent tuning, but an alternative is to make <a class="wiki_link" href="/7_4">7/4</a> just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et.<br /> | A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&amp;58. However described, diaschismic has wedgie &lt;&lt;2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. <a class="wiki_link" href="/58edo">58et</a> provides an excellent tuning, but an alternative is to make <a class="wiki_link" href="/7_4">7/4</a> just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et.<br /> | ||
<br /> | <br /> | ||
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EDOs: 46, 58, 104c, 162c<br /> | EDOs: 46, 58, 104c, 162c<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Diaschismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2> | ||
Commas: 126/125, 176/175, 896/891<br /> | Commas: 126/125, 176/175, 896/891<br /> | ||
<br /> | <br /> | ||
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EDOs: 46, 58, 104c, 162ce<br /> | EDOs: 46, 58, 104c, 162ce<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Diaschismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h2> | ||
Commas: 126/125, 196/195, 364/363, 2048/2025<br /> | Commas: 126/125, 196/195, 364/363, 2048/2025<br /> | ||
<br /> | <br /> | ||
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EDOs: <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/104edo">104c</a>, <a class="wiki_link" href="/162edo">162cef</a><br /> | EDOs: <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/104edo">104c</a>, <a class="wiki_link" href="/162edo">162cef</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Diaschismic-17-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->17-limit</h2> | ||
Commas: 126/125, 136/135, 176/175, 196/195, 256/255<br /> | Commas: 126/125, 136/135, 176/175, 196/195, 256/255<br /> | ||
<br /> | <br /> | ||
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EDOs: 46, 58, 104c<br /> | EDOs: 46, 58, 104c<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Keen"></a><!-- ws:end:WikiTextHeadingRule:34 -->Keen</h1> | ||
Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie &lt;&lt;2 -4 18 -11 23 53||. It may also be described as the 22&amp;56 temperament. <a class="wiki_link" href="/78edo">78et</a> is a good tuning choice, and remains a good one in the 11-limit, where keen, &lt;&lt;2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas.<br /> | Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie &lt;&lt;2 -4 18 -11 23 53||. It may also be described as the 22&amp;56 temperament. <a class="wiki_link" href="/78edo">78et</a> is a good tuning choice, and remains a good one in the 11-limit, where keen, &lt;&lt;2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas.<br /> | ||
<br /> | <br /> | ||
| Line 604: | Line 641: | ||
EDOs: 22, 56, 78, 134b, 212b, 290b<br /> | EDOs: 22, 56, 78, 134b, 212b, 290b<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Keen-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
Commas: 100/99, 385/384, 1232/1215<br /> | Commas: 100/99, 385/384, 1232/1215<br /> | ||
<br /> | <br /> | ||
| Line 612: | Line 649: | ||
EDOs: 22, 56, 78, 212bf, 290bf<br /> | EDOs: 22, 56, 78, 212bf, 290bf<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Bidia"></a><!-- ws:end:WikiTextHeadingRule:38 -->Bidia</h1> | ||
Bidia adds 3136/3125 to the commas, splitting the period into 1/4 octave. It may be called the 12&amp;56 temperament.<br /> | Bidia adds 3136/3125 to the commas, splitting the period into 1/4 octave. It may be called the 12&amp;56 temperament.<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0565<br /> | Badness: 0.0565<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Bidia-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> | ||
Commas: 176/175, 896/891, 1375/1372<br /> | Commas: 176/175, 896/891, 1375/1372<br /> | ||
<br /> | <br /> | ||
| Line 633: | Line 670: | ||
Badness: 0.0402<br /> | Badness: 0.0402<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Bidia-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2> | ||
Commas: 176/175, 325/324, 640/637, 896/891<br /> | Commas: 176/175, 325/324, 640/637, 896/891<br /> | ||
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| Line 642: | Line 679: | ||
Badness: 0.0411<br /> | Badness: 0.0411<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Echidna"></a><!-- ws:end:WikiTextHeadingRule:44 -->Echidna</h1> | ||
Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie &lt;&lt;6 -12 10 -33 -1 57|| and may be called the 22&amp;58 temperament. <a class="wiki_link" href="/58edo">58et</a> or <a class="wiki_link" href="/80edo">80et</a> make for good tunings, or their vals can be add to &lt;138 219 321 388|.<br /> | Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie &lt;&lt;6 -12 10 -33 -1 57|| and may be called the 22&amp;58 temperament. <a class="wiki_link" href="/58edo">58et</a> or <a class="wiki_link" href="/80edo">80et</a> make for good tunings, or their vals can be add to &lt;138 219 321 388|.<br /> | ||
<br /> | <br /> | ||
| Line 655: | Line 692: | ||
Badness: 0.0580<br /> | Badness: 0.0580<br /> | ||
<br /> | <br /> | ||
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Commas: 176/175, 896/891, 540/539<br /> | Commas: 176/175, 896/891, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 670: | Line 707: | ||
Badness: 0.0260<br /> | Badness: 0.0260<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Echidna-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | ||
Commas: 176/175, 351/350, 364/363, 540/539<br /> | Commas: 176/175, 351/350, 364/363, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 679: | Line 716: | ||
Badness: 0.0237<br /> | Badness: 0.0237<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Echidna-17-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->17-limit</h2> | ||
Commas: 136/135, 176/175, 221/220, 256/255, 540/539<br /> | Commas: 136/135, 176/175, 221/220, 256/255, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 688: | Line 725: | ||
Badness: 0.0203<br /> | Badness: 0.0203<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Echidnic"></a><!-- ws:end:WikiTextHeadingRule:52 -->Echidnic</h1> | ||
Commas: 686/675, 1029/1024<br /> | Commas: 686/675, 1029/1024<br /> | ||
<br /> | <br /> | ||
| Line 697: | Line 734: | ||
Badness: 0.0722<br /> | Badness: 0.0722<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Echidnic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2> | ||
Commas: 385/384, 441/440, 686/675<br /> | Commas: 385/384, 441/440, 686/675<br /> | ||
<br /> | <br /> | ||
| Line 706: | Line 743: | ||
Badness: 0.0451<br /> | Badness: 0.0451<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Echidnic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2> | ||
Commas: 91/90, 169/168, 385/384, 441/440<br /> | Commas: 91/90, 169/168, 385/384, 441/440<br /> | ||
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| Line 717: | Line 754: | ||
Compositions:<br /> | Compositions:<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:545:http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 --><a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow">http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3</a><!-- ws:end:WikiTextUrlRule:545 --><br /> | ||
(the description says &quot;lemba&quot; which has a similar sale structure but different mapping for 5)<br /> | (the description says &quot;lemba&quot; which has a similar sale structure but different mapping for 5)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Shrutar"></a><!-- ws:end:WikiTextHeadingRule:58 -->Shrutar</h1> | ||
Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie &lt;&lt;4 -8 14 -22 11 55||, it can also be described as 22&amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. <a class="wiki_link" href="/68edo">68edo</a> makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just.<br /> | Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie &lt;&lt;4 -8 14 -22 11 55||, it can also be described as 22&amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. <a class="wiki_link" href="/68edo">68edo</a> makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just.<br /> | ||
<br /> | <br /> | ||
| Line 732: | Line 769: | ||
EDOs: 22, 46, 68, 182b, 250bc<br /> | EDOs: 22, 46, 68, 182b, 250bc<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Shrutar-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2> | ||
Commas: 2048/2025, 245/243, 121/120<br /> | Commas: 2048/2025, 245/243, 121/120<br /> | ||
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| Line 740: | Line 777: | ||
EDOs: 22, 46, 68, 114, 296bce, 410bce<br /> | EDOs: 22, 46, 68, 114, 296bce, 410bce<br /> | ||
<br /> | <br /> | ||
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Commas: 121/120, 176/175, 196/195, 245/243<br /> | Commas: 121/120, 176/175, 196/195, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 749: | Line 786: | ||
Badness: 0.0281<br /> | Badness: 0.0281<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Shrutar-17-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->17-limit</h2> | ||
Commas: 121/120, 136/135, 154/153, 176/175, 196/195<br /> | Commas: 121/120, 136/135, 154/153, 176/175, 196/195<br /> | ||
<br /> | <br /> | ||
| Line 758: | Line 795: | ||
Badness: 0.0187<br /> | Badness: 0.0187<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Shrutar-19-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->19-limit</h2> | ||
Commas: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342<br /> | Commas: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342<br /> | ||
<br /> | <br /> | ||
| Line 767: | Line 804: | ||
Badness: 0.0175<br /> | Badness: 0.0175<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Sruti"></a><!-- ws:end:WikiTextHeadingRule:68 -->Sruti</h1> | ||
Commas: 2048/2025, 19683/19600<br /> | Commas: 2048/2025, 19683/19600<br /> | ||
<br /> | <br /> | ||
| Line 777: | Line 814: | ||
Badness: 0.1174<br /> | Badness: 0.1174<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Sruti-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->11-limit</h2> | ||
Commas: 176/175, 243/242, 896/891<br /> | Commas: 176/175, 243/242, 896/891<br /> | ||
<br /> | <br /> | ||
| Line 786: | Line 823: | ||
Badness: 0.0415<br /> | Badness: 0.0415<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Sruti-13-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->13-limit</h2> | ||
Commas: 144/143, 176/175, 351/350, 676/675<br /> | Commas: 144/143, 176/175, 351/350, 676/675<br /> | ||
<br /> | <br /> | ||
| Line 795: | Line 832: | ||
Badness: 0.0238<br /> | Badness: 0.0238<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h1&gt; --><h1 id="toc37"><a name="Anguirus"></a><!-- ws:end:WikiTextHeadingRule:74 -->Anguirus</h1> | ||
Commas: 49/48, 2048/2025<br /> | Commas: 49/48, 2048/2025<br /> | ||
<br /> | <br /> | ||
| Line 805: | Line 842: | ||
Badness: 0.0780<br /> | Badness: 0.0780<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Anguirus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->11-limit</h2> | ||
Commas: 49/48, 56/55, 243/242<br /> | Commas: 49/48, 56/55, 243/242<br /> | ||
<br /> | <br /> | ||
| Line 814: | Line 851: | ||
Badness: 0.0493<br /> | Badness: 0.0493<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Anguirus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->13-limit</h2> | ||
Commas: 49/48 56/55 91/90 352/351<br /> | Commas: 49/48 56/55 91/90 352/351<br /> | ||
<br /> | <br /> | ||
| Line 823: | Line 860: | ||
Badness: 0.0308<br /> | Badness: 0.0308<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h1&gt; --><h1 id="toc40"><a name="Shru"></a><!-- ws:end:WikiTextHeadingRule:80 -->Shru</h1> | ||
Commas: 392/375, 1323/1280<br /> | Commas: 392/375, 1323/1280<br /> | ||
<br /> | <br /> | ||
| Line 833: | Line 870: | ||
Badness: 0.1576<br /> | Badness: 0.1576<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Shru-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2> | ||
Commas: 56/55, 77/75, 1323/1280<br /> | Commas: 56/55, 77/75, 1323/1280<br /> | ||
<br /> | <br /> | ||
| Line 842: | Line 879: | ||
Badness: 0.0635<br /> | Badness: 0.0635<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Shru-13-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->13-limit</h2> | ||
Commas: 56/55, 77/75, 105/104, 507/500<br /> | Commas: 56/55, 77/75, 105/104, 507/500<br /> | ||
<br /> | <br /> | ||