Diaschismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 324362150 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 332699968 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-09 18:08:16 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>332699968</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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Map: [<2 0 11 4 -1 9|, <0 2 -4 1 5 -1|] | Map: [<2 0 11 4 -1 9|, <0 2 -4 1 5 -1|] | ||
EDOs: 10, 24, 34, 58d, 92def | EDOs: 10, 24, 34, 58d, 92def | ||
Badness: 0.0308</pre></div> | Badness: 0.0308 | ||
=Shru= | |||
Commas: 392/375, 1323/1280 | |||
POTE generator: ~64/63 = 50.135 | |||
Map: [<2 1 9 11|, <0 2 -4 -5|] | |||
Wedgie: <<4 -8 -10 -22 -27 -1|| | |||
EDOs: 22d, 24 | |||
Badness: 0.1576 | |||
==11-limit== | |||
Commas: 56/55, 77/75, 1323/1280 | |||
POTE generator: ~64/63 = 50.130 | |||
Map: [<2 1 9 11 8|, <0 2 -4 -5 -1|] | |||
EDOs: 22d, 24 | |||
Badness: 0.0635 | |||
==13-limit== | |||
Commas: 56/55, 77/75, 105/104, 507/500 | |||
POTE generator: ~64/63 = 50.535 | |||
Map: [<2 1 9 11 8 15|, <0 2 -4 -5 -1 -7|] | |||
EDOs: 24 | |||
Badness: 0.0457 | |||
</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:82:&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:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 1em;"><a href="#Srutal">Srutal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 2em;"><a href="#Srutal-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 2em;"><a href="#Srutal-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 1em;"><a href="#Pajara">Pajara</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 2em;"><a href="#Pajara-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Pajara-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#Pajara-Pajarous">Pajarous</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Pajara-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 2em;"><a href="#Pajara-Pajaro">Pajaro</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#Pajara-Hemipaj">Hemipaj</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 1em;"><a href="#Diaschismic">Diaschismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 2em;"><a href="#Diaschismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 2em;"><a href="#Diaschismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Diaschismic-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 1em;"><a href="#Keen">Keen</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Keen-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 1em;"><a href="#Bidia">Bidia</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 2em;"><a href="#Bidia-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Bidia-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 1em;"><a href="#Echidna">Echidna</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 2em;"><a href="#Echidna-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Echidna-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#Echidna-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 1em;"><a href="#Echidnic">Echidnic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Echidnic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 2em;"><a href="#Echidnic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 1em;"><a href="#Shrutar">Shrutar</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Shrutar-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 2em;"><a href="#Shrutar-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 2em;"><a href="#Shrutar-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Shrutar-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 1em;"><a href="#Sruti">Sruti</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Sruti-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Sruti-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Anguirus">Anguirus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Anguirus-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 2em;"><a href="#Anguirus-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 1em;"><a href="#Shru">Shru</a></div> | ||
< | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Shru-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Shru-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --></div> | |||
<!-- ws:end:WikiTextTocRule:124 -->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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Compositions:<br /> | Compositions:<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:523: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:523 --><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 /> | ||
| Line 786: | Line 821: | ||
Map: [&lt;2 0 11 4 -1 9|, &lt;0 2 -4 1 5 -1|]<br /> | Map: [&lt;2 0 11 4 -1 9|, &lt;0 2 -4 1 5 -1|]<br /> | ||
EDOs: 10, 24, 34, 58d, 92def<br /> | EDOs: 10, 24, 34, 58d, 92def<br /> | ||
Badness: 0.0308</body></html></pre></div> | Badness: 0.0308<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:76:&lt;h1&gt; --><h1 id="toc38"><a name="Shru"></a><!-- ws:end:WikiTextHeadingRule:76 -->Shru</h1> | |||
Commas: 392/375, 1323/1280<br /> | |||
<br /> | |||
POTE generator: ~64/63 = 50.135<br /> | |||
<br /> | |||
Map: [&lt;2 1 9 11|, &lt;0 2 -4 -5|]<br /> | |||
Wedgie: &lt;&lt;4 -8 -10 -22 -27 -1||<br /> | |||
EDOs: 22d, 24<br /> | |||
Badness: 0.1576<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Shru-11-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->11-limit</h2> | |||
Commas: 56/55, 77/75, 1323/1280<br /> | |||
<br /> | |||
POTE generator: ~64/63 = 50.130<br /> | |||
<br /> | |||
Map: [&lt;2 1 9 11 8|, &lt;0 2 -4 -5 -1|]<br /> | |||
EDOs: 22d, 24<br /> | |||
Badness: 0.0635<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Shru-13-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->13-limit</h2> | |||
Commas: 56/55, 77/75, 105/104, 507/500<br /> | |||
<br /> | |||
POTE generator: ~64/63 = 50.535<br /> | |||
<br /> | |||
Map: [&lt;2 1 9 11 8 15|, &lt;0 2 -4 -5 -1 -7|]<br /> | |||
EDOs: 24<br /> | |||
Badness: 0.0457</body></html></pre></div> | |||