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Diaschismic family: Difference between revisions

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**Imported revision 288693728 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 303163932 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-28 19:59:15 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-19 15:34:06 UTC</tt>.<br>
: The original revision id was <tt>288693728</tt>.<br>
: The original revision id was <tt>303163932</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: [&lt;2 1 9 -2 8 -10 6 -10|, &lt;0 2 -4 7 -1 16 2 17|]
Map: [&lt;2 1 9 -2 8 -10 6 -10|, &lt;0 2 -4 7 -1 16 2 17|]
EDOs: 22, 24, 46, 68, 114, 182bef
EDOs: 22, 24, 46, 68, 114, 182bef
Badness: 0.0175</pre></div>
Badness: 0.0175
 
=Sruti=
Commas: 2048/2025, 19683/19600
 
POTE generator: ~175/144 = 351.876
 
Map: [&lt;2 0 11 -15|, &lt;0 2 -4 13|]
Wedgie: &lt;&lt;4 -8 26 -22 30 83||
EDOs: 24, 34d, 58, 150cd, 208cd, 266cd
Badness: 0.1174
 
==11-limit==
Commas: 176/175, 243/242, 896/891
 
POTE generator: ~11/9 = 351.863
 
Map: [&lt;2 0 11 -15 -1|, &lt;0 2 -4 13 5|]
EDOs: 24, 34d, 58, 150cde, 208cde
Badness: 0.0415
 
==13-limit==
Commas: 144/143, 176/175, 351/350, 676/675
 
POTE generator: ~11/9 = 351.886
 
Map: [&lt;2 0 11 -15 -1 9|, &lt;0 2 -4 13 5 -1|]
EDOs: 24, 34d, 58, 150cdef, 208cdef
Badness: 0.0238
</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Diaschismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:50:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Pajara"&gt;Pajara&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt; | &lt;a href="#Diaschismic"&gt;Diaschismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Keen"&gt;Keen&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Bidia"&gt;Bidia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Echidna"&gt;Echidna&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Echidnic"&gt;Echidnic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Shrutar"&gt;Shrutar&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Diaschismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:56:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Pajara"&gt;Pajara&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Diaschismic"&gt;Diaschismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Keen"&gt;Keen&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Bidia"&gt;Bidia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt; | &lt;a href="#Echidna"&gt;Echidna&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt; | &lt;a href="#Echidnic"&gt;Echidnic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Shrutar"&gt;Shrutar&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt; | &lt;a href="#Sruti"&gt;Sruti&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;br /&gt;
The 5-limit parent comma for the &lt;strong&gt;diaschismic family&lt;/strong&gt; is 2048/2025, the &lt;a class="wiki_link" href="/diaschisma"&gt;diaschisma&lt;/a&gt;. Its monzo is |11 -4 -2&amp;gt;, and flipping that yields &amp;lt;&amp;lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or &lt;strong&gt;srutal&lt;/strong&gt;, 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. &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; is a good tuning choice, with &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; or &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; being other possibilities. Both &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; support it, and retuning them to a MOS of diaschismic gives two scale possibilities.&lt;br /&gt;
The 5-limit parent comma for the &lt;strong&gt;diaschismic family&lt;/strong&gt; is 2048/2025, the &lt;a class="wiki_link" href="/diaschisma"&gt;diaschisma&lt;/a&gt;. Its monzo is |11 -4 -2&amp;gt;, and flipping that yields &amp;lt;&amp;lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or &lt;strong&gt;srutal&lt;/strong&gt;, 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. &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; is a good tuning choice, with &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; or &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; being other possibilities. Both &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; support it, and retuning them to a MOS of diaschismic gives two scale possibilities.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Map: [&amp;lt;2 1 9 -2 8 -10 6 -10|, &amp;lt;0 2 -4 7 -1 16 2 17|]&lt;br /&gt;
Map: [&amp;lt;2 1 9 -2 8 -10 6 -10|, &amp;lt;0 2 -4 7 -1 16 2 17|]&lt;br /&gt;
EDOs: 22, 24, 46, 68, 114, 182bef&lt;br /&gt;
EDOs: 22, 24, 46, 68, 114, 182bef&lt;br /&gt;
Badness: 0.0175&lt;/body&gt;&lt;/html&gt;</pre></div>
Badness: 0.0175&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Sruti"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Sruti&lt;/h1&gt;
Commas: 2048/2025, 19683/19600&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~175/144 = 351.876&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 11 -15|, &amp;lt;0 2 -4 13|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;4 -8 26 -22 30 83||&lt;br /&gt;
EDOs: 24, 34d, 58, 150cd, 208cd, 266cd&lt;br /&gt;
Badness: 0.1174&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Sruti-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;11-limit&lt;/h2&gt;
Commas: 176/175, 243/242, 896/891&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 351.863&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 11 -15 -1|, &amp;lt;0 2 -4 13 5|]&lt;br /&gt;
EDOs: 24, 34d, 58, 150cde, 208cde&lt;br /&gt;
Badness: 0.0415&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Sruti-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;13-limit&lt;/h2&gt;
Commas: 144/143, 176/175, 351/350, 676/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 351.886&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 11 -15 -1 9|, &amp;lt;0 2 -4 13 5 -1|]&lt;br /&gt;
EDOs: 24, 34d, 58, 150cdef, 208cdef&lt;br /&gt;
Badness: 0.0238&lt;/body&gt;&lt;/html&gt;</pre></div>
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