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Diaschismic family: Difference between revisions

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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>2012-04-12 13:33:32 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-12 13:34:30 UTC</tt>.<br>
: The original revision id was <tt>319896024</tt>.<br>
: The original revision id was <tt>319896462</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>
<h4>Original Wikitext content:</h4>
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<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]
The 5-limit parent comma for the **diaschismic family** is 2048/2025, the [[diaschisma]]. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or **srutal**, 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. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.
The 5-limit parent comma for the **diaschismic family** is 2048/2025, the [[diaschisma]]. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or **srutal**, 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. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.


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<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:60:&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:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Pajara"&gt;Pajara&lt;/a&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;!-- 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="#Diaschismic"&gt;Diaschismic&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;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Keen"&gt;Keen&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;a href="#Bidia"&gt;Bidia&lt;/a&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; | &lt;a href="#Echidna"&gt;Echidna&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&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;a href="#Echidnic"&gt;Echidnic&lt;/a&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;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt; | &lt;a href="#Shrutar"&gt;Shrutar&lt;/a&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:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt; | &lt;a href="#Sruti"&gt;Sruti&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&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:60:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Pajara"&gt;Pajara&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Pajara-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Pajara-Pajarous"&gt;Pajarous&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Diaschismic"&gt;Diaschismic&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diaschismic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diaschismic-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Keen"&gt;Keen&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Keen-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bidia"&gt;Bidia&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Echidnic"&gt;Echidnic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Echidnic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:91 --&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;!-- ws:end:WikiTextTocRule:91 --&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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