378edo: Difference between revisions

Wikispaces>JosephRuhf
**Imported revision 601677382 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-08 00:07:19 UTC</tt>.<br>
 
: The original revision id was <tt>601677382</tt>.<br>
The equal temperament [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit and [[3136/3125]] in the 7-limit, so that it [[support]]s [[bischismic]], and in fact provides the [[optimal patent val]]. It tempers out [[441/440]] and [[8019/8000]] in the 11-limit and [[729/728]] and [[1001/1000]] in the 13-limit so that it supports 11- and 13-limit bischismatic, and it also gives the optimal patent val for 13-limit bischismic.
: 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>
=== Prime harmonics ===
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|378}}
<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">The //378 equal division// divides the octave into 378 equal parts of 3.175 cents each. It tempers out 32805/32768 in the 5-limit and 3136/3125 in the 7-limit, so that it supports [[Schismatic family#Bischismatic|bischismatic temperament]] and in fact provides the [[optimal patent val]]. It tempers out 441/440 and 8019/8000 in the 11-limit and 729/728 and 1001/1000 in the 13-limit so that it supports 11 and 13 limit bischismatic, and it also gives the optimal patent val for 13-limit bischismatic.</pre></div>
 
<h4>Original HTML content:</h4>
=== Subsets and supersets ===
<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;378edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;378 equal division&lt;/em&gt; divides the octave into 378 equal parts of 3.175 cents each. It tempers out 32805/32768 in the 5-limit and 3136/3125 in the 7-limit, so that it supports &lt;a class="wiki_link" href="/Schismatic%20family#Bischismatic"&gt;bischismatic temperament&lt;/a&gt; and in fact provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt;. It tempers out 441/440 and 8019/8000 in the 11-limit and 729/728 and 1001/1000 in the 13-limit so that it supports 11 and 13 limit bischismatic, and it also gives the optimal patent val for 13-limit bischismatic.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 378 factors into {{factorization|378}}, 378edo has subset edos {{EDOs| 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, and 189 }}.
 
[[Category:Bischismic]]