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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:genewardsmith|genewardsmith]] and made on <tt>2011-07-13 15:17:14 UTC</tt>.<br>
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| : The original revision id was <tt>241210949</tt>.<br>
| | If [[5/1|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s [[parakleismic]], the 99 & 316 temperament, and provides the [[optimal patent val]]. In the 11-limit it tempers out 12005/11979, [[16384/16335]], and [[41503/41472]]; and in the 13-limit, [[676/675]], [[1001/1000]], [[2080/2079]], 3584/3575, and [[10648/10647]]. |
| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | === Odd harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|415}} |
| <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 //415 equal division// divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, |8 14 -13>; in the 7-limit 3136/3125 and 4375/4374, so that it supports parakleismic temperament and provides the [[optimal patent val]]. </pre></div>
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| <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"><html><head><title>415edo</title></head><body>The <em>415 equal division</em> divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, |8 14 -13&gt;; in the 7-limit 3136/3125 and 4375/4374, so that it supports parakleismic temperament and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>.</body></html></pre></div>
| | Since 415 factors into {{factorization|415}}, 415edo contains [[5edo]] and [[83edo]] as subsets. |
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| | [[Category:Parakleismic]] |