122edo: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 214069270 - Original comment: **
m Subsets and supersets: 244 also corrects harmonic 7
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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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>2011-03-25 15:49:58 UTC</tt>.<br>
: The original revision id was <tt>214069270</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The //122 equal division// divides the octave into 122 equal parts of 9.836 cents each. It is the optimal patent val for 7- and 11-limit [[Marvel temperaments|tritonic temperament]], and tempers out 78732/78125 in the 5-limit, 225/224 in the 7-limit, 385/384 and 4000/3993 in the 11-limit, and 351/350 and 364/363 in the 13-limit.


122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * 61.</pre></div>
122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. As an equal temperament, it [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]]; [[225/224]] in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni|tritoni]] temperament, and the [[rank-3|planar]] temperament [[squalentine]].  
<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;122edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;122 equal division&lt;/em&gt; divides the octave into 122 equal parts of 9.836 cents each. It is the optimal patent val for 7- and 11-limit &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;tritonic temperament&lt;/a&gt;, and tempers out 78732/78125 in the 5-limit, 225/224 in the 7-limit, 385/384 and 4000/3993 in the 11-limit, and 351/350 and 364/363 in the 13-limit.&lt;br /&gt;
122 = [[55edo|55]] + [[67edo|67]], and so using the 122c [[val]] it is the [[convergent]] towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.
&lt;br /&gt;
 
122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * 61.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Odd harmonics ===
{{Harmonics in equal|122}}
 
Harmonic 25 (two 5/4 major thirds) is about halfway between 122edo's steps.
 
=== Subsets and supersets ===
Since 122 factors into {{factorization|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. [[244edo]] (double 122edo) provides a good correction to harmonics 7 and 25.  
 
[[Category:Tritonic]]
[[Category:Meantone]]