333edo: Difference between revisions

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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>2012-02-09 16:31:10 UTC</tt>.<br>
 
: The original revision id was <tt>300282248</tt>.<br>
The equal temperament tempers out [[15625/15552]] in the 5-limit and [[5120/5103]] in the 7-limit, so it [[support]]s [[countercata]]. In the 11-limit it tempers out 1375/1372 and [[4000/3993]], and in the 13-limit [[325/324]], [[364/363]], [[625/624]] and [[676/675]], and provides the [[optimal patent val]] for the rank-2 temperament [[novemkleismic]], for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324.
: 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|333}}
<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 //333 equal temperament// divides the octave into 333 equal parts of 3.604 cents each. It tempers out 15625/15552 in the 5-limit and 5120/5013 in the 7-limit, so it supports [[Kleismic family#Countercata|countercata temperament]]. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the [[optimal patent val]] for the rank three temperament tempering out 325/324, 625/624 and 676/675, the rank four temperament tempering out 325/324 and 1375/1372, and the rank five temperament tempering out 325/324.</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;333edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;333 equal temperament&lt;/em&gt; divides the octave into 333 equal parts of 3.604 cents each. It tempers out 15625/15552 in the 5-limit and 5120/5013 in the 7-limit, so it supports &lt;a class="wiki_link" href="/Kleismic%20family#Countercata"&gt;countercata temperament&lt;/a&gt;. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the rank three temperament tempering out 325/324, 625/624 and 676/675, the rank four temperament tempering out 325/324 and 1375/1372, and the rank five temperament tempering out 325/324.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 333 factors into 3<sup>2</sup> × 37, 333edo has subset edos {{EDOs| 3, 9, 37, and 111 }}.  
 
[[Category:Countercata]]
[[Category:Marveltwin]]