282edo: Difference between revisions

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**Imported revision 514613994 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The ''282 equal division'' divides the octave into 282 equal parts of 4.255 cents each. It tempers out 16875/16807, 19683/19600 and 65625/65536 in the 7-limit, and 540/539 and 5632/5625 in the 11-limit, so that it provides the [[Optimal_patent_val|optimal patent val]] for [[Porwell_family|jupiter temperament]]; it also tempers out 4000/3993 and 234375/234256, providing the optimal patent val for [[Porwell_temperaments#Septisuperfourth|septisuperfourth]] temperament. In the 13-limit it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079. It is the smallest equal temperament uniquely [[consistent|consistent]] through to the 23 limit, and also the smallest consistent to the 29 limit. 282 has proper divisors 1, 2, 3, 6, 47, 94, and 141. It therefore divides the steps of 94et into three, but is not contorted beyond the 3-limit.
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>2014-06-22 03:24:02 UTC</tt>.<br>
: The original revision id was <tt>514613994</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 //282 equal division// divides the octave into 282 equal parts of 4.255 cents each. It tempers out 16875/16807, 19683/19600 and 65625/65536 in the 7-limit, and 540/539 and 5632/5625 in the 11-limit, so that it provides the [[optimal patent val]] for [[Porwell family|jupiter temperament]]; it also tempers out 4000/3993 and 234375/234256, providing the optimal patent val for [[Porwell temperaments#Septisuperfourth|septisuperfourth]] temperament. In the 13-limit it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079. It is the smallest equal temperament uniquely [[consistent]] through to the 23 limit, and also the smallest consistent to the 29 limit. 282 has proper divisors 1, 2, 3, 6, 47, 94, and 141. It therefore divides the steps of 94et into three, but is not contorted beyond the 3-limit. </pre></div>
<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;282edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;282 equal division&lt;/em&gt; divides the octave into 282 equal parts of 4.255 cents each. It tempers out 16875/16807, 19683/19600 and 65625/65536 in the 7-limit, and 540/539 and 5632/5625 in the 11-limit, so that it provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for &lt;a class="wiki_link" href="/Porwell%20family"&gt;jupiter temperament&lt;/a&gt;; it also tempers out 4000/3993 and 234375/234256, providing the optimal patent val for &lt;a class="wiki_link" href="/Porwell%20temperaments#Septisuperfourth"&gt;septisuperfourth&lt;/a&gt; temperament. In the 13-limit it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079. It is the smallest equal temperament uniquely &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; through to the 23 limit, and also the smallest consistent to the 29 limit. 282 has proper divisors 1, 2, 3, 6, 47, 94, and 141. It therefore divides the steps of 94et into three, but is not contorted beyond the 3-limit.&lt;/body&gt;&lt;/html&gt;</pre></div>