127edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma|comma]]s it [[tempering_out|tempers out]]. In the [[5-limit|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence supports [[Würschmidt_family|würschmidt temperament]]. In the [[7-limit|7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit|11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[Optimal_patent_val|optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 02:11:10 UTC</tt>.<br>
: The original revision id was <tt>288887301</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">**127edo**, which divides the [[octave]] into 127 parts of 9.45 [[cents]] each, is another equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]. In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence supports [[Würschmidt family|würschmidt temperament]]. In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.


127edo is the 31st [[prime numbers|prime]] edo.
127edo is the 31st [[prime_numbers|prime]] edo.


[[MOS Scales of 127edo]]</pre></div>
[[MOS_Scales_of_127edo|MOS Scales of 127edo]]     [[Category:edo]]
<h4>Original HTML content:</h4>
[[Category:hemiwuerschmidt]]
<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;127edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;127edo&lt;/strong&gt;, which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 127 parts of 9.45 &lt;a class="wiki_link" href="/cents"&gt;cents&lt;/a&gt; each, is another equal division interesting because of its approximations, defined by the &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s it &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt;. In the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, it tempers out the würschmidt comma, 393216/390625 and hence supports &lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family"&gt;würschmidt temperament&lt;/a&gt;. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.&lt;br /&gt;
[[Category:minerva]]
&lt;br /&gt;
[[Category:prime_edo]]
127edo is the 31st &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo.&lt;br /&gt;
[[Category:theory]]
&lt;br /&gt;
[[Category:wuerschmidt]]
&lt;a class="wiki_link" href="/MOS%20Scales%20of%20127edo"&gt;MOS Scales of 127edo&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:wurschmidt]]

Revision as of 00:00, 17 July 2018

127edo, which divides the octave into 127 parts of 9.45 cents each, is another equal division interesting because of its approximations, defined by the commas it tempers out. In the 5-limit, it tempers out the würschmidt comma, 393216/390625 and hence supports würschmidt temperament. In the 7-limit, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the 11-limit, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

127edo is the 31st prime edo.

MOS Scales of 127edo