105edo

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Revision as of 17:59, 22 March 2011 by Wikispaces>genewardsmith (**Imported revision 212979694 - Original comment: **)
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This revision was by author genewardsmith and made on 2011-03-22 17:59:48 UTC.
The original revision id was 212979694.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

The 105 equal division divides the octave into 105 equal parts of 11.429 cents each. It is most notable as a tuning of meantone and in particular higher limit extensions of meantone, tempering out 81/80 in the 5-limit; 81/80, 126/125 and hence 225/224 in the 7-limit; 99/98, 176/175 and 441/440 in the 11-limit; and if we want to push that far, 144/143 in the 13-limit. This is the sharper fifth mapping (aka "huygens") of 11-limit meantone.

105edo gives the [[optimal patent val]] for 11-limit meantone (ie huygens rather than meanpop) and provides a good tuning in the 13-limit, though [[74edo]] is in that case the optimal patent val. 105 is highly composite, being the product 3*5*7 of the three smallest odd primes, with other divisors being 15, 21 and 35.

Original HTML content:

<html><head><title>105edo</title></head><body>The 105 equal division divides the octave into 105 equal parts of 11.429 cents each. It is most notable as a tuning of meantone and in particular higher limit extensions of meantone, tempering out 81/80 in the 5-limit; 81/80, 126/125 and hence 225/224 in the 7-limit; 99/98, 176/175 and 441/440 in the 11-limit; and if we want to push that far, 144/143 in the 13-limit. This is the sharper fifth mapping (aka &quot;huygens&quot;) of 11-limit meantone.<br />
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105edo gives the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit meantone (ie huygens rather than meanpop) and provides a good tuning in the 13-limit, though <a class="wiki_link" href="/74edo">74edo</a> is in that case the optimal patent val. 105 is highly composite, being the product 3*5*7 of the three smallest odd primes, with other divisors being 15, 21 and 35.</body></html>