105edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author JosephRuhf and made on 2016-12-07 17:34:16 UTC.
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Original Wikitext content:
**105edo** is the [[equal division of the octave]] into 105 equal parts of 11.429 [[cent]]s each. It is most notable as a tuning of meantone and in particular higher limit extensions of meantone, [[tempering out]] [[81_80|81/80]] in the [[5-limit]]; 81/80, [[126_125|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. As the common multiple of these three primes closest to 100, 105 is a perfect substitute for it when a "[[cent]]" is desired to include them all.
Original HTML content:
<html><head><title>105edo</title></head><body><strong>105edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 105 equal parts of 11.429 <a class="wiki_link" href="/cent">cent</a>s each. It is most notable as a tuning of meantone and in particular higher limit extensions of meantone, <a class="wiki_link" href="/tempering%20out">tempering out</a> <a class="wiki_link" href="/81_80">81/80</a> in the <a class="wiki_link" href="/5-limit">5-limit</a>; 81/80, <a class="wiki_link" href="/126_125">126/125</a> and hence 225/224 in the <a class="wiki_link" href="/7-limit">7-limit</a>; 99/98, 176/175 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>; and if we want to push that far, 144/143 in the <a class="wiki_link" href="/13-limit">13-limit</a>. This is the sharper fifth mapping (aka "huygens") of 11-limit meantone.<br /> <br /> 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. As the common multiple of these three primes closest to 100, 105 is a perfect substitute for it when a "<a class="wiki_link" href="/cent">cent</a>" is desired to include them all.</body></html>