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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''105edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 105 equal parts of 11.429 [[cent|cent]]s each. It is most notable as a tuning of meantone and in particular higher limit extensions of meantone, [[tempering_out|tempering out]] [[81/80|81/80]] in the [[5-limit|5-limit]]; 81/80, [[126/125|126/125]] and hence 225/224 in the [[7-limit|7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit|11-limit]]; and if we want to push that far, 144/143 in the [[13-limit|13-limit]]. This is the sharper fifth mapping (aka "huygens") of 11-limit meantone. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 17:34:16 UTC</tt>.<br>
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| : The original revision id was <tt>601660756</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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">**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.
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| 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.</pre></div> | | 105edo gives the [[Optimal_patent_val|optimal patent val]] for 11-limit meantone (ie huygens rather than meanpop) and provides a good tuning in the 13-limit, though [[74edo|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|cent]]" is desired to include them all. |
| <h4>Original HTML content:</h4>
| | [[Category:edo]] |
| <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"><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 &quot;huygens&quot;) of 11-limit meantone.<br />
| | [[Category:huygens]] |
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| | [[Category:meantone]] |
| 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 &quot;<a class="wiki_link" href="/cent">cent</a>&quot; is desired to include them all.</body></html></pre></div>
| | [[Category:theory]] |