105edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 212979694 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 239301961 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 08:11:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>239301961</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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"> | <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**, the 105 equal division divides 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.</pre></div> | 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.</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>105edo</title></head><body> | <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>, the 105 equal division divides the <a class="wiki_link" href="/octave">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 /> | ||
<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.</body></html></pre></div> | 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></pre></div> | ||
Revision as of 08:11, 29 June 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2011-06-29 08:11:18 UTC.
- The original revision id was 239301961.
- 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:
**105edo**, the 105 equal division divides 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.
Original HTML content:
<html><head><title>105edo</title></head><body><strong>105edo</strong>, the 105 equal division divides the <a class="wiki_link" href="/octave">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.</body></html>