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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 08:19:53 UTC</tt>.<br>
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| : The original revision id was <tt>239302685</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.</pre></div>
| | == Theory == |
| <h4>Original HTML content:</h4>
| | 105edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone, such as [[grosstone]] and [[huygens]]. It [[tempering out|tempers 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 of 11-limit meantone (a.k.a. huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning|CTE generator]] for meantone. |
| <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 />
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| | === Odd harmonics === |
| 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>
| | {{Harmonics in equal|105}} |
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| | === Subsets and supersets === |
| | 105 is the product of 3 × 5 × 7, the three smallest odd primes, with other divisors being 15, 21 and 35. |
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| | As such, the val [105 165 245 294], which is contorted in 2.n for each prime n in the subgroup, may be used to extend the concept of 21edo's 5-limit harmony to the 7-limit, producing an independent dimension for each prime. |
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| | == Intervals == |
| | {{Main|Table of 105edo intervals}} |
| | === 15-odd-limit interval mappings === |
| | {{Q-odd-limit intervals|105}} |
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| | == Instruments == |
| | === Lumatone === |
| | The [[lumatone]] can be used to play 105edo. For key mappings, see: [[Lumatone mapping for 105edo]]. |
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| | [[Category:105edo| ]] <!-- main article --> |
| | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> |
| | [[Category:Huygens]] |
| | [[Category:Meantone]] |