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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-23 00:14:46 UTC</tt>.<br>
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| : The original revision id was <tt>213074704</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | In the [[5-limit]] the equal temperament [[tempering out|tempers out]] 2048/2025 ([[diaschisma]]), in the [[7-limit]] [[245/243]], in the [[11-limit]] [[121/120]], [[176/175]] and notably the [[quartisma]], in the [[13-limit]] [[196/195]] and [[325/324]], in the [[17-limit]] [[136/135]] and [[154/153]], in the [[19-limit]] [[286/285]] and [[343/342]]. These commas make for 114edo being an excellent tuning for the [[shrutar]] temperament; it is in fact the [[optimal patent val]] for shrutar in the 11-, 13-, 17-, and 19-limit, as well as the rank-3 [[bisector]] temperament. |
| 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>
| | === Odd harmonics === |
| <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">The //114 equal division// divides the octave into 114 equal parts, each of 10.526 cents. In the 5-limit it tempers out 2048/2025, in the 7-limit 245/243, in the 11-limit 121/120 and 176/175, in the 13-limit 196/195 and 325/324, in the 17-limit 136/135 and 154/153, in the 19-limit 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic family|shrutar temperament]]; it is in fact the [[optimal patent val]] for shrutar in the 11- 13- 17- and 19-limit.</pre></div>
| | {{Harmonics in equal|114}} |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>114edo</title></head><body>The <em>114 equal division</em> divides the octave into 114 equal parts, each of 10.526 cents. In the 5-limit it tempers out 2048/2025, in the 7-limit 245/243, in the 11-limit 121/120 and 176/175, in the 13-limit 196/195 and 325/324, in the 17-limit 136/135 and 154/153, in the 19-limit 286/285 and 343/342. These commas make for 114edo being an excellent tuning for <a class="wiki_link" href="/Diaschismic%20family">shrutar temperament</a>; it is in fact the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for shrutar in the 11- 13- 17- and 19-limit.</body></html></pre></div>
| | === Subsets and supersets === |
| | Since 114 factors into {{factorization|114}}, 114 edo has subset edos {{EDOs| 2, 3, 6, 19, 38, and 57 }}. |
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| | == Intervals == |
| | {{Interval table}} |
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| | [[Category:Shrutar]] |
| | [[Category:Bisector]] |