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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>2012-05-28 14:36:34 UTC</tt>.<br>
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| : The original revision id was <tt>340182192</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | Since {{nowrap|86 {{=}} 2 × 43}}, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the [[patent val]] [[tempering out|tempers out]] 6144/6125, so that it [[support]]s the [[mohajira]] temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675. |
| 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>
| | It is perhaps more interesting to consider the alternative 86e val, which tempers out [[121/120]] and [[243/242]] and [[support]]s 11-limit mohajira. The 86de val is a less good entry for 11-limit [[migration]]. In any case, this tuning is between [[31edo]] and [[55edo]], and replaces 43edo's lopsided placement of [[11/9]] and [[27/22]] with a true neutral third. |
| <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 86 equal temperament divides the octave into 86 equal parts of 13.953 cents each. 86 = 2 * 43, and the patent val is a contorted [[43edo|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it supports mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.</pre></div>
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| <h4>Original HTML content:</h4>
| | 86edo is closely related to the [[8ed16/15|delta scale]], which is the equal division of the [[16/15|classic diatonic semitone]] into eight parts of 13.9664{{c}} each. |
| <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>86edo</title></head><body>The 86 equal temperament divides the octave into 86 equal parts of 13.953 cents each. 86 = 2 * 43, and the patent val is a contorted <a class="wiki_link" href="/43edo">43</a> in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it supports mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&amp;86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.</body></html></pre></div>
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| | === Odd harmonics === |
| | {{Harmonics in equal|86}} |
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| | === Subsets and supersets === |
| | 86edo contains [[2edo]] and [[43edo]] as subsets. [[258edo]], which triples it, is a notable tuning. |
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| | == Interval table == |
| | {{Interval table}} |
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| | == Instruments == |
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| | A [[Lumatone mapping for 86edo]] is available. |
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| | == Music == |
| | ; [[Bryan Deister]] |
| | * [https://www.youtube.com/shorts/5_W323Iea18 ''microtonal improvisation in 86edo''] (2025) |
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| | == See also == |
| | * [[343edo#343ed16|343ed16]] (octave-stretched version of 86edo) |