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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 13:44:32 UTC</tt>.<br>
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| : The original revision id was <tt>340167170</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | The [[3/1|harmonic 3]] is 6.5{{c}} sharp and the [[5/1|5]] is 4{{c}} sharp, with [[7/1|7]], [[11/1|11]], and [[13/1|13]] more accurate but a little flat. Using the [[patent val]], it [[tempering out|tempers out]] [[15625/15552]] in the 5-limit and [[686/675]], [[4000/3969]] and [[6144/6125]] in the 7-limit. In the 11-limit it tempers out [[121/120]], [[176/175]] and [[385/384]], and in the 13-limit [[91/90]], [[169/168]] and [[196/195]], and it provides the optimal patent val for the 11-limit {{nowrap|22 & 61}} temperament and the 13-limit 15 & 83 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>
| | Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]]. |
| <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 83 equal temperament divides the octave into 83 equal parts of 14.458 cents each. The 3 is six and a half cents sharp and the 5 four cents sharp, with 7, 11, and 13 more accurate but a little flat. It tempers out 15625/15552 in the 5-limit and 686/675, 4000/3969 and 6144/6125 in the 7-limit, and provides the optimal patent val for the 7-limit 27&56 temperament with wedgie <<5 18 17 17 13 -11||. In the 11-limit it tempers out 121/120, 176/175 and 385/384, and in the 13-limit 91/90, 169/168 and 196/195, and it provides the optimal patent val for the 11-limit 22&61 temperament and the 13-limit 15&83 temperament.</pre></div>
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| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>83edo</title></head><body>The 83 equal temperament divides the octave into 83 equal parts of 14.458 cents each. The 3 is six and a half cents sharp and the 5 four cents sharp, with 7, 11, and 13 more accurate but a little flat. It tempers out 15625/15552 in the 5-limit and 686/675, 4000/3969 and 6144/6125 in the 7-limit, and provides the optimal patent val for the 7-limit 27&amp;56 temperament with wedgie &lt;&lt;5 18 17 17 13 -11||. In the 11-limit it tempers out 121/120, 176/175 and 385/384, and in the 13-limit 91/90, 169/168 and 196/195, and it provides the optimal patent val for the 11-limit 22&amp;61 temperament and the 13-limit 15&amp;83 temperament.</body></html></pre></div>
| | {{Harmonics in equal|83}} |
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| | === Subsets and supersets === |
| | 83edo is the 23rd [[prime edo]], following [[79edo]] and before [[89edo]]. |
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| | == Intervals == |
| | {{Interval table}} |
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| | == Instruments == |
| | A [[Lumatone mapping for 83edo]] has now been demonstrated (see the Ripple and Miracle mapping for full gamut coverage). |
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| | == Music == |
| | * [https://youtube.com/shorts/vYhK-A74Kpg?si=n8bjn_AOYAPY69qx ''Microtonal improvisation in 83edo''] - [[Bryan Deister]] (Mar 2025) |
| | * [https://www.youtube.com/shorts/FFNFQ4H-2D4 ''83edo waltz''] (2025) |