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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>2011-08-05 14:34:57 UTC</tt>.<br>
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| : The original revision id was <tt>244520207</tt>.<br>
| | 306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]]. |
| : 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>
| | 306edo provides an excellent approximation of [[Well temperament#Historical well temperaments|Valotti temperament]] due to its representation of the [[Pythagorean comma]] as 6 steps. |
| <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">The //306 equal division// divides the octave into 306 equal parts of 3.922 cents each, and thereby provides a very accurate fifth, only 0.006 cents sharp. In the 5-limit, the [[patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179/306, the continued fraction convergent after 31/53 and before 389/665 in the sequence of continued fraction approximations to the log base 2 of 3/2. On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].</pre></div>
| | === Prime harmonics === |
| <h4>Original HTML content:</h4>
| | {{Harmonics in equal|306|prec=3}} |
| <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>306edo</title></head><body>The <em>306 equal division</em> divides the octave into 306 equal parts of 3.922 cents each, and thereby provides a very accurate fifth, only 0.006 cents sharp. In the 5-limit, the <a class="wiki_link" href="/patent%20val">patent val</a> tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179/306, the continued fraction convergent after 31/53 and before 389/665 in the sequence of continued fraction approximations to the log base 2 of 3/2. On the 2*306 subgroup 2.3.25.7.55 it takes the same values as <a class="wiki_link" href="/612edo">612edo</a>.</body></html></pre></div>
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| | === Subsets and supersets === |
| | Since 306 factors into {{factorization|306}}, 306edo has subset edos {{EDOs| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}. |
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| | [[Category:3-limit record edos|###]] <!-- 3-digit number --> |