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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>2015-08-18 01:26:25 UTC</tt>.<br>
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| : The original revision id was <tt>556856635</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">The 4296 equal division divides the octave into 4296 steps of 0.2793 cents each, which means that one cent is exactly 3.58 steps of 4296 edo. It is an extraordinarily strong 5-limit system, tempering out raider, |71 -99 37>, pirate, |-90 -15 49> and the Kirnberger atom, |161 -84 -12>. Not until [[73709edo|73709]] do we reach a division with a lower 5-limit relative error. In the 7-limit, it tempers out the landscape comma, 250047/250000, and so supports the 7-limit version of the 612&1848 temperament.
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| It 4296 = 12 * 358, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments. From that point of view, one might note that 81/80 is 77 steps, 531441/524288, the Pythagorean comma, 84 steps, and 32805/32768, the schisma, 7 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Senior, |-17 62 -35>, fortune, |-107 47 14> and the monzisma, |54 -37 2>, are all one step of 4296et. </pre></div>
| | 4296edo is an extraordinarily strong 5-limit system, tempering out raider, {{monzo| 71 -99 37 }}, pirate, {{monzo| -90 -15 49 }} and the [[Kirnberger's atom]], {{monzo| 161 -84 -12 }}. Not until [[73709edo|73709]] do we reach a division with a lower 5-limit relative error, and not until [[6796263edo|6796263]] do we find a lower logflat badness. It is uniquely [[consistent]] through the 9-odd-limit, and in the 7-limit, it tempers out the [[landscape comma]], 250047/250000, and so [[support]]s septimal [[atomic]], the 612 & 1848 temperament. |
| <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>4296edo</title></head><body>The 4296 equal division divides the octave into 4296 steps of 0.2793 cents each, which means that one cent is exactly 3.58 steps of 4296 edo. It is an extraordinarily strong 5-limit system, tempering out raider, |71 -99 37&gt;, pirate, |-90 -15 49&gt; and the Kirnberger atom, |161 -84 -12&gt;. Not until <a class="wiki_link" href="/73709edo">73709</a> do we reach a division with a lower 5-limit relative error. In the 7-limit, it tempers out the landscape comma, 250047/250000, and so supports the 7-limit version of the 612&amp;1848 temperament.<br />
| | 4296 = 12 × 358, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments, and |
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| | which means that one cent is exactly 3.58 steps of 4296edo. From that point of view, one might note that 81/80 is 77 steps, 531441/524288, the Pythagorean comma, 84 steps, and 32805/32768, the schisma, 7 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Senior, {{monzo| -17 62 -35 }}, fortune, {{monzo| -107 47 14 }} and the [[monzisma]], {{monzo| 54 -37 2 }}, are all one step of 4296et. |
| It 4296 = 12 * 358, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments. From that point of view, one might note that 81/80 is 77 steps, 531441/524288, the Pythagorean comma, 84 steps, and 32805/32768, the schisma, 7 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Senior, |-17 62 -35&gt;, fortune, |-107 47 14&gt; and the monzisma, |54 -37 2&gt;, are all one step of 4296et.</body></html></pre></div>
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| | === Prime harmonics === |
| | {{Harmonics in equal|4296|prec=4}} |