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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-06-17 05:15:55 UTC</tt>.<br>
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| : The original revision id was <tt>614809973</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 12276 division divides the octave into equal steps of size 0.097752 cents. This creates a unit known as the **prima,** useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three **tuning units**.
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| 12276 is a strong 11-limit system, with a lower 11-limit relative error than any division aside from [[6691edo|6691]]. It factors as 12276 = 2^2 * 3^2 * 11 * 31, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively. </pre></div> | | 12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo|6691]]. 12276 tempers out the [[Kirnberger's atom|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps. |
| <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>12276edo</title></head><body>The 12276 division divides the octave into equal steps of size 0.097752 cents. This creates a unit known as the <strong>prima,</strong> useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three <strong>tuning units</strong>. <br />
| | === Prime harmonics === |
| <br />
| | {{Harmonics in equal|12276|columns=11}} |
| 12276 is a strong 11-limit system, with a lower 11-limit relative error than any division aside from <a class="wiki_link" href="/6691edo">6691</a>. It factors as 12276 = 2^2 * 3^2 * 11 * 31, and among its divisors are <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/99edo">99</a> and <a class="wiki_link" href="/198edo">198</a>. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.</body></html></pre></div>
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| | === Subsets and supersets === |
| | 12276edo factors into primes as {{nowrap| 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31 }}, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s. |
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| | [[Category:3-limit record edos|#####]] <!-- 5-digit number --> |