12276edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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'''.  
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-06-17 05:15:55 UTC</tt>.<br>
: The original revision id was <tt>614809973</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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**.  


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 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.
<h4>Original HTML content:</h4>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;12276edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 12276 division divides the octave into equal steps of size 0.097752 cents. This creates a unit known as the &lt;strong&gt;prima,&lt;/strong&gt; 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 &lt;strong&gt;tuning units&lt;/strong&gt;. &lt;br /&gt;
&lt;br /&gt;
12276 is a strong 11-limit system, with a lower 11-limit relative error than any division aside from &lt;a class="wiki_link" href="/6691edo"&gt;6691&lt;/a&gt;. It factors as 12276 = 2^2 * 3^2 * 11 * 31, and among its divisors are &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt; and &lt;a class="wiki_link" href="/198edo"&gt;198&lt;/a&gt;. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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.

12276 is a strong 11-limit system, with a lower 11-limit relative error than any division aside from 6691. It factors as 12276 = 2^2 * 3^2 * 11 * 31, and among its divisors are 12, 22, 31, 99 and 198. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.