Pythagorean comma: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The Pythagorean or ditonic comma (about 23.460¢) is the interval 531441/524288 = |-19 12&gt; (see [[monzo|monzo]]). It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)^12/2^7 and it also can be written as the ratio between the [[2187/2048|apotome]] and the [[256/243|Pythagorean minor second]], (2187/2048)/(256/243). For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by [[24edo|24edo]], [[72edo|72edo]] and [[84edo|84edo]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-05 21:40:32 UTC</tt>.<br>
: The original revision id was <tt>282666442</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 Pythagorean or ditonic comma (about 23.460¢) is the interval 531441/524288 = |-19 12&gt; (see [[monzo]]). It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)^12/2^7 and it also can be written as the ratio between the [[2187_2048|apotome]] and the [[256_243|Pythagorean minor second]], (2187/2048)/(256/243). For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by [[24edo]], [[72edo]] and [[84edo]].


See: [[Gallery of Just Intervals]], [[comma]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[Comma|comma]]


[[http://en.wikipedia.org/wiki/Pythagorean_comma|Wikipedia article]]</pre></div>
[http://en.wikipedia.org/wiki/Pythagorean_comma Wikipedia article]     [[Category:comma]]
<h4>Original HTML content:</h4>
[[Category:pythagorean]]
<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;Pythagorean comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The Pythagorean or ditonic comma (about 23.460¢) is the interval 531441/524288 = |-19 12&amp;gt; (see &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt;). It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)^12/2^7 and it also can be written as the ratio between the &lt;a class="wiki_link" href="/2187_2048"&gt;apotome&lt;/a&gt; and the &lt;a class="wiki_link" href="/256_243"&gt;Pythagorean minor second&lt;/a&gt;, (2187/2048)/(256/243). For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; and &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;, &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pythagorean_comma" rel="nofollow"&gt;Wikipedia article&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The Pythagorean or ditonic comma (about 23.460¢) is the interval 531441/524288 = |-19 12> (see monzo). It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)^12/2^7 and it also can be written as the ratio between the apotome and the Pythagorean minor second, (2187/2048)/(256/243). For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by 24edo, 72edo and 84edo.

See: Gallery of Just Intervals, comma

Wikipedia article