Pythagorean comma
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Andrew_Heathwaite and made on 2011-12-05 21:40:11 UTC.
- The original revision id was 282666330.
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Original Wikitext content:
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 [[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]]. [[http://en.wikipedia.org/wiki/Pythagorean_comma|Wikipedia article]]
Original HTML content:
<html><head><title>Pythagorean comma</title></head><body>The Pythagorean or ditonic comma (about 23.460¢) is the interval 531441/524288 = |-19 12> (see <a class="wiki_link" href="/monzo">monzo</a>). 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 <a class="wiki_link" href="/2187_2048">apotome</a> and the <a class="wiki_link" href="/256_243">Pythagorean minor second</a>, (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 <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/72edo">72edo</a> and <a class="wiki_link" href="/84edo">84edo</a>.<br /> <br /> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pythagorean_comma" rel="nofollow">Wikipedia article</a></body></html>