1200edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2012-06-04 17:09:55 UTC.
- The original revision id was 342578710.
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Original Wikitext content:
The //1200 division// divides the octave in 1200 equal parts of exactly 1 [[cent]] each. It is notable mostly because it is the equal division corresponding to cents. 1200edo is uniquely [[consistent]] through the [[11-limit]], which means the intervals of the 11-limit[[tonality diamond| tonality diamond]], and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val <1200 1902 2786 3369 4141|. It is [[contorted]] in the [[5-limit]], having the same mapping as 600edo. In the [[7-limit]], it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by [[171edo]]. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by [[494edo]]. In the 7-limit, it provides a val, 1200cd, which is extremely closely close to the 7-limit POTE tuning of [[Kleismic family#Quadritikleismic|quadritikleismic temperament]]: <1200 1902 2785 3368|.
Original HTML content:
<html><head><title>1200edo</title></head><body>The <em>1200 division</em> divides the octave in 1200 equal parts of exactly 1 <a class="wiki_link" href="/cent">cent</a> each. It is notable mostly because it is the equal division corresponding to cents.<br /> <br /> 1200edo is uniquely <a class="wiki_link" href="/consistent">consistent</a> through the <a class="wiki_link" href="/11-limit">11-limit</a>, which means the intervals of the 11-limit<a class="wiki_link" href="/tonality%20diamond"> tonality diamond</a>, and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val <1200 1902 2786 3369 4141|. It is <a class="wiki_link" href="/contorted">contorted</a> in the <a class="wiki_link" href="/5-limit">5-limit</a>, having the same mapping as 600edo. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by <a class="wiki_link" href="/171edo">171edo</a>. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by <a class="wiki_link" href="/494edo">494edo</a>. In the 7-limit, it provides a val, 1200cd, which is extremely closely close to the 7-limit POTE tuning of <a class="wiki_link" href="/Kleismic%20family#Quadritikleismic">quadritikleismic temperament</a>: <1200 1902 2785 3368|.</body></html>