1200edo: Difference between revisions
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The '''1200 edo''' 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. | The '''1200 edo''' 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 | 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 4151|. 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, 1200ccd, which is extremely closely close to the 7-limit POTE tuning of [[Kleismic_family#Quadritikleismic|quadritikleismic temperament]]: <1200 1902 2785 3368|. It also provides the optimal patent val for the 224&752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721. | ||
[[Category:cents]] | [[Category:cents]] | ||
[[Category:edo]] | [[Category:edo]] | ||
[[Category:notation]] | [[Category:notation]] | ||
[[Category:theory]] | [[Category:theory]] | ||
Revision as of 06:21, 12 January 2019
The 1200 edo 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, 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 4151|. 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, 1200ccd, which is extremely closely close to the 7-limit POTE tuning of quadritikleismic temperament: <1200 1902 2785 3368|. It also provides the optimal patent val for the 224&752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721.