1200edo: Difference between revisions

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The ''1200 ~~division~~'' divides the octave in 1200 equal parts of exactly 1 [[~~cent|~~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|~~consistent]] through the [[~~11-limit|~~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|~~contorted]] in the [[~~5-limit|~~5-limit]], having the same mapping as 600edo. In the [[~~7-limit|~~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|~~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|~~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.

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, 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:edo]]

[[Category:notation]]

[[Category:theory]]

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-The ''1200 division'' divides the octave in 1200 equal parts of exactly 1 [[cent|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.
-edo is uniquely [[consistent|consistent]] through the [[11-limit|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 &lt;1200 1902 2786 3369 4141|. It is [[contorted|contorted]] in the [[5-limit|5-limit]], having the same mapping as 600edo. In the [[7-limit|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|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|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]]: &lt;1200 1902 2785 3368|. It also provides the optimal patent val for the 224&amp;752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721.
+edo 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 &lt;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, 1200ccd, which is extremely closely close to the 7-limit POTE tuning of [[Kleismic_family#Quadritikleismic|quadritikleismic temperament]]: &lt;1200 1902 2785 3368|. It also provides the optimal patent val for the 224&amp;752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721.
 [[Category:cents]]
 [[Category:edo]]
 [[Category:notation]]
 [[Category:theory]]