1200edo: Difference between revisions

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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]] {{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 [[support]]s 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]]: {{val| 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.

The divisors of 1200 are {{EDOs|1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600}}. These are all the EDOs whose step size is an integer amount of cents, and which can be played exactly on any digital audio workstation which offers detuning by cents.

[[Category:Equal divisions of the octave]]

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 edo 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]] {{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 [[support]]s 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]]: {{val| 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.
+The divisors of 1200 are {{EDOs|1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600}}. These are all the EDOs whose step size is an integer amount of cents, and which can be played exactly on any digital audio workstation which offers detuning by cents.
 [[Category:Equal divisions of the octave]]