1200edo: Difference between revisions

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== Theory ==

1200edo is distinctly [[consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val| 1200 1902 2786 3369 4151 }}. It is [[enfactored]] in the [[5-limit]], having the same mapping as [[600edo]]. Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 subgroup it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.

1200edo is distinctly [[consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val| 1200 1902 2786 3369 4151 }}. It is [[enfactored]] in the [[5-limit]], having the same mapping as [[600edo]].

1200et tempers out 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.

It also provides a 7-limit 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.

Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 subgroup it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.

=== Prime harmonics ===

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 == Theory ==
-edo is distinctly [[consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val| 1200 1902 2786 3369 4151 }}. It is [[enfactored]] in the [[5-limit]], having the same mapping as [[600edo]]. Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 subgroup it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.
+edo is distinctly [[consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val| 1200 1902 2786 3369 4151 }}. It is [[enfactored]] in the [[5-limit]], having the same mapping as [[600edo]].
 et tempers out 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.
 It also provides a 7-limit 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.
+Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 subgroup it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.
 === Prime harmonics ===