1200edo: Difference between revisions

Line 5:

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. The 47th harmonic is 6666 steps and 666 steps reduced – a funny mathematical coincidence in our decimal system.

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.

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.

Line 13:

=== Subsets and supersets ===

The divisors of 1200 are {{EDOs| 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, and 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 that offers detuning by cents.

The divisors of 1200 are {{EDOs| 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, and 600 }}. These are all the edos whose step size is an integer amount of cents, and thus can be played exactly on any digital audio workstation that offers detuning by cents.

== Regular temperament properties ==

@@ Line 5: / Line 5: @@
 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. The 47th harmonic is 6666 steps and 666 steps reduced – a funny mathematical coincidence in our decimal system.
-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.
+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.
@@ Line 13: / Line 13: @@
 === Subsets and supersets ===
-The divisors of 1200 are {{EDOs| 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, and 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 that offers detuning by cents.
+The divisors of 1200 are {{EDOs| 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, and 600 }}. These are all the edos whose step size is an integer amount of cents, and thus can be played exactly on any digital audio workstation that offers detuning by cents.
 == Regular temperament properties ==