12276edo

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12276edo

12277edo →

Prime factorization	22 × 32 × 11 × 31
Step size	0.0977517 ¢
Fifth	7181\12276 (701.955 ¢) (semiconvergent)
Semitones (A1:m2)	1163:923 (113.7 ¢ : 90.22 ¢)
Consistency limit	17
Distinct consistency limit	17

12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from 6691. 12276 tempers out the atom and the septimal ruthenia, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps.

Prime harmonics

Approximation of prime harmonics in 12276edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	+0.0000	+0.0010	-0.0087	+0.0017	+0.0393	+0.0299	+0.0432	-0.0241	+0.0416	+0.0280
	Relative (%)	+0.0	+0.0	+1.1	-8.9	+1.7	+40.2	+30.6	+44.2	-24.7	+42.5	+28.6
Steps (reduced)		12276 (0)	19457 (7181)	28504 (3952)	34463 (9911)	42468 (5640)	45427 (8599)	50178 (1074)	52148 (3044)	55531 (6427)	59637 (10533)	60818 (11714)

Interval size measure

12276edo factors as 2² × 3² × 11 × 31, and among its divisors are 12, 22, 31, 99 and 198. This creates a unit known as the prima, useful for measurement of 11-limit intervals and commas. A prima is almost exactly three tuning units.