2964edo

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2964edo

2965edo →

Prime factorization	22 × 3 × 13 × 19
Step size	0.404858¢
Fifth	1734\2964 (702.024¢) (→289\494)
Semitones (A1:m2)	282:222 (114.2¢ : 89.88¢)
Consistency limit	7
Distinct consistency limit	7

2964 equal divisions of the octave (abbreviated 2964edo or 2964ed2), also called 2964-tone equal temperament (2964tet) or 2964 equal temperament (2964et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2964 equal parts of about 0.405 ¢ each. Each step represents a frequency ratio of 2^1/2964, or the 2964th root of 2.

In the 13-limit, 2964edo shares the same patent val with 494edo except for the 7th harmonic, which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is a denominator to convergent to log₂7.

Prime harmonics

Approximation of prime harmonics in 2964edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.069	-0.079	+0.000	+0.099	-0.042	-0.097	+0.058	+0.066	-0.023	-0.096
	Relative (%)	+0.0	+17.1	-19.5	+0.0	+24.5	-10.3	-24.0	+14.3	+16.2	-5.6	-23.8
Steps (reduced)		2964 (0)	4698 (1734)	6882 (954)	8321 (2393)	10254 (1362)	10968 (2076)	12115 (259)	12591 (735)	13408 (1552)	14399 (2543)	14684 (2828)

Subsets and supersets

Since 2964 factors into 2² × 3 × 13 × 19, 2964edo has subset edos 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, and 1482.