11664edo

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11664edo

11665edo →

Prime factorization	24 × 36
Step size	0.102881¢
Fifth	6823\11664 (701.955¢)
Semitones (A1:m2)	1105:877 (113.7¢ : 90.23¢)
Consistency limit	27
Distinct consistency limit	27
Special properties	zeta peak

11664 equal divisions of the octave (abbreviated 11664edo or 11664ed2), also called 11664-tone equal temperament (11664tet) or 11664 equal temperament (11664et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 11664 equal parts of about 0.103 ¢ each. Each step represents a frequency ratio of 2^1/11664, or the 11664th root of 2.

11664edo is a very strong 7-limit system, with a lower 7-limit relative error than any division until 18355. It is a zeta peak edo unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27-odd-limit and with a lower 23-limit relative error than any division until 16808. Aside from this peculiar double threat property, it is also very composite, since 11664 = 2³ × 3⁶. Among its divisiors are 12, 16, 24, 27, 72, 81 and 243.

Prime harmonics

Approximation of prime harmonics in 11664edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+0.00000	-0.00027	+0.00316	+0.00125	+0.01951	+0.00732	-0.01714	+0.01785	+0.01783	-0.05045	+0.02616
	relative (%)	+0	-0	+3	+1	+19	+7	-17	+17	+17	-49	+25
Steps (reduced)		11664 (0)	18487 (6823)	27083 (3755)	32745 (9417)	40351 (5359)	43162 (8170)	47676 (1020)	49548 (2892)	52763 (6107)	56663 (10007)	57786 (11130)