11664edo

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← 11663edo 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

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 21/11664, 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 -0.3 +3.1 +1.2 +19.0 +7.1 -16.7 +17.3 +17.3 -49.0 +25.4
Steps
(reduced)
11664
(0)
18487
(6823)
27083
(3755)
32745
(9417)
40351
(5359)
43162
(8170)
47676
(1020)
49548
(2892)
52763
(6107)
56663
(10007)
57786
(11130)