11664edo
| ← 11663edo | 11664edo | 11665edo → |
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
| 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) | |