11664edo
|
This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 11663edo | 11664edo | 11665edo → |
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) | |