User:Overthink/5144edo
5144 equal divisions of the octave (abbreviated 5144edo or 5144ed2), also called 5144-tone equal temperament (5144tet) or 5144 equal temperament (5144et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5144 equal parts of about 0.233 ¢ each. Each step represents a frequency ratio of 21/5144, or the 5144th root of 2.
Theory
5144edo is consistent in the 27-odd-limit with a mostly flat tendency. It inherits its harmonic 5 from 643edo. It is usable as a full 23-limit system, but is best in the 2.3.5.7.13.17 subgroup, with less than 10% error on all primes.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.011 | +0.000 | -0.008 | -0.074 | -0.014 | +0.021 | -0.079 | -0.047 | -0.106 | -0.090 |
| Relative (%) | +0.0 | -4.7 | +0.2 | -3.4 | -31.6 | -6.2 | +9.1 | -33.9 | -20.3 | -45.4 | -38.6 | |
| Steps (reduced) |
5144 (0) |
8153 (3009) |
11944 (1656) |
14441 (4153) |
17795 (2363) |
19035 (3603) |
21026 (450) |
21851 (1275) |
23269 (2693) |
24989 (4413) |
25484 (4908) | |