User:Eliora/2592edo
| ← 2591edo | 2592edo | 2593edo → |
2592 equal divisions of the octave (abbreviated 2592edo or 2592ed2), also called 2592-tone equal temperament (2592tet) or 2592 equal temperament (2592et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2592 equal parts of about 0.463 ¢ each. Each step represents a frequency ratio of 21/2592, or the 2592nd root of 2.
2592edo is consistent in the 5-odd-limit, though its approximation of simple harmonics is rather poor. Nonetheless, there are strong direct approximations to 15/14, 10/9, 13/9, 13/10, 15/13.
Furthermore, in the 7-limit, it provides the optimal patent val for the 32nd-octave windrose temperament, even if inconsisent. 2592edo overall is best considered for its subsets due to many divisors, see below.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.103 | -0.203 | +0.156 | -0.206 | +0.071 | +0.213 | +0.157 | +0.137 | +0.172 | +0.052 | -0.034 |
| Relative (%) | -22.3 | -43.8 | +33.6 | -44.6 | +15.3 | +46.0 | +34.0 | +29.6 | +37.2 | +11.3 | -7.3 | |
| Steps (reduced) |
4108 (1516) |
6018 (834) |
7277 (2093) |
8216 (440) |
8967 (1191) |
9592 (1816) |
10127 (2351) |
10595 (227) |
11011 (643) |
11385 (1017) |
11725 (1357) | |
Subsets
Since 2592 factors as 25 × 34, 2592edo has subset edos 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296. Its abundancy index is around 1.94.