1323edo
| ← 1322edo | 1323edo | 1324edo → |
1323 equal divisions of the octave (1323edo), or 1323-tone equal temperament (1323tet), 1323 equal temperament (1323et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1323 equal parts of about 0.907 ¢ each.
Theory
1323edo is the smallest uniquely consistent EDO in the 29-odd-limit.
It provides the optimal patent val for the 11-limit trinealimmal temperament, which has a period of 1\27 octave. In additoin, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum.
1323's divisors are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, of which 441EDO is a member of the zeta edos. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.086 | +0.081 | -0.118 | +0.156 | +0.289 | +0.260 | -0.007 | +0.297 | -0.099 | -0.364 |
| relative (%) | +0 | +9 | +9 | -13 | +17 | +32 | +29 | -1 | +33 | -11 | -40 | |
| Steps (reduced) |
1323 (0) |
2097 (774) |
3072 (426) |
3714 (1068) |
4577 (608) |
4896 (927) |
5408 (116) |
5620 (328) |
5985 (693) |
6427 (1135) |
6554 (1262) | |
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 3 | 177\1323 | 160.544 | 154478651796875/140737488355328 | 441 & 1308 |
| 27 | 299\1323 (5\1323) |
271.201 (4.535) |
1375/1176 (?) |
Trinealimmal |