93edo
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.18 | +0.78 | -1.08 | +2.54 | +3.52 | -1.82 | -4.40 | -1.73 | -0.74 | -6.26 | +3.98 |
| Relative (%) | -40.2 | +6.1 | -8.4 | +19.7 | +27.3 | -14.1 | -34.1 | -13.4 | -5.7 | -48.6 | +30.9 | |
| Steps (reduced) |
147 (54) |
216 (30) |
261 (75) |
295 (16) |
322 (43) |
344 (65) |
363 (84) |
380 (8) |
395 (23) |
408 (36) |
421 (49) | |
93 = 3 * 31, and 93 is a contorted 31 through the 7 limit. In the 11-limit the patent val tempers out 4000/3993 and in the 13-limit 144/143, 1188/1183 and 364/363. It provides the optimal patent val for the 11-limit prajapati and 13-limit kumhar temperaments, and the 11 and 13 limit 43&50 temperament. It is the 13th no-3s zeta peak edo.
Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710 ¢, 103.226 ¢, and 296.774 ¢ respectively, octave-reduced), it also allows one to give a clearer harmonic identity to 31edo's excellent approximation of 13:17:19.
Temperament properties
Since 93edo has a step of 12.903 ¢, it also allows one to use its MOS scales as circulating temperaments, which it is the first edo to do. It is also the first edo to allow one to use a syntonic or Mavila MOS scale or a 17 tone MOS scale similar to a median between Pelog and the theories of Sundanese composer-musicologist-teacher Raden Machjar Angga Koesoemadinata as a circulating temperament.
| Tones | Pattern | L:s |
|---|---|---|
| 5 | 3L 2s | 19:18 |
| 6 | 3L 3s | 16:15 |
| 7 | 2L 5s | 14:13 |
| 8 | 5L 3s | 12:11 |
| 9 | 3L 6s | 11:10 |
| 10 | 3L 7s | 10:9 |
| 11 | 5L 6s | 9:8 |
| 12 | 9L 3s | 8:7 |
| 13 | 2L 11s | |
| 14 | 9L 5s | 7:6 |
| 15 | 3L 12s | |
| 16 | 13L 3s | 6:5 |
| 17 | 8L 9s | |
| 18 | 3L 15s | |
| 19 | 17L 2s | 5:4 |
| 20 | 13L 7s | |
| 21 | 9L 12s | |
| 22 | 5L 17s | |
| 23 | 1L 22s | |
| 24 | 21L 3s | 4:3 |
| 25 | 18L 7s | |
| 26 | 15L 11s | |
| 27 | 12L 15s | |
| 28 | 9L 19s | |
| 29 | 6L 23s | |
| 30 | 3L 27s | |
| 31 | 31edo | equal |
| 32 | 29L 3s | 3:2 |
| 33 | 27L 6s | |
| 34 | 25L 9s | |
| 35 | 23L 12s | |
| 36 | 21L 15s | |
| 37 | 19L 18s | |
| 38 | 17L 21s | |
| 39 | 15L 24s | |
| 40 | 13L 27s | |
| 41 | 12L 29s | |
| 42 | 9L 33s | |
| 43 | 7L 36s | |
| 44 | 5L 39s | |
| 45 | 3L 42s | |
| 46 | 1L 45s | |
| 47 | 46L 1s | 2:1 |
| 48 | 45L 3s | |
| 49 | 44L 5s | |
| 50 | 43L 7s | |
| 51 | 42L 9s | |
| 52 | 41L 11s | |
| 53 | 40L 13s | |
| 54 | 39L 15s | |
| 55 | 38L 17s | |
| 56 | 37L 19s | |
| 57 | 36L 21s | |
| 58 | 35L 23s | |
| 59 | 34L 25s | |
| 60 | 33L 27s | |
| 61 | 32L 29s | |
| 62 | 31L 31s | |
| 63 | 30L 33s | |
| 64 | 29L 35s | |
| 65 | 28L 37s | |
| 66 | 27L 39s | |
| 67 | 26L 41s | |
| 68 | 25L 43s | |
| 69 | 24L 45s | |
| 70 | 23L 47s | |
| 71 | 22L 49s | |
| 72 | 21L 51s | |
| 73 | 20L 53s | |
| 74 | 19L 55s |