102edo: Difference between revisions
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[[Category: | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Echidnic]] | |||
Revision as of 16:16, 2 July 2022
102edo is the equal division of the octave into 102 steps of size 11.765 cents each. In the 5-limit it tempers out the same commas (2048/2025, 15625/15552, 20000/19683) as 34edo. In the 7-limit it tempers out 686/675 and 1029/1024; in the 11-limit 385/384, 441/440 and 4000/3993; in the 13-limit 91/90 and 169/168; in the 17-limit 136/135 and 154/153; and in the 19-limit 133/132 and 190/189. It is the optimal patent val for 13-limit echidnic temperament, and the rank five temperament tempering out 91/90.
13-limit Echidnic
| Degree | Cents | Difference from 46edo |
|---|---|---|
| 2 | 23.529 | -2.5575¢ |
| 4 | 47.059 | -5.115¢ |
| 7 | 82.353 | 4.092¢ |
| 9 | 105.882 | 1.5345¢ |
| 11 | 129.412 | -1.023¢ |
| 13 | 152.941 | 8.184¢ |
| 16 | 188.235 | 5.627¢ |
| 18 | 211.765 | 3.069¢ |
| 20 | 235.294 | 0.511¢ |
| 22 | 258.824 | -2.046¢ |
| 24 | 282.353 | -4.604¢ |
| 27 | 317.647 | 4.604¢ |
| 29 | 341.176 | 2.046¢ |
| 31 | 364.706 | -0.5115¢ |
| 33 | 388.235 | -3.069¢ |
| 35 | 411.765 | -5.627¢ |
| 38 | 447.059 | 3.581¢ |
| 40 | 470.588 | 1.023¢ |
| 42 | 494.117 | -1.5345¢ |
| 44 | 517.647 | -4.092¢ |
| 47 | 552.941 | 5.115¢ |
| 49 | 576.471 | 2.5575¢ |
Since 102edo has a step of 11.765 cents, it also allows one to use its MOS scales as circulating temperaments. It is the first edo which truly allows one to use an MOS scale with 60 or more small steps as a circulating temperament.
| Tones | Pattern | L:s |
|---|---|---|
| 5 | 2L 3s | 21:20 |
| 6 | 6edo | equal |
| 7 | 4L 3s | 15:14 |
| 8 | 6L 2s | 13:12 |
| 9 | 3L 6s | 12:11 |
| 10 | 2L 8s | 11:10 |
| 11 | 3L 8s | 10:9 |
| 12 | 6L 6s | 9:8 |
| 13 | 11L 2s | 8:7 |
| 14 | 4L 10s | |
| 15 | 12L 3s | 7:6 |
| 16 | 6L 10s | |
| 17 | 17edo | equal |
| 18 | 10L 8s | 6:5 |
| 19 | 7L 12s | |
| 20 | 2L 18s | |
| 21 | 18L 3s | 5:4 |
| 22 | 14L 8s | |
| 23 | 10L 13s | |
| 24 | 6L 18s | |
| 25 | 2L 23s | |
| 26 | 24L 2s | 4:3 |
| 27 | 21L 6s | |
| 28 | 18L 10s | |
| 29 | 15L 14s | |
| 30 | 12L 18s | |
| 31 | 9L 22s | |
| 32 | 6L 26s | |
| 33 | 3L 30s | |
| 34 | 34edo | equal |
| 35 | 32L 3s | 3:2 |
| 36 | 30L 6s | |
| 37 | 28L 9s | |
| 38 | 26L 12s | |
| 39 | 24L 15s | |
| 40 | 22L 18s | |
| 41 | 20L 21s | |
| 42 | 18L 24s | |
| 43 | 16L 27s | |
| 44 | 14L 30s | |
| 45 | 12L 33s | |
| 46 | 10L 36s | |
| 47 | 8L 39s | |
| 48 | 6L 42s | |
| 49 | 4L 45s | |
| 50 | 2L 48s | |
| 51 | 51edo | equal |
| 52 | 50L 2s | 2:1 |
| 53 | 49L 4s | |
| 54 | 48L 6s | |
| 55 | 47L 8s | |
| 56 | 46L 10s | |
| 57 | 45L 12s | |
| 58 | 44L 14s | |
| 59 | 43L 16s | |
| 60 | 42L 18s | |
| 61 | 41L 20s | |
| 62 | 40L 22s | |
| 63 | 39L 24s | |
| 64 | 38L 26s | |
| 65 | 37L 28s | |
| 66 | 36L 30s | |
| 67 | 35L 32s | |
| 68 | 34L 34s | |
| 69 | 33L 36s | |
| 70 | 32L 38s | |
| 71 | 31L 40s | |
| 72 | 30L 42s | |
| 73 | 29L 44s | |
| 74 | 28L 46s | |
| 75 | 27L 48s | |
| 76 | 26L 50s | |
| 77 | 25L 52s | |
| 78 | 24L 54s | |
| 79 | 23L 56s | |
| 80 | 22L 58s | |
| 81 | 21L 60s |