110edo: Difference between revisions
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[[Category:Equal divisions of the octave]] | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | |||
Revision as of 16:20, 2 July 2022
110edo is the equal division of the octave into 110 parts of 10.9090909091 cents each. It tempers out 15625/15552 and 3486784401/3355443200 in the 5-limit. Using the patent val, it tempers out 1728/1715, 3125/3087, and 3645/3584 in the 7-limit.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.77 | -4.50 | +2.08 | +3.36 | +5.05 | -0.53 | +2.64 | +4.14 | -2.97 | -1.69 | +4.45 |
| Relative (%) | -34.6 | -41.2 | +19.1 | +30.8 | +46.3 | -4.8 | +24.2 | +37.9 | -27.2 | -15.5 | +40.8 | |
| Steps (reduced) |
174 (64) |
255 (35) |
309 (89) |
349 (19) |
381 (51) |
407 (77) |
430 (100) |
450 (10) |
467 (27) |
483 (43) |
498 (58) | |
Since 110edo has a step of 10.9090909091 cents, it also allows one to use its MOS scales as circulating temperaments. As 10*11edo, it is the first edo which allows one to use consecutive smaller edos as circulating temperaments.
| Tones | Pattern | L:s |
|---|---|---|
| 5 | 5edo | equal |
| 6 | 2L 4s | 19:18 |
| 7 | 5L 2s | 16:15 |
| 8 | 6L 2s | 14:13 |
| 9 | 2L 7s | 13:12 |
| 10 | 10edo | equal |
| 11 | 11edo | |
| 12 | 2L 10s | 10:9 |
| 13 | 5L 8s | 9:8 |
| 14 | 12L 2s | 8:7 |
| 15 | 5L 10s | |
| 16 | 14L 2s | 7:6 |
| 17 | 8L 9s | |
| 18 | 2L 16s | |
| 19 | 15L 4s | 6:5 |
| 20 | 10L 10s | |
| 21 | 5L 16s | |
| 22 | 22edo | equal |
| 23 | 18L 5s | 5:4 |
| 24 | 14L 10s | |
| 25 | 10L 15s | |
| 26 | 6L 20s | |
| 27 | 2L 25s | |
| 28 | 26L 2s | 4:3 |
| 29 | 23L 6s | |
| 30 | 20L 10s | |
| 31 | 17L 14s | |
| 32 | 14L 18s | |
| 33 | 11L 22s | |
| 34 | 8L 26s | |
| 35 | 5L 30s | |
| 36 | 2L 34s | |
| 37 | 36L 1s | 3:2 |
| 38 | 34L 4s | |
| 39 | 32L 7s | |
| 40 | 30L 10s | |
| 41 | 28L 13s | |
| 42 | 26L 16s | |
| 43 | 24L 19s | |
| 44 | 22L 22s | |
| 45 | 20L 25s | |
| 46 | 18L 28s | |
| 47 | 16L 31s | |
| 48 | 14L 34s | |
| 49 | 12L 37s | |
| 50 | 10L 40s | |
| 51 | 8L 43s | |
| 52 | 6L 46s | |
| 53 | 4L 49s | |
| 54 | 2L 52s | |
| 55 | 55edo | equal |
| 56 | 54L 2s | 2:1 |
| 57 | 53L 4s | |
| 58 | 52L 6s | |
| 59 | 51L 8s | |
| 60 | 50L 10s | |
| 61 | 49L 12s | |
| 62 | 48L 14s | |
| 63 | 47L 16s | |
| 64 | 46L 18s | |
| 65 | 45L 20s | |
| 66 | 44L 22s | |
| 67 | 43L 24s | |
| 68 | 42L 26s | |
| 69 | 41L 28s | |
| 70 | 40L 30s | |
| 71 | 39L 32s | |
| 72 | 38L 34s | |
| 73 | 37L 36s | |
| 74 | 36L 38s | |
| 75 | 35L 40s | |
| 76 | 34L 42s | |
| 77 | 33L 44s | |
| 78 | 32L 46s | |
| 79 | 31L 48s | |
| 80 | 30L 50s | |
| 81 | 29L 52s | |
| 82 | 28L 54s | |
| 83 | 27L 56s | |
| 84 | 26L 58s | |
| 85 | 25L 60s | |
| 86 | 24L 62s | |
| 87 | 23L 64s |