93edo: Difference between revisions
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Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710¢, 103.226¢, and 296.774¢ respectively), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19. | Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710¢, 103.226¢, and 296.774¢ respectively), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19. | ||
Since 93edo has a step of 12.903 cents, it also allows one to use its MOS scales as circulating temperaments, which it is the first edo to do. | |||
{| class="wikitable" | |||
|+Circulating temperaments in 93edo | |||
!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]] | |||
| rowspan="2" |8:7 | |||
|- | |||
|13 | |||
|[[2L 11s]] | |||
|- | |||
|14 | |||
|[[9L 5s]] | |||
| rowspan="2" |7:6 | |||
|- | |||
|15 | |||
|[[3L 12s]] | |||
|- | |||
|16 | |||
|13L 3s | |||
| rowspan="3" |6:5 | |||
|- | |||
|17 | |||
|[[8L 9s]] | |||
|- | |||
|18 | |||
|3L 15s | |||
|- | |||
|19 | |||
|[[17L 2s]] | |||
| rowspan="5" |5:4 | |||
|- | |||
|20 | |||
|[[13L 7s]] | |||
|- | |||
|21 | |||
|9L 12s | |||
|- | |||
|22 | |||
|[[5L 17s]] | |||
|- | |||
|23 | |||
|1L 22s | |||
|- | |||
|24 | |||
|21L 3s | |||
| rowspan="7" |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 | |||
| rowspan="15" |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 | |||
| rowspan="28" |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 | |||
|} | |||