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
|}