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113edo is the 30th [[prime EDO]].
113edo is the 30th [[prime EDO]].


Since 113edo has a step of 10.6195 cents, it also allows one to use its MOS scales as circulating temperaments. It is the first edo which allows one to use an MOS scale of 90 tones or more as a circulating temperament.
{| class="wikitable"
|+Circulating temperaments in 113edo
!Tones
!Pattern
!L:s
|-
|5
|[[3L 2s]]
|23:22
|-
|6
|[[5L 1s]]
|19:18
|-
|7
|[[1L 6s]]
|17:16
|-
|8
|[[1L 7s]]
|15:14
|-
|9
|[[5L 4s]]
|13:12
|-
|10
|[[3L 7s]]
|12:11
|-
|11
|[[3L 8s]]
|11:10
|-
|12
|[[5L 7s]]
|10:9
|-
|13
|[[9L 4s]]
| rowspan="2" |9:8
|-
|14
|[[1L 13s]]
|-
|15
|[[7L 8s]]
| rowspan="2" |8:7
|-
|16
|1L 15s
|-
|17
|[[11L 6s]]
| rowspan="2" |7:6
|-
|18
|5L 13s
|-
|19
|18L 1s
| rowspan="4" |6:5
|-
|20
|[[13L 7s]]
|-
|21
|[[8L 13s]]
|-
|22
|[[3L 19s]]
|-
|23
|21L 2s
| rowspan="6" |5:4
|-
|24
|[[17L 7s]]
|-
|25
|13L 12s
|-
|26
|9L 17s
|-
|27
|[[5L 22s]]
|-
|28
|1L 27s
|-
|29
|26L 3s
| rowspan="9" |4:3
|-
|30
|23L 7s
|-
|31
|20L 11s
|-
|32
|17L 15s
|-
|33
|14L 19s
|-
|34
|11L 23s
|-
|35
|8L 27s
|-
|36
|5L 31s
|-
|37
|2L 35s
|-
|38
|37L 1s
| rowspan="19" |3:2
|-
|39
|35L 4s
|-
|40
|33L 7s
|-
|41
|31L 10s
|-
|42
|29L 13s
|-
|43
|27L 16s
|-
|44
|25L 19s
|-
|45
|23L 22s
|-
|46
|21L 25s
|-
|47
|19L 28s
|-
|48
|17L 31s
|-
|49
|15L 34s
|-
|50
|13L 37s
|-
|51
|11L 40s
|-
|52
|9L  43s
|-
|53
|7L 46s
|-
|54
|5L 49s
|-
|55
|3L 52s
|-
|56
|1L 55s
|-
|57
|56L 1s
| rowspan="34" |2:1
|-
|58
|55L 3s
|-
|59
|54L 5s
|-
|60
|53L 7s
|-
|61
|52L 9s
|-
|62
|51L 11s
|-
|63
|50L 13s
|-
|64
|49L 15s
|-
|65
|48L 17s
|-
|66
|47L 19s
|-
|67
|46L 21s
|-
|68
|45L 23s
|-
|69
|44L 25s
|-
|70
|43L 27s
|-
|71
|42L 29s
|-
|72
|41L 31s
|-
|73
|40L 33s
|-
|74
|39L 35s
|-
|75
|38L 37s
|-
|76
|37L 39s
|-
|77
|36L 41s
|-
|78
|35L 43s
|-
|79
|34L 45s
|-
|80
|33L 47s
|-
|81
|32L 49s
|-
|82
|31L 51s
|-
|83
|30L 53s
|-
|84
|29L 55s
|-
|85
|28L 57s
|-
|86
|27L 59s
|-
|87
|26L 61s
|-
|88
|25L 63s
|-
|89
|24L 65s
|-
|90
|23L 67s
|}
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Prime EDO]]
[[Category:Prime EDO]]
[[Category:Theory]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/113edo"