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'''110edo''' is the [[EDO|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.
'''110edo''' is the [[EDO|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.


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.
{| class="wikitable"
|+Circulating temperaments in 110edo
!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]]
| rowspan="2" |equal
|-
|11
|[[11edo]]
|-
|12
|[[2L 10s]]
|10:9
|-
|13
|[[5L 8s]]
|9:8
|-
|14
|[[10L 4s]]
| rowspan="2" |8:7
|-
|15
|[[5L 10s]]
|-
|16
|14L 2s
| rowspan="3" |7:6
|-
|17
|[[8L 9s]]
|-
|18
|2L 16s
|-
|19
|[[15L 4s]]
| rowspan="3" |6:5
|-
|20
|10L 10s
|-
|21
|[[5L 16s]]
|-
|22
|[[22edo]]
|equal
|-
|23
|18L 5s
| rowspan="5" |5:4
|-
|24
|14L 10s
|-
|25
|10L 15s
|-
|26
|6L 20s
|-
|27
|2L 25s
|-
|28
|26L 2s
| rowspan="9" |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
| rowspan="18" |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
| rowspan="32" |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
|}
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
Retrieved from "https://en.xen.wiki/w/110edo"