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| {{Infobox ET}} | | {{Infobox ET}} |
| '''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.
| | {{ED intro}} |
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| == Theory == | | == Theory == |
| | The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) 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. |
| | |
| | === Odd harmonics === |
| {{Harmonics in equal|110}} | | {{Harmonics in equal|110}} |
| 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.
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| {| class="wikitable"
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| |+Circulating temperaments in 110edo
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| !Tones
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| !Pattern
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| !L:s
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| |-
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| |5
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| |[[5edo]]
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| |equal
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| |-
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| |6
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| |[[2L 4s]]
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| |19:18
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| |-
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| |7
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| |[[5L 2s]]
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| |16:15
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| |-
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| |8
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| |[[6L 2s]]
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| |14:13
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| |-
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| |9
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| |[[2L 7s]]
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| |13:12
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| |-
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| |10
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| |[[10edo]]
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| | rowspan="2" |equal
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| |-
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| |11
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| |[[11edo]]
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| |-
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| |12
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| |[[2L 10s]]
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| |10:9
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| |-
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| |13
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| |[[5L 8s]]
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| |9:8
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| |-
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| |14
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| |[[12L 2s]]
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| | rowspan="2" |8:7
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| |-
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| |15
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| |[[5L 10s]]
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| |-
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| |16
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| |14L 2s
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| | rowspan="3" |7:6
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| |-
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| |17
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| |[[8L 9s]]
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| |-
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| |18
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| |2L 16s
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| |-
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| |19
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| |[[15L 4s]]
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| | rowspan="3" |6:5
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| |-
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| |20
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| |10L 10s
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| |-
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| |21
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| |[[5L 16s]]
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| |-
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| |22
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| |[[22edo]]
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| |equal
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| |-
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| |23
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| |18L 5s
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| | rowspan="5" |5:4
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| |-
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| |24
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| |14L 10s
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| |-
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| |25
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| |10L 15s
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| |-
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| |26
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| |6L 20s
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| |-
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| |27
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| |2L 25s
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| |-
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| |28
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| |26L 2s
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| | rowspan="9" |4:3
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| |-
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| |29
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| |23L 6s
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| |-
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| |30
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| |20L 10s
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| |-
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| |31
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| |17L 14s
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| |-
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| |32
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| |14L 18s
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| |-
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| |33
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| |11L 22s
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| |-
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| |34
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| |8L 26s
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| |-
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| |35
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| |5L 30s
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| |-
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| |36
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| |2L 34s
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| |-
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| |37
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| |36L 1s
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| | rowspan="18" |3:2
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| |-
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| |38
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| |34L 4s
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| |-
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| |39
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| |32L 7s
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| |-
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| |40
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| |30L 10s
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| |-
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| |41
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| |28L 13s
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| |-
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| |42
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| |26L 16s
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| |-
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| |43
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| |24L 19s
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| |-
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| |44
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| |22L 22s
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| |-
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| |45
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| |20L 25s
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| |-
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| |46
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| |18L 28s
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| |-
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| |47
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| |16L 31s
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| |-
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| |48
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| |14L 34s
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| |-
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| |49
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| |12L 37s
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| |-
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| |50
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| |10L 40s
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| |-
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| |51
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| |8L 43s
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| |-
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| |52
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| |6L 46s
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| |-
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| |53
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| |4L 49s
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| |-
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| |54
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| |2L 52s
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| |-
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| |55
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| |[[55edo]]
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| |equal
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| |-
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| |56
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| |54L 2s
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| | rowspan="32" |2:1
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| |-
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| |57
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| |53L 4s
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| |-
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| |58
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| |52L 6s
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| |-
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| |59
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| |51L 8s
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| |-
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| |60
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| |50L 10s
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| |-
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| |61
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| |49L 12s
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| |-
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| |62
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| |48L 14s
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| |-
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| |63
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| |47L 16s
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| |-
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| |64
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| |46L 18s
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| |-
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| |65
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| |45L 20s
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| |-
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| |66
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| |44L 22s
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| |-
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| |67
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| |43L 24s
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| |-
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| |68
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| |42L 26s
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| |-
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| |69
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| |41L 28s
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| |-
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| |70
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| |40L 30s
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| |-
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| |71
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| |39L 32s
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| |-
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| |72
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| |38L 34s
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| |-
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| |73
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| |37L 36s
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| |-
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| |74
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| |36L 38s
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| |-
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| |75
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| |35L 40s
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| |-
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| |76
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| |34L 42s
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| |-
| |
| |77
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| |33L 44s
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| |-
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| |78
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| |32L 46s
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| |-
| |
| |79
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| |31L 48s
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| |-
| |
| |80
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| |30L 50s
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| |-
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| |81
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| |29L 52s
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| |-
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| |82
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| |28L 54s
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| |-
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| |83
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| |27L 56s
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| |-
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| |84
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| |26L 58s
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| |-
| |
| |85
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| |25L 60s
| |
| |-
| |
| |86
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| |24L 62s
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| |-
| |
| |87
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| |23L 64s
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| |}
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| [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | | === Subsets and supersets === |
| | Since 110 factors into {{factorization|110}}, 110edo has subset edos {{EDOs| 2, 5, 10, 11, 22, and 55 }}. |
| | |
| | == Intervals == |
| | {{Interval table}} |
| | |
| | == Instruments == |
| | * [[Lumatone mapping for 110edo]] |
| | |
| | {{stub}} |