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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.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| | == 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. |
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| 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.
| | === Odd harmonics === |
| {| class="wikitable" | | {{Harmonics in equal|110}} |
| |+Circulating temperaments in 110edo
| | |
| !Tones
| | === Subsets and supersets === |
| !Pattern
| | Since 110 factors into {{factorization|110}}, 110edo has subset edos {{EDOs| 2, 5, 10, 11, 22, and 55 }}. |
| !L:s
| | |
| |-
| | == Intervals == |
| |5
| | {{Interval table}} |
| |[[5edo]]
| | |
| |equal
| | == Instruments == |
| |- | | * [[Lumatone mapping for 110edo]] |
| |6
| | |
| |[[2L 4s]]
| | {{stub}} |
| |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]]
| |