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'''116edo''' is the [[EDO|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments|submajor temperament]].
'''116edo''' is the [[EDO|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments|submajor temperament]].
 
Since 116edo has a step of 10.3448 cents, it also allows one to use its MOS scales as circulating temperaments.
{| class="wikitable"
|+Circulating temperaments in 116edo
!Tones
!Pattern
!L:s
|-
|5
|[[1L 4s]]
|24:23
|-
|6
|[[2L 4s]]
|20:19
|-
|7
|[[4L 3s]]
|17:16
|-
|8
|[[4L 4s]]
|15:14
|-
|9
|[[8L 1s]]
|13:12
|-
|10
|[[6L 4s]]
|12:11
|-
|11
|[[6L 5s]]
|11:10
|-
|12
|[[8L 4s]]
|10:9
|-
|13
|[[12L 1s]]
| rowspan="2" |9:8
|-
|14
|[[4L 10s]]
|-
|15
|[[11L 4s]]
| rowspan="2" |8:7
|-
|16
|4L 12s
|-
|17
|[[14L 3s]]
| rowspan="3" |7:6
|-
|18
|8L 10s
|-
|19
|[[2L 17s]]
|-
|20
|16L 4s
| rowspan="4" |6:5
|-
|21
|11L 10s
|-
|22
|[[6L 16s]]
|-
|23
|1L 22s
|-
|24
|20L 4s
| rowspan="5" |5:4
|-
|25
|16L 9s
|-
|26
|12L 14s
|-
|27
|8L 19s
|-
|28
|4L 24s
|-
|29
|[[29edo]]
|equal
|-
|30
|26L 4s
| rowspan="9" |4:3
|-
|31
|23L 8s
|-
|32
|20L 12s
|-
|33
|17L 16s
|-
|34
|14L 20s
|-
|35
|11L 24s
|-
|36
|8L 28s
|-
|37
|5L 32s
|-
|38
|2L 36s
|-
|39
|38L 1s
| rowspan="19" |3:2
|-
|40
|36L 4s
|-
|41
|34L 7s
|-
|42
|32L 10s
|-
|43
|30L 13s
|-
|44
|28L 16s
|-
|45
|26L 19s
|-
|46
|24L 22s
|-
|47
|22L 25s
|-
|48
|20L 28s
|-
|49
|18L 31s
|-
|50
|16L 34s
|-
|51
|14L 37s
|-
|52
|12L 40s
|-
|53
|10L 43s
|-
|54
|8L 46s
|-
|55
|6L 49s
|-
|56
|4L 52s
|-
|57
|2L 55s
|-
|58
|[[58edo]]
|equal
|-
|59
|57L 2s
| rowspan="34" |2:1
|-
|60
|56L 4s
|-
|61
|55L 6s
|-
|62
|54L 8s
|-
|63
|53L 10s
|-
|64
|52L 12s
|-
|65
|51L 14s
|-
|66
|50L 16s
|-
|67
|49L 18s
|-
|68
|48L 20s
|-
|69
|47L 22s
|-
|70
|46L 24s
|-
|71
|45L 26s
|-
|72
|44L 28s
|-
|73
|43L 30s
|-
|74
|42L 32s
|-
|75
|41L 34s
|-
|76
|40L 36s
|-
|77
|39L 38s
|-
|78
|38L 40s
|-
|79
|37L 42s
|-
|80
|36L 44s
|-
|81
|35L 46s
|-
|82
|34L 48s
|-
|83
|33L 50s
|-
|84
|32L 52s
|-
|85
|31L 54s
|-
|86
|30L 56s
|-
|87
|29L 58s
|-
|88
|28L 60s
|-
|89
|27L 62s
|-
|90
|26L 64s
|-
|91
|25L 66s
|-
|92
|24L 68s
|}
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
Retrieved from "https://en.xen.wiki/w/116edo"