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Aside from tuning, 108 is the smallest number with a prime factorization of the form <math>p^p \cdot q^q</math>. Being close to 100, it is a good substitute for a relative cent if you desire the measure to have such a property. Also, multiplying it by 12 gives the fourth power of an integer.
Aside from tuning, 108 is the smallest number with a prime factorization of the form <math>p^p \cdot q^q</math>. Being close to 100, it is a good substitute for a relative cent if you desire the measure to have such a property. Also, multiplying it by 12 gives the fourth power of an integer.
Since 108edo has a step of 11.111 cents, it also allows one to use its MOS scales as circulating temperaments.
{| class="wikitable"
|+Circulating temperaments in 108edo
!Tones
!Pattern
!L:s
|-
|5
|[[3L 2s]]
|22:21
|-
|6
|[[6edo]]
|equal
|-
|7
|[[3L 4s]]
|16:15
|-
|8
|[[4L 4s]]
|14:13
|-
|9
|[[9edo]]
|equal
|-
|10
|[[8L 2s]]
|11:10
|-
|11
|[[9L 2s]]
|10:9
|-
|12
|[[12edo]]
|equal
|-
|13
|[[3L 10s]]
|9:8
|-
|14
|[[10L 4s]]
| rowspan="2" |8:7
|-
|15
|[[3L 12s]]
|-
|16
|12L 4s
| rowspan="2" |7:6
|-
|17
|[[6L 11s]]
|-
|18
|[[18edo]]
|equal
|-
|19
|[[13L 6s]]
| rowspan="3" |6:5
|-
|20
|8L 12s
|-
|21
|3L 18s
|-
|22
|20L 2s
| rowspan="5" |5:4
|-
|23
|16L 7s
|-
|24
|12L 12s
|-
|25
|8L 17s
|-
|26
|4L 22s
|-
|27
|[[27edo]]
|equal
|-
|28
|24L 4s
| rowspan="8" |4:3
|-
|29
|21L 8s
|-
|30
|18L 12s
|-
|31
|15L 16s
|-
|32
|12L 20s
|-
|33
|9L 24s
|-
|34
|6L 28s
|-
|35
|3L 32s
|-
|36
|[[36edo]]
|equal
|-
|37
|34L 3s
| rowspan="17" |3:2
|-
|38
|32L 6s
|-
|39
|30L 9s
|-
|40
|28L 12s
|-
|41
|26L 15s
|-
|42
|24L 18s
|-
|43
|22L 21s
|-
|44
|20L 24s
|-
|45
|18L 27s
|-
|46
|16L 30s
|-
|47
|14L 33s
|-
|48
|12L 36s
|-
|49
|10L 39s
|-
|50
|8L 42s
|-
|51
|6L 45s
|-
|52
|4L 48s
|-
|53
|2L 51s
|-
|54
|[[54edo]]
|equal
|-
|55
|53L 2s
| rowspan="33" |2:1
|-
|56
|52L 4s
|-
|57
|51L 6s
|-
|58
|50L 8s
|-
|59
|49L 10s
|-
|60
|48L 12s
|-
|61
|47L 14s
|-
|62
|46L 16s
|-
|63
|45L 18s
|-
|64
|44L 20s
|-
|65
|43L 22s
|-
|66
|42L 24s
|-
|67
|41L 26s
|-
|68
|40L 28s
|-
|69
|39L 30s
|-
|70
|38L 32s
|-
|71
|37L 34s
|-
|72
|36L 36s
|-
|73
|35L 38s
|-
|74
|34L 40s
|-
|75
|33L 42s
|-
|76
|32L 44s
|-
|77
|31L 46s
|-
|78
|30L 48s
|-
|79
|29L 50s
|-
|80
|28L 52s
|-
|81
|27L 54s
|-
|82
|26L 56s
|-
|83
|25L 58s
|-
|84
|24L 60s
|-
|85
|23L 62s
|-
|86
|22L 64s
|-
|87
|21L 66s
|}
[[Category:valentine]]
[[Category:valentine]]
Retrieved from "https://en.xen.wiki/w/108edo"