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| Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19. | | Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19. |
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| == Temperament properties ==
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| Since 93edo has a step of 12.903{{cent}}, it also allows one to use its MOS scales as circulating temperaments, which it is the first edo to do. It is also the first edo to allow one to use a syntonic or Mavila MOS scale or a 17 tone MOS scale similar to a median between [http://www.neuroscience-of-music.se/pelog_main.htm Pelog] and the theories of Sundanese composer-musicologist-teacher [https://en.wikipedia.org/wiki/Raden_Machjar_Angga_Koesoemadinata Raden Machjar Angga Koesoemadinata] as a circulating temperament.
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| {| class="wikitable"
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| |+Circulating temperaments in 93edo
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| !Tones
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| !Pattern
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| !L:s
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| |-
| |
| |5
| |
| |[[3L 2s]]
| |
| |19:18
| |
| |-
| |
| |6
| |
| |[[3L 3s]]
| |
| |16:15
| |
| |-
| |
| |7
| |
| |[[2L 5s]]
| |
| |14:13
| |
| |-
| |
| |8
| |
| |[[5L 3s]]
| |
| |12:11
| |
| |-
| |
| |9
| |
| |[[3L 6s]]
| |
| |11:10
| |
| |-
| |
| |10
| |
| |[[3L 7s]]
| |
| |10:9
| |
| |-
| |
| |11
| |
| |[[5L 6s]]
| |
| |9:8
| |
| |-
| |
| |12
| |
| |[[9L 3s]]
| |
| | rowspan="2" |8:7
| |
| |-
| |
| |13
| |
| |[[2L 11s]]
| |
| |-
| |
| |14
| |
| |[[9L 5s]]
| |
| | rowspan="2" |7:6
| |
| |-
| |
| |15
| |
| |[[3L 12s]]
| |
| |-
| |
| |16
| |
| |13L 3s
| |
| | rowspan="3" |6:5
| |
| |-
| |
| |17
| |
| |[[8L 9s]]
| |
| |-
| |
| |18
| |
| |3L 15s
| |
| |-
| |
| |19
| |
| |[[17L 2s]]
| |
| | rowspan="5" |5:4
| |
| |-
| |
| |20
| |
| |[[13L 7s]]
| |
| |-
| |
| |21
| |
| |9L 12s
| |
| |-
| |
| |22
| |
| |[[5L 17s]]
| |
| |-
| |
| |23
| |
| |1L 22s
| |
| |-
| |
| |24
| |
| |21L 3s
| |
| | rowspan="7" |4:3
| |
| |-
| |
| |25
| |
| |18L 7s
| |
| |-
| |
| |26
| |
| |15L 11s
| |
| |-
| |
| |27
| |
| |12L 15s
| |
| |-
| |
| |28
| |
| |9L 19s
| |
| |-
| |
| |29
| |
| |6L 23s
| |
| |-
| |
| |30
| |
| |3L 27s
| |
| |-
| |
| |31
| |
| |[[31edo]]
| |
| |equal
| |
| |-
| |
| |32
| |
| |29L 3s
| |
| | rowspan="15" |3:2
| |
| |-
| |
| |33
| |
| |27L 6s
| |
| |-
| |
| |34
| |
| |25L 9s
| |
| |-
| |
| |35
| |
| |23L 12s
| |
| |-
| |
| |36
| |
| |21L 15s
| |
| |-
| |
| |37
| |
| |19L 18s
| |
| |-
| |
| |38
| |
| |17L 21s
| |
| |-
| |
| |39
| |
| |15L 24s
| |
| |-
| |
| |40
| |
| |13L 27s
| |
| |-
| |
| |41
| |
| |12L 29s
| |
| |-
| |
| |42
| |
| |9L 33s
| |
| |-
| |
| |43
| |
| |7L 36s
| |
| |-
| |
| |44
| |
| |5L 39s
| |
| |-
| |
| |45
| |
| |3L 42s
| |
| |-
| |
| |46
| |
| |1L 45s
| |
| |-
| |
| |47
| |
| |46L 1s
| |
| | rowspan="28" |2:1
| |
| |-
| |
| |48
| |
| |45L 3s
| |
| |-
| |
| |49
| |
| |44L 5s
| |
| |-
| |
| |50
| |
| |43L 7s
| |
| |-
| |
| |51
| |
| |42L 9s
| |
| |-
| |
| |52
| |
| |41L 11s
| |
| |-
| |
| |53
| |
| |40L 13s
| |
| |-
| |
| |54
| |
| |39L 15s
| |
| |-
| |
| |55
| |
| |38L 17s
| |
| |-
| |
| |56
| |
| |37L 19s
| |
| |-
| |
| |57
| |
| |36L 21s
| |
| |-
| |
| |58
| |
| |35L 23s
| |
| |-
| |
| |59
| |
| |34L 25s
| |
| |-
| |
| |60
| |
| |33L 27s
| |
| |-
| |
| |61
| |
| |32L 29s
| |
| |-
| |
| |62
| |
| |31L 31s
| |
| |-
| |
| |63
| |
| |30L 33s
| |
| |-
| |
| |64
| |
| |29L 35s
| |
| |-
| |
| |65
| |
| |28L 37s
| |
| |-
| |
| |66
| |
| |27L 39s
| |
| |-
| |
| |67
| |
| |26L 41s
| |
| |-
| |
| |68
| |
| |25L 43s
| |
| |-
| |
| |69
| |
| |24L 45s
| |
| |-
| |
| |70
| |
| |23L 47s
| |
| |-
| |
| |71
| |
| |22L 49s
| |
| |-
| |
| |72
| |
| |21L 51s
| |
| |-
| |
| |73
| |
| |20L 53s
| |
| |-
| |
| |74
| |
| |19L 55s
| |
| |}
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|
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| [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> |