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| {{Infobox ET}} | | {{Infobox ET}} |
| {{EDO intro|115}} | | {{ED intro}} |
| ==Theory==
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| 115edo tempers out 1594323/1562500 (unicorn comma) and 2109375/2097152 (semicomma) in the 5-limit, as well as 43046721/41943040 and 30958682112/30517578125 ([[Trisedodge family|trisedodge comma]]); 225/224, 1728/1715, and 9920232/9765625 in the 7-limit. 115edo [[support]]s the [[Semicomma family|newspeak temperament]], tempering out 441/440, 1375/1372, and 1944/1925 in the 11-limit. The wizardharry comma, 4000/3993 is also tempered out in 115edo.
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| === Miscellany === | | == Theory == |
| Since 115edo has a step of 10.4348 cents, it also allows one to use its MOS scales as circulating temperaments.
| | The equal temperament [[tempering out|tempers out]] 1594323/1562500 ([[unicorn comma]]) and 2109375/2097152 ([[semicomma]]) in the 5-limit, as well as 43046721/41943040 ([[python comma]]) and {{monzo| 19 10 -15 }} ([[trisedodge comma]]); [[225/224]], [[1728/1715]], and 9920232/9765625 in the 7-limit. Using the [[patent val]], it [[support]]s the [[semicomma family #Newspeak|newspeak temperament]], tempering out [[441/440]], [[1375/1372]], and 1944/1925 in the 11-limit. The wizardharry comma, [[4000/3993]] is also tempered out. |
| {| class="wikitable collapsible mw-collapsed"
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| |+Circulating temperaments in 115edo
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| !Tones
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| !Pattern
| |
| !L:s
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| |-
| |
| |5
| |
| |[[5edo]]
| |
| |equal | |
| |-
| |
| |6
| |
| |[[1L 5s]]
| |
| |20:19
| |
| |-
| |
| |7
| |
| |[[3L 4s]]
| |
| |17:16
| |
| |-
| |
| |8
| |
| |[[2L 6s]]
| |
| |15:14
| |
| |-
| |
| |9
| |
| |[[7L 2s]]
| |
| |13:12
| |
| |-
| |
| |10 | |
| |[[5L 5s]]
| |
| |12:11
| |
| |-
| |
| |11
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| |[[5L 6s]]
| |
| |11:10
| |
| |-
| |
| |12
| |
| |[[7L 5s]]
| |
| |10:9
| |
| |-
| |
| |13
| |
| |[[11L 2s]]
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| | rowspan="2" |9:8
| |
| |-
| |
| |14
| |
| |[[3L 11s]]
| |
| |-
| |
| |15
| |
| |[[10L 5s]]
| |
| | rowspan="2" |8:7
| |
| |-
| |
| |16
| |
| |[[3L 13s]]
| |
| |-
| |
| |17
| |
| |13L 4s | |
| | rowspan="3" |7:6
| |
| |-
| |
| |18
| |
| |7L 11s
| |
| |-
| |
| |19
| |
| |1L 18s
| |
| |-
| |
| |20
| |
| |15L 5s
| |
| | rowspan="3" |6:5
| |
| |-
| |
| |21
| |
| |[[10L 11s]]
| |
| |-
| |
| |22
| |
| |[[5L 17s]]
| |
| |-
| |
| |23
| |
| |[[23edo]]
| |
| |equal
| |
| |-
| |
| |24
| |
| |[[19L 5s]]
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| | rowspan="5" |5:4
| |
| |-
| |
| |25
| |
| |15L 10s
| |
| |-
| |
| |26
| |
| |11L 15s
| |
| |-
| |
| |27
| |
| |7L 20s
| |
| |-
| |
| |28
| |
| |3L 25s
| |
| |-
| |
| |29
| |
| |28L 1s
| |
| | rowspan="10" |4:3
| |
| |-
| |
| |30
| |
| |25L 5s
| |
| |-
| |
| |31
| |
| |22L 9s
| |
| |-
| |
| |32
| |
| |19L 13s
| |
| |-
| |
| |33
| |
| |16L 17s
| |
| |-
| |
| |34
| |
| |13L 21s
| |
| |-
| |
| |35
| |
| |10L 25s
| |
| |-
| |
| |36
| |
| |7L 29s
| |
| |-
| |
| |37
| |
| |4L 33s
| |
| |-
| |
| |38
| |
| |1L 37s
| |
| |-
| |
| |39
| |
| |37L 2s
| |
| | rowspan="19" |3:2
| |
| |-
| |
| |40
| |
| |35L 5s
| |
| |-
| |
| |41
| |
| |33L 8s
| |
| |-
| |
| |42
| |
| |31L 11s
| |
| |-
| |
| |43
| |
| |29L 14s
| |
| |-
| |
| |44
| |
| |27L 17s
| |
| |-
| |
| |45
| |
| |25L 20s
| |
| |-
| |
| |46
| |
| |23L 23s
| |
| |-
| |
| |47
| |
| |21L 26s
| |
| |-
| |
| |48
| |
| |19L 29s
| |
| |-
| |
| |49
| |
| |17L 32s
| |
| |-
| |
| |50
| |
| |15L 35s
| |
| |-
| |
| |51
| |
| |13L 38s
| |
| |-
| |
| |52
| |
| |11L 41s
| |
| |-
| |
| |53
| |
| |9L 44s
| |
| |-
| |
| |54
| |
| |7L 47s
| |
| |-
| |
| |55
| |
| |5L 50s
| |
| |-
| |
| |56
| |
| |3L 53s
| |
| |-
| |
| |57
| |
| |1L 56s
| |
| |-
| |
| |58
| |
| |57L 1s
| |
| | rowspan="34" |2:1
| |
| |-
| |
| |59
| |
| |56L 3s
| |
| |-
| |
| |60
| |
| |55L 5s
| |
| |-
| |
| |61
| |
| |54L 7s
| |
| |-
| |
| |62
| |
| |53L 9s
| |
| |-
| |
| |63
| |
| |52L 11s
| |
| |-
| |
| |64
| |
| |51L 13s
| |
| |-
| |
| |65
| |
| |50L 15s
| |
| |-
| |
| |66
| |
| |49L 17s
| |
| |-
| |
| |67
| |
| |48L 19s
| |
| |-
| |
| |68
| |
| |47L 21s
| |
| |-
| |
| |69
| |
| |46L 23s
| |
| |-
| |
| |70
| |
| |45L 25s
| |
| |-
| |
| |71
| |
| |44L 27s
| |
| |-
| |
| |72
| |
| |43L 29s
| |
| |-
| |
| |73
| |
| |42L 31s
| |
| |-
| |
| |74
| |
| |41L 33s
| |
| |-
| |
| |75
| |
| |40L 35s
| |
| |-
| |
| |76
| |
| |39L 37s
| |
| |-
| |
| |77
| |
| |38L 39s
| |
| |-
| |
| |78
| |
| |37L 41s
| |
| |-
| |
| |79
| |
| |36L 43s
| |
| |-
| |
| |80
| |
| |35L 45s
| |
| |-
| |
| |81
| |
| |34L 47s
| |
| |-
| |
| |82
| |
| |33L 49s
| |
| |-
| |
| |83
| |
| |32L 51s
| |
| |-
| |
| |84
| |
| |31L 53s
| |
| |-
| |
| |85
| |
| |30L 55s
| |
| |-
| |
| |86
| |
| |29L 57s
| |
| |-
| |
| |87
| |
| |28L 59s
| |
| |-
| |
| |88
| |
| |27L 61s
| |
| |-
| |
| |89
| |
| |26L 63s
| |
| |-
| |
| |90
| |
| |25L 65s
| |
| |-
| |
| |91
| |
| |24L 67s
| |
| |}
| |
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| |
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| [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
| | === Odd harmonics === |
| | {{Harmonics in equal|115}} |
| | |
| | == Intervals == |
| | {{Interval table}} |