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'''112EDO''' has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27|28:27]] while -8 fifths gives a near-just [[39/32|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17|17:21]].
'''112EDO''' has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27|28:27]] while -8 fifths gives a near-just [[39/32|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17|17:21]].


One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.
One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.




Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as circulating temperaments.  
Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as circulating temperaments.
{| class="wikitable"
{| class="wikitable"
|+Circulating temperaments in 112edo
|+Circulating temperaments in 112edo
!Tones
! Tones
!Pattern
! Pattern
!L:s
! L:s
|-
|-
|5
| 5
|[[2L 3s]]
| [[2L 3s]]
|23:22
| 23:22
|-
|-
|6
| 6
|[[4L 2s]]
| [[4L 2s]]
|19:18
| 19:18
|-
|-
|7
| 7
|[[7edo]]
| [[7edo]]
| rowspan="2" |equal
| rowspan="2" | equal
|-
|-
|8
| 8
|[[8edo]]
| [[8edo]]
|-
|-
|9
| 9
|[[4L 5s]]
| [[4L 5s]]
|13:12
| 13:12
|-
|-
|10
| 10
|[[2L 8s]]
| [[2L 8s]]
|12:11
| 12:11
|-
|-
|11
| 11
|[[2L 9s]]
| [[2L 9s]]
|11:10
| 11:10
|-
|-
|12
| 12
|[[4L 8s]]
| [[4L 8s]]
|10:9
| 10:9
|-
|-
|13
| 13
|[[8L 5s]]
| [[8L 5s]]
|9:8
| 9:8
|-
|-
|14
| 14
|[[14edo]]
| [[14edo]]
|equal
| equal
|-
|-
|15
| 15
|[[6L 9s]]
| [[6L 9s]]
|8:7
| 8:7
|-
|-
|16
| 16
|[[16edo]]
| [[16edo]]
|equal
| equal
|-
|-
|17
| 17
|[[10L 7s]]
| [[10L 7s]]
| rowspan="2" |7:6
| rowspan="2" | 7:6
|-
|-
|18
| 18
|4L 14s
| 4L 14s
|-
|-
|19
| 19
|[[17L 2s]]
| [[17L 2s]]
| rowspan="4" |6:5
| rowspan="4" | 6:5
|-
|-
|20
| 20
|12L 8s
| 12L 8s
|-
|-
|21
| 21
|7L 14s
| 7L 14s
|-
|-
|22
| 22
|2L 20s
| 2L 20s
|-
|-
|23
| 23
|20L 3s
| 20L 3s
| rowspan="5" |5:4
| rowspan="5" | 5:4
|-
|-
|24
| 24
|16L 8s
| 16L 8s
|-
|-
|25
| 25
|12L 13s
| 12L 13s
|-
|-
|26
| 26
|8L 18s
| 8L 18s
|-
|-
|27
| 27
|4L 23s
| 4L 23s
|-
|-
|28
| 28
|[[28edo]]
| [[28edo]]
|equal
| equal
|-
|-
|29
| 29
|25L 4s
| 25L 4s
| rowspan="9" |4:3
| rowspan="9" | 4:3
|-
|-
|30
| 30
|22L 8s
| 22L 8s
|-
|-
|31
| 31
|19L 12s
| 19L 12s
|-
|-
|32
| 32
|16L 16s
| 16L 16s
|-
|-
|33
| 33
|13L 20s
| 13L 20s
|-
|-
|34
| 34
|10L 24s
| 10L 24s
|-
|-
|35
| 35
|7L 28s
| 7L 28s
|-
|-
|36
| 36
|4L 32s
| 4L 32s
|-
|-
|37
| 37
|1L 36s
| 1L 36s
|-
|-
|38
| 38
|36L 2s
| 36L 2s
| rowspan="18" |3:2
| rowspan="18" | 3:2
|-
|-
|39
| 39
|34L 5s
| 34L 5s
|-
|-
|40
| 40
|32L 8s
| 32L 8s
|-
|-
|41
| 41
|30L 11s
| 30L 11s
|-
|-
|42
| 42
|28L 14s
| 28L 14s
|-
|-
|43
| 43
|26L 17s
| 26L 17s
|-
|-
|44
| 44
|24L 20s
| 24L 20s
|-
|-
|45
| 45
|22L 23s
| 22L 23s
|-
|-
|46
| 46
|20L 26s
| 20L 26s
|-
|-
|47
| 47
|18L 29s
| 18L 29s
|-
|-
|48
| 48
|16L 32s
| 16L 32s
|-
|-
|49
| 49
|14L 35s
| 14L 35s
|-
|-
|50
| 50
|12L 38s
| 12L 38s
|-
|-
|51
| 51
|10L 41s
| 10L 41s
|-
|-
|52
| 52
|8L 44s
| 8L 44s
|-
|-
|53
| 53
|6L 47s
| 6L 47s
|-
|-
|54
| 54
|4L 50s
| 4L 50s
|-
|-
|55
| 55
|2L 53s
| 2L 53s
|-
|-
|56
| 56
|[[56edo]]
| [[56edo]]
|equal
| equal
|-
|-
|57
| 57
|55L 2s
| 55L 2s
| rowspan="33" |2:1
| rowspan="33" | 2:1
|-
|-
|58
| 58
|54L 4s
| 54L 4s
|-
|-
|59
| 59
|53L 6s
| 53L 6s
|-
|-
|60
| 60
|52L 8s
| 52L 8s
|-
|-
|61
| 61
|51L 10s
| 51L 10s
|-
|-
|62
| 62
|50L 12s
| 50L 12s
|-
|-
|63
| 63
|49L 14s
| 49L 14s
|-
|-
|64
| 64
|48L 16s
| 48L 16s
|-
|-
|65
| 65
|47L 18s
| 47L 18s
|-
|-
|66
| 66
|46L 20s
| 46L 20s
|-
|-
|67
| 67
|45L 22s
| 45L 22s
|-
|-
|68
| 68
|44L 24s
| 44L 24s
|-
|-
|69
| 69
|43L 26s
| 43L 26s
|-
|-
|70
| 70
|42L 28s
| 42L 28s
|-
|-
|71
| 71
|41L 30s
| 41L 30s
|-
|-
|72
| 72
|40L 32s
| 40L 32s
|-
|-
|73
| 73
|39L 34s
| 39L 34s
|-
|-
|74
| 74
|38L 36s
| 38L 36s
|-
|-
|75
| 75
|37L 38s
| 37L 38s
|-
|-
|76
| 76
|36L 40s
| 36L 40s
|-
|-
|77
| 77
|35L 42s
| 35L 42s
|-
|-
|78
| 78
|34L 44s
| 34L 44s
|-
|-
|79
| 79
|33L 46s
| 33L 46s
|-
|-
|80
| 80
|32L 48s
| 32L 48s
|-
|-
|81
| 81
|31L 50s
| 31L 50s
|-
|-
|82
| 82
|30L 52s
| 30L 52s
|-
|-
|83
| 83
|29L 54s
| 29L 54s
|-
|-
|84
| 84
|28L 56s
| 28L 56s
|-
|-
|85
| 85
|27L 58s
| 27L 58s
|-
|-
|86
| 86
|26L 60s
| 26L 60s
|-
|-
|87
| 87
|25L 62s
| 25L 62s
|-
|-
|88
| 88
|24L 64s
| 24L 64s
|-
|-
|89
| 89
|23L 66s
| 23L 66s
|}
|}


==Music in 112EDO==
== Music in 112EDO ==


*[https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv Circulating 2.3.7.11.13 Floaty Piano Improv] by [[Cam Taylor]]
* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv Circulating 2.3.7.11.13 Floaty Piano Improv] by [[Cam Taylor]]


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:what is]]
[[Category:wiki]]
Retrieved from "https://en.xen.wiki/w/112edo"