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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]]

Revision as of 12:37, 4 December 2021

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 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of 7edo) and +9 fifths gives a close approximation to 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.


Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as circulating temperaments.

Circulating temperaments in 112edo
Tones Pattern L:s
5 2L 3s 23:22
6 4L 2s 19:18
7 7edo equal
8 8edo
9 4L 5s 13:12
10 2L 8s 12:11
11 2L 9s 11:10
12 4L 8s 10:9
13 8L 5s 9:8
14 14edo equal
15 6L 9s 8:7
16 16edo equal
17 10L 7s 7:6
18 4L 14s
19 17L 2s 6:5
20 12L 8s
21 7L 14s
22 2L 20s
23 20L 3s 5:4
24 16L 8s
25 12L 13s
26 8L 18s
27 4L 23s
28 28edo equal
29 25L 4s 4:3
30 22L 8s
31 19L 12s
32 16L 16s
33 13L 20s
34 10L 24s
35 7L 28s
36 4L 32s
37 1L 36s
38 36L 2s 3:2
39 34L 5s
40 32L 8s
41 30L 11s
42 28L 14s
43 26L 17s
44 24L 20s
45 22L 23s
46 20L 26s
47 18L 29s
48 16L 32s
49 14L 35s
50 12L 38s
51 10L 41s
52 8L 44s
53 6L 47s
54 4L 50s
55 2L 53s
56 56edo equal
57 55L 2s 2:1
58 54L 4s
59 53L 6s
60 52L 8s
61 51L 10s
62 50L 12s
63 49L 14s
64 48L 16s
65 47L 18s
66 46L 20s
67 45L 22s
68 44L 24s
69 43L 26s
70 42L 28s
71 41L 30s
72 40L 32s
73 39L 34s
74 38L 36s
75 37L 38s
76 36L 40s
77 35L 42s
78 34L 44s
79 33L 46s
80 32L 48s
81 31L 50s
82 30L 52s
83 29L 54s
84 28L 56s
85 27L 58s
86 26L 60s
87 25L 62s
88 24L 64s
89 23L 66s

Music in 112EDO

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