116edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
No edit summary
Line 1: Line 1:
'''116edo''' is the [[EDO|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments|submajor temperament]].
'''116edo''' is the [[EDO|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments|submajor temperament]].
 
Since 116edo has a step of 10.3448 cents, it also allows one to use its MOS scales as circulating temperaments.
{| class="wikitable"
|+Circulating temperaments in 116edo
!Tones
!Pattern
!L:s
|-
|5
|[[1L 4s]]
|24:23
|-
|6
|[[2L 4s]]
|20:19
|-
|7
|[[4L 3s]]
|17:16
|-
|8
|[[4L 4s]]
|15:14
|-
|9
|[[8L 1s]]
|13:12
|-
|10
|[[6L 4s]]
|12:11
|-
|11
|[[6L 5s]]
|11:10
|-
|12
|[[8L 4s]]
|10:9
|-
|13
|[[12L 1s]]
| rowspan="2" |9:8
|-
|14
|[[4L 10s]]
|-
|15
|[[11L 4s]]
| rowspan="2" |8:7
|-
|16
|4L 12s
|-
|17
|[[14L 3s]]
| rowspan="3" |7:6
|-
|18
|8L 10s
|-
|19
|[[2L 17s]]
|-
|20
|16L 4s
| rowspan="4" |6:5
|-
|21
|11L 10s
|-
|22
|[[6L 16s]]
|-
|23
|1L 22s
|-
|24
|20L 4s
| rowspan="5" |5:4
|-
|25
|16L 9s
|-
|26
|12L 14s
|-
|27
|8L 19s
|-
|28
|4L 24s
|-
|29
|[[29edo]]
|equal
|-
|30
|26L 4s
| rowspan="9" |4:3
|-
|31
|23L 8s
|-
|32
|20L 12s
|-
|33
|17L 16s
|-
|34
|14L 20s
|-
|35
|11L 24s
|-
|36
|8L 28s
|-
|37
|5L 32s
|-
|38
|2L 36s
|-
|39
|38L 1s
| rowspan="19" |3:2
|-
|40
|36L 4s
|-
|41
|34L 7s
|-
|42
|32L 10s
|-
|43
|30L 13s
|-
|44
|28L 16s
|-
|45
|26L 19s
|-
|46
|24L 22s
|-
|47
|22L 25s
|-
|48
|20L 28s
|-
|49
|18L 31s
|-
|50
|16L 34s
|-
|51
|14L 37s
|-
|52
|12L 40s
|-
|53
|10L 43s
|-
|54
|8L 46s
|-
|55
|6L 49s
|-
|56
|4L 52s
|-
|57
|2L 55s
|-
|58
|[[58edo]]
|equal
|-
|59
|57L 2s
| rowspan="34" |2:1
|-
|60
|56L 4s
|-
|61
|55L 6s
|-
|62
|54L 8s
|-
|63
|53L 10s
|-
|64
|52L 12s
|-
|65
|51L 14s
|-
|66
|50L 16s
|-
|67
|49L 18s
|-
|68
|48L 20s
|-
|69
|47L 22s
|-
|70
|46L 24s
|-
|71
|45L 26s
|-
|72
|44L 28s
|-
|73
|43L 30s
|-
|74
|42L 32s
|-
|75
|41L 34s
|-
|76
|40L 36s
|-
|77
|39L 38s
|-
|78
|38L 40s
|-
|79
|37L 42s
|-
|80
|36L 44s
|-
|81
|35L 46s
|-
|82
|34L 48s
|-
|83
|33L 50s
|-
|84
|32L 52s
|-
|85
|31L 54s
|-
|86
|30L 56s
|-
|87
|29L 58s
|-
|88
|28L 60s
|-
|89
|27L 62s
|-
|90
|26L 64s
|-
|91
|25L 66s
|-
|92
|24L 68s
|}
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]

Revision as of 21:46, 21 April 2021

116edo is the equal division of the octave into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for submajor temperament. Since 116edo has a step of 10.3448 cents, it also allows one to use its MOS scales as circulating temperaments.

Circulating temperaments in 116edo
Tones Pattern L:s
5 1L 4s 24:23
6 2L 4s 20:19
7 4L 3s 17:16
8 4L 4s 15:14
9 8L 1s 13:12
10 6L 4s 12:11
11 6L 5s 11:10
12 8L 4s 10:9
13 12L 1s 9:8
14 4L 10s
15 11L 4s 8:7
16 4L 12s
17 14L 3s 7:6
18 8L 10s
19 2L 17s
20 16L 4s 6:5
21 11L 10s
22 6L 16s
23 1L 22s
24 20L 4s 5:4
25 16L 9s
26 12L 14s
27 8L 19s
28 4L 24s
29 29edo equal
30 26L 4s 4:3
31 23L 8s
32 20L 12s
33 17L 16s
34 14L 20s
35 11L 24s
36 8L 28s
37 5L 32s
38 2L 36s
39 38L 1s 3:2
40 36L 4s
41 34L 7s
42 32L 10s
43 30L 13s
44 28L 16s
45 26L 19s
46 24L 22s
47 22L 25s
48 20L 28s
49 18L 31s
50 16L 34s
51 14L 37s
52 12L 40s
53 10L 43s
54 8L 46s
55 6L 49s
56 4L 52s
57 2L 55s
58 58edo equal
59 57L 2s 2:1
60 56L 4s
61 55L 6s
62 54L 8s
63 53L 10s
64 52L 12s
65 51L 14s
66 50L 16s
67 49L 18s
68 48L 20s
69 47L 22s
70 46L 24s
71 45L 26s
72 44L 28s
73 43L 30s
74 42L 32s
75 41L 34s
76 40L 36s
77 39L 38s
78 38L 40s
79 37L 42s
80 36L 44s
81 35L 46s
82 34L 48s
83 33L 50s
84 32L 52s
85 31L 54s
86 30L 56s
87 29L 58s
88 28L 60s
89 27L 62s
90 26L 64s
91 25L 66s
92 24L 68s
Retrieved from "https://en.xen.wiki/index.php?title=116edo&oldid=68172"