| Prime factorization
|
2 × 3 × 19
|
| Step size
|
10.5263 ¢
|
| Fifth
|
67\114 (705.263 ¢)
|
| Semitones (A1:m2)
|
13:7 (136.8 ¢ : 73.68 ¢)
|
| Consistency limit
|
7
|
| Distinct consistency limit
|
7
|
114edo is the equal division of the octave into 114 parts, each of 10.52632 cents. In the 5-limit it tempers out 2048/2025, in the 7-limit 245/243, in the 11-limit 121/120, 176/175 and 117440512/117406179, in the 13-limit 196/195 and 325/324, in the 17-limit 136/135 and 154/153, in the 19-limit 286/285 and 343/342. These commas make for 114edo being an excellent tuning for shrutar temperament; it is in fact the optimal patent val for shrutar in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.
Period of 19-limit Shrutar
| Degree
|
Cents
|
Difference from 68edo
|
| 2
|
21.05263
|
3.40557¢
|
| 3
|
31.57895
|
-3.71517¢
|
| 5
|
52.63158
|
-0.3096¢
|
| 7
|
73.68421
|
3.096¢
|
| 8
|
84.21053
|
-4.02477¢
|
| 10
|
105.26316
|
-0.619195¢
|
| 12
|
126.31579
|
2.78638¢
|
| 13
|
136.842105
|
-4.334365¢
|
| 15
|
157.89474
|
-0.9288¢
|
| 17
|
178.94737
|
2.47678¢
|
| 18
|
189.47369
|
-4.644¢
|
| 20
|
210.52632
|
-1.23839¢
|
| 22
|
231.57895
|
2.16718¢
|
| 23
|
242.10526
|
-4.953560372
|
| 25
|
263.157895
|
-1.548¢
|
| 27
|
284.21053
|
1.857585¢
|
| 29
|
305.26316
|
5.26316¢
|
| 30
|
315.78947
|
-1.857585¢
|
| 32
|
336.842105
|
1.548¢
|
| 34
|
357.89474
|
4.95356¢
|
| 35
|
368.42105
|
-2.16718¢
|
| 37
|
389.47368
|
1.23839¢
|
| 39
|
410.52632
|
4.64396¢
|
| 40
|
421.05263
|
-2.47678¢
|
| 42
|
442.10526
|
0.92879¢
|
| 44
|
463.157895
|
4.334365¢
|
| 45
|
473.68421
|
-2.78638¢
|
| 47
|
494.73684
|
0.619195¢
|
| 49
|
515.78947
|
4.02477¢
|
| 50
|
526.31579
|
-3.095975¢
|
| 52
|
547.36842
|
0.3096¢
|
| 54
|
568.42105
|
3.71517¢
|
| 55
|
578.94737
|
-3.40557¢
|
Since 114edo has a step of 10.52632 cents, it also allows one to use its MOS scales as circulating temperaments.
Circulating temperaments in 114edo
| Tones
|
Pattern
|
L:s
|
| 5
|
4L 1s
|
23:22
|
| 6
|
6edo
|
equal
|
| 7
|
2L 5s
|
17:16
|
| 8
|
2L 6s
|
15:14
|
| 9
|
6L 3s
|
13:12
|
| 10
|
4L 6s
|
12:11
|
| 11
|
4L 7s
|
11:10
|
| 12
|
6L 6s
|
10:9
|
| 13
|
10L 3s
|
9:8
|
| 14
|
2L 12s
|
| 15
|
9L 6s
|
8:7
|
| 16
|
2L 14s
|
| 17
|
12L 5s
|
7:6
|
| 18
|
6L 12s
|
| 19
|
19edo
|
equal
|
| 20
|
14L 6s
|
6:5
|
| 21
|
9L 12s
|
| 22
|
4L 18s
|
| 23
|
22L 1s
|
5:4
|
| 24
|
18L 6s
|
| 25
|
14L 11s
|
| 26
|
10L 16s
|
| 27
|
6L 21s
|
| 28
|
2L 26s
|
| 29
|
27L 2s
|
4:3
|
| 30
|
24L 6s
|
| 31
|
21L 10s
|
| 32
|
18L 14s
|
| 33
|
15L 18s
|
| 34
|
12L 22s
|
| 35
|
9L 26s
|
| 36
|
6L 30s
|
| 37
|
3L 34s
|
| 38
|
38edo
|
equal
|
| 39
|
36L 3s
|
3:2
|
| 40
|
34L 6s
|
| 41
|
32L 9s
|
| 42
|
30L 12s
|
| 43
|
28L 15s
|
| 44
|
26L 18s
|
| 45
|
24L 21s
|
| 46
|
22L 24s
|
| 47
|
20L 27s
|
| 48
|
18L 30L
|
| 49
|
16L 33s
|
| 50
|
14L 36s
|
| 51
|
12L 39s
|
| 52
|
10L 42s
|
| 53
|
8L 45s
|
| 54
|
6L 48s
|
| 55
|
4L 52s
|
| 56
|
2L 54s
|
| 57
|
57edo
|
equal
|
| 58
|
56L 2s
|
2:1
|
| 59
|
55L 4s
|
| 60
|
54L 6s
|
| 61
|
53L 8s
|
| 62
|
52L 10s
|
| 63
|
51L 12s
|
| 64
|
50L 14s
|
| 65
|
49L 16s
|
| 66
|
48L 18s
|
| 67
|
47L 20s
|
| 68
|
46L 22s
|
| 69
|
45L 24s
|
| 70
|
44L 26s
|
| 71
|
43L 28s
|
| 72
|
42L 30s
|
| 73
|
41L 32s
|
| 74
|
40L 34s
|
| 75
|
39L 36s
|
| 76
|
38L 38s
|
| 77
|
37L 40s
|
| 78
|
36L 42s
|
| 79
|
35L 44s
|
| 80
|
34L 46s
|
| 81
|
33L 48s
|
| 82
|
32L 50s
|
| 83
|
31L 52s
|
| 84
|
30L 54s
|
| 85
|
29L 56s
|
| 86
|
28L 58s
|
| 87
|
27L 60s
|
| 88
|
26L 62s
|
| 89
|
25L 64s
|
| 90
|
24L 66s
|
| 91
|
23L 68s
|