| Prime factorization
|
31 (prime)
|
| Step size
|
61.3534¢
|
| Octave
|
20\31edt (1227.07¢)
|
| Consistency limit
|
2
|
| Distinct consistency limit
|
2
|
31edt divides the tritave into equal parts of 61.353 cents, corresponding to the non-octave third tone scale of 39edo where each degree gets ~.185 cents flatter than the corresponding degree of 39edo. It supports the same higher-limit meantone temperament as 12 edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father scales.
Intervals
See also: Specific intervals in 31edt
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1, 50/49, 55/54, 78/77
|
| 1
|
61.3534
|
21/20, 27/26, 55/52, 81/77
|
| 2
|
122.707
|
52/49
|
| 3
|
184.06
|
10/9, 11/10, 12/11, 39/35, 49/45, 54/49, 55/49
|
| 4
|
245.414
|
7/6, 15/13, 33/28, 63/55, 81/70
|
| 5
|
306.767
|
63/52
|
| 6
|
368.12
|
11/9, 26/21, 40/33, 60/49
|
| 7
|
429.474
|
9/7, 13/10, 14/11, 33/26, 35/27, 49/39, 50/39, 55/42, 63/50, 77/60
|
| 8
|
490.827
|
27/20, 35/26
|
| 9
|
552.18
|
66/49
|
| 10
|
613.534
|
7/5, 10/7, 13/9, 55/39, 77/54, 78/55
|
| 11
|
674.887
|
3/2, 49/33, 77/52, 81/55
|
| 12
|
736.241
|
81/52
|
| 13
|
797.594
|
11/7, 14/9, 39/25, 52/33, 78/49
|
| 14
|
858.947
|
5/3, 18/11, 21/13, 33/20, 49/30, 81/49, 81/50
|
| 15
|
920.301
|
45/26
|
| 16
|
981.654
|
26/15
|
| 17
|
1043.01
|
9/5, 11/6, 13/7, 20/11, 49/27, 50/27, 70/39
|
| 18
|
1104.36
|
21/11, 25/13, 27/14, 49/26, 77/40
|
| 19
|
1165.71
|
52/27
|
| 20
|
1227.07
|
2/1, 55/27
|
| 21
|
1288.42
|
15/7, 21/10, 27/13, 55/26, 70/33, 77/36
|
| 22
|
1349.77
|
49/22
|
| 23
|
1411.13
|
20/9, 78/35
|
| 24
|
1472.48
|
7/3, 26/11, 30/13, 33/14, 50/21, 81/35
|
| 25
|
1533.83
|
27/11, 49/20, 63/26
|
| 26
|
1595.19
|
52/21
|
| 27
|
1656.54
|
13/5, 18/7, 28/11, 55/21, 70/27, 77/30
|
| 28
|
1717.89
|
11/4, 27/10, 30/11, 35/13, 49/18
|
| 29
|
1779.25
|
|
| 30
|
1840.6
|
20/7, 26/9, 77/27
|
| 31
|
1901.96
|
3/1, 55/18, 77/26
|