31edt

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← 30edt31edt32edt →
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