Prime factorization

31 (prime)

Step size

61.3534 ¢

Octave

20\31edt (1227.07 ¢)

Consistency limit

3

Distinct consistency limit

3

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	Hekts	Approximate ratios
0	0	0	1/1
1	61.4	41.9	27/26
2	122.7	83.9
3	184.1	125.8	10/9, 19/17
4	245.4	167.7	15/13
5	306.8	209.7
6	368.1	251.6	21/17, 26/21
7	429.5	293.5	9/7
8	490.8	335.5
9	552.2	377.4	26/19
10	613.5	419.4	10/7, 27/19
11	674.9	461.3
12	736.2	503.2	23/15, 26/17
13	797.6	545.2	27/17
14	858.9	587.1	18/11
15	920.3	629	17/10
16	981.7	671	23/13
17	1043	712.9	11/6, 20/11
18	1104.4	754.8	17/9, 19/10
19	1165.7	796.8
20	1227.1	838.7
21	1288.4	880.6	19/9, 21/10
22	1349.8	922.6
23	1411.1	964.5
24	1472.5	1006.5	7/3
25	1533.8	1048.4	17/7
26	1595.2	1090.3
27	1656.5	1132.3	13/5
28	1717.9	1174.2	27/10
29	1779.2	1216.1
30	1840.6	1258.1	26/9
31	1902	1300	3/1