31edt

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31edt

32edt →

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
1	61.353	27/26
2	122.707
3	184.06	10/9, 19/17
4	245.414	15/13
5	306.767
6	368.12	21/17, 26/21
7	429.474	9/7
8	490.827
9	552.18	26/19
10	613.534	10/7, 27/19
11	674.887
12	736.241	23/15, 26/17
13	797.594	27/17
14	858.947	18/11
15	920.301	17/10
16	981.654	23/13
17	1043.008	11/6, 20/11
18	1104.361	17/9, 19/10
19	1165.714
20	1227.068
21	1288.421	19/9, 21/10
22	1349.775
23	1411.128
24	1472.481	7/3
25	1533.835	17/7
26	1595.188
27	1656.541	13/5
28	1717.895	27/10
29	1779.248
30	1840.602	26/9
31	1901.955	3/1

Harmonics

Approximation of harmonics in 31edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+27.1	+0.0	-7.2	-25.4	+27.1	+5.6	+19.8	+0.0	+1.7	+20.7	-7.2
	Relative (%)	+44.1	+0.0	-11.8	-41.4	+44.1	+9.1	+32.4	+0.0	+2.7	+33.8	-11.8
Steps (reduced)		20 (20)	31 (0)	39 (8)	45 (14)	51 (20)	55 (24)	59 (28)	62 (0)	65 (3)	68 (6)	70 (8)

Approximation of harmonics in 31edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-23.1	-28.7	-25.4	-14.4	+3.3	+27.1	-5.2	+28.7	+5.6	-13.6	-29.2
	Relative (%)	-37.6	-46.7	-41.4	-23.5	+5.4	+44.1	-8.4	+46.8	+9.1	-22.1	-47.6
Steps (reduced)		72 (10)	74 (12)	76 (14)	78 (16)	80 (18)	82 (20)	83 (21)	85 (23)	86 (24)	87 (25)	88 (26)