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	61.4	27/26
2	122.7
3	184.1	10/9, 19/17
4	245.4	15/13
5	306.8
6	368.1	21/17, 26/21
7	429.5	9/7
8	490.8
9	552.2	26/19
10	613.5	10/7, 27/19
11	674.9
12	736.2	23/15, 26/17
13	797.6	27/17
14	858.9	18/11
15	920.3	17/10
16	981.7	23/13
17	1043	11/6, 20/11
18	1104.4	17/9, 19/10
19	1165.7
20	1227.1
21	1288.4	19/9, 21/10
22	1349.8
23	1411.1
24	1472.5	7/3
25	1533.8	17/7
26	1595.2
27	1656.5	13/5
28	1717.9	27/10
29	1779.2
30	1840.6	26/9
31	1902	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)