32ed7

← 31ed7

32ed7

33ed7 →

Prime factorization	25
Step size	105.276¢
Octave	11\32ed7 (1158.03¢)
Twelfth	18\32ed7 (1894.96¢) (→9\16ed7)
Consistency limit	3
Distinct consistency limit	3

Division of the 7th harmonic into 32 equal parts (32ed7) is related to 18edt, but with the 7/1 rather than the 3/1 being just. The step size is about 105.2758 cents, corresponding to 11.3986 edo.

Intervals

Intervals of 32ed7

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	105.2758	17/16
2	210.5516
3	315.8274	6/5
4	421.1032	51/40
5	526.3790
6	631.6549	36/25
7	736.9307
8	842.2065
9	947.4823	140/81
10	1052.7581
11	1158.0339	125/64
12	1263.3097	56/27
13	1368.5855
14	1473.8613	225/96
15	1579.1371
16	1684.4130	119/45, 45/17
17	1789.6888	45/16
18	1894.9646
19	2000.2404
20	2105.5162	27/8
21	2210.7920
22	2316.0678
23	2421.3436	81/20
24	2526.6194
25	2631.8952	32/7
26	2737.1710	175/36
27	2842.4469
28	2947.7227	192/35
29	3052.9985	35/6
30	3158.2743
31	3263.5501
32	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of prime harmonics in 32ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-42.0	-7.0	-49.1	+0.0	-45.6	-18.9	+43.0	-44.3	+46.1	-39.4	-49.6
	Relative (%)	-39.9	-6.6	-46.7	+0.0	-43.3	-18.0	+40.9	-42.1	+43.8	-37.4	-47.1
Steps (reduced)		11 (11)	18 (18)	26 (26)	32 (0)	39 (7)	42 (10)	47 (15)	48 (16)	52 (20)	55 (23)	56 (24)

Approximation of prime harmonics in 32ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-40.1	-7.2	+15.6	-33.1	-30.6	-5.7	+41.9	-15.3	-10.4	+46.8	+15.3
	Relative (%)	-38.1	-6.9	+14.8	-31.5	-29.0	-5.4	+39.8	-14.5	-9.9	+44.4	+14.6
Steps (reduced)		59 (27)	61 (29)	62 (30)	63 (31)	65 (1)	67 (3)	68 (4)	69 (5)	70 (6)	71 (7)	72 (8)

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