32ed7/3

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32ed7/3

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Prime factorization	25
Step size	45.8397¢
Octave	26\32ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth	41\32ed7/3 (1879.43¢)
Consistency limit	4
Distinct consistency limit	4

32 equal divisions of 7/3 (abbreviated 32ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 32 equal parts of about 45.8 ¢ each. Each step represents a frequency ratio of (7/3)^1/32, or the 32nd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	45.84
2	91.679	20/19
3	137.519
4	183.359	19/17
5	229.199	8/7, 25/22
6	275.038	7/6, 20/17
7	320.878
8	366.718
9	412.557	19/15
10	458.397	13/10, 17/13
11	504.237	4/3
12	550.077	26/19
13	595.916
14	641.756
15	687.596
16	733.435	23/15, 26/17
17	779.275
18	825.115
19	870.955
20	916.794	17/10, 22/13
21	962.634	7/4
22	1008.474
23	1054.313
24	1100.153
25	1145.993
26	1191.833	2/1
27	1237.672
28	1283.512
29	1329.352
30	1375.191
31	1421.031	25/11
32	1466.871	7/3

Harmonics

Approximation of harmonics in 32ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.2	-22.5	-16.3	+9.9	+15.1	-22.5	+21.3	+0.8	+1.7	+20.1	+7.0
	Relative (%)	-17.8	-49.1	-35.6	+21.6	+33.0	-49.1	+46.5	+1.7	+3.8	+43.8	+15.2
Steps (reduced)		26 (26)	41 (9)	52 (20)	61 (29)	68 (4)	73 (9)	79 (15)	83 (19)	87 (23)	91 (27)	94 (30)

Approximation of harmonics in 32ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.9	+15.1	-12.6	+13.2	-0.1	-7.4	-9.3	-6.4	+0.8	+11.9	-19.2
	Relative (%)	+12.9	+33.0	-27.5	+28.7	-0.2	-16.1	-20.3	-14.0	+1.7	+26.0	-41.9
Steps (reduced)		97 (1)	100 (4)	102 (6)	105 (9)	107 (11)	109 (13)	111 (15)	113 (17)	115 (19)	117 (21)	118 (22)