32ed7/4

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32ed7/4

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Prime factorization	25
Step size	30.2758¢
Octave	40\32ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth	63\32ed7/4 (1907.38¢)
Consistency limit	3
Distinct consistency limit	3

32 equal divisions of 7/4 (abbreviated 32ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 32 equal parts of about 30.3 ¢ each. Each step represents a frequency ratio of (7/4)^1/32, or the 32nd root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	30.3
2	60.6	27/26, 28/27
3	90.8
4	121.1	14/13, 15/14
5	151.4	23/21, 25/23
6	181.7	10/9, 21/19
7	211.9	17/15
8	242.2	15/13
9	272.5
10	302.8	25/21
11	333	17/14, 23/19
12	363.3	21/17, 27/22
13	393.6
14	423.9	14/11
15	454.1	13/10, 22/17
16	484.4	25/19
17	514.7	23/17, 27/20
18	545	15/11
19	575.2	7/5
20	605.5
21	635.8	13/9
22	666.1	22/15, 25/17
23	696.3	3/2
24	726.6
25	756.9	14/9, 17/11
26	787.2	11/7
27	817.4
28	847.7
29	878	5/3
30	908.3	22/13
31	938.6	19/11
32	968.8

Harmonics

Approximation of harmonics in 32ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.0	+5.4	-8.2	-0.9	-13.8	-8.2	+2.8	+10.8	+10.1	-3.5	-2.8
	Relative (%)	+36.4	+17.9	-27.1	-3.1	-45.7	-27.1	+9.3	+35.8	+33.3	-11.7	-9.2
Steps (reduced)		40 (8)	63 (31)	79 (15)	92 (28)	102 (6)	111 (15)	119 (23)	126 (30)	132 (4)	137 (9)	142 (14)

Approximation of harmonics in 32ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.0	+2.8	+4.5	+13.9	-0.3	-8.4	-11.2	-9.2	-2.8	+7.5	-8.9
	Relative (%)	+33.1	+9.3	+14.8	+45.8	-0.9	-27.7	-36.9	-30.2	-9.2	+24.8	-29.4
Steps (reduced)		147 (19)	151 (23)	155 (27)	159 (31)	162 (2)	165 (5)	168 (8)	171 (11)	174 (14)	177 (17)	179 (19)