32ed5/2

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32ed5/2

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Prime factorization	25
Step size	49.5723¢
Octave	24\32ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth	38\32ed5/2 (1883.75¢) (→19\16ed5/2)
Consistency limit	5
Distinct consistency limit	3

32 equal divisions of 5/2 (abbreviated 32ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 32 equal parts of about 49.6 ¢ each. Each step represents a frequency ratio of (5/2)^1/32, or the 32nd root of 5/2.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	49.572
2	99.145
3	148.717
4	198.289	9/8, 19/17, 28/25
5	247.862	22/19
6	297.434	13/11, 25/21
7	347.006
8	396.578
9	446.151	22/17
10	495.723	4/3
11	545.295	26/19
12	594.868
13	644.44
14	694.012	3/2
15	743.585	26/17
16	793.157
17	842.729
18	892.301	5/3
19	941.874	19/11
20	991.446	16/9, 23/13
21	1041.018
22	1090.591	15/8
23	1140.163
24	1189.735
25	1239.308
26	1288.88	21/10
27	1338.452
28	1388.024	20/9
29	1437.597
30	1487.169	26/11
31	1536.741	17/7
32	1586.314	5/2

Harmonics

Approximation of harmonics in 32ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.3	-18.2	-20.5	-10.3	+21.1	+2.1	+18.8	+13.2	-20.5	+12.8	+10.8
	Relative (%)	-20.7	-36.7	-41.4	-20.7	+42.6	+4.2	+37.9	+26.5	-41.4	+25.7	+21.9
Steps (reduced)		24 (24)	38 (6)	48 (16)	56 (24)	63 (31)	68 (4)	73 (9)	77 (13)	80 (16)	84 (20)	87 (23)

Approximation of harmonics in 32ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+21.0	-8.2	+21.1	+8.5	+2.7	+2.9	+8.4	+18.8	-16.1	+2.5	+24.7
	Relative (%)	+42.3	-16.5	+42.6	+17.2	+5.5	+5.8	+17.0	+37.9	-32.5	+5.0	+49.8
Steps (reduced)		90 (26)	92 (28)	95 (31)	97 (1)	99 (3)	101 (5)	103 (7)	105 (9)	106 (10)	108 (12)	110 (14)