32ed5/4

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32ed5/4

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Prime factorization	25
Step size	12.0723¢
Octave	99\32ed5/4 (1195.16¢)
Twelfth	158\32ed5/4 (1907.42¢) (→79\16ed5/4)
Consistency limit	2
Distinct consistency limit	2

32 equal divisions of 5/4 (abbreviated 32ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 32 equal parts of about 12.1 ¢ each. Each step represents a frequency ratio of (5/4)^1/32, or the 32nd root of 5/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	12.1
2	24.1
3	36.2
4	48.3
5	60.4	26/25
6	72.4	22/21
7	84.5	19/18, 20/19, 23/22
8	96.6
9	108.7
10	120.7	14/13
11	132.8
12	144.9	12/11, 13/12, 25/23
13	156.9	23/21
14	169	11/10
15	181.1	21/19
16	193.2	19/17
17	205.2	26/23
18	217.3
19	229.4	25/22
20	241.4
21	253.5	15/13, 22/19
22	265.6	7/6
23	277.7	20/17
24	289.7	13/11
25	301.8	25/21
26	313.9	6/5
27	326
28	338	17/14, 23/19
29	350.1
30	362.2	26/21
31	374.2	21/17
32	386.3

Harmonics

Approximation of harmonics in 32ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.84	+5.47	+2.39	+2.39	+0.63	-0.65	-2.45	-1.13	-2.45	+1.55	-4.21
	Relative (%)	-40.1	+45.3	+19.8	+19.8	+5.2	-5.4	-20.3	-9.4	-20.3	+12.9	-34.9
Steps (reduced)		99 (3)	158 (30)	199 (7)	231 (7)	257 (1)	279 (23)	298 (10)	315 (27)	330 (10)	344 (24)	356 (4)

Approximation of harmonics in 32ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	-5.50	-4.21	+4.78	-3.60	-5.98	-3.00	+4.78	+4.82	-3.29	+4.26
	Relative (%)	+17.2	-45.5	-34.9	+39.6	-29.8	-49.5	-24.9	+39.6	+39.9	-27.2	+35.3
Steps (reduced)		368 (16)	378 (26)	388 (4)	398 (14)	406 (22)	414 (30)	422 (6)	430 (14)	437 (21)	443 (27)	450 (2)