37ed7/4

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37ed7/4

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Prime factorization	37 (prime)
Step size	26.1845¢
Octave	46\37ed7/4 (1204.49¢)
Twelfth	73\37ed7/4 (1911.47¢)
Consistency limit	4
Distinct consistency limit	3

37 equal divisions of 7/4 (abbreviated 37ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 37 equal parts of about 26.2⁠ ⁠¢ each. Each step represents a frequency ratio of (7/4)^1/37, or the 37th root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	26.2
2	52.4
3	78.6	22/21
4	104.7
5	130.9	13/12, 14/13
6	157.1	12/11
7	183.3	29/26
8	209.5	9/8, 17/15
9	235.7	8/7, 23/20
10	261.8	7/6
11	288	13/11, 20/17
12	314.2
13	340.4	11/9
14	366.6	16/13, 26/21
15	392.8
16	419	14/11
17	445.1
18	471.3	21/16, 29/22
19	497.5	4/3
20	523.7	19/14, 23/17
21	549.9	11/8, 26/19
22	576.1
23	602.2
24	628.4
25	654.6	16/11, 19/13
26	680.8
27	707	3/2
28	733.2	23/15, 29/19
29	759.4	14/9
30	785.5	11/7
31	811.7
32	837.9	13/8, 21/13
33	864.1
34	890.3
35	916.5	17/10, 22/13
36	942.6	19/11
37	968.8	7/4

Harmonics

Approximation of harmonics in 37ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.5	+9.5	+9.0	-10.8	-12.2	+9.0	-12.7	-7.2	-6.3	+12.0	-7.7
	Relative (%)	+17.1	+36.3	+34.3	-41.1	-46.5	+34.3	-48.6	-27.3	-24.0	+45.9	-29.4
Steps (reduced)		46 (9)	73 (36)	92 (18)	106 (32)	118 (7)	129 (18)	137 (26)	145 (34)	152 (4)	159 (11)	164 (16)

Approximation of harmonics in 37ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.8	-12.7	-1.2	-8.2	-8.5	-2.7	+8.5	-1.8	-7.7	-9.7	-8.1
	Relative (%)	+41.4	-48.6	-4.8	-31.5	-32.3	-10.2	+32.3	-6.8	-29.4	-37.0	-30.9
Steps (reduced)		170 (22)	174 (26)	179 (31)	183 (35)	187 (2)	191 (6)	195 (10)	198 (13)	201 (16)	204 (19)	207 (22)