37ed11/5

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37ed11/5

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Prime factorization	37 (prime)
Step size	36.892¢
Octave	33\37ed11/5 (1217.44¢)
Twelfth	52\37ed11/5 (1918.38¢)
Consistency limit	3
Distinct consistency limit	3

37 equal divisions of 11/5 (abbreviated 37ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 37 equal parts of about 36.9⁠ ⁠¢ each. Each step represents a frequency ratio of (11/5)^1/37, or the 37th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	36.9
2	73.8
3	110.7
4	147.6
5	184.5	10/9, 29/26
6	221.4	25/22
7	258.2
8	295.1
9	332	17/14, 23/19
10	368.9	21/17, 26/21
11	405.8	29/23
12	442.7
13	479.6
14	516.5	23/17, 27/20
15	553.4	29/21
16	590.3
17	627.2
18	664.1	19/13, 22/15
19	700.9	3/2
20	737.8	26/17, 29/19
21	774.7
22	811.6
23	848.5
24	885.4	5/3
25	922.3	29/17
26	959.2
27	996.1
28	1033
29	1069.9	13/7
30	1106.8
31	1143.7
32	1180.5
33	1217.4
34	1254.3	29/14
35	1291.2
36	1328.1
37	1365	11/5

Harmonics

Approximation of harmonics in 37ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+17.4	+16.4	-2.0	+17.5	-3.0	-11.7	+15.4	-4.0	-2.0	+17.5	+14.4
	Relative (%)	+47.3	+44.5	-5.5	+47.4	-8.2	-31.6	+41.8	-10.9	-5.4	+47.4	+39.1
Steps (reduced)		33 (33)	52 (15)	65 (28)	76 (2)	84 (10)	91 (17)	98 (24)	103 (29)	108 (34)	113 (2)	117 (6)

Approximation of harmonics in 37ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-13.5	+5.8	-3.0	-4.0	+1.7	+13.4	-6.4	+15.5	+4.8	-2.0	-5.1
	Relative (%)	-36.6	+15.7	-8.1	-10.9	+4.6	+36.3	-17.4	+41.9	+12.9	-5.4	-14.0
Steps (reduced)		120 (9)	124 (13)	127 (16)	130 (19)	133 (22)	136 (25)	138 (27)	141 (30)	143 (32)	145 (34)	147 (36)