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	36.892
2	73.784
3	110.676
4	147.568
5	184.46	10/9, 29/26
6	221.352	25/22
7	258.244
8	295.136
9	332.028	17/14, 23/19
10	368.92	21/17, 26/21
11	405.812	29/23
12	442.704
13	479.596
14	516.488	23/17, 27/20
15	553.38	29/21
16	590.272
17	627.164
18	664.056	19/13, 22/15
19	700.948	3/2
20	737.84	26/17, 29/19
21	774.732
22	811.624
23	848.516
24	885.408	5/3
25	922.3	29/17
26	959.192
27	996.084
28	1032.976
29	1069.868	13/7
30	1106.76
31	1143.652
32	1180.544
33	1217.436
34	1254.328	29/14
35	1291.22
36	1328.112
37	1365.004	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)