37ed5/2

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37ed5/2

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Prime factorization	37 (prime)
Step size	42.8733¢
Octave	28\37ed5/2 (1200.45¢) (convergent)
Twelfth	44\37ed5/2 (1886.43¢)
Consistency limit	6
Distinct consistency limit	6

37 equal divisions of 5/2 (abbreviated 37ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 37 equal parts of about 42.9 ¢ each. Each step represents a frequency ratio of (5/2)^1/37, or the 37th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	42.9
2	85.7	20/19, 21/20, 22/21
3	128.6	14/13
4	171.5	11/10, 21/19
5	214.4	17/15, 25/22, 26/23
6	257.2	22/19, 29/25
7	300.1	19/16, 25/21
8	343	28/23
9	385.9	5/4
10	428.7
11	471.6	21/16, 25/19, 29/22
12	514.5
13	557.4	11/8, 29/21
14	600.2	17/12, 24/17
15	643.1	16/11, 29/20
16	686
17	728.8	29/19
18	771.7	25/16
19	814.6	8/5
20	857.5	23/14
21	900.3
22	943.2	19/11
23	986.1	23/13
24	1029	20/11, 29/16
25	1071.8	13/7
26	1114.7	19/10, 21/11
27	1157.6
28	1200.5	2/1
29	1243.3
30	1286.2	21/10
31	1329.1	28/13
32	1371.9	11/5
33	1414.8	25/11
34	1457.7
35	1500.6	19/8
36	1543.4
37	1586.3	5/2

Harmonics

Approximation of harmonics in 37ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.5	-15.5	+0.9	+0.5	-15.1	+18.2	+1.4	+11.8	+0.9	+7.4	-14.6
	Relative (%)	+1.1	-36.2	+2.1	+1.1	-35.2	+42.4	+3.2	+27.6	+2.1	+17.3	-34.1
Steps (reduced)		28 (28)	44 (7)	56 (19)	65 (28)	72 (35)	79 (5)	84 (10)	89 (15)	93 (19)	97 (23)	100 (26)

Approximation of harmonics in 37ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+18.3	+18.6	-15.1	+1.8	-17.4	+12.3	+4.4	+1.4	+2.6	+7.9	+16.6
	Relative (%)	+42.7	+43.4	-35.2	+4.2	-40.6	+28.6	+10.3	+3.2	+6.2	+18.3	+38.8
Steps (reduced)		104 (30)	107 (33)	109 (35)	112 (1)	114 (3)	117 (6)	119 (8)	121 (10)	123 (12)	125 (14)	127 (16)