37ed7/3

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37ed7/3

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Prime factorization	37 (prime)
Step size	39.6452¢
Octave	30\37ed7/3 (1189.35¢)
Twelfth	48\37ed7/3 (1902.97¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	3

37 equal divisions of 7/3 (abbreviated 37ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 37 equal parts of about 39.6⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/37, or the 37th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	39.6
2	79.3	22/21, 23/22
3	118.9	15/14, 29/27
4	158.6	23/21
5	198.2	19/17, 28/25
6	237.9
7	277.5	27/23
8	317.2	6/5
9	356.8	27/22
10	396.5	29/23
11	436.1	9/7
12	475.7	29/22
13	515.4
14	555	29/21
15	594.7
16	634.3	13/9
17	674
18	713.6
19	753.3	17/11
20	792.9
21	832.5	21/13, 29/18
22	872.2
23	911.8	22/13
24	951.5	19/11, 26/15
25	991.1	23/13
26	1030.8
27	1070.4	13/7
28	1110.1
29	1149.7
30	1189.4
31	1229
32	1268.6	25/12, 27/13, 29/14
33	1308.3
34	1347.9
35	1387.6	29/13
36	1427.2
37	1466.9	7/3

Harmonics

Approximation of harmonics in 37ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.6	+1.0	+18.4	-11.2	-9.6	+1.0	+7.7	+2.0	+17.8	+11.4	+19.4
	Relative (%)	-26.9	+2.6	+46.3	-28.1	-24.3	+2.6	+19.4	+5.1	+45.0	+28.8	+48.9
Steps (reduced)		30 (30)	48 (11)	61 (24)	70 (33)	78 (4)	85 (11)	91 (17)	96 (22)	101 (27)	105 (31)	109 (35)

Approximation of harmonics in 37ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-0.3	-9.6	-10.1	-2.9	+11.0	-8.6	+16.7	+7.2	+2.0	+0.8	+3.1
	Relative (%)	-0.7	-24.3	-25.6	-7.4	+27.9	-21.7	+42.2	+18.2	+5.1	+2.0	+7.9
Steps (reduced)		112 (1)	115 (4)	118 (7)	121 (10)	124 (13)	126 (15)	129 (18)	131 (20)	133 (22)	135 (24)	137 (26)