37ed7/3

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 36ed7/3

37ed7/3

38ed7/3 →

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	39.645
2	79.29	22/21, 23/22
3	118.935	15/14, 29/27
4	158.581	23/21
5	198.226	19/17, 28/25
6	237.871
7	277.516	27/23
8	317.161	6/5
9	356.806	27/22
10	396.452	29/23
11	436.097	9/7
12	475.742	29/22
13	515.387
14	555.032	29/21
15	594.677
16	634.323	13/9
17	673.968
18	713.613
19	753.258	17/11
20	792.903
21	832.548	21/13, 29/18
22	872.194
23	911.839	22/13
24	951.484	19/11, 26/15
25	991.129	23/13
26	1030.774
27	1070.419	13/7
28	1110.064
29	1149.71
30	1189.355
31	1229
32	1268.645	25/12, 27/13, 29/14
33	1308.29
34	1347.935
35	1387.581	29/13
36	1427.226
37	1466.871	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)