37ed4

← 35ed4

37ed4

39ed4 →

Prime factorization	37 (prime)
Step size	64.8649 ¢
Octave	19\37ed4 (1232.43 ¢)
Twelfth	29\37ed4 (1881.08 ¢)
Consistency limit	1
Distinct consistency limit	1

37ED4 is an equal tuning which divides the 4/1 double octave into 37 steps of approximately 64.865¢. As an ED4 system, it is equivalent to taking every other tone of 37edo. All the intervals of 37ED4 are thus the same as or an octave away from a corresponding interval in 37edo.

65cET is a slightly stretched version of 37ED4, in which the 37th degree is 5¢ sharp of 4/1.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	64.9	26/25
2	129.7
3	194.6	19/17, 29/26
4	259.5	7/6, 22/19, 29/25
5	324.3	23/19
6	389.2
7	454.1	22/17
8	518.9	23/17
9	583.8	7/5
10	648.6
11	713.5
12	778.4	11/7
13	843.2
14	908.1
15	973
16	1037.8
17	1102.7
18	1167.6
19	1232.4
20	1297.3
21	1362.2	11/5
22	1427	25/11
23	1491.9	26/11
24	1556.8
25	1621.6
26	1686.5
27	1751.4
28	1816.2
29	1881.1
30	1945.9
31	2010.8
32	2075.7
33	2140.5
34	2205.4	25/7
35	2270.3	26/7
36	2335.1
37	2400

Harmonics

Approximation of harmonics in 37ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+32.4	-20.9	+0.0	+2.9	+11.6	+4.1	+32.4	+23.1	-29.6	+0.0	-20.9
	Relative (%)	+50.0	-32.2	+0.0	+4.4	+17.8	+6.4	+50.0	+35.6	-45.6	+0.1	-32.2
Steps (reduced)		19 (19)	29 (29)	37 (0)	43 (6)	48 (11)	52 (15)	56 (19)	59 (22)	61 (24)	64 (27)	66 (29)

Approximation of harmonics in 37ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-29.7	-28.3	-18.0	+0.0	+24.8	-9.3	+26.8	+2.9	-16.7	-32.4	+20.4
	Relative (%)	-45.8	-43.6	-27.7	+0.0	+38.2	-14.4	+41.3	+4.4	-25.8	-49.9	+31.4
Steps (reduced)		68 (31)	70 (33)	72 (35)	74 (0)	76 (2)	77 (3)	79 (5)	80 (6)	81 (7)	82 (8)	84 (10)

Music

• Happy Birthday by Todd Harrop