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	64.865	26/25
2	129.73
3	194.595	19/17, 29/26
4	259.459	7/6, 22/19, 29/25
5	324.324	23/19
6	389.189
7	454.054	22/17
8	518.919	23/17
9	583.784	7/5
10	648.649
11	713.514
12	778.378	11/7
13	843.243
14	908.108
15	972.973
16	1037.838
17	1102.703
18	1167.568
19	1232.432
20	1297.297
21	1362.162	11/5
22	1427.027	25/11
23	1491.892	26/11
24	1556.757
25	1621.622
26	1686.486
27	1751.351
28	1816.216
29	1881.081
30	1945.946
31	2010.811
32	2075.676
33	2140.541
34	2205.405	25/7
35	2270.27	26/7
36	2335.135
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