37ed4

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← 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