37edt

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← 36edt37edt38edt →
Prime factorization 37 (prime)
Step size 51.4042¢ 
Octave 23\37edt (1182.3¢)
Consistency limit 2
Distinct consistency limit 2

37EDT is the equal division of the third harmonic into 37 parts of 51.4042 cents each, corresponding to 23.4355 edo. The tunings supplied by 111EDT (or 70edo) cannot be used for all low-limit just intervals, but they can be used on the 17-limit 8.3.100.70.22.52.68 just intonation subgroup, tempering out 289/288, 325/324, 352/351, 385/384, 561/560, 595/594, 625/624, 676/675, 1089/1088, 1156/1155, 1225/1224, and 1331/1326.

Harmonics

Approximation of prime harmonics in 37edt
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -17.7 +0.0 -10.5 +23.9 +12.4 -19.8 -21.6 -8.5 +20.6 -20.9 +17.9
Relative (%) -34.4 +0.0 -20.4 +46.4 +24.2 -38.5 -41.9 -16.5 +40.0 -40.7 +34.7
Steps
(reduced)
23
(23)
37
(0)
54
(17)
66
(29)
81
(7)
86
(12)
95
(21)
99
(25)
106
(32)
113
(2)
116
(5)
Approximation of prime harmonics in 37edt
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) +20.0 -3.5 +16.8 +17.0 +14.7 -16.8 -23.1 +20.1 +22.5 -25.6 -8.1
Relative (%) +38.8 -6.9 +32.7 +33.1 +28.5 -32.7 -45.0 +39.1 +43.8 -49.8 -15.8
Steps
(reduced)
122
(11)
125
(14)
127
(16)
130
(19)
134
(23)
137
(26)
138
(27)
142
(31)
144
(33)
144
(33)
147
(36)

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 51.404
2 102.808 18/17
3 154.213 23/21
4 205.617
5 257.021 22/19, 29/25
6 308.425 6/5
7 359.829 27/22
8 411.234 14/11, 19/15
9 462.638 17/13
10 514.042
11 565.446 18/13, 25/18
12 616.85
13 668.254 22/15, 25/17, 28/19
14 719.659
15 771.063 14/9
16 822.467 29/18
17 873.871
18 925.275 17/10, 29/17
19 976.68
20 1028.084
21 1079.488 28/15
22 1130.892 25/13, 27/14
23 1182.296
24 1233.701
25 1285.105
26 1336.509 13/6
27 1387.913 29/13
28 1439.317
29 1490.721
30 1542.126 22/9
31 1593.53 5/2
32 1644.934
33 1696.338
34 1747.742
35 1799.147 17/6
36 1850.551 29/10
37 1901.955 3/1