37ed7/4

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← 36ed7/437ed7/438ed7/4 →
Prime factorization 37 (prime)
Step size 26.1845¢ 
Octave 46\37ed7/4 (1204.49¢)
Twelfth 73\37ed7/4 (1911.47¢)
Consistency limit 4
Distinct consistency limit 3

37 equal divisions of 7/4 (abbreviated 37ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 37 equal parts of about 26.2 ¢ each. Each step represents a frequency ratio of (7/4)1/37, or the 37th root of 7/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 26.184
2 52.369
3 78.553 22/21
4 104.738
5 130.922 13/12, 14/13
6 157.107 12/11
7 183.291 29/26
8 209.476 9/8, 17/15
9 235.66 8/7, 23/20
10 261.845 7/6
11 288.029 13/11, 20/17
12 314.214
13 340.398 11/9
14 366.583 16/13, 26/21
15 392.767
16 418.952 14/11
17 445.136
18 471.321 21/16, 29/22
19 497.505 4/3
20 523.69 19/14, 23/17
21 549.874 11/8, 26/19
22 576.059
23 602.243
24 628.428
25 654.612 16/11, 19/13
26 680.797
27 706.981 3/2
28 733.166 23/15, 29/19
29 759.35 14/9
30 785.535 11/7
31 811.719
32 837.903 13/8, 21/13
33 864.088
34 890.272
35 916.457 17/10, 22/13
36 942.641 19/11
37 968.826 7/4

Harmonics

Approximation of harmonics in 37ed7/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.5 +9.5 +9.0 -10.8 -12.2 +9.0 -12.7 -7.2 -6.3 +12.0 -7.7
Relative (%) +17.1 +36.3 +34.3 -41.1 -46.5 +34.3 -48.6 -27.3 -24.0 +45.9 -29.4
Steps
(reduced)
46
(9)
73
(36)
92
(18)
106
(32)
118
(7)
129
(18)
137
(26)
145
(34)
152
(4)
159
(11)
164
(16)
Approximation of harmonics in 37ed7/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +10.8 -12.7 -1.2 -8.2 -8.5 -2.7 +8.5 -1.8 -7.7 -9.7 -8.1
Relative (%) +41.4 -48.6 -4.8 -31.5 -32.3 -10.2 +32.3 -6.8 -29.4 -37.0 -30.9
Steps
(reduced)
170
(22)
174
(26)
179
(31)
183
(35)
187
(2)
191
(6)
195
(10)
198
(13)
201
(16)
204
(19)
207
(22)