37ed7/4
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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
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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
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) |
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) |