31ed7/3
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Prime factorization
31 (prime)
Step size
47.3184¢
Octave
25\31ed7/3 (1182.96¢)
Twelfth
40\31ed7/3 (1892.74¢)
Consistency limit
3
Distinct consistency limit
3
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31 equal divisions of 7/3 (abbreviated 31ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 31 equal parts of about 47.3 ¢ each. Each step represents a frequency ratio of (7/3)1/31, or the 31st root of 7/3.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 47.318 | |
2 | 94.637 | |
3 | 141.955 | 25/23 |
4 | 189.274 | 10/9, 19/17 |
5 | 236.592 | |
6 | 283.91 | 13/11 |
7 | 331.229 | 23/19 |
8 | 378.547 | 26/21 |
9 | 425.866 | 9/7 |
10 | 473.184 | 17/13, 25/19 |
11 | 520.503 | 23/17, 27/20 |
12 | 567.821 | |
13 | 615.139 | 10/7 |
14 | 662.458 | 19/13, 22/15, 25/17 |
15 | 709.776 | 3/2 |
16 | 757.095 | 14/9, 17/11 |
17 | 804.413 | |
18 | 851.731 | |
19 | 899.05 | |
20 | 946.368 | 19/11, 26/15 |
21 | 993.687 | 23/13 |
22 | 1041.005 | |
23 | 1088.324 | |
24 | 1135.642 | 25/13, 27/14 |
25 | 1182.96 | |
26 | 1230.279 | |
27 | 1277.597 | 21/10, 23/11 |
28 | 1324.916 | 15/7 |
29 | 1372.234 | 11/5 |
30 | 1419.552 | 25/11 |
31 | 1466.871 | 7/3 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -17.0 | -9.2 | +13.2 | +5.5 | +21.1 | -9.2 | -3.8 | -18.4 | -11.6 | +12.7 | +4.0 |
Relative (%) | -36.0 | -19.5 | +28.0 | +11.6 | +44.5 | -19.5 | -8.0 | -39.0 | -24.4 | +26.8 | +8.5 | |
Steps (reduced) |
25 (25) |
40 (9) |
51 (20) |
59 (28) |
66 (4) |
71 (9) |
76 (14) |
80 (18) |
84 (22) |
88 (26) |
91 (29) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +7.4 | +21.1 | -3.7 | -20.8 | +16.2 | +11.8 | +12.9 | +18.7 | -18.4 | -4.3 | +13.3 |
Relative (%) | +15.6 | +44.5 | -7.9 | -44.0 | +34.2 | +25.0 | +27.2 | +39.5 | -39.0 | -9.2 | +28.2 | |
Steps (reduced) |
94 (1) |
97 (4) |
99 (6) |
101 (8) |
104 (11) |
106 (13) |
108 (15) |
110 (17) |
111 (18) |
113 (20) |
115 (22) |