13ed7/3
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Prime factorization
13 (prime)
Step size
112.836¢
Octave
11\13ed7/3 (1241.2¢)
Twelfth
17\13ed7/3 (1918.22¢)
Consistency limit
3
Distinct consistency limit
3
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| ← 12ed7/3 | 13ed7/3 | 14ed7/3 → |
13 equal divisions of 7/3 (abbreviated 13ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 13 equal parts of about 113 ¢ each. Each step represents a frequency ratio of (7/3)1/13, or the 13th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 112.836 | 15/14 |
| 2 | 225.672 | |
| 3 | 338.509 | 6/5, 11/9, 23/19 |
| 4 | 451.345 | 9/7, 17/13 |
| 5 | 564.181 | 7/5 |
| 6 | 677.017 | 3/2, 19/13, 22/15 |
| 7 | 789.854 | 11/7, 14/9 |
| 8 | 902.69 | 5/3 |
| 9 | 1015.526 | 9/5 |
| 10 | 1128.362 | 21/11 |
| 11 | 1241.198 | |
| 12 | 1354.035 | 11/5 |
| 13 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +41.2 | +16.3 | -30.4 | +34.6 | -55.4 | +16.3 | +10.8 | +32.5 | -37.0 | +23.6 | -14.2 |
| Relative (%) | +36.5 | +14.4 | -27.0 | +30.7 | -49.1 | +14.4 | +9.5 | +28.8 | -32.8 | +20.9 | -12.6 | |
| Steps (reduced) |
11 (11) |
17 (4) |
21 (8) |
25 (12) |
27 (1) |
30 (4) |
32 (6) |
34 (8) |
35 (9) |
37 (11) |
38 (12) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | -55.4 | +50.9 | +52.0 | -53.0 | -39.1 | -19.9 | +4.2 | +32.5 | -48.0 | -12.1 |
| Relative (%) | -35.4 | -49.1 | +45.1 | +46.0 | -47.0 | -34.7 | -17.6 | +3.7 | +28.8 | -42.6 | -10.8 | |
| Steps (reduced) |
39 (0) |
40 (1) |
42 (3) |
43 (4) |
43 (4) |
44 (5) |
45 (6) |
46 (7) |
47 (8) |
47 (8) |
48 (9) | |