13ed7/4
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Prime factorization
13 (prime)
Step size
74.5251¢
Octave
16\13ed7/4 (1192.4¢)
(semiconvergent)
Twelfth
26\13ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 12ed7/4 | 13ed7/4 | 14ed7/4 → |
(semiconvergent)
13 equal divisions of 7/4 (abbreviated 13ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 13 equal parts of about 74.5 ¢ each. Each step represents a frequency ratio of (7/4)1/13, or the 13th root of 7/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 74.5 | 20/19, 22/21, 23/22 |
| 2 | 149.1 | 12/11, 13/12, 23/21 |
| 3 | 223.6 | 8/7, 15/13, 17/15 |
| 4 | 298.1 | 13/11, 19/16 |
| 5 | 372.6 | 5/4, 21/17 |
| 6 | 447.2 | 17/13, 22/17 |
| 7 | 521.7 | 15/11, 19/14, 23/17 |
| 8 | 596.2 | 7/5, 10/7, 17/12 |
| 9 | 670.7 | 22/15 |
| 10 | 745.3 | 17/11, 23/15 |
| 11 | 819.8 | 8/5, 21/13 |
| 12 | 894.3 | 22/13 |
| 13 | 968.8 | 7/4, 23/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.6 | +35.7 | -15.2 | -28.9 | +28.1 | -15.2 | -22.8 | -3.1 | -36.5 | +22.1 | +20.5 |
| Relative (%) | -10.2 | +47.9 | -20.4 | -38.8 | +37.7 | -20.4 | -30.6 | -4.2 | -49.0 | +29.6 | +27.5 | |
| Steps (reduced) |
16 (3) |
26 (0) |
32 (6) |
37 (11) |
42 (3) |
45 (6) |
48 (9) |
51 (12) |
53 (1) |
56 (4) |
58 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +31.0 | -22.8 | +6.8 | -30.4 | +13.7 | -10.7 | -29.8 | +30.4 | +20.5 | +14.5 | +12.1 |
| Relative (%) | +41.6 | -30.6 | +9.1 | -40.8 | +18.4 | -14.4 | -40.0 | +40.8 | +27.5 | +19.4 | +16.2 | |
| Steps (reduced) |
60 (8) |
61 (9) |
63 (11) |
64 (12) |
66 (1) |
67 (2) |
68 (3) |
70 (5) |
71 (6) |
72 (7) |
73 (8) | |