17/13
In 17-limit just intonation, 17/13 is the septendecimal subfourth, measuring about 464.4¢. It differs from the 4/3 perfect fourth by the comma 52/51, about 33.6¢. It is the mediant between 13/10 and 4/3 and falls in the categorically-ambiguous zone between supermajor third and perfect fourth that Margo Schulter calls interseptimal. It appears in the harmonic series between the 13th and 17th harmonics.
| Interval information |
[sound info]
It is less than 0.1 cents flat of 31edo's subfourth of 464.52¢ (12\31). In fact, a circle of 31 pure 17/13's closes with an error of only 2.74c (relative error 7.1%).
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 5 | 2\5 | 480.00 | +15.57 | +6.49 |
| 8 | 3\8 | 450.00 | -14.43 | -9.62 |
| 13 | 5\13 | 461.54 | -2.89 | -3.13 |
| 18 | 7\18 | 466.67 | +2.24 | +3.36 |
| 23 | 9\23 | 469.57 | +5.14 | +9.85 |
| 26 | 10\26 | 461.54 | -2.89 | -6.26 |
| 31 | 12\31 | 464.52 | +0.09 | +0.23 |
| 36 | 14\36 | 466.67 | +2.24 | +6.72 |
| 39 | 15\39 | 461.54 | -2.89 | -9.39 |
| 44 | 17\44 | 463.64 | -0.79 | -2.90 |
| 49 | 19\49 | 465.31 | +0.88 | +3.59 |
| 57 | 22\57 | 463.16 | -1.27 | -6.03 |
| 62 | 24\62 | 464.52 | +0.09 | +0.46 |
| 67 | 26\67 | 465.67 | +1.24 | +6.95 |
| 70 | 27\70 | 462.86 | -1.57 | -9.16 |
| 75 | 29\75 | 464.00 | -0.43 | -2.67 |
| 80 | 31\80 | 465.00 | +0.57 | +3.82 |