17/15
Jump to navigation
Jump to search
| Interval information |
[sound info]
In 17-limit just intonation, 17/15 is the diatismic whole tone measuring about 216.7 ¢. It exceeds the Pythagorean whole tone (9/8) by a diatisma (136/135), hence the name. It is the mediant of 9/8 and 8/7, as it is (9 + 8)/(8 + 7). It is found in the harmonic series between the 17th and 15th harmonics. 11edo's second degree, measuring approximately 218.2¢, is close in size to 17/15 – indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 5 | 1\5 | 240.00 | +23.31 | +9.71 |
| 6 | 1\6 | 200.00 | -16.69 | -8.34 |
| 11 | 2\11 | 218.18 | +1.50 | +1.37 |
| 17 | 3\17 | 211.76 | -4.92 | -6.97 |
| 22 | 4\22 | 218.18 | +1.50 | +2.74 |
| 28 | 5\28 | 214.29 | -2.40 | -5.60 |
| 33 | 6\33 | 218.18 | +1.50 | +4.11 |
| 39 | 7\39 | 215.38 | -1.30 | -4.23 |
| 44 | 8\44 | 218.18 | +1.50 | +5.48 |
| 50 | 9\50 | 216.00 | -0.69 | -2.86 |
| 55 | 10\55 | 218.18 | +1.50 | +6.85 |
| 61 | 11\61 | 216.39 | -0.29 | -1.49 |
| 66 | 12\66 | 218.18 | +1.50 | +8.22 |
| 67 | 12\67 | 214.93 | -1.76 | -9.83 |
| 72 | 13\72 | 216.67 | -0.02 | -0.12 |
| 77 | 14\77 | 218.18 | +1.50 | +9.59 |
| 78 | 14\78 | 215.38 | -1.30 | -8.46 |