15/11
(Redirected from 15 11)
| Interval information |
undecimal grave infra-augmented fourth
[sound info]
The interval 15/11, known most frequently as the undecimal augmented fourth, is the difference between the 11th and 15th partials of the harmonic series. It is 536.95 cents wide, exactly 45/44 larger than a perfect fourth, and almost exactly a sixth-tone sharper than a 12edo fourth. It is narrower than 11/8 by exactly 121/120, and is wider than 27/20 by exactly 100/99. Additionally, it is narrower than 243/176 by exactly 81/80, which lends to it being called the undecimal grave infra-augmented fourth. 15/11 can be called a superfourth, as it falls between the interval categories of perfect fourth and tritone. 4 steps of 9edo is an excellent approximation for 15/11.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 9 | 4\9 | 533.33 | -3.62 | -2.71 |
| 11 | 5\11 | 545.45 | +8.50 | +7.80 |
| 18 | 8\18 | 533.33 | -3.62 | -5.43 |
| 20 | 9\20 | 540.00 | +3.05 | +5.08 |
| 27 | 12\27 | 533.33 | -3.62 | -8.14 |
| 29 | 13\29 | 537.93 | +0.98 | +2.37 |
| 38 | 17\38 | 536.84 | -0.11 | -0.34 |
| 47 | 21\47 | 536.17 | -0.78 | -3.06 |
| 49 | 22\49 | 538.78 | +1.82 | +7.45 |
| 56 | 25\56 | 535.71 | -1.24 | -5.77 |
| 58 | 26\58 | 537.93 | +0.98 | +4.74 |
| 65 | 29\65 | 535.38 | -1.57 | -8.48 |
| 67 | 30\67 | 537.31 | +0.36 | +2.02 |
| 76 | 34\76 | 536.84 | -0.11 | -0.69 |
| 78 | 35\78 | 538.46 | +1.51 | +9.82 |