17/15
Jump to navigation
Jump to search
Ratio | 17/15 |
Factorization | 3^{-1} × 5^{-1} × 17 |
Monzo | [0 -1 -1 0 0 0 1⟩ |
Size in cents | 216.68669¢ |
Name | diatismic whole tone |
Color name | 17og3, sogu 3rd |
FJS name | [math]\text{d3}^{17}_{5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 7.99435 |
Weil height (log_{2} max(n, d)) | 8.17493 |
Wilson height (sopfr (nd)) | 25 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.2035 bits |
[sound info] | |
open this interval in xen-calc |
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.).