17/15
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Ratio
17/15
Factorization
3-1 × 5-1 × 17
Monzo
[0 -1 -1 0 0 0 1⟩
Size in cents
216.6867¢
Name
diatismic whole tone
Color name
17og3, sogu 3rd
FJS name
[math]\text{d3}^{17}_{5}[/math]
Special properties
reduced
Tenney height (log2 nd)
7.99435
Weil height (log2 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
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
[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.).