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 | 216.68669¢ |
| 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 | |
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.).