17/9
Ratio | 17/9 |
Subgroup monzo | 3.17 [-2 1⟩ |
Size in cents | 1101.0454¢ |
Name | large septendecimal major seventh |
Color name | 17o8, iso octave |
FJS name | [math]\text{d8}^{17}[/math] |
Special properties | reduced |
Tenney height (log2 nd) | 7.25739 |
Weil height (log2 max(n, d)) | 8.17493 |
Wilson height (sopfr (nd)) | 23 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.23138 bits |
[sound info] | |
open this interval in xen-calc |
In 17-limit just intonation, 17/9 is the septendecimal diminished octave or the septendecimal major seventh, depending on how one views it. It measures about 1101¢. It is the mediant between 15/8 and 2/1. Its inversion is 18/17, the "small septendecimal semitone".
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 4096/2187, the Pythagorean diminished octave. The major seventh view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 243/128, the Pythagorean major seventh.
In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded circle-of-fifths notation is to prepare a Pythagorean comma accidental so that the interval can be notated in either category.