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.