32/17
| Ratio | 32/17 |
| Subgroup monzo | 2.17 [5 -1⟩ |
| Size in cents | 1095.0446¢ |
| Names | septendecimal major seventh, septendecimal diminished octave |
| Color name | 17u7, su 7th |
| FJS name | [math]\text{M7}_{17}[/math] |
| Special properties | reduced, reduced subharmonic |
| Tenney height (log2 nd) | 9.08746 |
| Weil height (log2 max(n, d)) | 10 |
| Wilson height (sopfr(nd)) | 27 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.22906 bits |
[sound info] | |
| open this interval in xen-calc | |
In 17-limit just intonation, 32/17 is the septendecimal major seventh or the septendecimal diminished octave, depending on how one views it. It is also the octave-reduced 17th subharmonic. Its inversion is 17/16, the octave-reduced 17th harmonic. Measuring about 1095 ¢, it is the mediant between 15/8 and 17/9.
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 32/17 should be a major seventh or a diminished octave. The major seventh view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 243/128, the Pythagorean major seventh. The diminished octave view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 4096/2187, the Pythagorean diminished octave.
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.