32/17

Interval information

Ratio	32/17
Subgroup monzo	2.17 [5 -1⟩
Size in cents	1095.045¢
Names	septendecimal major seventh, septendecimal diminished octave
Color name	17u7, su 7th
FJS name	[math]\displaystyle{ \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
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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

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.

See also

• 17/16 – its octave complement
• Gallery of just intervals