32/17

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Interval information
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
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.

See also