17/9

Interval information

Ratio	17/9
Subgroup monzo	3.17 [-2 1⟩
Size in cents	1101.045¢
Name	large septendecimal major seventh
Color name	17o8, iso octave
FJS name	[math]\displaystyle{ \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
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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

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.

See also

• 18/17 – its octave complement
• Gallery of Just Intervals