17/16

Interval information

Ratio	17/16
Subgroup monzo	2.17 [-4 1⟩
Size in cents	104.9554¢
Name	large septendecimal semitone
Color name	17o2, iso 2nd
FJS name	[math]\displaystyle{ \text{m2}^{17} }[/math]
Special properties	superparticular, reduced, reduced harmonic
Tenney height (log2 nd)	8.08746
Weil height (log2 max(n, d))	8.17493
Wilson height (sopfr(nd))	25
[sound info]
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In 17-limit just intonation, 17/16 is the 17th harmonic, octave reduced, and may be called the large septendecimal semitone. Measuring about 105¢, it is close to the 12edo semitone of 100¢, and thus 12edo can be said to approximate it closely. In a chord, it can function similarly to a jazz "minor ninth" – for instance, 8:10:12:14:17 (although here the interval is 17/8, which is a little less harsh sounding than 17/16). In 17-limit JI, it is treated as the next basic consonance after 13 and 15.

17/16 is one of two superparticular semitones in the 17-limit; the other is 18/17, which measures about 99¢. The difference between them is 289/288, about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out.

There exists a disagreement in different notation systems on whether 17/16 should be notated as a diatonic semitone or a chromatic semitone. In Functional Just System, it is a diatonic semitone, whereas in Helmholtz-Ellis notation, it is a chromatic semitone.

See also

• 32/17 – its octave complement
• 24/17 – its fifth complement
• 17/8 – same interval, one octave higher
• Gallery of just intervals
• List of superparticular intervals