17/16

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Interval information
Ratio 17/16
Subgroup monzo 2.17 [-4 1
Size in cents 104.95541¢
Name large septendecimal semitone
minor diatonic semitone
Color name 17o2, iso 2nd
FJS name [math]\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
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.28419 bits

[sound info]
open this interval in xen-calc
English Wikipedia has an article on:

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, although an even better approximation is available in 23edo. 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, 17/1 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, the small septendecimal semitone, 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.

17/16 is almost exactly 1/3 of the 6/5 minor third. The difference between 6/5 and three 17/16 semitones is 24576/24565, an interval of approximately 0.8¢. 17/16 is also almost exactly 1/8 of 13/8, with the difference between 13/8 and (17/16)8 being approximately 0.9¢. The difference between ten 17/16's and 11/6 is approximately 0.2¢, while the difference between thirteen 17/16's and 11/5 is approximately 0.6¢.

Terminology and notation

Conceptualization systems disagree on whether 17/16 should be a diatonic semitone or a chromatic semitone, and as a result the disagreement propagates to all intervals of HC17. See 17-limit for a detailed discussion.

For 17/16 specifically:

The term large septendecimal semitone omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal semitone of 18/17.

See also