17/16
| Interval information |
minor diatonic semitone
reduced,
reduced harmonic
[sound info]
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, 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, 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¢. It is 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 17/16s and 11/6 is approximately 0.2¢, while the difference between 13 17/16s and 11/5 is approximately 0.6¢.
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 17/16 should be a diatonic semitone or a chromatic semitone. In Functional Just System, it is a diatonic semitone, separated by 4131/4096 from 256/243, the Pythagorean diatonic semitone. It is also called the minor diatonic semitone, which contrasts the 5-limit major diatonic semitone of 16/15 by 256/255, about 6.8¢. In Helmholtz-Ellis notation, it is a chromatic semitone, separated by 2187/2176 from 2187/2048, the Pythagorean chromatic semitone. The term "large septendecimal semitone" omits the diatonic/chromatic part and only describes its melodic property i.e. the size.
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
- 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