17/12
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
In 17-limit just intonation, 17/12 is the large septendecimal tritone, measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, 24/17, and the interval that separates them is the small comma 289/288, about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered edo system contains a close approximation to these intervals.
17/12 is the mediant between the two septimal tritones 7/5 and 10/7.
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 17/12 specifically:
- In Functional Just System, it is a diminished fifth, separated by 4131/4096 from the Pythagorean diminished fifth (1024/729).
- In Helmholtz-Ellis notation, it is an augmented fourth, separated by 2187/2176 from the Pythagorean augmented fourth (729/512).
The term large septendecimal tritone omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.