24/17
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
In 17-limit just intonation, 24/17 is the small septendecimal tritone, measuring very nearly 597¢. It is the mediant between 7/5 and 17/12, the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered edo systems, including 12edo. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. 22edo is another good edo system for using the half-octave in this way.
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 24/17 specifically:
- In Functional Just System, it is an augmented fourth, separated by 4131/4096 from the Pythagorean augmented fourth (729/512).
- In Helmholtz-Ellis notation, it is a diminished fifth, separated by 2187/2176 from the Pythagorean diminished fifth (1024/729).
The term small septendecimal tritone omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of 17/12.