24/17
Ratio | 24/17 |
Subgroup monzo | 2.3.17 [3 1 -1⟩ |
Size in cents | 596.99959¢ |
Name | small septendecimal tritone |
Color name | 17u4, su 4th |
FJS name | [math]\text{A4}_{17}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 8.67243 |
Weil height (log_{2} max(n, d)) | 9.16993 |
Wilson height (sopfr (nd)) | 26 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.21179 bits |
[sound info] | |
open this interval in xen-calc |
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.