From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
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 (log2 nd) 8.67243
Weil height (log2 max(n, d)) 9.16993
Wilson height (sopfr (nd)) 26
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.54683 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:

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.

See also