17/12
Ratio | 17/12 |
Subgroup monzo | 2.3.17 [-2 -1 1⟩ |
Size in cents | 603.00041¢ |
Name | larger septendecimal tritone |
Color name | 17o5, iso 5th |
FJS name | [math]\text{d5}^{17}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 7.67243 |
Weil height (log_{2} max(n, d)) | 8.17493 |
Wilson height (sopfr (nd)) | 24 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.23204 bits |
[sound info] | |
open this interval in xen-calc |
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.