14:21:24

Chord information

Harmonics	14:21:24
Subharmonics	1/(12:8:7)
Intervals from root	1/1–3/2–12/7
Cents from root	0¢–702¢–933¢
Step intervals	3/2, 8/7
Step cents	702¢, 231¢
Prime limit	7
Genus	3⋅7 (21)
Intervallic odd limit	7
Otonal odd limit	21
Utonal odd limit	7
Consistent edos (d ≥ 2)	5edo**, 10edo*, 22edo*, 26edo*, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

14:21:24 is a 7-limit chord found as a subset of the subharmonic sixth chord, 70:84:105:120, or of the septimal major sixth chord, 14:18:21:24. Due to having no fives, it is the first utonal chord that deviates from traditional harmony. As such, it is a candidate for metallic harmony, a form of extraclassical tonality that employs 7 instead of 5 as its other prime.

Its first rotation, 21:24:28, is significant because it consists of the intervals 8/7 and 7/6 stacked on top of each other. The intervals in this chord divide the perfect fourth rather than the perfect fifth, and contrast by 49/48, similarly to how 6/5 and 5/4 contrast by 25/24 in 10:12:15. By swapping the order of 8/7 and 7/6, we get the otonal inverse of 21:24:28, that being 6:7:8.

Another notable setting is the open voicing 7:12:21, which shares the property with 21:24:28 that its intervals, 12/7 and 7/4, contrast by 49/48, but they divide the perfect twelfth instead. Its otonal version is 4:7:12, an open voicing of 4:6:7.

Its second rotation, 12:14:21, is also significant because it functions as the fifthless version of the septimal minor seventh chord, 12:14:18:21.