10:12:15

Chord information

Harmonics	10:12:15
Subharmonics	1/(6:5:4)
Intervals from root	1/1–6/5–3/2
Cents from root	0¢–316¢–702¢
Step intervals	6/5, 5/4
Step cents	316¢, 386¢
Color name	gu or g
Prime limit	5
Genus	3⋅5 (15)
Intervallic odd limit	5
Otonal odd limit	15
Utonal odd limit	5
Consistent edos (d ≥ 2)	3edo*, 12edo*, 15edo*, 19edo**, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

10:12:15 is the classical minor triad, and can also be referred to as the Ptolemaic minor triad. It is found on the iii (5⁄4) and vi (5⁄3) of Ptolemy's intense diatonic scale (Zarlino), which is perhaps the most common 5-limit diatonic. Unlike 27:32:40, which appears on the ii of the same scale, 10:12:15 is utonal.

However, there are other 5-limit diatonic scales which don't have the Ptolemaic minor triad occurring in all the same places. For instance, Aura is known to use a diatonic minor scale in which this chord only occurs on the i and iv scale degrees while using a Pythagorean minor triad (that is, 54:64:81) on the v. Conversely, in the diatonic major scale that Aura uses, this chord only really appears on the iii. Compared to its Pythagorean counterpart, the Ptolemaic major triad sounds like it's more consonant. Because of these properties, the Ptolemaic major triad has earned its status as a bread-and-butter chord in 5-limit harmony.

There are a number of possible tetrads which can be reasonably built off of this triad, such as 10:12:15:18 in the 5-limit, as well as 70:84:105:120 in the 7-limit and 110:132:165:192 in the 11-limit.