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 a utonal minor triad, known as the just minor triad, classical minor triad, or Ptolemaic minor triad. It is a common chord that appears as a counterpart to the widespread otonal major triad of 4:5:6, the major third swapped with a minor third.

Rotations around the octave

10:12:15 "Root position"

12:15:20 "1st inversion"

15:20:24 "2nd inversion"

Voicings and rotations around two octaves

Voicing Rotation	Root	'3	'15	'3'15
On 3	12:15:40	6:10:15	6:15:20	12:15:20
On 5	10:12:15	10:15:24	5:6:15	5:12:15
On 15	15:40:48	15:24:40	15:20:24	15:20:48

Related chords

Common tetrads based on this triad (5-limit except where noted):

• 4:5:6 – chord inversion
• 10:12:15:18 adds 9/5
• 30:36:45:50 adds 5/3
• 60:70:84:105 – adds 8/7 below root (7-limit)
• 70:84:105:120 – adds 12/7 (7-limit); homonym of 60:70:84:105