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, with the major third replaced by a minor third.

Audio of close voicings

10:12:15 Root position

12:15:20 1st inversion

15:20:24 2nd inversion

Notable voicings

Voicings are identified with Hi-lo notation. AOV and CAOV stand for (condensed) all-odd voicing.

3 voices:

• 10:12:15 (6:5:4) - close voicing
• 6:10:15 (5:3:2) - lo3, CAOV
• 3:5:15 (5:3:1) - lo3hi5, AOV
• 12:15:20 (5:4:3) - 1st inversion
• 15:20:24 (8:6:5) - 2nd inversion
• 10:15:24 (12:8:5) - hi3

4 voices:

• 10:12:15:20 (6:5:4:3) - add8
• 10:15:20:24 (12:8:6:5) - hi3add8

Related chords

Melodic inversion: 4:5:6.

Plausible homonyms: 12:15:20 (1/1 - 5/4 - 5/3), a maj6no5 chord.

Notable extensions (5-limit except where noted):

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