10:12:15
| Chord information |
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. It occurs as a minor triad in the diatonic scale of meantone temperament, as the minor third formed from stacking three perfect fourths octave reduced, 32/27, is equated with 6/5 due to vanishing of 81/80.
It is not the only minor triad in just intonation; other minor triads include 54:64:81 (Pythagorean minor triad), 6:7:9 (septimal minor triad), and 16:19:24.
Audio of close voicings
Notable voicings
Voicings are sorted by Wilson norm. This list is only a brief overview, see Voicings of 10:12:15 for a more comprehensive list.
| Voices | EFR | Hi-lo name | Special properties |
|---|---|---|---|
| 3 voices | 3:5:15 | lo3hi5 | AOV (all-odd voicing) |
| 6:10:15 | lo3 | CAOV (condensed AOV) | |
| 10:12:15 | basic | ||
| 10:15:24 | hi3 | ||
| 12:15:20 | hiR | 1st inversion | |
| 15:20:24 | lo5 | 2nd inversion | |
| 4 voices | 10:12:15:20 | add8 | |
| 10:15:20:24 | 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 (1/(12:10:8:7)) – adds 12/7 (7-limit)
- 60:70:84:105 (1/(7:6:5:4)) – a homonym of the previous chord