10:12:15: Difference between revisions

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{{Infobox Chord|ColorName=gu or g}}
{{Infobox Chord|ColorName=gu or g}}


'''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.  
'''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 [[5L 2s|diatonic]] scale of [[meantone]] temperament, as the minor third formed from stacking three [[4/3|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 ==
== Audio of close voicings ==

Latest revision as of 09:32, 30 December 2025

Chord information
Harmonics 10:12:15
Subharmonics 1/(6:5:4)
Intervals from root 1/16/53/2
Cents from root 316¢702¢
Step intervals 6/5, 5/4
Step cents 316¢, 386¢
Color name gu or g
Prime limit 5
Genus 35 (15)
Intervallic odd limit 5
Otonal odd limit 15
Utonal odd limit 5
Consistent edos (d ≥ 2) 3edo*, 12edo*, 15edo*, 19edo**, …

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

10:12:15 Root position
12:15:20 1st inversion
15:20:24 2nd inversion

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):