10:12:15: Difference between revisions
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{{Infobox Chord}} | {{Infobox Chord|ColorName=gu or g}} | ||
'''10:12:15''' is a 5 | '''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 == | |||
[[File:SculpEufaDem10-12-15-onD.mp3|none|thumb|10:12:15 Root position]] | |||
[[File:SculpEufaDem12-15-20-onD.mp3|none|thumb|12:15:20 1st inversion]] | |||
[[File:SculpEufaDem15-20-24-onD.mp3|none|thumb|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. | |||
{| class="wikitable" | |||
|+ | |||
!Voices | |||
![[EFR]] | |||
![[Kite's thoughts on hi-lo notation|Hi-lo name]] | |||
!Special properties | |||
|- | |||
| rowspan="6" |3 voices | |||
|3:5:15 | |||
|lo3hi5 | |||
|AOV ([[Odd limit#Proposed extensions|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 | |||
|- | |||
| rowspan="2" |4 voices | |||
|10:12:15:20 | |||
|add8 | |||
| | |||
|- | |||
|10:15:20:24 | |||
|hi3add8 | |||
| | |||
|} | |||
== Related chords == | |||
Melodic inversion: [[4:5:6]]. | |||
Plausible [[Chord homonym|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 | |||
[[Category:Minor triads|#@]] <!-- 2-digit first number --> | |||