10:12:15: Difference between revisions

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 {{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 ==
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 == Notable voicings ==
-Voicings are identified with [[Kite's thoughts on hi-lo notation|Hi-lo notation]]. AOV  and CAOV stand for (condensed) [[Odd limit#Proposed extensions|all-odd voicing]].
+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:
+|+
+!Voices
-* 10:12:15 (6:5:4) - basic voicing
+![[EFR]]
-* 6:10:15 (5:3:2) - lo3, CAOV
+![[Kite's thoughts on hi-lo notation|Hi-lo name]]
-* 3:5:15 (5:3:1) - lo3hi5, AOV
+!Special properties
-* 12:15:20 (5:4:3) - 1st inversion
+|-
-* 15:20:24 (8:6:5) - 2nd inversion
+| rowspan="6" |3 voices
-* 10:15:24 (12:8:5) - hi3
+|3:5:15
+|lo3hi5
-voices:
+|AOV ([[Odd limit#Proposed extensions|all-odd voicing]])
+|-
-* 10:12:15:20 (6:5:4:3) - add8
+|6:10:15
-* 10:15:20:24 (12:8:6:5) - hi3add8
+|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 ==
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 * [[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)
+* [[70:84:105:120]] (1/(12:10:8:7)) – adds 12/7 (7-limit)
-* [[60:70:84:105]] (7:6:5:4) – a homonym of the previous chord
+* [[60:70:84:105]] (1/(7:6:5:4)) – a homonym of the previous chord
 [[Category:Minor triads|#@]] <!-- 2-digit first number -->