10:12:15: Difference between revisions

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'''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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* [[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|#@]]

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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 ==
@@ Line 61: / Line 63: @@
 * [[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 -->