10:12:15: Difference between revisions

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'''10:12:15''' is the ~~just~~ [[minor triad]], also known as the '''~~Ptolemaic~~ minor triad'''.

'''10:12:15''' is the utonal [[minor triad]], also known as the '''classical minor triad, classical minor triad,''' or more generally - albeit less precisely - as the '''just major triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.

== Rotations around the octave ==

[[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"]]

== Voicings and rotations around two octaves ==

{| class="wikitable sortable" style="text-align:center;"

|+

! style="width:90px;" {{diagonal split header|Rotation|Voicing}}

! style="width:90px;" | Root

! style="width:90px;" | '3

! style="width:90px;" | '15

! style="width:90px;" | '''<nowiki/>'''<nowiki/>'3'15

|-

! style="width:90px;" | On 3

| style="width:90px;" data-sort-value="012-015-040" | 12:15:40

| style="width:90px;" data-sort-value="006-010-015" | 6:10:15

| style="width:90px;" data-sort-value="006-015-020" | 6:15:20

| style="width:90px;" data-sort-value="012-015-020" | ''12:15:20''

|-

! style="width:90px;" | On 5

| style="width:90px;" data-sort-value="010-012-015" | ''10:12:15''

| style="width:90px;" data-sort-value="010-015-024" | 10:15:24

| style="width:90px;" data-sort-value="005-006-015" | 5:6:15

| style="width:90px;" data-sort-value="005-012-015" | 5:12:15

|-

! style="width:90px;" | On 15

| style="width:90px;" data-sort-value="015-040-048" | 15:40:48

| style="width:90px;" data-sort-value="015-024-040" | 15:24:40

| style="width:90px;" data-sort-value="015-020-024" | ''15:20:24''

| style="width:90px;" data-sort-value="015-020-048" | 15:20:48

|}

== Related chords ==

Common tetrads based on this triad (5-limit except where noted):

* [[10:12:15:18]] adds 9/5

* [[4:5:6]] - chord inversion

* [[30:36:45:50]] adds 5/3

* [[10:12:15:18]] adds [[9/5]]

* [[70:84:105~~:120~~]] ~~(12:10:~~8~~:7) adds 12~~/7 (7-limit)

* [[30:36:45:50]] adds [[5/3]]

* [[60:70:84:105]] - adds 8/7 (7-limit)

~~{{todo|inline=1|expand}}~~

[[Category:Minor triads|#@]]

@@ Line 1: / Line 1: @@
 {{Infobox Chord|ColorName=gu or g}}
-'''10:12:15''' is the just [[minor triad]], also known as the '''Ptolemaic minor triad'''.
+'''10:12:15''' is the utonal [[minor triad]], also known as the '''classical minor triad, classical minor triad,''' or more generally - albeit less precisely - as the '''just major triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.
+== Rotations around the octave ==
+[[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"]]
+== Voicings and rotations around two octaves ==
+{| class="wikitable sortable" style="text-align:center;"
+|+
+! style="width:90px;" {{diagonal split header|Rotation|Voicing}}
+! style="width:90px;" | Root
+! style="width:90px;" | '3
+! style="width:90px;" | '15
+! style="width:90px;" | '''<nowiki/>'''<nowiki/>'3'15
+|-
+! style="width:90px;" | On 3
+| style="width:90px;" data-sort-value="012-015-040" | 12:15:40
+| style="width:90px;" data-sort-value="006-010-015" | 6:10:15
+| style="width:90px;" data-sort-value="006-015-020" | 6:15:20
+| style="width:90px;" data-sort-value="012-015-020" | ''12:15:20''
+|-
+! style="width:90px;" | On 5
+| style="width:90px;" data-sort-value="010-012-015" | ''10:12:15''
+| style="width:90px;" data-sort-value="010-015-024" | 10:15:24
+| style="width:90px;" data-sort-value="005-006-015" | 5:6:15
+| style="width:90px;" data-sort-value="005-012-015" | 5:12:15
+|-
+! style="width:90px;" | On 15
+| style="width:90px;" data-sort-value="015-040-048" | 15:40:48
+| style="width:90px;" data-sort-value="015-024-040" | 15:24:40
+| style="width:90px;" data-sort-value="015-020-024" | ''15:20:24''
+| style="width:90px;" data-sort-value="015-020-048" | 15:20:48
+|}
+== Related chords ==
 Common tetrads based on this triad (5-limit except where noted):
-* [[10:12:15:18]] adds 9/5
+* [[4:5:6]] - chord inversion
-* [[30:36:45:50]] adds 5/3
+* [[10:12:15:18]] adds [[9/5]]
-* [[70:84:105:120]] (12:10:8:7) adds 12/7 (7-limit)
+* [[30:36:45:50]] adds [[5/3]]
+* [[60:70:84:105]] - adds 8/7 (7-limit)
-{{todo|inline=1|expand}}
 [[Category:Minor triads|#@]] <!-- 2-digit first number -->