10:12:15: Difference between revisions

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'''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.

'''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]].

~~== Rotations around~~ the ~~octave ==~~

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]].

[[~~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~~ ==

== Audio of close voicings ==

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

[[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"

|+

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

!Voices

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

![[EFR]]

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

![[Kite's thoughts on hi-lo notation|Hi-lo name]]

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

!Special properties

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

|-

| 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

|-

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

|15:20:24

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

|lo5

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

|2nd inversion

| ~~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~~

| rowspan="2" |4 voices

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

|10:12:15:20

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

|add8

| ~~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~~

|10:15:20:24

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

|hi3add8

~~| 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):

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):

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

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

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

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

* [[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|#@]]

@@ Line 1: / Line 1: @@
 {{Infobox Chord|ColorName=gu or g}}
-'''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.
+'''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]].
-== Rotations around the octave ==
+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]].
-[[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 ==
+== Audio of close voicings ==
-{| class="wikitable sortable" style="text-align:center;"
+[[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"
 |+
-! style="width:90px;" {{diagonal split header|Rotation|Voicing}}
+!Voices
-! style="width:90px;" | Root
+![[EFR]]
-! style="width:90px;" | '3
+![[Kite's thoughts on hi-lo notation|Hi-lo name]]
-! style="width:90px;" | '15
+!Special properties
-! style="width:90px;" | '''<nowiki/>'''<nowiki/>'3'15
+|-
+| 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
 |-
-! style="width:90px;" | On 3
+|15:20:24
-| style="width:90px;" data-sort-value="012-015-040" | 12:15:40
+|lo5
-| style="width:90px;" data-sort-value="006-010-015" | 6:10:15
+|2nd inversion
-| 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
+| rowspan="2" |4 voices
-| style="width:90px;" data-sort-value="010-012-015" | ''10:12:15''
+|10:12:15:20
-| style="width:90px;" data-sort-value="010-015-024" | 10:15:24
+|add8
-| 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
+|10:15:20:24
-| style="width:90px;" data-sort-value="015-040-048" | 15:40:48
+|hi3add8
-| 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):
+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):
-* [[4:5:6]] - chord inversion
 * [[10:12:15:18]] adds [[9/5]]
 * [[30:36:45:50]] adds [[5/3]]
-* [[60:70:84:105]] - adds 8/7 (7-limit)
+* [[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 -->