4:5:6: Difference between revisions

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'''4:5:6''' is an otonal [[major triad]], known as the '''just major triad''', '''classical major triad''', or '''Ptolemaic major triad'''. It is the most consonant triad, and it is the most common triad in music. It is also an [[~~isodifferential~~]] ~~chord~~.

'''4:5:6''' is an otonal [[major triad]], known as the '''just major triad''', '''classical major triad''', or '''Ptolemaic major triad'''. It is the most consonant triad, and it is the most common triad in music. In close voicing root position, it is an [[Delta-rational chord #Isoharmonic chord|isoharmonic chord]]. It occurs as a major triad in the [[meantone]] diatonic scale, as the major third formed by stacking four [[3/2|perfect fifths]] octave reduced, [[81/64]], is equated with [[5/4]]. It serves as the fundamental major root chord in classical music, and approximating is key in [[5-limit]] temperaments. This chord is approximated with all intervals having less than 20{{c}} of error in [[edo]]s {{EDOs|12, 15, 19, 22, 24, 26, 27}}, etc.

This chord is formed by stacking [[5/4]] and [[6/5]] in that order. Swapping the order of these intervals results in [[10:12:15]], the classical minor triad. The minor triad can also be obtained from 4:5:6 by flattening the third by [[25/24]], the diptolemaic chromatic semitone.

== Audio of close voicings ==

[[File:SculpEufaDem4-5-6-onD.mp3|none|thumb|4:5:6, Root position]]

== Approximation by edos ==

[[7edo]] contains a rough approximation to 4:5:6, which equates the 5/4 and 6/5 steps. The smallest edo to approximate it with acceptable accuracy is [[12edo]], with [[19edo]] being the next edo to improve on it.

== Notable voicings ==

Voicings are arranged from simple to complex using [[Wilson norm]]. AOV and CAOV stand for [[Odd limit #Proposed extensions|all-odd voicing]] and ''condensed'' AOV respectively. Numbers in '''bold''' denote doubled pitches. This list is only a brief overview, see [[Voicings of 4:5:6]] for a more comprehensive list and audio examples.

Voicings written in [[enumeration]] and written [[Kite's thoughts on hi-lo notation|Hi-lo notation]]. AOV and CAOV stand for [[Odd limit#Proposed extensions|all-odd voicing]] and ''condensed'' AOV respectively {{idiosyncratic}} . Integers in '''bold''' denote the pitch-classes of the chord.

{| class="wikitable"

!Voices

! Voices

!~~Enumeration~~

! [[EFR]]

!Hi-lo

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

!Special properties

! Special properties

|-

~~| rowspan="3" |3 voices~~

~~|'''1:3:5'''~~

~~|hi3loR~~

~~|AOV, isodifferential~~

|-

~~|'''2:3:5'''~~

~~|hi3~~

~~| rowspan="2" |CAOV~~

|-

~~|'''3:5:8'''~~

~~|hiRlo5~~

|-

~~| rowspan="7" |4 voices~~

~~|3:'''4:5:6'''~~

~~|addlo5~~

~~|isodifferential~~

|-

|~~'''~~4:5~~:6''':8~~

| rowspan="4" |3 voices

|~~add8~~

| 1:3:5

|

| hi3loR

| AOV, [[Delta-rational chord #Isoharmonic chord|isoharmonic]]

|-

|~~'''5~~:6:~~8''':10~~

| 2:3:5

|~~hiRaddhi3~~

| hi3

|

| CAOV

|-

|~~'''2:~~3~~'''~~:4:~~'''~~5~~'''~~

| 3:4:5

|~~hi3add8~~

| lo5

|~~isodifferential~~

| 1st inversion, isoharmonic

|-

|~~2:'''~~4~~'''~~:~~'''~~5:6~~'''~~

| 4:5:6

|~~addloR~~

| basic

|

| isoharmonic

|-

|3:'''~~5:6:8~~'''

| rowspan="4" |4 voices

|~~hiRaddlo5~~

| 2:3:'''4''':5

|

| hi3add8

| isoharmonic

|-

|'''~~5:8:12~~''':16

| 2:'''4''':5:6

|~~lo3addhi8~~

| addloR

|

|-

| ~~rowspan="2" |5 voices~~

| 3:4:5:'''6'''

~~|2:~~3:~~'''~~4:5:6'''

| addlo5

|~~addloR5~~

| isoharmonic

|~~isodifferential~~

|-

|~~'''~~4:5:6''':8~~:10~~

| 4:5:6:'''8'''

|~~addhiR3~~

| add8

|

|}

~~See a more comprehensive list [[Voicings of 4:5:6|in this page]].~~

== Related chords ==

Melodic inversion: 1/(6:5:4) = [[10:12:15]].

Plausible [[~~Chord~~ homonym|homonyms]]: None.

Plausible [[chord homonym|homonyms]]: None.

Lower limit soundalikes: [[64:81:96]] (3-limit) ~~[Pythagorean major chord]~~

Lower limit soundalikes: [[64:81:96]] (3-limit)

Notable extensions (5-limit except where noted):

* [[12:15:18:20]] - adds 5/3

* [[12:15:18:20]] – adds 5/3

* [[8:10:12:15]] - adds 15/8

* [[8:10:12:15]] – adds 15/8

* [[36:45:54:64]] - adds 16/9

* [[36:45:54:64]] – adds 16/9

* [[20:25:30:36]] - adds 9/5

* [[20:25:30:36]] – adds 9/5

* [[4:5:6:7]] - adds 7/4 (7-limit)

* [[4:5:6:7]] – adds 7/4 (7-limit)

~~[[Category:Major triads|#]] ~~

[[Category:Major triads|#]]

@@ Line 1: / Line 1: @@
 {{Infobox Chord|ColorName=yo or y}}
-'''4:5:6''' is an otonal [[major triad]], known as the '''just major triad''', '''classical major triad''', or '''Ptolemaic major triad'''. It is the most consonant triad, and it is the most common triad in music. It is also an [[isodifferential]] chord.
+'''4:5:6''' is an otonal [[major triad]], known as the '''just major triad''', '''classical major triad''', or '''Ptolemaic major triad'''. It is the most consonant triad, and it is the most common triad in music. In close voicing root position, it is an [[Delta-rational chord #Isoharmonic chord|isoharmonic chord]]. It occurs as a major triad in the [[meantone]] diatonic scale, as the major third formed by stacking four [[3/2|perfect fifths]] octave reduced, [[81/64]], is equated with [[5/4]]. It serves as the fundamental major root chord in classical music, and approximating is key in [[5-limit]] temperaments. This chord is approximated with all intervals having less than 20{{c}} of error in [[edo]]s {{EDOs|12, 15, 19, 22, 24, 26, 27}}, etc.
+This chord is formed by stacking [[5/4]] and [[6/5]] in that order. Swapping the order of these intervals results in [[10:12:15]], the classical minor triad. The minor triad can also be obtained from 4:5:6 by flattening the third by [[25/24]], the diptolemaic chromatic semitone.
 == Audio of close voicings ==
 [[File:SculpEufaDem4-5-6-onD.mp3|none|thumb|4:5:6, Root position]]
 [[File:SculpEufaDem5-6-8-onD.mp3|none|thumb|5:6:8, 1st inversion]][[File:SculpEufaDem3-4-5-onD.mp3|none|thumb|3:4:5, 2nd inversion]]
+== Approximation by edos ==
+[[7edo]] contains a rough approximation to 4:5:6, which equates the 5/4 and 6/5 steps. The smallest edo to approximate it with acceptable accuracy is [[12edo]], with [[19edo]] being the next edo to improve on it.
+{{chord edo approximation}}
 == Notable voicings ==
+Voicings are arranged from simple to complex using [[Wilson norm]]. AOV and CAOV stand for [[Odd limit #Proposed extensions|all-odd voicing]] and ''condensed'' AOV respectively. Numbers in '''bold''' denote doubled pitches. This list is only a brief overview, see [[Voicings of 4:5:6]] for a more comprehensive list and audio examples.
-Voicings written in [[enumeration]] and written [[Kite's thoughts on hi-lo notation|Hi-lo notation]]. AOV and CAOV stand for [[Odd limit#Proposed extensions|all-odd voicing]] and ''condensed'' AOV respectively {{idiosyncratic}} . Integers in '''bold''' denote the pitch-classes of the chord.
 {| class="wikitable"
-!Voices
+! Voices
-!Enumeration
+! [[EFR]]
-!Hi-lo
+! [[Kite's thoughts on hi-lo notation|Hi-lo name]]
-!Special properties
+! Special properties
-|-
-| rowspan="3" |3 voices
-|'''1:3:5'''
-|hi3loR
-|AOV, isodifferential
-|-
-|'''2:3:5'''
-|hi3
-| rowspan="2" |CAOV
-|-
-|'''3:5:8'''
-|hiRlo5
-|-
-| rowspan="7" |4 voices
-|3:'''4:5:6'''
-|addlo5
-|isodifferential
 |-
-|'''4:5:6''':8
+| rowspan="4" |3 voices
-|add8
+| 1:3:5
-|
+| hi3loR
+| AOV, [[Delta-rational chord #Isoharmonic chord|isoharmonic]]
 |-
-|'''5:6:8''':10
+| 2:3:5
-|hiRaddhi3
+| hi3
-|
+| CAOV
 |-
-|'''2:3''':4:'''5'''
+| 3:4:5
-|hi3add8
+| lo5
-|isodifferential
+| 1st inversion, isoharmonic
 |-
-|2:'''4''':'''5:6'''
+| 4:5:6
-|addloR
+| basic
-|
+| isoharmonic
 |-
-|3:'''5:6:8'''
+| rowspan="4" |4 voices
-|hiRaddlo5
+| 2:3:'''4''':5
-|
+| hi3add8
+| isoharmonic
 |-
-|'''5:8:12''':16
+| 2:'''4''':5:6
-|lo3addhi8
+| addloR
 |
 |-
-| rowspan="2" |5 voices
+| 3:4:5:'''6'''
-|2:3:'''4:5:6'''
+| addlo5
-|addloR5
+| isoharmonic
-|isodifferential
 |-
-|'''4:5:6''':8:10
+| 4:5:6:'''8'''
-|addhiR3
+| add8
 |
 |}
-See a more comprehensive list [[Voicings of 4:5:6|in this page]].
 == Related chords ==
 Melodic inversion: 1/(6:5:4) = [[10:12:15]].
-Plausible [[Chord homonym|homonyms]]: None.
+Plausible [[chord homonym|homonyms]]: None.
-Lower limit soundalikes: [[64:81:96]] (3-limit) [Pythagorean major chord]
+Lower limit soundalikes: [[64:81:96]] (3-limit)
 Notable extensions (5-limit except where noted):
-* [[12:15:18:20]] - adds 5/3
+* [[12:15:18:20]] – adds 5/3
-* [[8:10:12:15]] - adds 15/8
+* [[8:10:12:15]] – adds 15/8
-* [[36:45:54:64]] - adds 16/9
+* [[36:45:54:64]] – adds 16/9
-* [[20:25:30:36]] - adds 9/5
+* [[20:25:30:36]] – adds 9/5
-* [[4:5:6:7]] - adds 7/4 (7-limit)
+* [[4:5:6:7]] – adds 7/4 (7-limit)
-[[Category:Major triads|#]] <!-- 1-digit first number -->
 [[Category:Major triads|#]] <!-- 1-digit first number -->