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4:5:6: Difference between revisions

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"Just major triad" isn't less precise. 3:4:5 isn't more concordant than 4:5:6 for multiple good reasons; HE isn't everything.
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{{Infobox Chord|ColorName=yo or y}}
{{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 among the most consonant triads, and it is among the most common triads in music.  
'''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.


Its second rotation, 3:4:5, reportedly has a lower [[harmonic entropy]]. However, 3:4:5 is not typically considered to be consonant in counterpoint and some derived theories (but not necessarily modern pop or xenharmonic theory), as it is not only [[rooted interval|nonrooted]] but the fourth above the root contrasts and therefore wants to move to the missing major third.  
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.


== Rotations around the octave ==
== Audio of close voicings ==
[[File:SculpEufaDem3-4-5-onD.mp3|none|thumb|3:4:5, "2nd inversion"]]
[[File:SculpEufaDem4-5-6-onD.mp3|none|thumb|4:5:6, Root position]]
[[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]]
[[File:SculpEufaDem5-6-8-onD.mp3|none|thumb|5:6:8, "1st inversion"]]


== Voicings and rotations around two octaves ==
== Approximation by edos ==
{| class="wikitable sortable" style="text-align:center;"
[[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}}
! style="width:90px;" {{diagonal split header|Rotation|Voicing}}
 
! style="width:90px;" | Root
== Notable voicings ==
! style="width:90px;" | '3
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.
! style="width:90px;" | '''<nowiki/>'5'''
 
! style="width:90px;" | '3'5
{| class="wikitable"
! Voices
! [[EFR]]
! [[Kite's thoughts on hi-lo notation|Hi-lo name]]
! Special properties
|-
| rowspan="4" |3 voices
| 1:3:5
| hi3loR
| AOV, [[Delta-rational chord #Isoharmonic chord|isoharmonic]]
|-
| 2:3:5
| hi3
| CAOV
|-
| 3:4:5
| lo5
| 1st inversion, isoharmonic
|-
| 4:5:6
| basic
| isoharmonic
|-
|-
! style="width:90px;" | On 1
| rowspan="4" |4 voices
| style="width:90px;" data-sort-value="004-005-006" | ''4:5:6''
| 2:3:'''4''':5
| style="width:90px;" data-sort-value="004-005-012" | 4:5:12
| hi3add8
| style="width:90px;" data-sort-value="002-003-005" | 2:3:5
| isoharmonic
| style="width:90px;" data-sort-value="002-005-006" | 2:5:6
|-
|-
! style="width:90px;" | On 3
| 2:'''4''':5:6
| style="width:90px;" data-sort-value="003-004-005" | 3:8:10
| addloR
| style="width:90px;" data-sort-value="003-004-005" | ''3:4:5''
|  
| style="width:90px;" data-sort-value="003-005-008" | 3:5:8
| style="width:90px;" data-sort-value="003-004-010" | 3:4:10
|-
|-
! style="width:90px;" | On 5
| 3:4:5:'''6'''
| style="width:90px;" data-sort-value="005-006-016" | 5:6:16
| addlo5
| style="width:90px;" data-sort-value="005-012-016" | 5:12:16
| isoharmonic
| style="width:90px;" data-sort-value="005-008-012" | 5:8:12
|-
| style="width:90px;" data-sort-value="005-006-008" | ''5:6:8''
| 4:5:6:'''8'''
| add8
|
|}
|}
== Related chords ==
Melodic inversion: 1/(6:5:4) = [[10:12:15]].


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


== Related chords ==
Lower limit soundalikes: [[64:81:96]] (3-limit)
Chords related to this triad (5-limit except where noted):
 
* [[10:12:15]] - chord inversion
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 -->
[[Category:Major triads|#]] <!-- 1-digit first number -->
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