4:5:6: Difference between revisions

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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 the most consonant triad, and it is the most common triad in music. In close voicing root position it's an [[Delta-rational chord#Isoharmonic chord|isoharmonic]] 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]].  


== Audio of close voicings ==
== Audio of close voicings ==
[[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]][[File:SculpEufaDem3-4-5-onD.mp3|none|thumb|3:4:5, 2nd inversion]]
== Notable voicings ==
== 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.


Voicings are arranged from simple to complex using [[Wilson norm#Example|Wilson height]]. 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.
{| class="wikitable"
{| class="wikitable"
!Voices
! Voices
!Ratio
! Ratio
![[Kite's thoughts on hi-lo notation|Hi-lo name]]
! [[Kite's thoughts on hi-lo notation|Hi-lo name]]
!Special properties
! Special properties
|-
|-
| rowspan="4" |3 voices
| rowspan="4" |3 voices
|1:3:5
| 1:3:5
|hi3loR
| hi3loR
|AOV, [[Delta-rational chord#Isoharmonic chord|isoharmonic]]
| AOV, [[Delta-rational chord #Isoharmonic chord|isoharmonic]]
|-
|-
|2:3:5
| 2:3:5
|hi3
| hi3
|CAOV
| CAOV
|-
|-
|3:4:5
| 3:4:5
|lo5
| lo5
|1st inversion, isoharmonic
| 1st inversion, isoharmonic
|-
|-
|4:5:6
| 4:5:6
|basic
| basic
|isoharmonic
| isoharmonic
|-
|-
| rowspan="4" |4 voices
| rowspan="4" |4 voices
|2:3:'''4''':5
| 2:3:'''4''':5
|hi3add8
| hi3add8
|isoharmonic
| isoharmonic
|-
|-
|2:'''4''':5:6
| 2:'''4''':5:6
|addloR
| addloR
|
|  
|-
|-
|3:4:5:'''6'''
| 3:4:5:'''6'''
|addlo5
| addlo5
|isoharmonic
| isoharmonic
|-
|-
|4:5:6:'''8'''
| 4:5:6:'''8'''
|add8
| add8
|
|  
|}
|}
== Related chords ==
== Related chords ==
Melodic inversion: 6:5:4 = [[10:12:15]].
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)
Lower limit soundalikes: [[64:81:96]] (3-limit)


Notable extensions (5-limit except where noted):
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 -->

Revision as of 09:15, 24 November 2025

Chord information
Harmonics 4:5:6
Subharmonics 1/(15:12:10)
Intervals from root 1/1–5/4–3/2
Cents from root 0¢–386¢–702¢
Step intervals 5/4, 6/5
Step cents 386¢, 316¢
Color name yo or y
Prime limit 5
Genus 3⋅5 (15)
Intervallic odd limit 5
Otonal odd limit 5
Utonal odd limit 15
Consistent edos (d ≥ 2) 3edo*, 12edo*, 15edo*, 19edo**, …

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 isoharmonic chord.

Audio of close voicings

4:5:6, Root position
5:6:8, 1st inversion
3:4:5, 2nd inversion

Notable voicings

Voicings are arranged from simple to complex using Wilson norm. AOV and CAOV stand for 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.

Voices Ratio Hi-lo name Special properties
3 voices 1:3:5 hi3loR AOV, isoharmonic
2:3:5 hi3 CAOV
3:4:5 lo5 1st inversion, isoharmonic
4:5:6 basic isoharmonic
4 voices 2:3:4:5 hi3add8 isoharmonic
2:4:5:6 addloR
3:4:5:6 addlo5 isoharmonic
4:5:6:8 add8

Related chords

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

Plausible homonyms: None.

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

Notable extensions (5-limit except where noted):

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