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 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.  


Its second rotation, 3:4:5, has a lower [[harmonic entropy]] and is sometimes considered to be more consonant (for example, by [[Lériendil]]). 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. It is also not considered to be stable in [[Shasavistic theory]] unlike 4:5:6.
== 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]]
== Notable voicings ==


== Rotations around the octave ==
Voicings are identified with [[Kite's thoughts on hi-lo notation|Hi-lo notation]]. AOV  and CAOV stand for (condensed) [[Odd limit#Proposed extensions|all-odd voicing]].
[[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:SculpEufaDem5-6-8-onD.mp3|none|thumb|5:6:8, "1st inversion"]]


== Voicings and rotations around two octaves ==
3 voices:
{| 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;" | '''<nowiki/>'5'''
! style="width:90px;" | '3'5
|-
! style="width:90px;" | On 1
| style="width:90px;" data-sort-value="004-005-006" | ''4:5:6''
| style="width:90px;" data-sort-value="004-005-012" | 4:5:12
| style="width:90px;" data-sort-value="002-003-005" | 2:3:5
| style="width:90px;" data-sort-value="002-005-006" | 2:5:6
|-
! style="width:90px;" | On 3
| style="width:90px;" data-sort-value="003-004-005" | 3:8:10
| 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
| style="width:90px;" data-sort-value="005-006-016" | 5:6:16
| style="width:90px;" data-sort-value="005-012-016" | 5:12:16
| 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 - close voicing
* 2:3:5 - hi3, CAOV
* 1:3:5 - hi3loR, AOV
* 3:4:5 - lo5 or 2nd inversion
4 voices:
* 4:5:6:8 - add8
* 2:3:4:5 - hi3add8
* 2:4:5:6 - addloR
* 3:4:5:6 - addlo5


== Related chords ==
== Related chords ==
Chords related to this triad (5-limit except where noted):
Melodic inversion: 6:5:4 = [[10:12:15]].
* [[10:12:15]] - chord inversion
 
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

Revision as of 01:20, 19 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.

Audio of close voicings

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

Notable voicings

Voicings are identified with Hi-lo notation. AOV and CAOV stand for (condensed) all-odd voicing.

3 voices:

  • 4:5:6 - close voicing
  • 2:3:5 - hi3, CAOV
  • 1:3:5 - hi3loR, AOV
  • 3:4:5 - lo5 or 2nd inversion

4 voices:

  • 4:5:6:8 - add8
  • 2:3:4:5 - hi3add8
  • 2:4:5:6 - addloR
  • 3:4:5:6 - addlo5

Related chords

Melodic inversion: 6:5:4 = 10:12:15.

Extensions (5-limit except where noted):

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