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 the classical [[major triad]], also known as the '''Ptolemaic major triad''', or imprecisely as the '''just major triad'''. It is the most consonant of all the just intonation [[Triad|triads]].
'''4:5:6''' is the otonal [[major triad]], also known as the '''classical''' '''major triad''', '''Ptolemaic major triad''', or more generally - albeit less precisely - as the '''just major triad'''. It is among the most consonant triads, and it is among the most common triads in music.


Common tetrads based on this triad (5-limit except where noted):
Its most consonant rotation, 3:4:5, is not typically considered to be consonant, at least in more classical tonal music, where the fourth above the root is considered a dissonance. Acoustically speaking however, 3:4:5 has the least [[harmonic entropy]].


* [[12:15:18:20]] adds 5/3
== Rotations around the octave ==
* [[8:10:12:15]] adds 15/8
[[File:SculpEufaDem3-4-5-onD.mp3|none|thumb|3:4:5, "2nd inversion"]]
* [[36:45:54:64]] adds 16/9
[[File:SculpEufaDem4-5-6-onD.mp3|none|thumb|4:5:6, "Root position"]]
* [[20:25:30:36]] adds 9/5
[[File:SculpEufaDem5-6-8-onD.mp3|none|thumb|5:6:8, "1st inversion"]]
* [[4:5:6:7]] adds 7/4 (7-limit)


== Related chords ==
Chords related to this triad (5-limit except where noted):
* 2:3:5 - open voicing
* [[10:12:15]] - chord inversion
* [[12:15:18:20]] - adds 5/3
* [[8:10:12:15]] - adds 15/8
* [[36:45:54:64]] - adds 16/9
* [[20:25:30:36]] - adds 9/5
* [[4:5:6:7]] - adds 7/4 (7-limit)
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[[Category:Major triads|#]] <!-- 1-digit first number -->
[[Category:Major triads|#]] <!-- 1-digit first number -->

Revision as of 23:14, 1 November 2025

Chord information
Harmonics 4:5:6
Subharmonics 1/(15:12:10)
Intervals from root 1/15/43/2
Cents from root 386¢702¢
Step intervals 5/4, 6/5
Step cents 386¢, 316¢
Color name yo or y
Prime limit 5
Genus 35 (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 the otonal major triad, also known as the classical major triad, Ptolemaic major triad, or more generally - albeit less precisely - as the just major triad. It is among the most consonant triads, and it is among the most common triads in music.

Its most consonant rotation, 3:4:5, is not typically considered to be consonant, at least in more classical tonal music, where the fourth above the root is considered a dissonance. Acoustically speaking however, 3:4:5 has the least harmonic entropy.

Rotations around the octave

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

Related chords

Chords related to this triad (5-limit except where noted):