4:5:6 - Revision history

Overthink: sectioning; brief explanation

2026-05-31T23:53:01Z

sectioning; brief explanation

← Older revision		Revision as of 23:53, 31 May 2026
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	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.		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.
	~~{{chord edo approximation}}~~

	== 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]]

			== 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 ==		== Notable voicings ==

Overthink: - extra whitespace

2026-05-31T23:50:50Z

- extra whitespace

← Older revision		Revision as of 23:50, 31 May 2026
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	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.		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.

	{{chord edo approximation}}		{{chord edo approximation}}

Pailiaq at 21:54, 31 May 2026

2026-05-31T21:54:21Z

← Older revision		Revision as of 21:54, 31 May 2026
Line 3:		Line 3:

	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.		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.

			{{chord edo approximation}}

	== Audio of close voicings ==		== Audio of close voicings ==

Eufalesio at 20:27, 30 January 2026

2026-01-30T20:27:23Z

← Older revision		Revision as of 20:27, 30 January 2026
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	== 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]]. 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.

	{\| class="wikitable"		{\| class="wikitable"

Overthink: + approximations by EDOs

2025-12-26T07:30:26Z

+ approximations by EDOs

← Older revision		Revision as of 07:30, 26 December 2025
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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 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.		'''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.		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.

Overthink: expand description

2025-12-22T09:04:05Z

expand description

← Older revision		Revision as of 09:04, 22 December 2025
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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 is 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]]. 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.

			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 ==		== Audio of close voicings ==

FloraC: "Inversion"

2025-11-24T09:28:39Z

"Inversion"

← Older revision		Revision as of 09:28, 24 November 2025
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	\|}		\|}
	== 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.

TallKite at 09:22, 24 November 2025

2025-11-24T09:22:52Z

← Older revision		Revision as of 09:22, 24 November 2025
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	\|}		\|}
	== Related chords ==		== Related chords ==
	Melodic inversion: ~~1/(~~6:5:4) = [[10:12:15]].		Melodic inversion: 6:5:4 = [[10:12:15]].

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

TallKite at 09:22, 24 November 2025

2025-11-24T09:22:17Z

← Older revision		Revision as of 09:22, 24 November 2025
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	{\| class="wikitable"		{\| class="wikitable"
	! Voices		! Voices
	! ~~Ratio~~		! [[EFR]]
	! [[Kite's thoughts on hi-lo notation\|Hi-lo name]]		! [[Kite's thoughts on hi-lo notation\|Hi-lo name]]
	! Special properties		! Special properties

FloraC: Cleanup

2025-11-24T09:15:13Z

Cleanup

← Older revision		Revision as of 09:15, 24 November 2025
Line 1:		Line 1:
	{{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 -->