Perfect fourth - Revision history

FloraC: Infobox placement; style

2026-03-30T12:00:16Z

Infobox placement; style

← Older revision		Revision as of 12:00, 30 March 2026
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	{{About\|the [[interval region]]\|the just perfect fourth\|4/3}}		{{About\|the [[interval region]]\|the just perfect fourth\|4/3}}
			{{Wikipedia}}

			A '''perfect fourth''' ('''P4''') is the smaller and most common of the two fourths – intervals spanning 4 degrees or 3 scale steps in the diatonic scale. It is found between the 1st and 4th degrees of all diatonic modes except Lydian. Another diatonic interval around the same size is the '''augmented third''' ('''A3'''). More generally, an interval close to 500 cents can be called a perfect fourth.

			== As an interval region ==
	{{Infobox interval region		{{Infobox interval region
	\| Name = Perfect fourth		\| Name = Perfect fourth
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	\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]		\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]
	\| Complement = [[Perfect fifth]]		\| Complement = [[Perfect fifth]]
	\| Lower region = [[~~Major_third_(interval region)\|~~Major ~~Third~~]]		\| Lower region = [[Major third]]
	\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]		\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]
	}}		}}
	A '''perfect fourth''' ('''P4''') is the smaller and most common of the two "fourths" - intervals spanning 4 degrees or 3 scale steps in the diatonic scale. It is found between the 1st and 4th degrees of all diatonic modes except Lydian. Another diatonic interval around the same size is the '''augmented third (A3).''' More generally, an interval close to 500 cents can be called a perfect fourth.{{Wikipedia}}

	~~== As an interval region ==~~
	As an [[interval region]], the perfect fourth is typically near 500{{c}} in size, distinct from the [[semiaugmented fourth]] of roughly 550{{c}}. A rough tuning range for the perfect fourth is about 470 to 530{{c}} according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 480 to 514{{c}}, which generates a diatonic scale.		As an [[interval region]], the perfect fourth is typically near 500{{c}} in size, distinct from the [[semiaugmented fourth]] of roughly 550{{c}}. A rough tuning range for the perfect fourth is about 470 to 530{{c}} according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 480 to 514{{c}}, which generates a diatonic scale.

	This article covers intervals from 450 to 540{{c}}.		This article covers intervals from 450 to 540{{c}}.

	=== In ~~MOS~~ scales ===		=== In mos scales ===
	Intervals between 450 and 545 cents generate the following [[mos~~\|MOS~~]] ~~scales~~:		Intervals between 450 and 545 cents generate the following [[mos scale]]s:

	These tables start from the last monolarge mos generated by the interval range.		These tables start from the last monolarge mos generated by the interval range.
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	\|-		\|-
	! Range		! Range
	! colspan="6" \| ~~MOS~~		! colspan="6" \| Mos
	\|-		\|-
	\| 450–480{{c}}		\| 450–480{{c}}
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	=== Scale info ===		=== Scale info ===
	The diatonic scale contains six perfect fourths. In the Ionian mode, perfect fourths are found on all but the fourth degree of the scale, which has an [[~~Tritone\|~~augmented fourth]]. The strong presence of perfect fourths as opposed to their augmented counterparts leads to fourths (along with fifths) being the most fundamental intervals for diatonic harmony.		The diatonic scale contains six perfect fourths. In the Ionian mode, perfect fourths are found on all but the fourth degree of the scale, which has an [[augmented fourth]]. The strong presence of perfect fourths as opposed to their augmented counterparts leads to fourths (along with fifths) being the most fundamental intervals for diatonic harmony.

	== In just intonation ==		== In just intonation ==
	=== By prime limit ===		=== By prime limit ===
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	Other "out of tune" fourths in higher [[prime limit\|limits]] include:		Other "out of tune" fourths in higher [[prime limit\|limits]] include:

	* The 5-limit '''acute fourth''' is a ratio of [[27/20]], and is about 520{{c}}		* The 5-limit '''acute fourth''' is a ratio of [[27/20]], and is about 520{{c}}
	* The 7-limit '''subfourth''' is a ratio of [[21/16]], and is about 471{{c}}.		* The 7-limit '''subfourth''' is a ratio of [[21/16]], and is about 471{{c}}.
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	== In edos ==		== In edos ==
	The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[edo]]s.		The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[edo]]s.

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

Jdood: removed the "(interval region)" text from infobox

2025-12-03T18:25:55Z

removed the "(interval region)" text from infobox

← Older revision		Revision as of 18:25, 3 December 2025
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	\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]		\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]
	\| Complement = [[Perfect fifth]]		\| Complement = [[Perfect fifth]]
	\| Lower region = [[Major ~~third (interval region)~~]]		\| Lower region = [[Major_third_(interval region)\|Major Third]]
	\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]		\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]
	}}		}}

VectorGraphics at 06:17, 18 June 2025

2025-06-18T06:17:31Z

Show changes

VectorGraphics at 06:06, 18 June 2025

2025-06-18T06:06:14Z

← Older revision		Revision as of 06:06, 18 June 2025
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	\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]		\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]
	\| Complement = [[Perfect fifth]]		\| Complement = [[Perfect fifth]]
	\| Lower region = [[Major third]]		\| Lower region = [[Major third (interval region)]]
	\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]		\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]
	}}		}}

Lériendil: added schismic and superpyth

2025-03-17T01:58:49Z

added schismic and superpyth

← Older revision		Revision as of 01:58, 17 March 2025
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	=== Temperaments that use 4/3 as a generator ===		=== Temperaments that use 4/3 as a generator ===
	* [[Archy]], the temperament flattening 4/3 such that three 4/3's stack to [[7/6]] octave-reduced		* [[Archy]], the temperament flattening 4/3 such that three 4/3's stack to [[7/6]] (and furthermore, in [[superpyth]], where eight stack to 6/5) octave-reduced
			* [[Schismic]], the temperament tuning 4/3 such that eight 4/3's stack to [[5/4]] octave-reduced
	* [[Meantone]], the temperament sharpening 4/3 such that three 4/3's stack to [[6/5]] octave-reduced		* [[Meantone]], the temperament sharpening 4/3 such that three 4/3's stack to [[6/5]] octave-reduced
	* [[Mavila]], the temperament sharpening 4/3 such that three 4/3's stack to [[5/4]] octave-reduced		* [[Mavila]], the temperament sharpening 4/3 such that three 4/3's stack to [[5/4]] octave-reduced

Lériendil: added lynx

2025-03-17T01:51:00Z

added lynx

← Older revision		Revision as of 01:51, 17 March 2025
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	Other "out of tune" fourths in higher [[prime limit\|limits]] include:		Other "out of tune" fourths in higher [[prime limit\|limits]] include:

	* The 5-limit '''acute fourth''' is a ratio of 27/20, and is about 520{{c}}		* The 5-limit '''acute fourth''' is a ratio of [[27/20]], and is about 520{{c}}
	* The 7-limit '''subfourth''' is a ratio of 21/16, and is about 471{{c}}.		* The 7-limit '''subfourth''' is a ratio of [[21/16]], and is about 471{{c}}.
	* The 11-limit '''augmented fourth''' is a ratio of 15/11, and is about 537{{c}}.		* The 11-limit '''augmented fourth''' is a ratio of [[15/11]], and is about 537{{c}}, and may better be analyzed as a [[superfourth]].
	** There is also an 11-limit '''grave fourth,''' which is a ratio of 33/25, and is about 480{{c}}.		** There is also an 11-limit '''grave fourth,''' which is a ratio of [[33/25]], and is about 480{{c}}.
	* The 13-limit '''infrafourth''' is a ratio of 13/10, and is about 454{{c}}, but it might be better analyzed as an [[major third\|ultramajor third]]. Despite that, it is also here for completeness.		* The 13-limit '''infrafourth''' is a ratio of [[13/10]], and is about 454{{c}}, but it might be better analyzed as an [[major third\|ultramajor third]]. Despite that, it is also here for completeness.

	=== By delta ===		=== By delta ===

Lériendil at 01:50, 17 March 2025

2025-03-17T01:50:04Z

← Older revision		Revision as of 01:50, 17 March 2025
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	=== Temperaments that use wolf fourths as generators ===		=== Temperaments that use wolf fourths as generators ===
	* [[Buzzard]], the temperament generated by sharpening 21/16 so that four of it stack to [[3/1]].		* [[Buzzard]], the temperament generated by sharpening 21/16 so that four of it stack to [[3/1]].
	* [[Gravity]], the temperament generated by flattening 27/20 so that two of it stack to [[20/11]] ~~and six~~ of which reach [[3/2]].		* [[Gravity]], the temperament generated by flattening 27/20 so that two of it stack to [[20/11]], three of which in turn reach [[3/2]].

	== In mos scales ==		== In mos scales ==

Lériendil: added some wolf-gen temps

2025-03-17T01:30:57Z

added some wolf-gen temps

← Older revision		Revision as of 01:30, 17 March 2025
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	=== Temperaments that use 4/3 as a generator ===		=== Temperaments that use 4/3 as a generator ===
	* [[Archy]], the temperament flattening 4/3 such that three 4/3's stack to [[7/6]]		* [[Archy]], the temperament flattening 4/3 such that three 4/3's stack to [[7/6]] octave-reduced
	* [[Meantone]], the temperament sharpening 4/3 such that three 4/3's stack to [[6/5]]		* [[Meantone]], the temperament sharpening 4/3 such that three 4/3's stack to [[6/5]] octave-reduced
	* [[Mavila]], the temperament sharpening 4/3 such that three 4/3's stack to [[5/4]]		* [[Mavila]], the temperament sharpening 4/3 such that three 4/3's stack to [[5/4]] octave-reduced
	* Various historical [[well temperament]]s generated by tempered 4/3's or 3/2's, equivalent to 12edo as compton and meantone		* Various historical [[well temperament]]s generated by tempered 4/3's or 3/2's, equivalent to 12edo as compton and meantone

			=== Temperaments that use wolf fourths as generators ===
			* [[Buzzard]], the temperament generated by sharpening 21/16 so that four of it stack to [[3/1]].
			* [[Gravity]], the temperament generated by flattening 27/20 so that two of it stack to [[20/11]] and six of which reach [[3/2]].

	== In mos scales ==		== In mos scales ==

Lériendil: compton does not technically use 4/3 or 3/2 as a generator; its period is 1\12 which identifies as 256/243 and 2187/2048

2025-03-17T01:26:36Z

compton does not technically use 4/3 or 3/2 as a generator; its *period* is 1\12 which identifies as 256/243 and 2187/2048

← Older revision		Revision as of 01:26, 17 March 2025
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	=== Temperaments that use 4/3 as a generator ===		=== Temperaments that use 4/3 as a generator ===
	* [[Compton]], the temperament of the Pythagorean comma, equivalent to 12edo
	** The 3-limit [[circular temperament]]s in general
	* [[Archy]], the temperament flattening 4/3 such that three 4/3's stack to [[7/6]]		* [[Archy]], the temperament flattening 4/3 such that three 4/3's stack to [[7/6]]
	* [[Meantone]], the temperament sharpening 4/3 such that three 4/3's stack to [[6/5]]		* [[Meantone]], the temperament sharpening 4/3 such that three 4/3's stack to [[6/5]]

FloraC: Fix

2025-03-14T11:10:46Z

Fix

← Older revision		Revision as of 11:10, 14 March 2025
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	\| JI intervals = 4/3		\| JI intervals = 4/3
	\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]		\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]
	\| Complement = [[Perfect ~~fourth~~]]		\| Complement = [[Perfect fifth]]
	\| Lower region = [[Major third]]		\| Lower region = [[Major third]]
	\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]		\| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]