Major third - Revision history

FloraC: + interwiki

2026-03-30T14:42:11Z

+ interwiki

← Older revision		Revision as of 14:42, 30 March 2026
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			{{Interwiki
			\| en = Major third
			\| zh = 大三度
			}}
	{{Wikipedia}}		{{Wikipedia}}
	A '''major third''' ('''M3''') is the larger of the two thirds – intervals spanning 3 degrees or 2 scale steps in the diatonic scale. It is found between the 1st and 3rd notes of the major scale, hence its name. Another diatonic interval around the same size is the '''diminished fourth''' ('''d4'''). More generally, an interval close to 400 cents in size can be called a major third.		A '''major third''' ('''M3''') is the larger of the two thirds – intervals spanning 3 degrees or 2 scale steps in the diatonic scale. It is found between the 1st and 3rd notes of the major scale, hence its name. Another diatonic interval around the same size is the '''diminished fourth''' ('''d4'''). More generally, an interval close to 400 cents in size can be called a major third.

FloraC: - abuse of bold

2026-03-30T13:02:31Z

- abuse of bold

← Older revision		Revision as of 13:02, 30 March 2026
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	=== In mos scales ===		=== In mos scales ===
	Intervals between 360 and 480 cents generate the following [[mos scale]]s:		Intervals between 360 and 480 cents generate the following [[mos scale]]s. These tables start from the last monolarge mos generated by the interval range. Scales with more than 12 notes are not included.

	These tables start from the last monolarge mos generated by the interval range.

	Scales with more than 12 notes are not included.

	{\| class="wikitable"		{\| class="wikitable"
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	The major third can be stacked with a [[minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.		The major third can be stacked with a [[minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

	In [[TAMNAMS]], this interval is called the '''major 2-diastep'''.		In [[TAMNAMS]], this interval is called the ''major 2-diastep''.

	The diminished fourth is enharmonic with the major third, ranging from 240 to 514{{c}} (2\5 to 3\7). It is generated by stacking 8 fourths octave reduced, and is as such not found in the diatonic scale. Regardless, in TAMNAMS, it may be called the '''diminished 3-diastep'''.		The diminished fourth is enharmonic with the major third, ranging from 240 to 514{{c}} (2\5 to 3\7). It is generated by stacking 8 fourths octave reduced, and is as such not found in the diatonic scale. Regardless, in TAMNAMS, it may be called the ''diminished 3-diastep''.

	In [[just intonation]], an interval may be classified as a diminished fourth if it is reasonably mapped to '''three''' steps of the diatonic scale and four steps of the chromatic scale, or formally 3\7 and [[24edo\|8\24]].		In just intonation, an interval may be classified as a diminished fourth if it is reasonably mapped to ''three'' steps of the diatonic scale and four steps of the chromatic scale, or formally 3\7 and [[24edo\|8\24]].

	=== Scale info ===		=== Scale info ===
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	Much [[odd limit\|simpler]] major thirds and diminished fourths exist in higher [[prime limit\|limits]], however, for example:		Much [[odd limit\|simpler]] major thirds and diminished fourths exist in higher [[prime limit\|limits]], however, for example:
	* The 5-limit ~~'''~~classical major third~~'''~~ is a ratio of [[5/4]], and is about 386{{c}}.		* The 5-limit classical major third is a ratio of [[5/4]], and is about 386{{c}}.
	* The 7-limit ~~'''~~(septimal) supermajor third~~'''~~ is a ratio of [[9/7]], and is almost exactly 435{{c}}.		* The 7-limit (septimal) supermajor third is a ratio of [[9/7]], and is almost exactly 435{{c}}.
	* The 11-limit ~~'''~~neogothic major third~~'''~~ is a ratio of [[14/11]], and is about 418{{c}}. (Note that this is often considered an imperfect or diminished fourth.)		* The 11-limit neogothic major third is a ratio of [[14/11]], and is about 418{{c}}. (Note that this is often considered an imperfect or diminished fourth.)
	* The 13-limit ~~'''~~(tridecimal) ultramajor third~~'''~~ is a ratio of [[13/10]], and is about 454{{c}}.		* The 13-limit (tridecimal) ultramajor third is a ratio of [[13/10]], and is about 454{{c}}.
	** There is also a 13-limit ~~'''~~(tridecimal) submajor third~~'''~~, which is a ratio of [[26/21]], and is about 370{{c}}.		** There is also a 13-limit (tridecimal) submajor third, which is a ratio of [[26/21]], and is about 370{{c}}.
	* The 17-limit ~~'''~~(septendecimal) submajor third~~'''~~ is a ratio of [[21/17]], and is about 366{{c}}.		* The 17-limit (septendecimal) submajor third is a ratio of [[21/17]], and is about 366{{c}}.
	* The 23-limit ~~'''~~vicesimoterial supermajor~~'''~~ third is a ratio of [[23/18]], and is about 424{{c}}.		* The 23-limit vicesimoterial supermajor third is a ratio of [[23/18]], and is about 424{{c}}.

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

FloraC: +1

2026-03-30T12:58:33Z

Show changes

FloraC: Page merge followup

2026-03-30T11:35:45Z

Page merge followup

← Older revision		Revision as of 11:35, 30 March 2026
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			{{Wikipedia}}
			A '''major third''' ('''M3''') is the larger of the two thirds – intervals spanning 3 degrees or 2 scale steps in the diatonic scale. It is found between the 1st and 3rd notes of the major scale, hence its name. Another diatonic interval around the same size is the '''diminished fourth''' ('''d4'''). More generally, an interval close to 400 cents in size can be called a major third.

			Many JI intervals are called major thirds, but the term usually refers to one of these three intervals:
			* [[5/4]], the classical major third of about 386 cents.
			* [[9/7]], the septimal major third of about 435 cents.
			* [[81/64]], the Pythagorean major third of about 408 cents.

			== As an interval region ==
	{{Infobox interval region		{{Infobox interval region
	\| Name = Major third		\| Name = Major third
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	\| Complement = [[Minor sixth]]		\| Complement = [[Minor sixth]]
	\| Subregions = [[Submajor third]] <br> [[Supermajor third]] <br> [[Ultramajor third]]		\| Subregions = [[Submajor third]] <br> [[Supermajor third]] <br> [[Ultramajor third]]
	}}~~{{Wikipedia}}~~		}}
	A major third (M3) is the larger of the two "thirds" - intervals spanning 3 degrees or 2 scale steps in the diatonic scale. It is found between the 1st and 3rd notes of the major scale, hence its name. Another diatonic interval around the same size is the '''diminished fourth.''' More generally, an interval close to 400 cents in size can be called a major third.

	~~== As an interval region ==~~
	As an [[interval region]], a major third is typically near 400{{c}} in size. A rough tuning range for the major third is about 370 to 440{{c}} according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350–450{{c}} range as a whole, and to a specific subdivision within it (~370–415{{c}}) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".		As an [[interval region]], a major third is typically near 400{{c}} in size. A rough tuning range for the major third is about 370 to 440{{c}} according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350–450{{c}} range as a whole, and to a specific subdivision within it (~370–415{{c}}) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".

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	! 5/4		! 5/4
	! 9/7		! 9/7
	!Diatonic major third		! Diatonic major third
	\|-		\|-
	\| 12		\| 12
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	\| 375{{c}}		\| 375{{c}}
	\| 450{{c}}		\| 450{{c}}
	\|*		\| *
	\|-		\|-
	\| 17		\| 17
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	\| 379{{c}}		\| 379{{c}}
	\| 442{{c}}		\| 442{{c}}
	\|379{{c}}		\| 379{{c}}
	\|-		\|-
	\| 22		\| 22
	\| 382{{c}}		\| 382{{c}}
	\| 436{{c}}		\| 436{{c}}
	\|436{{c}}		\| 436{{c}}
	\|-		\|-
	\| 24		\| 24
	\| 400{{c}}		\| 400{{c}}
	\| 450{{c}}		\| 450{{c}}
	\|400{{c}}		\| 400{{c}}
	\|-		\|-
	\| 25		\| 25
	\| 384{{c}}		\| 384{{c}}
	\| 432{{c}}		\| 432{{c}}
	\|*		\| *
	\|-		\|-
	\| 26		\| 26
	\| 369{{c}}		\| 369{{c}}
	\| 415{{c}}		\| 415{{c}}
	\|369{{c}}		\| 369{{c}}
	\|-		\|-
	\| 27		\| 27
	\| 400{{c}}		\| 400{{c}}
	\| 444{{c}}		\| 444{{c}}
	\|444{{c}}		\| 444{{c}}
	\|-		\|-
	\| 29		\| 29
	\| 372{{c}}		\| 372{{c}}
	\| 455{{c}}		\| 455{{c}}
	\|{{nowrap\|414{{c}} ≈ 81/64, 14/11}}		\| {{nowrap\|414{{c}} ≈ 81/64, 14/11}}
	\|-		\|-
	\| 31		\| 31
	\| 387{{c}}		\| 387{{c}}
	\| 426{{c}}		\| 426{{c}}
	\|387{{c}}		\| 387{{c}}
	\|-		\|-
	\| 34		\| 34
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	\| 381{{c}}		\| 381{{c}}
	\| 439{{c}}		\| 439{{c}}
	\|{{nowrap\|410{{c}} ≈ 81/64}}		\| {{nowrap\|410{{c}} ≈ 81/64}}
	\|-		\|-
	\| 53		\| 53
	\| 385{{c}}		\| 385{{c}}
	\| 430{{c}}		\| 430{{c}}
	\|408{{c}} ≈ 81/64		\| 408{{c}} ≈ 81/64
	\|}		\|}
	<nowiki>*</nowiki> There is a valid interval in this edo, but it is well outside the range of a major third.		<nowiki>*</nowiki> There is a valid interval in this edo, but it is well outside the range of a major third.

	~~<nowiki/>~~
	== In regular temperaments ==		== In regular temperaments ==
	The two simplest major third ratios are 5/4 and 9/7. The following notable temperaments are generated by them:		The two simplest major third ratios are 5/4 and 9/7. The following notable temperaments are generated by them:
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	* [[Sensi]], generated by sharp supermajor thirds representing [[9/7]] and [[13/10]], such that a stack of two gives a major sixth approximating [[5/3]], and a stack of seven gives [[6/1]].		* [[Sensi]], generated by sharp supermajor thirds representing [[9/7]] and [[13/10]], such that a stack of two gives a major sixth approximating [[5/3]], and a stack of seven gives [[6/1]].
	* [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]].		* [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]].

	~~== See also ==~~
	* [[Major third]] (disambiguation page)

	{{Navbox intervals}}		{{Navbox intervals}}

FloraC: FloraC moved page Major third (interval region) to Major third: One page

2026-03-30T11:28:21Z

FloraC moved page Major third (interval region) to Major third: One page

← Older revision	Revision as of 11:28, 30 March 2026
(No difference)

Lucius Chiaraviglio: /* By prime limit */ Fix formatting to be consistent with the other entries

2025-12-26T21:25:50Z

By prime limit: Fix formatting to be consistent with the other entries

← Older revision		Revision as of 21:25, 26 December 2025
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	** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.		** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.
	* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.		* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.
	* The 23-limit '''vicesimoterial''' ~~super major~~ third is a ratio of [[23/18]], and is about 424{{c}}.		* The 23-limit '''vicesimoterial supermajor''' third is a ratio of [[23/18]], and is about 424{{c}}.

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

Lucius Chiaraviglio: /* By prime limit */ Fix corrupted character

2025-12-26T21:24:42Z

By prime limit: Fix corrupted character

← Older revision		Revision as of 21:24, 26 December 2025
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	** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.		** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.
	* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.		* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.
	* The 23-limit '''vicesimoterial'''~~0super~~ major third is a ratio of [[23/18]], and is about 424{{c}}.		* The 23-limit '''vicesimoterial''' super major third is a ratio of [[23/18]], and is about 424{{c}}.

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

Lucius Chiaraviglio: /* By prime limit */ Add 23/18

2025-12-26T21:24:09Z

By prime limit: Add 23/18

← Older revision		Revision as of 21:24, 26 December 2025
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	** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.		** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.
	* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.		* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.
			* The 23-limit '''vicesimoterial'''0super major third is a ratio of [[23/18]], and is about 424{{c}}.

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

Jdood: why does it say both neutral and minor thirds? my thoughts exactly...

2025-12-03T18:21:29Z

why does it say both neutral and minor thirds? my thoughts exactly...

← Older revision		Revision as of 18:21, 3 December 2025
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	\| MOSes = [[3L 4s]], [[7L 3s]], [[3L 7s]], [[3L 5s]], [[5L 3s]]		\| MOSes = [[3L 4s]], [[7L 3s]], [[3L 7s]], [[3L 5s]], [[5L 3s]]
	\| JI intervals = 5/4, 9/7		\| JI intervals = 5/4, 9/7
	\| Lower region = [[Neutral~~ third]] <br> [[Minor~~ third]]		\| Lower region = [[Neutral third]]
	\| Higher region = [[Perfect fourth]]		\| Higher region = [[Perfect fourth]]
	\| Complement = [[Minor sixth]]		\| Complement = [[Minor sixth]]

Lériendil at 13:32, 5 September 2025

2025-09-05T13:32:54Z

← Older revision		Revision as of 13:32, 5 September 2025
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	* [[Dicot]], an exotemperament which generates 3/2 by stacking two 5/4's so that the mapping dictates that 5/4 and [[6/5]] are equated.		* [[Dicot]], an exotemperament which generates 3/2 by stacking two 5/4's so that the mapping dictates that 5/4 and [[6/5]] are equated.
	* [[Father]], an exotemperament which equates [[4/3]] and 5/4 as a single "fourth-third" interval, from which it derives its name.		* [[Father]], an exotemperament which equates [[4/3]] and 5/4 as a single "fourth-third" interval, from which it derives its name.
	* [[Augmented (temperament)\|Augmented]], which splits the octave into three equal parts, each representing [[5/4]].
	** The 5-limit [[circular temperament]]s in general

	=== Temperaments that use 9/7 as a generator ===		=== Temperaments that use 9/7 as a generator ===
	* [[Sensi]], generated by sharp supermajor thirds representing [[9/7]] and [[13/10]], such that a stack of two gives a major sixth approximating [[5/3]].		* [[Sensi]], generated by sharp supermajor thirds representing [[9/7]] and [[13/10]], such that a stack of two gives a major sixth approximating [[5/3]], and a stack of seven gives [[6/1]].
	* [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]].		* [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]].