Major third (diatonic interval category) - Revision history

FloraC: Changed redirect target from Major third (interval region) to Major third

2026-03-30T12:20:01Z

Changed redirect target from Major third (interval region) to Major third

← Older revision		Revision as of 12:20, 30 March 2026
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	#REDIRECT [[Major third ~~(interval region)]]~~		#REDIRECT [[Major third]]
	~~[[Category:Diatonic interval categories~~]]

VectorGraphics: All the content of this page has been migrated to the other page for a while at this point

2025-06-18T06:05:28Z

All the content of this page has been migrated to the other page for a while at this point

Show changes

FloraC: Paragraphing

2025-04-17T13:16:41Z

Paragraphing

← Older revision		Revision as of 13:16, 17 April 2025
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	\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	}}		}}
	A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and [[24edo\|8\24]]. The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]).

			In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and [[24edo\|8\24]]. The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	The major third can be stacked with a [[minor third (diatonic interval category)\|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 (diatonic interval category)\|minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

FloraC: Linking

2025-04-17T12:51:26Z

Linking

← Older revision		Revision as of 12:51, 17 April 2025
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	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 = Function on root \| Data 6 = Mediant		\| Header 6 = Function on root \| Data 6 = Mediant
	\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[major third (interval region)\|major third]], [[naiadic]]		\| Header 7 = Interval regions \| Data 7 = [[Neutral third (interval region)\|Neutral third]], [[major third (interval region)\|major third]], [[naiadic]]
	\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]		\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]
	\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]

FloraC: More cleanup

2025-04-17T12:46:29Z

More cleanup

← Older revision		Revision as of 12:46, 17 April 2025
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	Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale.		Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale.

	The tuning range of the diatonic major third ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major third can be found by {{~~sfrac~~\|''n'' + 2400\|4}}. For example, the third 384{{c}} gives us {{nowrap\|~~{{sfrac\|~~384 + 2400\|4}} {{=}} ~~{{sfrac\|~~2784\|4}} {{=}} 696{{c}}}}, corresponding to 50edo.		The tuning range of the diatonic major third ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major third can be found by {{nowrap\| (''n'' + 2400)/4 }}. For example, the third 384{{c}} gives us {{nowrap\| (384 + 2400)/4 {{=}} 2784/4 {{=}} 696{{c}} }}, corresponding to 50edo.

	Several example tunings are provided below:		Several example tunings are provided below:
	{\| class="wikitable"		{\| class="wikitable center-all left-1"
	\|+ style="font-size: 105%;" \| Tunings of the major third		\|+ style="font-size: 105%;" \| Tunings of the major third
	\|-		\|-
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	If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major third leads to the following temperaments:		If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major third leads to the following temperaments:

	{\| class="wikitable"		{\| class="wikitable center-2 center-5"
	\|-		\|-
	! Just interval		! Just<br>interval
	! Cents		! Cents
	! Temperament		! Temperament
	! ~~Tempered~~ comma		! Vanishing<br>comma
	! Generator (eigenmonzo tuning)		! Generator<br>(eigenmonzo tuning)
	\|-		\|-
	\| [[27/22]]		\| [[27/22]]
Line 96:		Line 96:
	\| [[Io]]		\| [[Io]]
	\| [[33/32]]		\| [[33/32]]
	\| {{nowrap\|~~Perfect fifth~~ ≈ 689{{c}}}}		\| {{nowrap\| P5 ≈ 689{{c}} }}
	\|-		\|-
	\| [[16/13]]		\| [[16/13]]
Line 102:		Line 102:
	\| [[Superflat]]		\| [[Superflat]]
	\| [[1053/1024]]		\| [[1053/1024]]
	\| {{nowrap\|~~Perfect fifth~~ ≈ 690{{c}}}}		\| {{nowrap\| P5 ≈ 690{{c}} }}
	\|-		\|-
	\| [[21/17]]		\| [[21/17]]
Line 108:		Line 108:
	\| Temperament of 459/448		\| Temperament of 459/448
	\| 459/448		\| 459/448
	\| {{nowrap\|~~Perfect fifth~~ ≈ 692{{c}}}}		\| {{nowrap\| P5 ≈ 692{{c}} }}
	\|-		\|-
	\| [[5/4]]		\| [[5/4]]
Line 114:		Line 114:
	\| [[Meantone]]		\| [[Meantone]]
	\| [[81/80]]		\| [[81/80]]
	\| {{nowrap\|~~Perfect fifth~~ ≈ 697{{c}}}}		\| {{nowrap\| P5 ≈ 697{{c}} }}
	\|-		\|-
	\| [[81/64]]		\| [[81/64]]
	\| 408{{c}}		\| 408{{c}}
	\| [[Pythagorean tuning~~\|Pythagorean~~]]		\| [[Pythagorean tuning]]
	\| [[1/1]]		\| [[1/1]]
	\| {{nowrap\|~~Perfect fifth~~ ≈ 702{{c}}}}		\| {{nowrap\| P5 ≈ 702{{c}} }}
	\|-		\|-
	\| [[14/11]]		\| [[14/11]]
	\| 418{{c}}		\| 418{{c}}
	\| [[~~Parapyth]]/[[pentacircle~~]]		\| [[Pepperoni]]
	\| [[896/891]]		\| [[896/891]]
	\| {{nowrap\|~~Perfect fifth~~ ≈ 705{{c}}}}		\| {{nowrap\| P5 ≈ 705{{c}} }}
	\|-		\|-
	\| [[9/7]]		\| [[9/7]]
Line 132:		Line 132:
	\| [[Superpyth\|Archy/superpyth]]		\| [[Superpyth\|Archy/superpyth]]
	\| [[64/63]]		\| [[64/63]]
	\| {{nowrap\|~~Perfect fifth~~ ≈ 709{{c}}}}		\| {{nowrap\| P5 ≈ 709{{c}} }}
	\|-		\|-
	\| [[13/10]]		\| [[13/10]]
	\| 454{{c}}		\| 454{{c}}
	\| [[Oceanfront]]/~~Temperament~~ of 416/405		\| [[Oceanfront]] / temperament of 416/405
	\| [[416/405]]		\| [[416/405]]
	\| {{nowrap\|~~Perfect fifth~~ ≈ 714{{c}}}}		\| {{nowrap\| P5 ≈ 714{{c}} }}
	\|}		\|}

FloraC: Invert the wording on diatonic/chromatic scale steps for beginner-friendliness

2025-04-17T12:37:44Z

Invert the wording on diatonic/chromatic scale steps for beginner-friendliness

← Older revision		Revision as of 12:37, 17 April 2025
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	\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	}}		}}
	A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] ~~(precisely two steps of the diatonic scale and four steps of the chromatic scale)~~. The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and [[24edo\|8\24]]. The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	The major third can be stacked with a [[minor third (diatonic interval category)\|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 (diatonic interval category)\|minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

FloraC: The next region is naiadic or interseptimal third-fourth (the corresponding interval region page doesn't exist. May standardize later)

2025-04-17T12:23:49Z

The next region is naiadic or interseptimal third-fourth (the corresponding interval region page doesn't exist. May standardize later)

← Older revision		Revision as of 12:23, 17 April 2025
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	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 = Function on root \| Data 6 = Mediant		\| Header 6 = Function on root \| Data 6 = Mediant
	\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[~~Major~~ third (interval region)\|~~Major~~ third]], [[~~Perfect fourth~~]]		\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[major third (interval region)\|major third]], [[naiadic]]
	\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]		\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]
	\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]

FloraC: No major centrism

2025-04-17T12:20:13Z

No major centrism

← Older revision		Revision as of 12:20, 17 April 2025
Line 7:		Line 7:
	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 = Function on root \| Data 6 = Mediant		\| Header 6 = Function on root \| Data 6 = Mediant
	\| Header 7 ~~= Positions in major scale \| Data 7 = 1, 4, 5~~		\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]
	~~\| Header 8~~ = Interval regions \| Data 8 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]		\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]
	\| Header 9 = Associated just intervals \| Data 9 = [[5/4]], [[81/64]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	\| Header 10 = Octave complement \| Data 10 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	}}		}}
	A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

FloraC: Chromatically adjacent interval not as useful as octave complement. -duplicate sentence components. Fix linking

2025-04-17T12:14:13Z

Chromatically adjacent interval not as useful as octave complement. -duplicate sentence components. Fix linking

← Older revision		Revision as of 12:14, 17 April 2025
Line 6:		Line 6:
	\| Header 4 = Tuning range \| Data 4 = 343–480{{c}}		\| Header 4 = Tuning range \| Data 4 = 343–480{{c}}
	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 ~~= Chromatically adjacent interval \| Data 6 = [[Minor third (diatonic interval category)\|Diatonic minor third]]~~		\| Header 6 = Function on root \| Data 6 = Mediant
	~~\| Header 7~~ = Function on root \| Data 7 = Mediant		\| Header 7 = Positions in major scale \| Data 7 = 1, 4, 5
	\| Header 8 = Positions in major scale \| Data 8 = 1, 4, 5		\| Header 8 = Interval regions \| Data 8 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]
	\| Header 9 = Interval regions \| Data 9 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]		\| Header 9 = Associated just intervals \| Data 9 = [[5/4]], [[81/64]]
	\| Header 10 = Associated just intervals \| Data 10 = [[5/4]], [[81/64]]		\| Header 10 = Octave complement \| Data 10 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	}}		}}
	A '''major third''' ('''M3''')~~, in the diatonic scale,~~ is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	The major third can be stacked with a [[minor third (diatonic interval)\|~~diatonic~~ 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 (diatonic interval category)\|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'''.

BudjarnLambeth: Categorised uncategorised page

2025-03-17T09:05:38Z

Categorised uncategorised page

← Older revision		Revision as of 09:05, 17 March 2025
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	== See also ==		== See also ==
	* [[Major third]] (disambiguation page)		* [[Major third]] (disambiguation page)

			[[Category:Diatonic interval categories]]

← Older revision		Revision as of 13:16, 17 April 2025
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	\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	}}		}}
	A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and [[24edo\|8\24]]. The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]).

			In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and [[24edo\|8\24]]. The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	The major third can be stacked with a [[minor third (diatonic interval category)\|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 (diatonic interval category)\|minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

← Older revision		Revision as of 12:51, 17 April 2025
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	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 = Function on root \| Data 6 = Mediant		\| Header 6 = Function on root \| Data 6 = Mediant
	\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[major third (interval region)\|major third]], [[naiadic]]		\| Header 7 = Interval regions \| Data 7 = [[Neutral third (interval region)\|Neutral third]], [[major third (interval region)\|major third]], [[naiadic]]
	\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]		\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]
	\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]

← Older revision		Revision as of 12:23, 17 April 2025
Line 7:		Line 7:
	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 = Function on root \| Data 6 = Mediant		\| Header 6 = Function on root \| Data 6 = Mediant
	\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[~~Major~~ third (interval region)\|~~Major~~ third]], [[~~Perfect fourth~~]]		\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[major third (interval region)\|major third]], [[naiadic]]
	\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]		\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]
	\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]

← Older revision		Revision as of 12:20, 17 April 2025
Line 7:		Line 7:
	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 = Function on root \| Data 6 = Mediant		\| Header 6 = Function on root \| Data 6 = Mediant
	\| Header 7 ~~= Positions in major scale \| Data 7 = 1, 4, 5~~		\| Header 7 = Interval regions \| Data 7 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]
	~~\| Header 8~~ = Interval regions \| Data 8 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]		\| Header 8 = Associated just intervals \| Data 8 = [[5/4]], [[81/64]]
	\| Header 9 = Associated just intervals \| Data 9 = [[5/4]], [[81/64]]		\| Header 9 = Octave complement \| Data 9 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	\| Header 10 = Octave complement \| Data 10 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	}}		}}
	A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

← Older revision		Revision as of 12:14, 17 April 2025
Line 6:		Line 6:
	\| Header 4 = Tuning range \| Data 4 = 343–480{{c}}		\| Header 4 = Tuning range \| Data 4 = 343–480{{c}}
	\| Header 5 = Basic tuning \| Data 5 = 400{{c}}		\| Header 5 = Basic tuning \| Data 5 = 400{{c}}
	\| Header 6 ~~= Chromatically adjacent interval \| Data 6 = [[Minor third (diatonic interval category)\|Diatonic minor third]]~~		\| Header 6 = Function on root \| Data 6 = Mediant
	~~\| Header 7~~ = Function on root \| Data 7 = Mediant		\| Header 7 = Positions in major scale \| Data 7 = 1, 4, 5
	\| Header 8 = Positions in major scale \| Data 8 = 1, 4, 5		\| Header 8 = Interval regions \| Data 8 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]
	\| Header 9 = Interval regions \| Data 9 = [[Neutral third]], [[Major third (interval region)\|Major third]], [[Perfect fourth]]		\| Header 9 = Associated just intervals \| Data 9 = [[5/4]], [[81/64]]
	\| Header 10 = Associated just intervals \| Data 10 = [[5/4]], [[81/64]]		\| Header 10 = Octave complement \| Data 10 = [[Minor sixth (diatonic interval category)\|Minor sixth]]
	}}		}}
	A '''major third''' ('''M3''')~~, in the diatonic scale,~~ is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''major third''' ('''M3''') is an interval that spans two scale steps in the [[5L 2s\|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction\|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo\|2\7]] to [[5edo\|2\5]]). In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo\|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	The major third can be stacked with a [[minor third (diatonic interval)\|~~diatonic~~ 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 (diatonic interval category)\|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'''.