User:VectorGraphics/Diatonic major third - Revision history

VectorGraphics at 22:23, 25 February 2025

2025-02-25T22:23:57Z

← Older revision		Revision as of 22:23, 25 February 2025
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	{{Infobox\|Title=Diatonic major third\|Data 5=400c\|Data 8=[[~~Diminished 2-pentstep~~]]\|Header 9=Daughter intervals\|Header 8=Parent interval\|Data 7=[[~~Minor 2-pelstep~~]], [[~~Minor 4-oneirostep~~]]\|Data 6=[[Diatonic minor third]]\|Header 7=Adjacent tunings\|Header 6=Chromatically adjacent interval\|Data 4=343c - 480c\|Header 1=MOS\|Data 3=+4 generators\|Data 2=Major 2-diastep\|Header 5=Basic tuning\|Header 4=Tuning range\|Header 3=Generator span\|Header 2=Other names\|Data 1=[[5L 2s]]\|Data 9=[[M-chromatic minor ~~4-step~~]], [[P-chromatic major ~~4-step~~]]\|Header 10=Associated just intervals\|Data 10=[[5/4]], [[81/64]]}}		{{Infobox\|Title=Diatonic major third\|Data 5=400c\|Data 8=[[Pentic diminished third]]\|Header 9=Daughter intervals\|Header 8=Parent interval\|Data 7=[[Antidiatonic minor third]], [[oneirotonic minor fifth]]\|Data 6=[[Diatonic minor third]]\|Header 7=Adjacent tunings\|Header 6=Chromatically adjacent interval\|Data 4=343c - 480c\|Header 1=MOS\|Data 3=+4 generators\|Data 2=Major 2-diastep\|Header 5=Basic tuning\|Header 4=Tuning range\|Header 3=Generator span\|Header 2=Other names\|Data 1=[[5L 2s]]\|Data 9=[[M-chromatic minor fifth]], [[P-chromatic major fifth]]\|Header 10=Associated just intervals\|Data 10=[[5/4]], [[81/64]]}}

	In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.		In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.
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	Being an abstract MOS degree, and not a specific interval, the diatonic major third doesn't 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 doesn't 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 cents to 480 cents. Sharp of this, it becomes a [[minor ~~4-oneirostep~~]], and flat of this, it becomes a [[minor ~~2-pelstep~~]].		The tuning range of the diatonic major third ranges from 342.8 cents to 480 cents. Sharp of this, it becomes an [[oneirotonic minor fifth]], and flat of this, it becomes an [[antidiatonic minor third]].

	The diatonic major third is itself a type of [[diminished ~~2-pentstep~~]], and contains the categories of [[m-chromatic minor ~~4-step~~]] and [[p-chromatic major ~~4-step~~]], corresponding to the flat-of-basic and sharp-of-basic tunings of the major third respectively.		The diatonic major third is itself a type of [[pentic diminished third]], and contains the categories of [[m-chromatic minor fifth]] and [[p-chromatic major fifth]], corresponding to the flat-of-basic and sharp-of-basic tunings of the major third respectively.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Tunings of the major 2-diastep		\|+Tunings of the major 2-diastep
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	\|[[Io]]		\|[[Io]]
	\|[[33/32]]		\|[[33/32]]
	\|Perfect ~~4-diastep~~ ≈ 689c		\|Perfect fifth ≈ 689c
	\|-		\|-
	\|[[16/13]]		\|[[16/13]]
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	\|[[Superflat]]		\|[[Superflat]]
	\|[[1053/1024]]		\|[[1053/1024]]
	\|Perfect ~~4-diastep~~ ≈ 690c		\|Perfect fifth ≈ 690c
	\|-		\|-
	\|[[21/17]]		\|[[21/17]]
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	\|Temperament of 459/448		\|Temperament of 459/448
	\|459/448		\|459/448
	\|Perfect ~~4-diastep~~ ≈ 692c		\|Perfect fifth ≈ 692c
	\|-		\|-
	\|[[5/4]]		\|[[5/4]]
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	\|[[Meantone]]		\|[[Meantone]]
	\|[[81/80]]		\|[[81/80]]
	\|Perfect ~~4-diastep~~ ≈ 697c		\|Perfect fifth ≈ 697c
	\|-		\|-
	\|[[81/64]]		\|[[81/64]]
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	\|[[Pythagorean tuning\|Pythagorean]]		\|[[Pythagorean tuning\|Pythagorean]]
	\|[[1/1]]		\|[[1/1]]
	\|Perfect ~~4-diastep~~ ≈ 702c		\|Perfect fifth ≈ 702c
	\|-		\|-
	\|[[14/11]]		\|[[14/11]]
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	\|[[Parapyth]]/[[Pentacircle]]		\|[[Parapyth]]/[[Pentacircle]]
	\|[[896/891]]		\|[[896/891]]
	\|Perfect ~~4-diastep~~ ≈ 705c		\|Perfect fifth ≈ 705c
	\|-		\|-
	\|[[9/7]]		\|[[9/7]]
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	\|[[Superpyth\|Archy/Superpyth]]		\|[[Superpyth\|Archy/Superpyth]]
	\|[[64/63]]		\|[[64/63]]
	\|Perfect ~~4-diastep~~ ≈ 709c		\|Perfect fifth ≈ 709c
	\|-		\|-
	\|[[13/10]]		\|[[13/10]]
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	\|[[Oceanfront]]/Temperament of 416/405		\|[[Oceanfront]]/Temperament of 416/405
	\|[[416/405]]		\|[[416/405]]
	\|Perfect ~~4-diastep~~ ≈ 714c		\|Perfect fifth ≈ 714c
	\|}		\|}

VectorGraphics at 02:49, 25 February 2025

2025-02-25T02:49:49Z

← Older revision		Revision as of 02:49, 25 February 2025
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	{{Infobox\|Title=Diatonic major third\|Data 5=400c\|Data 8=[[Diminished 2-pentstep]]\|Header 9=Daughter intervals\|Header 8=Parent interval\|Data 7=[[Minor 2-pelstep]], [[Minor 4-oneirostep]]\|Data 6=[[Diatonic minor third]]\|Header 7=Adjacent tunings\|Header 6=Chromatically adjacent interval\|Data 4=343c - 480c\|Header 1=MOS\|Data 3=+4 generators\|Data 2=Major 2-diastep\|Header 5=Basic tuning\|Header 4=Tuning range\|Header 3=Generator span\|Header 2=Other names\|Data 1=[[5L 2s]]\|Data 9=[[M-chromatic minor 4-step]], [[P-chromatic major 4-step]]}}		{{Infobox\|Title=Diatonic major third\|Data 5=400c\|Data 8=[[Diminished 2-pentstep]]\|Header 9=Daughter intervals\|Header 8=Parent interval\|Data 7=[[Minor 2-pelstep]], [[Minor 4-oneirostep]]\|Data 6=[[Diatonic minor third]]\|Header 7=Adjacent tunings\|Header 6=Chromatically adjacent interval\|Data 4=343c - 480c\|Header 1=MOS\|Data 3=+4 generators\|Data 2=Major 2-diastep\|Header 5=Basic tuning\|Header 4=Tuning range\|Header 3=Generator span\|Header 2=Other names\|Data 1=[[5L 2s]]\|Data 9=[[M-chromatic minor 4-step]], [[P-chromatic major 4-step]]\|Header 10=Associated just intervals\|Data 10=[[5/4]], [[81/64]]}}

	In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.		In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

VectorGraphics at 02:48, 25 February 2025

2025-02-25T02:48:25Z

← Older revision		Revision as of 02:48, 25 February 2025
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	In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.		In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

	~~Infobox TBD~~

	== Name ==		== Name ==

VectorGraphics at 02:47, 25 February 2025

2025-02-25T02:47:58Z

← Older revision		Revision as of 02:47, 25 February 2025
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			{{Infobox\|Title=Diatonic major third\|Data 5=400c\|Data 8=[[Diminished 2-pentstep]]\|Header 9=Daughter intervals\|Header 8=Parent interval\|Data 7=[[Minor 2-pelstep]], [[Minor 4-oneirostep]]\|Data 6=[[Diatonic minor third]]\|Header 7=Adjacent tunings\|Header 6=Chromatically adjacent interval\|Data 4=343c - 480c\|Header 1=MOS\|Data 3=+4 generators\|Data 2=Major 2-diastep\|Header 5=Basic tuning\|Header 4=Tuning range\|Header 3=Generator span\|Header 2=Other names\|Data 1=[[5L 2s]]\|Data 9=[[M-chromatic minor 4-step]], [[P-chromatic major 4-step]]}}

	In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.		In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth\|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

VectorGraphics at 02:39, 25 February 2025

2025-02-25T02:39:20Z

← Older revision		Revision as of 02:39, 25 February 2025
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	\|[[81/64]]		\|[[81/64]]
	\|408c		\|408c
	\|[[Pythagorean]]		\|[[Pythagorean tuning\|Pythagorean]]
	\|[[1/1]]		\|[[1/1]]
	\|Perfect 4-diastep ≈ 702c		\|Perfect 4-diastep ≈ 702c

VectorGraphics at 02:37, 25 February 2025

2025-02-25T02:37:12Z

← Older revision		Revision as of 02:37, 25 February 2025
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	\|[[1053/1024]]		\|[[1053/1024]]
	\|Perfect 4-diastep ≈ 690c		\|Perfect 4-diastep ≈ 690c
			\|-
			\|[[21/17]]
			\|366c
			\|Temperament of 459/448
			\|459/448
			\|Perfect 4-diastep ≈ 692c
	\|-		\|-
	\|[[5/4]]		\|[[5/4]]

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In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

Infobox TBD

== Name ==
In [[TAMNAMS]], this interval is called the '''major 2-diastep'''. However, because the diatonic scale is the standard scale of Western theory, it is more commonly called a '''major third''', such as in standard Western notation, [[chain-of-fifths notation]] and [[quasi-diatonic MOS notation]].

== Tunings ==
Being an abstract MOS degree, and not a specific interval, the diatonic major third doesn't 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 cents to 480 cents. Sharp of this, it becomes a [[minor 4-oneirostep]], and flat of this, it becomes a [[minor 2-pelstep]].

The diatonic major third is itself a type of [[diminished 2-pentstep]], and contains the categories of [[m-chromatic minor 4-step]] and [[p-chromatic major 4-step]], corresponding to the flat-of-basic and sharp-of-basic tunings of the major third respectively.
{| class="wikitable"
|+Tunings of the major 2-diastep
!Tuning
!Step ratio
!Edo
!Cents
|-
|Equalized
|1:1
|7
|343c
|-
|Supersoft
|4:3
|26
|369c
|-
|Soft
|3:2
|19
|379c
|-
|Semisoft
|5:3
|31
|387c
|-
|Basic
|2:1
|12
|400c
|-
|Semihard
|5:2
|29
|414c
|-
|Hard
|3:1
|17
|424c
|-
|Superhard
|4:1
|22
|436c
|-
|Collapsed
|1:0
|5
|480c
|}

== In regular 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"
|+
!Just interval
!Cents
!Temperament
!Tempered comma
!Generator (eigenmonzo tuning)
|-
|[[27/22]]
|355c
|[[Io]]
|[[33/32]]
|Perfect 4-diastep ≈ 689c
|-
|[[16/13]]
|359c
|[[Superflat]]
|[[1053/1024]]
|Perfect 4-diastep ≈ 690c
|-
|[[5/4]]
|386c
|[[Meantone]]
|[[81/80]]
|Perfect 4-diastep ≈ 697c
|-
|[[81/64]]
|408c
|[[Pythagorean]]
|[[1/1]]
|Perfect 4-diastep ≈ 702c
|-
|[[14/11]]
|418c
|[[Parapyth]]/[[Pentacircle]]
|[[896/891]]
|Perfect 4-diastep ≈ 705c
|-
|[[9/7]]
|435c
|[[Superpyth|Archy/Superpyth]]
|[[64/63]]
|Perfect 4-diastep ≈ 709c
|-
|[[13/10]]
|454c
|[[Oceanfront]]/Temperament of 416/405
|[[416/405]]
|Perfect 4-diastep ≈ 714c
|}