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{{Infobox
{{Infobox
| Title = Diatonic major third
| Title = Diatonic major third
| Header 1 = MOS | Data 1 = [[5L 2s]]
| Header 1 = MOS | Data 1 = [[5L 2s]]
| Header 2 = Other names | Data 2 = Major 2-diastep
| Header 2 = Other names | Data 2 = Major 2-diastep
| Header 3 = Generator span | Data 3 = +4 generators
| Header 3 = Generator span | Data 3 = +4 generators
| Header 4 = Tuning range | Data 4 = 343c – 480c
| Header 4 = Tuning range | Data 4 = 343–480{{c}}
| Header 5 = Basic tuning | Data 5 = 400c
| 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 = Chromatically adjacent interval | Data 6 = [[Minor third (diatonic interval category)|Diatonic minor third]]
| Header 7 = Function on root | Data 7 = Mediant
| Header 7 = Function on root | Data 7 = Mediant
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| Header 10 = Associated just intervals | Data 10 = [[5/4]], [[81/64]]
| Header 10 = Associated just intervals | Data 10 = [[5/4]], [[81/64]]
}}
}}
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'''), 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]].


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)|diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.
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Several example tunings are provided below:
Several example tunings are provided below:
{| class="wikitable"
{| class="wikitable"
|+Tunings of the major third
|+ style="font-size: 105%;" | Tunings of the major third
|-
! Tuning
! Tuning
! Step ratio
! Step ratio
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| 1:1
| 1:1
| 7
| 7
| 343c
| 343{{c}}
|-
|-
| Supersoft
| Supersoft
| 4:3
| 4:3
| 26
| 26
| 369c
| 369{{c}}
|-
|-
| Soft
| Soft
| 3:2
| 3:2
| 19
| 19
| 379c
| 379{{c}}
|-
|-
| Semisoft
| Semisoft
| 5:3
| 5:3
| 31
| 31
| 387c
| 387{{c}}
|-
|-
| Basic
| Basic
| 2:1
| 2:1
| 12
| 12
| 400c
| 400{{c}}
|-
|-
| Semihard
| Semihard
| 5:2
| 5:2
| 29
| 29
| 414c
| 414{{c}}
|-
|-
| Hard
| Hard
| 3:1
| 3:1
| 17
| 17
| 424c
| 424{{c}}
|-
|-
| Superhard
| Superhard
| 4:1
| 4:1
| 22
| 22
| 436c
| 436{{c}}
|-
|-
| Collapsed
| Collapsed
| 1:0
| 1:0
| 5
| 5
| 480c
| 480{{c}}
|}
|}


== In regular temperaments ==
== In regular temperaments ==
=== P5 = 3/2 ===
=== P5 {{=}} 3/2 ===
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"
|+
|-
! Just interval
! Just interval
! Cents
! Cents
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| [[Io]]
| [[Io]]
| [[33/32]]
| [[33/32]]
| Perfect fifth ≈ 689c
| {{nowrap|Perfect fifth ≈ 689{{c}}}}
|-
|-
| [[16/13]]
| [[16/13]]
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| [[Superflat]]
| [[Superflat]]
| [[1053/1024]]
| [[1053/1024]]
| Perfect fifth ≈ 690c
| {{nowrap|Perfect fifth ≈ 690{{c}}}}
|-
|-
| [[21/17]]
| [[21/17]]
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| Temperament of 459/448
| Temperament of 459/448
| 459/448
| 459/448
| Perfect fifth ≈ 692c
| {{nowrap|Perfect fifth ≈ 692{{c}}}}
|-
|-
| [[5/4]]
| [[5/4]]
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| [[Meantone]]
| [[Meantone]]
| [[81/80]]
| [[81/80]]
| Perfect fifth ≈ 697c
| {{nowrap|Perfect fifth ≈ 697{{c}}}}
|-
|-
| [[81/64]]
| [[81/64]]
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| [[Pythagorean tuning|Pythagorean]]
| [[Pythagorean tuning|Pythagorean]]
| [[1/1]]
| [[1/1]]
| Perfect fifth ≈ 702c
| {{nowrap|Perfect fifth ≈ 702{{c}}}}
|-
|-
| [[14/11]]
| [[14/11]]
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| [[Parapyth]]/[[pentacircle]]
| [[Parapyth]]/[[pentacircle]]
| [[896/891]]
| [[896/891]]
| Perfect fifth ≈ 705c
| {{nowrap|Perfect fifth ≈ 705{{c}}}}
|-
|-
| [[9/7]]
| [[9/7]]
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| [[Superpyth|Archy/superpyth]]
| [[Superpyth|Archy/superpyth]]
| [[64/63]]
| [[64/63]]
| Perfect fifth ≈ 709c
| {{nowrap|Perfect fifth ≈ 709{{c}}}}
|-
|-
| [[13/10]]
| [[13/10]]
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| [[Oceanfront]]/Temperament of 416/405
| [[Oceanfront]]/Temperament of 416/405
| [[416/405]]
| [[416/405]]
| Perfect fifth ≈ 714c
| {{nowrap|Perfect fifth ≈ 714{{c}}}}
|}
|}


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