Major third: Difference between revisions
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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 | ||
| Line 11: | Line 20: | ||
| Complement = [[Minor sixth]] | | Complement = [[Minor sixth]] | ||
| Subregions = [[Submajor third]] <br> [[Supermajor third]] <br> [[Ultramajor third]] | | Subregions = [[Submajor third]] <br> [[Supermajor third]] <br> [[Ultramajor third]] | ||
}} | }} | ||
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 | ||
| Line 235: | Line 241: | ||
| 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 | ||
| Line 279: | Line 285: | ||
| 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. | ||
== 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]]. | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||