Major third: Difference between revisions

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A '''major third (M3)''' ~~is an interval that spans two steps of~~ 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]]s ([[7edo|2\7]] to [[5edo|2\5]]).

A '''major third (M3)''' in the [[5L 2s|diatonic scale]] is an interval that spans two scale steps 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]]s ([[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]].

As a concrete [[interval region]], it is typically near 400 cents in size, distinct from the [[minor third]] of roughly 300 cents and the [[neutral third]] of roughly 350 cents. A rough tuning range for the major third is about 370 to 440 cents according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350-450 cent range as a whole, and to a specific subdivision within it (~370–415 cents) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".

As a concrete [[interval region]], it is typically near 400 [[cents]] in size, distinct from the [[minor third]] of roughly 300 cents and the [[neutral third]] of roughly 350 cents. A rough tuning range for the major third is about 370 to 440 cents according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350-450 cent range as a whole, and to a specific subdivision within it (~370–415 cents) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".

This article covers intervals between 360 and 460 cents. The outer range of this might be too extreme to call "major thirds", but this is done so that one can find what they're looking for easily.

== In just intonation ==

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-A '''major third (M3)''' is an interval that spans two steps of 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]]s ([[7edo|2\7]] to [[5edo|2\5]]).
+A '''major third (M3)''' in the [[5L 2s|diatonic scale]] is an interval that spans two scale steps 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]]s ([[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]].
-As a concrete [[interval region]], it is typically near 400 cents in size, distinct from the [[minor third]] of roughly 300 cents and the [[neutral third]] of roughly 350 cents. A rough tuning range for the major third is about 370 to 440 cents according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350-450 cent range as a whole, and to a specific subdivision within it (~370–415 cents) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".
+As a concrete [[interval region]], it is typically near 400 [[cents]] in size, distinct from the [[minor third]] of roughly 300 cents and the [[neutral third]] of roughly 350 cents. A rough tuning range for the major third is about 370 to 440 cents according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350-450 cent range as a whole, and to a specific subdivision within it (~370–415 cents) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".
+This article covers intervals between 360 and 460 cents. The outer range of this might be too extreme to call "major thirds", but this is done so that one can find what they're looking for easily.
 == In just intonation ==