Major third (diatonic interval category): Difference between revisions

Line 6:

| Header 4 = Tuning range | Data 4 = 343–480{{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'''.

@@ Line 6: / Line 6: @@
 | Header 4 = Tuning range | Data 4 = 343–480{{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'''.