The interval of a Major Sixth bumped up an octave. The difference between a Major Sixth and a Major Thirteenth is its function within a chord. A major Sixth takes the place of a Major Seventh in either a Major Seven or a Major Seventh Sharp Eleven chord in the case of the root being in the melody. The half-step between the Major seventh and the root in those chords creates an icky sound (unless that’s what you’re looking for...), which is alleviated by the Major Sixth, effectively making it a Major Six or chord. The Major Thirteen is used as an extension, above the seventh, ninth, and sharp eleventh (a Major Seven chord does not take an eleven, since it changes the focus from the I Maj 7 to the IV Maj 7 #11, a V7 does not take an eleven because it mellows dominant pull).


Thirteenths in parentheses

C Maj 13: C E G B D (A)

F Maj 13#11: F A C E G B (D)

G13 G B D F A (E)

E Maj 13 E G# B D# F# (C#)