The larger of the two diatonic intervals which encompass 6 degrees of the of the diatonic scale. The major-6th is composed of 4 tones (i.e., whole-tones) and 1 diatonic semitone, and is one chromatic semitone larger than the minor-6th.
______ major-6th _____ | | C D E F G A B C t t s t t M2 M2 m2 M2 M2 major-6th = 4t + s = 4(t-s) + 5s = 4(M2) + m2 = 4(+1) + 5(m2)
Thus, the major-6th contains 4 chromatic semitones and 5 diatonic semitones (or equivalently, 4 augmented-primes and 5 minor-2nds). In 12-edo, the major-6th encompasses 9 equal semitones.
Widening the "major-6th" by one more chromatic semitone results in the "augmented-6th".