The larger of the two diatonic intervals which encompass 7 degrees of the of the diatonic scale. The major-7th is composed of 5 tones (i.e., whole-tones) and 1 diatonic semitone, and is one chromatic semitone larger than the minor-7th.
________ major-7th ________ | | C D E F G A B C t t s t t t M2 M2 m2 M2 M2 M2 major-7th = 5t + s = 5(t-s) + 6s = 5(M2) + m2 = 5(+1) + 6(m2)
Thus, the major-7th contains 5 chromatic semitones and 6 diatonic semitones (or equivalently, 5 augmented-primes and 6 minor-2nds). In 12-edo, the major-7th encompasses 11 equal semitones.
Widening the "major-7th" by one more chromatic semitone results in the "augmented-7th", an interval rarely found in the standard repertoire.