A diatonic interval which is one chromatic semitone larger than the perfect-4th of the diatonic scale. The augmented-4th is composed of 3 tones (i.e., whole-tones).
The augmented 4th occurs naturally in every diatonic major and harmonic-minor scale, between the "subdominant" (4th degree or "IV") and the "leading-tone" (7th degree or "VII"). Example, in the key of C-major ("t" = tone, "s" = semitone) :
M2 M2 m2 M2 M2 M2 m2 t t s t t t s C D E F G A B C |___________| augmented 4th augmented-4th = 3t = 3(t-s) + 3s = 3(M2) = 3(+1) + 3(m2)
Thus, the augmented-4th contains 3 chromatic semitones and 3 diatonic semitones (or equivalently, 3 augmented-primes and 3 minor-2nds). In 12-edo, the augmented-4th encompasses 6 equal semitones.
The augmented-4th is also known as the "tritone", which see for more information.