A diatonic interval which is one chromatic semitone larger than the perfect-5th of the diatonic scale. The augmented-5th is composed of 3 tones (i.e., whole-tones), one diatonic semitone, and one chromatic semitone. For example, in the key of A-minor:
--------- perfect-5th --------- | | A B C D E F G A = A-natural-minor diatonic scale t t t t s t t M2 M2 M2 M2 m2 M2 M2 chromatic semitone / \ G G# A (t-s) s +1 m2 M2 M2 M2 M2 m2 +2 m2 t t t t s t+(t-s) t A B C D E F G# A = A-harmonic-minor diatonic scale | | ---------- augmented-5th ----------- augmented-5th = 3t + s + (t-s) = 4(t-s) + 4s = 3(M2) + m2 + (+1) = 4(+1) + 4(m2)
The augmented-5th thus contains 4 chromatic semitones and 4 diatonic semitones (or equivalently, 4 augmented-primes and 4 minor-2nds). In 12-edo, the augmented-5th encompasses 8 equal semitones, which makes it enharmonically equivalent to (i.e., exactly the same size as) the minor-6th -- but the augmented-5th is not properly the same as the minor-6th, and in all other tunings of the diatonic scale they are different intervals.
The augmented-5th arose primarily out of "common-practice" harmony as part of the harmonic-minor scale, where the 7th degree ("leading-tone") is raised a half-step so as to approach more closely to the tonic, the note to which it normally resolves.
The augmented-5th is the most prominent feature of the "augmented chord", which arises naturally as the triad built on the 3rd degree (III) of the harmonic-minor diatonic scale.
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