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Encyclopedia of Microtonal Music Theory

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augmented-4th / aug4 / #4 / +4

[Joe Monzo]

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.

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