Essentials of Music Theory: Elementary

by Carl E. Gardner

8. The augmented third is analogous to the perfect fourth. This interval is found in the altered minor triad between the third and the raised fifth of the triad. Derivation of the augmented third:—

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Exercise:—

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9. The augmented sixth is analogous to the minor seventh. This interval is found in the augmented sixth chord. Origin of the augmented sixth chord:—

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The diminished sixth, which is the inversion of the augmented third and analogous to the perfect fifth, is not used melodically. The diminished third, which is the inversion of the augmented sixth and analogous to the major second, is but seldom used melodically.