Augmented and Diminished Intervals

Theoretical Information

Augmented and Diminished Intervals A2, d7, A5, d4 are formed only in harmonic major and minor, necessarily with the participation of a harmonic step.

An augmented second (A2) is an interval that is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone.
A diminished seventh is an interval produced by narrowing a minor seventh by a chromatic semitone. For instance, the interval from A to G is a minor seventh, ten semitones wide, and both the intervals from A♯ to G, and from A to G♭ are diminished sevenths, spanning nine semitones. Being diminished, it is considered a dissonant interval. The diminished seventh is enharmonically equivalent to a major sixth. Its inversion is the augmented second.    
An augmented fifth is an interval produced by widening a perfect fifth by a chromatic semitone.For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C♭ to G, and from C to G♯ are augmented fifths, spanning eight semitones. Being augmented, it is considered a dissonant interval.   
Its inversion is the diminished fourth, and its enharmonic equivalent is the minor sixth.

These intervals are resolved into stable steps.

The augmented second is resolved into a perfect fourth : A2-P4
diminished seventh — perfect fifth: d7-P5
augmented fifth — major Sixth t: A5-M6
diminished fourth — minor third: d4-m3

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