Augmented and diminished intervals
An interval is the distance between any two pitches.

A melodic interval is the distance between two successive pitches and a harmonic interval is one between two simultaneous pitches.

Intervals are named according to the number of letter names they encompass and the quality or size of the interval.

For example, the interval from C to E is a third because it covers three letters (C, D, E).

Thirds have different possible qualities: C natural to E natural is 4 half steps, called a major third.

C natural to Eb would be only three half steps, or a minor third.

C to E# would also be a third, but it's one half step larger than major, making it augmented.

C# to Eb would be still another third, but with only 2 half steps: it's a diminished third.

Seconds, thirds, sixths, and sevenths can be diminished, minor, majr, or augmented.

Unisons, fourths, fifths, and octaves can only be diminished, perfect, or augmented.

For example, a perfect fifth like C - G covers 7 half steps. A diminished fifth like C# - G has only 6.

You'll have noticed that some intervals are enharmonically equivalent to others. On a piano you use the same keys to play both C-E# and C-F. The augmented third is enharmonically equivalent to the perfect fourth.

The traditions of melodic writing in counterpoint generally discourage writing any diminished or augmented melodic intervals, which are thought to be awkward. This is true even if the interval is enharmonically equivalent to a better interval.

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