The Harmonic Minor scale is natural minor with a raised 7th. The augmented 2nd between b6 and 7 gives it a classical, exotic, and slightly Middle Eastern quality. It exists to provide a leading tone in minor keys.
Scale Formula
1 2 b3 4 5 b6 7 - minor with natural 7. Semitone pattern: W H W W H WH H
Fretboard (C Harmonic Minor)
Toggle to interval view and notice the augmented 2nd gap between b6 and 7. This 3-semitone jump is what separates harmonic minor from natural minor and melodic minor.
Common Chords
Minor triad (1 b3 5), Minor-major 7th (1 b3 5 7), Diminished 7th (built on 7th degree).
Diatonic Harmony
Improvisation Context
Play over minor-major 7th chords or tonic minor chords when you want that classical minor sound. The natural 7 creates strong resolution to the root.
Practice
Play C Harmonic Minor ascending and descending, paying attention to the augmented 2nd between Ab and B. Compare it with C Aeolian (Bb instead of B) and C Melodic Minor (A instead of Ab). Each raises one note from natural minor, producing a distinct flavor. Over a Cm(maj7) drone, practice resolving the natural 7 (B) up to the root (C) -- that strong leading tone resolution is the whole reason this scale exists.