The harmonic minor scale is obtained by raising by a semitone the seventh degree of a natural minor scale.
The second augmented interval created between the sixth and seventh degrees of the scale gives it an unmistakable, very oriental sound.
The A harmonic minor scale is formed by the notes (A, B, C, D, E, D, G#).
The interval sequence in tones and semitones to build it is as follow (T, S, T, T, S, T, T and 1/2).
To obtain the harmonic minor scale in any other key, it will be enough to apply the tones and semitones sequence starting from the chosen tonic note.
The C harmonic minor scale, for example, will be (C, D, Eb, F, G, Ab, B).