The harmonic major scale is the major scale with a lowered 6th or the harmonic minor scale with a raised 3rd:
major scale = 1 2 3 4 5 6 7 (C D E F G A B)
harmonic major scale = 1 2 3 4 5 b6 7 (C D E F G Ab B)
harmonic minor scale = 1 2 b3 4 5 b6 7 (C D Eb F G Ab B)
harmonic major scale = 1 2 3 4 5 b6 7 (C D E F G Ab B)
*I don't personally use this scale that much, but i may have to experiment more with it because it is used in jazz music
The harmonic minor scale is the natural minor scale with a raised 7th:
natural minor = 1 2 b3 4 5 b6 b7 (C D Eb F G Ab Bb)
harmonic minor = 1 2 b3 4 5 b6 7 (C D Eb F G Ab B)