You see, they learn harmonic minor first and remember that it has raised 7th scale degree. Only about 3 years later they are introduced to harmonic major which has lowered 6th scale degree. And that's when it's starts to be confusing. Raised 6th or lowered 6th? Raised 7th or lowered 7th?
The quality of harmonic major is very distinctive. Often it is used to depict romance and love, especially in movies.
Since the 6th scale degree is part of the Subdominant chord, lowered 6th scale degree makes this chord appear like minor. That's when very colorful relationship arise - from minor dissonant chord and its major resolution.
If you have a curious mind, pick a key, a meter, and with your right hand start to play one voice melody with suitable rhythms in that key. Use only the notes of the harmonic major (for example, in C major: C, D, E, F, G, Ab, B, C). With your left hand play only 2 chords in alternation - the Tonic (C-E-G) and minor Subdominant (F-Ab-C).
Seeking a smooth voice leading, depending on which inversion of the Tonic chord do you start, keep the common note of both chords (C) stationary while moving the other 2 notes downward in a stepwise motion to the nearest chordal notes of the Tonic chord.
Let me know how does your experiment go.
Transposing Sequence in E Minor: IV6-V65-i