One of the fundamental uses for the Harmonic minor scale is to add a IV minor chord into a Major key. In C Major it is F minor (from A Harmonic minor). It makes use of an enharmonic equivalent, G# being spelled as Ab, to create the minor chord, but this is just the basic principle. The next step is to use the IV minor chords from adjacent Harmonic minor scales.
I cover this principle in great detail in Section III of the Modal Method, where the focus is not only on using scales from either side of the key that the music is in, but also the same with the substitute scales such as the Harmonic minor here being used for its IV minor chord.
So for example, the IV minor chord in C Major is F minor (A Harm min), in D Harmonic minor (the key back a 5th) it is Bb min and in E Harmonic minor it is C min. But it doesn't stop there.
Another very useful key is the parallel minor, in C Major it is C minor. Then the IV minor chord from C Harmonic minor, Ab minor, is used.
Using the scales from keys either side of the one we are in is an art, with basically two approaches. Forward and back motion, or incremental use, eg:
A H min- E H min - A H min - D H min - A H min - C H min - A H min is a nice simple way of getting the scales in while the other is more of a surprise approach, or implied use: C Maj - E H min - C H min - C Maj.
The example below is based around the progression: C Major - D Harmonic minor - C Major - A Harmonic minor - C Harmonic minor - C Major. The chords from the relevant Harmonic minor scales are listed below the notes.
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