The harmonic minor scale is a more complicated (sophisticated?) scale than the major scale. This post will show all the relative chords to the harmonic minor scale (in the key of A).
First, let’s see what it looks like:
As you can see, the only real difference between the harmonic minor scale and the minor scale is that the 7th is sharpened. This gives a very “eastern” tone, and is indeed used in many Eastern European and Middle Eastern songs.
However, the fact that that the 7th is sharpened completely changes the chords that are structured around this scale. Following the 1st-3rd-5th rule outlined in Music Theory for Guitar we get the following chords over the A harmonic minor scale:
Am, Bdim, Caug, Dm, E, F, G#dim
Compared that to the chords of the A minor scale:
Am, Bdim, C, Dm, Em, F, G
The one thing to remember is that the diminished chord should probably be used sparingly because it doesn’t have a very pleasant tone (we will see why in an upcoming post about note frequencies) — but if you’re going for unpleasant or evil sounds, maybe this chord is right for you.
The augmented chord has a very cool, jazzy tone to it, and again, depending on the sound you are looking for, it may or may not work for you.
I feel like I am just scratching the surface of music theory, but at the same time having a lot of fun discovering this stuff by myself in a very mathematical fashion.