Can anyone shed some light on what makes this chord progression work?
I know that bVI is a common bit of modal mixture, and minor iv often replaces IV, but I'm wondering what makes them work together here.
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Like with anything else in music, follow the notes and the common tones and they'll tell you all you need to know. The basic idea that is presented in this progression combination of chromatizim though modal mixture along with the traditional resolutions we expect. Let's put a key to this progression. If we were in C major, this progression would map to C, Fm, A♭, and G.
Notice that the C is common in all chords except the G which is taking you right back C chord and is approached by all notes moving down by half step. Also note while we are keeping C as a common tone, we are introducing other tones borrowed from the parallel minor which is adding a contrasting color to the progression. If you were to just move each note to the next closest tone, you would find this.
As you can see, two of the 3 notes don't move at all except moving away by half step and back. This if used effectively can create a lot of motion though use of chords not typically found in C major without actually having the notes move to far.