One way to figure out how a chord will sound is to look at which other chords have the same notes, but what happens when chords that are supposed to be similar refuse to share? The best example of this is the Chromatic Mediant, two chords that seem like they should be mostly the same, but with some changes made to their common tones to push them a little further apart. They're a great tool for both functional and non-functional harmony, giving you a sound that's simultaneously connected and detached, smooth yet bold, and they just sound great. Plus there's something called a hexatonic pole!
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Also, thanks to Jareth Arnold and Inés Dawson for proofreading the script to make sure this all makes sense hopefully!