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I am a DJ and the software I dj with just introduced key analyzation (Serato DJ). So now I have the key to every song in my library. Someone invented a way for DJ's to mix music in key without having to memorize classical keys. It's called a Camelot Wheel. (MixedinKey.com)
The way it basically works is: mixing songs immediately to the left or right or up produces a good harmonic mix. So, if you're playing a song in Ab minor (1A), it'll sound good with 12A, 2A or 1B.
So, my question is why do certain keys sound harmonically good together?
Why does, say, Ab Minor sound good with either Db Minor or Eb Minor?
P.S.: I am grad student in mathematics so I'd prefer if you can get technical mathematically. Not necessary though.