Genre Analysis

For the longest time, I have been interested in genres. I like thinking about what it is that tells you that a song is reggae and not grunge or dirty south gangsta rap or whatever. Obviously, the easiest way to do this is with math, because math is awesome! I started by thinking about several common genres, and what makes them different. I came up with several dimensional scales with which a genre or artist might fall. I may think of more (and I am open do suggestions!), but here is what I have so far:

Focus on Melody vs Focus on Rhythm

Power Metal vs Dance

Focus on Lyrics vs Focus on Instrumentation

Rap vs Classical

Natural vs. Artificial Instrumentation

Folk vs Electronic

Those are the clear cut ones. The others are a little more subjective:

Complexity

Progressive vs Punk

Aggressiveness

Blackened Death Metal vs Bubblegum Pop

The last one may be the hardest to judge, is a lot more subjective, and may be completely unnecessary. I'm looking for a broad genre that would have the same output as a different one, but haven't found one yet. As an either-or (binary system) instead of a scale, this allows for 32 different options, which even for broad genres doesn't seem like enough. I am open for thoughts on this.