This sounds like a project idea with a lot of potential!
The ways that you've mentioned- treble clef to bass clef and chord progressions- seem like a good place to start. I'd suggest also looking up the 'Circle of Fifths', which is a diagram that could help you break down the music into different categories based on note transitions. As for chords, there is usually a base note out of which the chord is constructed; looking up 'Chord Theory' might tell you more, as I'm not too familiar with music theory.
Alternately, you could pick out one series of notes as being the melody, then record those notes as numbers- A to 1, B to 2, and so on and so forth, with flats and sharps being decimals; A sharp would be 1.5, in that sense. After turning the music into a string of numbers, you could code in essentially any kind of analysis that you were interested in- frequency of different interval jumps, frequency of discordant notes, and so on.
I'm typing up this reply in a little bit of a hurry, so I may have made something unclear; if so, please don't hesitate to ask!
Hope this helped, and good luck,
Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.