Another mathematical theory using group theory is: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola.
He shows that music lives in the Z12 group and chords are invariant subgroups. Interesting read.
The joke about Mazzola is that people who know enough about music to see through his theories are bamboozled by his maths, and vice versa.
If you want to explore that space, Tymoczko's A Geometry of Music is more rewarding.
But this misses the point. Music isn't just mathematical consonance and dissonance. Music is the practice of using consonance, dissonance, timbre, rhythm, form, and historic and cultural references, with aesthetic intent - i.e. creating metaphors and other complex cognitive experiences out of musical material.
The difference between a composer and a dabbler is that composers either work at this level consciously and deliberately, or they have unusually effective musical instincts and use them to decide if something "sounds right" or "works."
Any naive mathematical description - which includes all of the work on ML in music - misses this ability of musical material to create those extra levels of expression and meaning.
Hmm, i suppose it would be hard to generate music with ML that make cultural or emotional references, the ML would need to resemble a human in order to understand these, or otherwise understand humans like we understand ourselves. However, current ML sytems might succeed in making references in its music involving a simpler context, like an arcade game, or common physics.
