So I'm mainly a drummer, but I like to dabble in tonal music every now and then. My question is this: would an advanced theory of rhythm be possible? There is such structure in tonal music (harmony, modulation etc), but there doesn't seem to be any similar thing for rhythm. Sure, we have cadences and 'rock star endings', but nothing on the scale of tonal music. If you were to formalise and give theoretical structure to rhythm, similar to what we have for tonal music, how would you do it? That's a good question. C-mexx Software The Visualizer there.

African drumming, Steve Reich's phasing, Indian music, maybe Elliott Carter's metric modulation.serialism can be applied to rhythm. There's definitely advanced rhythmic STUFF out there, and since theory just explains what music does, there must be some descriptions of advanced rhythm theory like what you're talking about. I'm not not sure there is a theory for just rhythm instruments independent of tonal content - should there be? My (very limited) understanding of Indian tala is that even the super complex drum rhythms happen underneath melodic phrases.

India Tala seems closest to what you're asking for. Pulse and syncopation can be pretty complicated in their own right. I wouldn't call them basic. Basic is note duration, like Quarter notes and Eighth notes, and how these durations fit within a meter.

I would consider drum corps level rhythms to be the highest level of advanced rhythm, so maybe look into that. I know in the marching percussion stuff I write, I like to create 'ambiguity' of the pulse and its division. So, for example, I might have a bar of 4/4 time.