With regard to tonality: you might enjoy some microtonal works, traditional turkish music [0], electronic music [1] and many other non-european musical traditions (indian, arab).
For rhythm there's a wide range for experimentation: from really slow tempos [2] to really fast and (seemingly) chaotic [3]. I like this study from Conlon Nancarrow [4], where the tempo between two voices evolve in time in coordination with each other.
So this 'different' music exists, and has existed for a long time in human history, it's just not very popular. E.G. In [1], apart from Wendy Carlos's invented microtonal scales there are some songs that take from other cultures [5] (See how the 7th track is similar to [3] interestingly enough).
And it makes sense for not being popular actually, given how human ears perceive chords as really fast polyrhythms. The simpler the more harmonic they sound. [6]
0: https://www.youtube.com/watch?v=JxWUgqduqYM
1: https://soundcloud.com/roberto-la-forgia/sets/beauty-in-the-...
2: https://www.youtube.com/watch?v=wEiRKpflgQA
3: https://www.youtube.com/watch?v=Zg1sgrw1PGM (1:50 onwards)
4: https://www.youtube.com/watch?v=f2gVhBxwRqg
5: https://en.wikipedia.org/wiki/Beauty_in_the_Beast
6: https://www.youtube.com/watch?v=JiNKlhspdKg