I'm a tabla player in (classical) training (still noob though). One of my favorite tala is called "Sardha Roopak", and it's a cycle of 10.5 beats which is trippy. There are other X.5 beat cycles as well.
Here's a video of someone playing a tabla solo in 10.5 beats
Here's a video of someone playing a tabla solo in 10.5 beats
https://youtu.be/8e2L2mr3_W0?t=33