Thanks or your post...

Just an aside,,, the "square root of 2" appears heavily throughout electronics theorey, amplification, etc. I wonder if that value show up in music as well.
Fascinating, can you explain why it comes up so often?
As for music, no. Well, I don't know all of the musics of the world, but for Western common practice period, no they're all rational numbers/ratios. Well, they are in theory, or* if we are truly and perfectly in tune for any specific key. (See, if you are "tempered" like a piano, then you are perfectly out* of tune, because if you are perfectly in tune in one key, you will sound awful in another; string quartets however can play perfectly in tune no matter what the key.)
What's sorta neat is that the most basic of the intervals are also the EXACT same thing as the most basic of polyrhythms. For instance, I'm pretty sure zumbo is drummer, and therefore I simply assume he can play 2 against 3, 3 against 4, and 4 against 5, for instance.
If I record him playing 2vs3, take this recording, and simply speed it up, we will HEAR a perfect fifth (difference between adjacent strings on a violin). If I record him playing 3vs4, speed up the recording, it will be a perfect fourth (difference between adjacent strings on a guitar). Yes, the world seems to be fractal at times!
edit: it's not just polyrhythms but all rhythms. Eighth notes to the quarters, recorded, sped up, sounds like an octave. Because it is an octave. (But again, on a piano, there are no octaves that are perfectly in tune).