Sound quantization

Sounds. They're everywhere. At least everywhere I've been.

Attempt to map sounds to numbers bijectively. Given a finite sampling rate, it's possible, right? So I wonder... how to map it?

The individual, "purer" sounds would be integers. Countable, even if infinite. Clinks, steps, single instrument notes. Those sound like integers to me.

Then music pieces... sequences of integers... often cut into parts, mixed and matched, harmonized together... likened to rationals? Maybe?

But sounds in nature never stop. They go on forever. The wind through a tree's branches, a river stream. Like... irrationals. Pi and e should be out there somewhere.

Just a conceptual whim.