>Sound is just air pressure wobbling.
Sorry man, if you approach things from that angle then no wonder music is a mystery to you.
The issue with "deriving from first principles" is that it very much depends on what you consider "principles" and which you pick. Take two people who want to derive sth "from first principles" and they will arrive at wildly different things. Because they start very differently. That's why this "ignore everything that came before" approach (different name for "from first principles) is so flawed and limited. There is so much insight to gain from the wisdom that came before you that ignoring it isn't going to help.
> the simpler the fraction, the better it sounds
That's comically wrong. If everything was just an octave, you wouldn't even have music.
Sorry, I stopped reading there. It's as if a physics student tries to derive medicine "from first principles" by starting at atoms and thinking hard. It doesn't work and won't fix your appendix.