> waves with wavelengths that form a simple ratio interact to form periodic waveforms

That is certainly not the case. The superposition of waves is linear, and waves of separate frequencies do not really "interact" besides being linearly combined. The fact that a waveform is periodic is not perceptible in our ears. We hear the frequencies separately and the ratio between them does not matter.

This is not a theoretical concept, but a physical observation that anybody can check. You can readily try it with a synthesizer. Create two waveforms f(x)=sin(x)+sin(2x) and g(x)=sin(x)+sin((2+e)x) where "e" is a small irrational number. The wave f is periodic and the wave g isn't. They sound just the same: you cannot tell which one is periodic just by hearing them.

Stable simple waveforms are observably more consonant than those with many transients. Nobody would have this dumb, stubborn discussion about rhythms.

You are right, this is not a discussion worth having when you can do the experience. If you have a digital synthesizer, just try the experiment that I describe and listen whether you can tell the periodic from the non-periodic waveform. You say that they are perfectly distinguishable, but I just did the experiment (even drawing the lissajous figures) and there's no real difference except the perceived pitch.

I didn't say they were perfectly distinguishable. You have reasons simple ratios don't result in physical waveform attributes relevant to music. I posit you should just really think about that for like five seconds. Otherwise I don't know what to tell you. Look up Pythagoras or maybe what a wave is or something.