I think if that were true, we’d see other orbitals that are harmonics of the lower fundamental, but not a harmonic of the s orbital... which we I don’t think we see in practice? (If we did, we wouldn’t consider the s orbital to be fundamental.)

This is very interesting.

So, if we interpret all matter to be different expressions of a fundamental frequency, it means us, the observers are also made up of the same, and to observe you would be basically sampling reality. Even if you consider measurement instruments to be an observer, they also sample other things that are made up of the same.

Then maybe there's a fundamental limit to what we can sample, hence observe. And that could explain why we only observe harmonics of the s orbital.

In this case, the lower fundamental would be something that permeates space (zero-point energy?), so the orbitals that are harmonics of the lower fundamental but not an atom's s orbital would be on other atoms entirely.

No, because the energy of the electron is known and is always quantized.

When you say this what do you mean?

Here are some statements of my own, typed quickly on a phone before I head to work:

-Electrons do not in general have quantized energy; only bound electrons have a discrete energy spectrum

-Electrons do not necessarily have a single energy; although energy eigenstates form a basis that can describe all states, very often the electron won't be in a pure eigenstate

-Single electron models are simplifications; in general, atoms will have multielectron states that are very difficult to write down or reason about; it's deep and non-obvious why single electron models do so well at describing behavior of multielectron wavefunctions

By the way you seem really smart and I love the enthusiasm, I don’t want to seem like a downer.. if you haven’t already taken some classes in physics, you should