It would be cool to see exactly what sort of model would produce behavior like this. I'm a theoretical physicist, and at first glance I have absolutely no idea

It would be cool to see exactly what sort of model would produce behavior like this. I'm a theoretical physicist, and at first glance I have absolutely no idea how one could write down a model that had "energy at a frequency that isn't a harmonic": it doesn't really fit with anything that I know about quantum systems or quantum field theory, which pretty solidly force us into discrete energy spectra for the types of systems that you're talking about. But I'd love to see a mathematically consistent model that does what you're talking about: it sounds fresh and different, if it turns out to be possible at all. If you come up with some math to share, please do! (Hmm... in the back of my mind, there was some interest years ago in "unparticle" models that might maybe possibly be related, or maybe I'm just completely fuzzy on what that idea was about.)