Well, nobody's going to argue that music is not sound (and that any sound can be perceived as having "musical properties" depending on the context and the ear/mindset combination that receives such signals), but I cannot agree that all sound is harmonic. Is this what you are suggesting? As far as I am concerned, there are sounds with definite pitch (perceived frequency) or indefinite pitch (let us call it inharmonic spectra). I will pass on commenting on the rest of your post.
I used to play a game, and I still do; I would try to hear the "pitch" of noises in the environment. Some of them had pitches, but with some of them, like vacuum cleaners, which produced a constant roar of noise which contained a lot of harmonics, I realized that I could hear it as almost any pitch I wanted. Later, I realized what was happening. I was "filtering" the sound with my brain, and just tuning in to the pitch I wanted to hear.
As Dim7 was asking, all "noise" is, is sound with a whole bunch of harmonics and no definite pitch; and yes, there are degrees of this.
Stockhausen did a piece called Mikrophonie, where he struck a gong (pretty noisy), and got a flat-head condenser mike, and ran it over the surface, not touchin, but very close. Through the amps, it sounded like a single tone. This is because the mike was picking up whatever harmonic was present in that particular spot.
He invites us to get microphones ourselves, and become "microscopic sound explorers."
