As much as I am rusty, I do recall a certain beauty to Fourier transforms. Both in what they represent in terms of spectrum, and how you could multiply something by a sine wave, and it would come out to zero, on average, if there were no correllation, and come out to something if there were a correllation. A lot of advanced math made me want to crawl into a cave, but Fourier was simple and beautiful. I like the way your ear does it mechanically and instictively to allow you to percieve music.

Of course, all the other stuff in your post was complete gibberish to me.