But that requires an outside, arbitrary, socially-constructed definition of what a "popular song" is.
Maybe I wasn't clear. The point was that the rules produced music that most people liked when they heard it. One might say it produced "catchy" tunes.
I didn't say it was unexplainable. I'm simply saying that it
isn't science. That isn't to say there is nothing physical going on. It's that there comes a moment of arbitrary imposition that is not science.
I agree. The dividing line between noise and music is often fuzzy, especially in some modern musical works, but there is a distinction there. Too, as you say, how musical sounds are organized is also largely a matter of custom. Personally, I expect that these things could be described in an organized way and the description could be verified by observation.
There is probably an interesting discussion here, but I suppose it's off-topic for this thread. Pity.