A practical definition is that classical music is the kind that gets subsidies from governments and foundations, whereas people like popular music enough to pay for it themselves by buying tickets and records and sheet music. Another use of the word classical is an exemplary work of lasting value. By this standard, there is a case that the American Popular Song as defined here, is also classical music. The implication of Rise and Fall in the title is deliberate. These songs are an art form that passed through development, florescence, and decline, but one that may survive in repertory like grand opera and baroque concerti.
Popular music is a universal constant.
American colonists and immigrants brought their national musics with them, and they imported African music along with slavery. We also imported the European custom of sheet music to be played on the living room piano or organ. Popular music included political songs and so-called parlor songs, mostly using song forms from the British Isles. I heard an unfamiliar piece on the radio the other day, and my first thought was that it was from The Beggar's Opera of 1728 England. I learned that it was our own Stephen Foster, a century and a half newer.