The "Barbershop Quartet" harmonies are really derived from classical music, rather that traditional music--From the time that records were first made, Quartets, like the Peerless Quartet, American Quartet, and the Hayden Quartet, were among the most popular recording artists--invariably, when a song was popular, there would be recordings available by a number of quartets, the arrangements were of the "light classical" sort(in truth, what passed for Quartet singing actually featured more than four singers)--
Back in those days, recordings were a sort of novelty though, and if you wanted music, you had to make your own, so informal group singing, often with simple improvised harmonies, was a common social activity--no quartets though, everyone joined in--
This wonderful custom began to disappear as recordings, radio, and movies became the standard entertainments, and the automobile culture broke up the old neigborhoods--but it was fondly, if not accurately, remembered, and recreated, often ironically, in the movies, on radio, and in recordings--
For one thing, the singing tended to occur in barrooms, not barbershops, for another, the songs were inclined to be more boisterous, colorful, and raw--the book, My Pious Friends and Drunken Companions is a collection that gives a more accurate picture of what was sung--