If one were to trace the roots of the earliest western traditions of music one might break it down into two basic categories--church music and secular music. It's really not quite that simple, and there was a great deal of cross influence between the two. The early settlers of the United States who came from the British Isles brought with them the popular music traditions of their respective homelands.
The early music of Britain, Ireland, Scotland, and surrounding areas descended from the music of the medieval minstrels and troubadours. As some of the more musically inclined citizenry began developing the various regional styles, they would pass on ballads and chanteys and the like for singing; and jigs, reels, and other instrumental styles for dancing and other festive occasions. This was the music they carried to their new homes in the Appalachians and other regions of North America.
As the country opened up and transportation networks were vastly improved, musical innovations were spread more quickly to all parts of the country. Like the roving troubadours of medieval times, new bands of minstrels toured the country popularizing new songs that were combinations of the many styles of white and black America. Publishing sheet music became a big business as those who were trained in music wanted to be able to play the popular songs in their own homes.