Peter's qustion is really a good one. The notions of chords now has sort of become the tail that wags the dog. It was between about 1575 and 1600 that professioal composers gave up on all but major and minor modes, because the other were too hard to write harmonies for. It seems to me that this is practical proof that melodies came first (for about a millenium) before harmonies were considered a nice frill.

Traditonal singers singing to instrumental in the British- American milieu, seems to have started in the south and west of the USA in the 1920s. That as yet to be noted in the Bitish Isles. Traditional singing to instrumental accompaniment is older in some other countries.