I've recently asked when the polyphonic music came up. Now I've encountered this accompaniment of Seikilos Epitaph. This sounds exactly like I was imagining that the Greeks would have accompanied their songs, as they had lyres with different tuned strings that could have played chords.
I also remember a movie about King David playing the Psalms to heal Saul from sickness. The sound was quite like this one:
Are these examples just fakes, or did the antique music sound like this?
And if they were able to accompany chords like this they also could be able to sing the voice lines of the chords: this would mean that the Greek choir songs were heterophony?