Ancient musicians had two completely separate systems of musical notation: one for voice, and another for instruments.
The Yale Musical Papyrus, P. Yale CtYBR inv. 4510, a fragment of probably two Greek songs from circa 125 CE, "contains the sort of musical notation sometimes used by professional singers in antiquity. In between the lines of Greek text can be seen symbols which resemble ancient Greek letters but which are in fact vocal musical notation. The papyrus is a fragment from what was apparently a collection of songs for performance, intended for a baritone voice with a wide range" (William A. Johnson, Fragments of Ancient Greek Songs from the Early Empire).
♦ When I last visited Prof. Johnson's website, in December 2013, I could hear a midi rendition of how the song might have been sung by clicking on a line in the reproduction of the papyrus. When I retunred that music had been transferred to YouTube: