Well yes, but not in the strict sense, because of the technical difficulties in recreating the actual tune.
The oldest complete tune actually recognized as such is the Song of Seikilos
http://www.youtube.com/watch?v=BWyXPpf7Vjohttp://en.wikipedia.org/wiki/Seikilos_epitaphThe Seikilos epitaph is the oldest surviving example of a complete musical composition, including musical notation, from anywhere in the world. The song, the melody of which is recorded, alongside its lyrics, in the ancient Greek musical notation, was found engraved on a tombstone, near Aidin, Turkey (not far from Ephesus). The find has been dated variously from around 200 BC to around AD 100.
Also on the tombstone is an indication that states in Greek "Εἰκὼν ἡ λίθος εἰμί.Τίθησί με Σείκιλος ἔνθα μνήμης ἀθανάτου σῆμα πολυχρόνιον" , "I am a tombstone, an icon. Seikilos placed me here as an everlasting sign of deathless remembrance".
While older music with notation exists (for example the Delphic Hymns), all of it is in fragments; the Seikilos epitaph is unique in that it is a complete, though short, composition. Ὅσον ζῇς, φαίνου,
Hoson zês, phainou,
While you live, shine, μηδὲν ὅλως σὺ λυποῦ·
mêden holôs su lupou;
don't suffer anything at all; πρὸς ὀλίγον ἐστὶ τὸ ζῆν,
pros oligon esti to zên,
life exists only a short while, τὸ τέλος ὁ xρόνος ἀπαιτεῖ.
to telos ho chronos apaitei.
and time demands its tollAnd yet, some 2,000 years later I can play this tune in my lyre....
Yes Eff, it does not matter which one is oldest, but it does matter that we walk in our ancestor's sandals and realize they were men and women as we are...
Drink, and don't be sad.. in 2,000 years men will wonder about us and what kind of people we were...
Glaukos