The number nine is neither original nor universal. An older Boeotian tradition worshipped three Muses on Helicon under the names Melete, Mneme and Aoide, practice, memory and song, which reads as a description of what a singer actually does rather than as a division of the arts. Pausanias reports that count as the local one and gives the nine as the later arrangement. It is Hesiod who names the nine that antiquity settled on, at the opening of the Theogony: Clio, Euterpe, Thalia, Melpomene, Terpsichore, Erato, Polyhymnia, Urania and Calliope, daughters of Zeus and of Mnemosyne, memory, born of nine nights. Hesiod assigns them no separate departments. Calliope alone is singled out, as the eldest and as the one who attends kings, and the rest are a chorus.
The matching of one Muse to one art is much later, a systematising habit of the Hellenistic and Roman periods that hardened in late antique commentary and passed from there into the handbooks the Renaissance read. Even then the assignments were not stable. Erato is given lyric, love poetry or the hymn depending on the source, while Urania with astronomy and Clio with history are the two that stayed put. The attributes that identify them in art, the tragic and comic masks, the writing tablet, the lyre, the globe and compasses, follow the same late fixing. A visitor looking at a Roman sarcophagus is looking at a scheme, not at a cult.