If you want to know why there are nine Muses, you just have to ask Homer. Homer knows either one or several nameless Muses of some indefinite number, as at Iliad 1.604 (“the antiphonal sweet sound of the Muses singing”) or Iliad 2.484 (“Tell me now, you Muses, who have your homes on Olympus”), Iliad 2.761 (“Tell me, then, Muse, …”), or Odyssey 1.1 (“Sing to me, Muse”). They remain in this indefinite state until the last book of the Odyssey, where the Muses are said by Agamemnon's psychē in the Underworld to appear finally on Earth – already a peculiar topographical and narrative inversion in itself – in order to lead a thrēnos at the funeral of Achilles. Only, they do so both as a chorus of nine and in the seemingly abstract and faceless singular:

Hesiod follows suit in the Theogony, either conferring or transmitting the nine distinct names of nine Muses, otherwise not functionally distinct, in a gesture that was destined to become canonical.

Elsewhere, their number varies wildly. Ephorus knows three Muses, others give four, five, seven or eight. And the iconography is in agreement. Sappho sometimes makes a tenth, but that is as far as it goes.