The singing woman in "The Idea of Order at Key West," and the near-divinity ascribed to her by the speaker, have led to frequent comparisons to the Muses of classical mythology. The Muses were nine sisters who were the patron deities of all music, performance, poetry, song and dance. They are described most fully in the Theogony by Hesiod, a Greek epic poem from the seventh century BC, as the daughters of Zeus, king of the gods, and Mnemosyne, the goddess of memory. Other Greek poets sometimes considered them as earlier offspring of the first-generation gods, Uranus and Gaia (heaven and earth)—a good indicator of how ancient and fundamental the Muses are in myth. Alternatively, they were also sometimes worshiped as water nymphs, an aquatic connection that may be echoed in the seaside setting of Stevens' poem.
So closely were the Muses linked to poetry that for millennia, poets invoked the Muses at the start of their work. This tradition appears most famously in Homer's Iliad and Odyssey ("Sing to me of the man, Muse, the man of twists and turns...") (trans. Robert Fagles), contemporary to Hesiod, and reappears in Ovid's Metamorphoses, Virgil's Aeneid, Dante's Inferno, and as late as Shakespeare and Milton's Paradise Lost in the 17th century AD. In modern times, the Muses remain symbolically attached to art and performance, and are at the root of the English words music, museum, and muse as a verb or noun ('to muse upon an idea').
The common idea behind invocations of the Muses in poetry was that the artist was calling upon the goddesses' inspiration: their wisdom would flow directly through the artist and be transmitted to audiences. With this background, Wallace Stevens undoubtedly made very deliberate choices in writing "The Idea of Order at Key West:" 1) to focus on a woman, and 2) to have her singing. Both of these lead to strong comparisons with the Muses. In this poem, Stevens seems to challenge the notion of a divine spirit flowing through a human artist who merely acts as a conduit: he claims instead that the wonders of creativity begin and end with the human intellect. Song is a particularly effective type of art for the poem to focus on, as it helps Stevens consider art as a holistic category, and to erase the distinctions between song and poetry: after all, in Homer's time, poems were performed much like song, and song and dance were routinely incorporated into theater. He can think about what it means for the woman, and by extension himself, to be a poet in the broadest sense.
It is curious, though, that while the woman acts as a sort of muse to Stevens, the poem primarily focuses on the woman's own creative process. Stevens seems to be deconstructing the idea of what a "muse" is: even if the woman is a Muse, where does her inspiration come from? For this poem, it is too easy an answer to say that it all stems from a mysterious, unseen force in nature. By assigning the woman godlike powers but making clear that she is human, not a spirit, Stevens reformulates the entire concept of inspiration and the Muses, suggesting that the creativity associated with the Muses has always been found in the human mind.