Muse is a band. Muse Records was a record label that released jazz and blues. A "Muse" refers to one of the Muses (Ancient Greek αἱ μοῦσαι, hai moũsai: perhaps from the Proto-Indo-European root *men- "think") in Greek mythology, poetry, and literature who are the goddesses or spirits who inspire the creation of literature and the arts. They were considered the source of the knowledge, related orally for centuries in the ancient culture, that was contained in poetic lyrics and myths.
Originally said to be three in number, by the Classical times of the 400s BC, their number had grown and become set at nine goddesses who embody the arts and inspire the creation process with their graces through remembered and improvised song and stage, writing, traditional music, and dance.
In one myth, King Pieride, once king of Mazedonia, had nine daughters he named after the nine Muses, believing that their skills were a great match to the Muses (mousi). He thus challenged the Muses to a match, resulting in his daughters being turned into magpies and jackdaws. In Greek Mythology these nine daughters of the king usually are referred to as the i]Pierides.
Sometimes they are referred to as water nymphs, associated with the springs of Helicon and with Pieris.
The Olympian myths set Apollo as their leader, Apollon Mousagetēs. Not only are the Muses explicitly used in modern English to refer to an inspiration, as when one cites one's own artistic muse, but they also are implicit in words and phrases such as "amuse", "museum"(changed from muselon--a place were the muses were worshipped), "music", and "musing upon".
According to Hesiod's Theogony (seventh century BC), they were daughters of Zeus, the second generation king of the gods, and the offspring of Mnemosyne, goddess of memory. For Alcman and Mimnermus, they were even more primordial, springing from the early deities, Uranus and Gaia. Gaia is Mother Earth, an early mother goddess who was worshipped at Delphi from prehistoric times, long before the site was rededicated to Apollo, possibly indicating a transfer to association with him after that time. Pausanias records a tradition of two generations of Muses; the first being daughters of Uranus and Gaia, the second of Zeus and Mnemosyne. Another, rarer genealogy is that they are daughters of Harmonia (the daughter of Aphrodite and Ares) which contradicts the myth in which they were dancing at the wedding of Harmonia and Cadmus. This later inconsistency is an example of how clues to the true dating, or chronology, of myths may be determined by the appearance of figures and concepts in Greek myths.
Compare the Roman inspiring nymphs of springs, the Camenae, the Völva of Norse Mythology and also the apsaras in the mythology of classical India. .