Organized sound; one of the oldest human behaviors on record.
Documented
The art of the Muses
Greek mousike (techne) meant the craft belonging to the Muses, the nine daughters of Zeus and Mnemosyne (Memory) who governed song, dance, poetry, history, and astronomy. The word passed through Latin musica into French musique and then English. Same root gives museum, a temple of the Muses, and amusement, originally a state of being absorbed, spellbound, by one. Even the ending is a job title: -ic descends from Greek -ike, "the art of," the same suffix in arithmetic, rhetoric, and logic.
Assessment: Fully documented across Greek, Latin, and Old French records. Note the mother of the Muses: Memory. The Greeks filed art under remembering.
Interesting claims
Muse plus sick: spellbound or afflicted?
A circulating claim breaks music into "muse" and "sick," sometimes adding that the Muses "afflict" listeners with trance, and that the word encodes music as a sickness or spell cast on the mind. It spreads because it feels hidden and slightly dangerous.
Assessment: Half a true thing. The muse element is genuine. The sick element is not: -ic comes from Greek -ike, "art of," unrelated to sickness. But the intuition behind the myth, that music seizes people involuntarily, is one the Greeks themselves held. Plato wanted certain musical modes banned for exactly that power. The etymology is wrong; the observation is ancient.
Stories
Pythagoras and the blacksmith's hammers
The founding legend of Western music theory: Pythagoras passing a forge heard hammers ring in harmony and discovered that weight ratios made consonance, four, two, one, the octave in a smithy. From that myth comes the whole tradition of music as audible mathematics.
Assessment: Told by Nicomachus and repeated for two millennia, and physically false: hammer weight does not tune anvil tone. The legend survives because it says something true about the Pythagorean conviction that the cosmos is ratio.
Sources and further reading
OED, music, from Greek mousike tekhne, art of the Muses
Plato, Republic 398d-403c, on mousike
Worth asking
English still houses its arts inside the temple: music, museum, amusement. What else in your vocabulary quietly reports to a goddess?