Definitions of music are by no means rare.
The most usual, the official one, is this: “Music is the art of combining sounds in a manner agreeable to the ear.”
According to Hugo Reimann, music is “the manifestation of Beauty through the medium of sound.”
Another German has it that “Die Musik ist eine klingende Arithmetik” (Music is a sonorous arithmetic).
Spencer, on the other hand, considered music as a natural development of the accent imparted to the human voice by passion.
To Mazzini music was “the faith of a world whose poetry is but high philosophy.”
To the average listener, music is melody, that is to say, a mere “pretext to sing.”
And lastly, we have the famous definition of Théophile Gautier, that “music is the most expensive of all noises.”
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Feeling constrained to give a definition myself, I should say that, in my opinion, music is the art of combining sounds both in time and space (successively and simultaneously) according to the composer’s creative egoism and his complete indifference to every law that opposes his sincerity.
From L’Evoluzione della Musica, A traverso la storia della Cadenza perfetta (“The Evolution of Music, Throughout the History of the Perfect Cadence”), by Alfredo Casella, 1919. (Emphasis in the original.) A fun party game: try and match each definition with a subsequent 20th-century musical style, vocabulary, or school. Even Gautier’s.