When and why it was written

When

Written in 1888, published 1889.

Why

Nietzsche was a composer as well as a philosopher, and treated music as evidence rather than decoration.

What it means

Read as enthusiasm this is charming and small. Read against Nietzsche's project it is a real claim: he held that life needs justifying, and that art is what does the justifying.

Music is his strongest case because it persuades without argument, which is exactly the kind of persuasion he thought philosophy had lost the ability to perform.