It's not "my definition" of art, it's an historical fact. Art without function is a recent development. Great works of transcendent beauty were born out of function: Sistine chapel, the Pieta, Bach's Masses.
I am not convinced that it is a fact. Music has never seemed particularly "functional" to me, and it seems to have stymied a lot of people who actually try to figure this stuff out. And just because some artist gets commissioned to create the work isn't a functional definition of the art itself.
If I throw a dinner party and hire Composer X to supply some music for it, and that music is still played 200 years later, but in concert halls, the original "function" of the music is totally lost. But the music itself still works. That tells me that the function is irrelevant, and it is the music for its own sake that matters.
Some of the oldest human artistic products that I know about are designs found on ancient pottery shards, and there's no apparent reason they are there, other than for the pleasure people must have taken in making them, and the pleasure the users of the pottery have in looking at them. I've never read any convincing "functional" reason of why people all over the globe all seem to have started decorating their functional utensils with extraneous designs at a certain level of their development, but they do.