Then fine-tune it on a particular artist's style. It will then mimic that artist. Depending how strongly you fine tune it, you can bias more strongly towards the target artist or towards general music.
You could then generate music in the same general style as an artist but taking any amount of inspiration from the rest of the world of music. I imagine with enough data and the right algorithms it would work very well and sound fantastic.
The same applies to visual works which I'm sure the reader is familiar with.
Just remember the algorithms we have today are the starting point not the ending point.