The solution would be to recognize private property as a detriment to the human experience and dissolve it.
Why would you do such a thing? Because it's a trap that separates and divides people and has wrecked all semblance of natural community we once possessed.
Why would artists continue to make music? That's the beautiful thing, people would still continue to make music because making music is an end in itself. It's therapeutic, expressive, and binds a community together through stories, experiences, and emotions. Those who did well in their craft would continue to reap rewards in the form of grants and favors for just being good and sharing their creation with their community. Their work would probably be less widespread, but therefore more unique and special. And, as a pleasant by-product, mass-produced pop and other, let's say "less artistic" brands of music would cease to be worthwhile and would cease to pollute the airways.
Not the answer you were looking for? Perhaps you could reason that as long as an artist is making a reasonable living, he is deserving of no more, and should be satisfied with his living and his contribution to human experience. Certainly pirating does at least widen the artists' exposure, and therefore potentially draws more income for live shows (where many artists make the majority of their money in any case- hey, that's not a bad thought). Perhaps you could reason that the artist makes more art when he makes less money per art object made, and therefore stealing from him is actually incentivizing his creativity and career acclaim, thereby also benefiting humanity because the artist will produce more. Finally, I throw a real curveball in there and say that pirating music is the justified precursor to an innovation in music marketing that has not yet been realized, and by participating in pirating, the pirate is actually spurring the industry ever closer, with each megabit downloaded, to an optimized delivery system that will eliminate the need for piracy by satisfying all concerned parties effectively. Or we do it simply because we can, and it is therefore good. Will to power and all that.