I think that's something you could do, the only drawback is that if you are promoting the music itself, the commissions for each individual purchase probably will be small, so you would need quite a bit of volume. I'm thinking of a scenario where you talk about an artist's music and then have an affiliate link to purchase it - either on CD (through Amazon, etc.) or by download. And I don't know whether there are affiliate programs for music downloads, so you would want to check into that.

However, you might be able to promote other products relating to the artist that would offer better commissions. I know some ticket brokers have affiliate programs, so you could review an artist's music and promote tickets to their show. Another option would be things like vintage concert posters, etc. I don't know if they have affiliate programs, but I know there are companies that specialize in stuff like that and the prices can be pretty high (e.g., sometimes $1K+).

You could also talk about ancillary products relating to the music. I think I saw a site promoting high-end record players for serious music fans. There probably are other products you could tie in with also, but you would want to make sure you keep the focus on the music and be able to show a strong connection between the music and the product being promoted.