You could have a monthly fee and decide what percentage of it you want to go to specific artists. If you listen a lot to an artist the app could ask you if you want to transfer some percents from one artist to this one. That is a feature that I would personally love to use.
So, you want the twitch.tv model then?
I actually don't see that as a bad concept. It might make Amazon/Twitch curious about how they might do the same, but competition is good.