Twitter have just launched a whole new service to called #music, yes that includes the hashtag. This new service is all about music discovery.
#music allows users to discover popular and new music from Twitter. You can find new tracks without having to sign in. But when you do sign in you can find music tweeted by the people and artists you follow. You can search for emerging music, stuff which is yet to become mainstream.
When you find a track and hit the play button, you can only listen to a little preview. You're then given option to buy it on iTunes. But if you have a Spotify or Rdio account, you can sign in with those and start listening to full tracks. So it's a great form of integration with the services.
Along with the web service, there is also an iOS app which allows you to do pretty much the same. Unfortunately there seems to be no Android app yet.