A recent Tweet from Beats Music Support to a follower stating, "We're working with Google to add Chromecast" pretty much suggests we'll see a Beats Music app in no time.
A similar Tweet from Rdio was posted but later removed; it's likely an Rdio app will make a Chromecast appearance as well, but wants it to remain under wraps for now.
Pandora and Google Play Music are already in the cast-mix, and only a few other music apps remain - including the top dog in the music streaming industry, Spotify.
Spotify seems to have "several prevailing priorities" at the moment so it will probably be awhile until you see it on your TV.
Via The Verge