Who has rights to the old music?

Does Bungie have rights to the familiar melodies of previous Halo Soundtracks, like the original Halo theme, or some of the other reoccuring songs, like A Walk in the Woods? Or can 343 use them, but they chose not to? Because I haven’t heard anything familiar in the Halo 4 music so far.

Microsoft.

It was strictly 343’s choice to include unique music in the game.

Microsoft owns the Halo IP, that includes the music. Bungie sold the IP rights to MS so they could regain their creative freedom.