The graph below shows the frequency that various terms used to describe music and cinema appear in the sources contained in Google Books. This was produced using the Google Labs Ngram Reader. I inputted five terms: film music, cinema music, moving picture music, motion picture music and movie music. One of the more interesting aspects of this graph is that it suggests that "film music" does not become the dominant term until after 1930—that is, its terminological dominance coincides with the change over to sound film production.
(Click to see a larger image.)
You can make your own graph and change the variables here.