A copyright gives the originator of a piece of intellectual property the right to produce and authorize others to: make recordings, print, perform, make derivative works, and to display the work publicly when regarding movies and visual art.
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There are, however, certain limitations to the copyright owner. The government has put in a place compulsory license, which allows someone to create and exploit their own version of a recording as long as the compulsory royalties are paid to the originator and notice is given. With each original recording, there are two rights to be considered: that of the actual recording, and that of the composition itself. Record companies usually hold to rights to the recordings, and the songwriters and composers hold the rights to the compositions. Since the Audi commercial did not use Eminem's actual recording, we are dealing with an issue regarding the song itself, and Audi only has to deal with the music publisher and not the record label. Musicologists should be called in as expert witnesses to make arguments on each litigants behalf.
The advertising agency who produced this commercial probably sent a commercial music house the "Lose Yourself" track as a reference for the composers, in order to give an example of the feel they wanted for the music. This is common practice in commercial music. After listening to the final song submissions, the ad agency probably felt that the song was similar enough to "Loose Yourself" to fit the direction of the commercial, but dissimilar enough to not be infringement. Take a look below. You be the judge: