There is a difference between having a score or recording and having permission to perform it!
"Fair use" does not apply to music licensed for performance or broadcast. Always confirm that you have a performance license or written permission!
Q310 What is the difference between the composer’s rights and royalties, those of the music publishing company, and the recording company?
Under U.S. copyright law, the copyright in a work initially vests with the author (i.e., the composer). The author is the owner of the copyright and is entitled to the exclusive rights provided under the Copyright Act: reproduction, distribution, adaptation, performance, and display. If the work in question is a sound recording, the owner also has the right of public performance via digital transmission.
The composer usually transfers to the music publisher only the rights of reproduction and distribution for the composition. The publisher then collects royalties for sales of copies of the sheet music and pays a share of the royalties back to the composer. Generally, the composer retains all of the other rights, such as public performance, and so continues to collect royalties for the public performance of his or her music. The composer typically signs a license with one of the performance-royalty-collecting agencies: the Association of Composers, Authors and Publishers (ASCAP), Broadcast Music Inc. (BMI), or SESAC Inc. They collect royalties for public performances of music and distribute them back to the composer.
A sound recording of the performance of a musical composition embodies at least two and sometimes three separate copyrights: the underlying musical composition, the recording of the performance of the music, and the arrangement of the music for the sound recording. The performer, who may or may not be the composer, normally transfers the copyright in the performance of the music to the recording company that collects royalties for the sale of the recordings. The composer is compensated for the sale of recordings through the mechanical license, a compulsory license under the statute. The composer normally continues to own the copyright in the musical composition, however.
When music is played on radio or television, royalties are paid to the composer in the form of a blanket license with the performance royalty organizations. There are no performance rights in sound recordings except for digital transmission. So, traditionally, the recording company makes its money from the sale of records and not from performance. But both the recording company and the performers share the royalties for digital transmission of sound recording (e.g., from webcasting).
[From Laura N. Gasaway, Copyright Questions and Answers for Information Professionals (Purdue Univ. Press, 2013). Used by permission.]