American Music Fairness Act of 2023 This bill establishes that the copyright holder of a sound recording shall have the exclusive right to perform the sound recording through an audio transmission. (Currently, the public performance right only covers performances through a digital audio transmission in certain instances, which means that nonsubscription terrestrial radio stations generally do not have to get a license to publicly perform a copyright-protected sound recording.) Under the bill, a nonsubscription broadcast transmission must have a license to publicly perform such sound recordings. The Copyright Royalty Board must periodically determine the royalty rates for such a license. When determining the rates, the board must base its decision on certain information presented by the parties, including the radio stations' effect on other streams of revenue related to the sound recordings. Terrestrial broadcast stations (and the owners of such stations) that fall below certain revenue thresholds may pay certain flat fees, instead of the board-established rate, for a license to publicly perform copyright-protected sound recordings.