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Say you like contemporary classical music, but the National Symphony’s recent offerings favor Mozart and Beethoven. Don’t fret—the New York City Ballet has you covered. This weekend, the company performs to works by American icon John Adams, contemporary Russian composer Leonid Desyatnikov, and 20th-century classics by Bernstein and Gerswhin. But there’s a catch: You have to stare at gorgeous ballerinas while you listen. Through Sunday, the New York City Ballet, which started performances on Tuesday, presents two programs notable for their live music as much as their movement. Tonight’s show includes “Fearful Symmetries,” Adams’ mesmerizing, synthesized mini-symphony, with choreography by company director Peter Martins. It’s sandwiched between two homages to Broadway: “Who Cares?”, a suite of Gershwin’s songs choreographed by George Balanchine, and an abridged version of Bernstein’s West Side Story, with choreography that Jerome Robbins adapted from the film. (Don’t expect Tony-worthy vocals, but yes, the dancers sing!) Saturday evening and Sunday afternoon, the company performs three 21st-century ballets, leading with another Martins/Adams collaboration, the piano duet “Hallelujah Junction.” Martins’ choreography can be a bit bland, but recent works by Christopher Wheeldon and Alexei Ratmansky add considerable intrigue. The company performs at 7:30 p.m. tonight, 1:30 p.m. and 7:30 p.m. Saturday, and 1:30 p.m. Sunday at the Kennedy Center Opera House, 2700 F St. NW. $25–$85. kennedy-center.org.(202) 467-4600.