Twyla Tharp’s new ballet, which will receive its world premiere at American Ballet Theatre on June 3, will be set to a commissioned score by Danny Elfman, known primarily for his compositions for film and television, including scores for “Chicago,” “Edward Scissorhands,” and “The Simpsons.” It will mark Mr. Elfman’s first composition for ballet. The piece will also feature costumes by fashion designer Norma Kamali.