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Born in Chicago, William Schmidt was originally a saxophonist. He studied in his hometown, and served as a Navy band musician in both World War II and the Korean War, after which he moved to Los Angeles and studied composition at USC with Halsey Stevens and Ingolf Dahl. He founded his own publishing companies and composed numerous works for winds; his Double Concerto for Trumpet, Piano, and Chamber Orchestra was commissioned by the Pasadena Chamber Orchestra and nominated for a Pulitzer Prize in 1981.

His Variants with Solo Cadenzas for trumpet quartet comes from that period. (It was first recorded in 1980 and published the year before. It has since become widely popular with college students and professionals alike; the Royal Concertgebouw Orchestra trumpets recently released an astonishing live recording.) The title describes the form, and each of the four players rotates out for one of the cadenzas. In attitude it is a mix of spiky fanfares and the sometimes bluesy, sometimes aggressively driven solos, adding up to a tightly wound but technically kaleidoscopic challenge to both solo and ensemble playing.