Born in Richmond Hill, New York, Gould was recognized early as a child prodigy with abilities in improvisation and composition. His first composition was published at age six. Gould studied at the Institute of Musical Art, although his most important teachers were Abby Whiteside and Vincent Jones.
During the Depression, Gould, while a teenager, worked in New York City playing piano in movie theaters, as well as with vaudeville acts. When Radio City Music Hall opened, Gould was hired as the staff pianist. By 1935, he was conducting and arranging orchestral programs for New York's WOR radio station, where he reached a national audience via the Mutual Broadcasting System, combining popular programming with classical music.
In the 1940s, Gould appeared on the Cresta Blanca Carnival program as well as The Chrysler Hour on CBS where he reached an audience of millions. Gould composed Broadway scores such as Billion Dollar Baby and Arms and the Girl; film music such as Delightfully Dangerous, Cinerama Holiday, and Windjammer; music for television series such as World War One; and ballet scores including Interplay, Fall River Legend, and I'm Old Fashioned.
Gould's music, commissioned by symphony orchestras all over the United States, was also commissioned by the Library of Congress, The Chamber Music Society of Lincoln Center, the American Ballet Theatre, and the New York City Ballet. His ability to seamlessly combine multiple musical genres into formal classical structure, while maintaining their distinctive elements, was unsurpassed, and Gould received three commissions for the United States Bicentennial. As a conductor, Gould led all of the major American orchestras as well as those of Canada, Mexico, Europe, Japan, and Australia. With his orchestra, he recorded music of many classical standards, including Gershwin's "Rhapsody in Blue" on which he also played the piano. He won a Grammy Award in 1966 for his recording of Charles Ives' first symphony, with the Chicago Symphony Orchestra. In 1983, Gould received the American Symphony Orchestra League's Gold Baton Award. In 1986, he was president of ASCAP, a position he held until 1994. In 1986 he was elected to the American Academy and Institute of Arts and Letters.
Incorporating new styles into his repertoire as they emerged, Gould incorporated wildly disparate elements, including a rapping narrator and a singing fire department into commissions for the Pittsburgh Youth Symphony. In 1993, his work "Ghost Waltzes" was commissioned for the ninth Van Cliburn International Piano Competition. In 1994, Gould received the Kennedy Center Honor in recognition of lifetime contributions to American culture.
In 1995, Gould was awarded the Pulitzer Prize for Music for Stringmusic, a composition commissioned by the National Symphony Orchestra in recognition of the final season of director Mstislav Rostropovich. In 2005, he was honored with the Grammy Lifetime Achievement Award. He also was a member of the board of the American Symphony Orchestra League and of the National Endowment for the Arts music panel. Most of his compositions and arrangements were issued by RCA Records, some of which are available from BMG.
Gould died in 1996 in Orlando, Florida.