Dizzy Gillespie was a giant in the jazz world—a virtuoso player, composer, arranger, innovator of bebop, and forerunner of Afro-Cuban music. While he received musical training as a child, he taught himself to play trumpet. In 1935 he joined a Philadelphia band where he picked up the “Dizzy” moniker for his onstage antics.

Gillespie made his first recording with the Teddy Hill Band in 1937, “King Porter Stomp.” He joined Cab Calloway’s band in 1939 and began to veer away from the traditional trumpet style that he had picked up from Louis Armstrong, Charlie Shavers, and Roy Eldridge. There he also met trumpeter Mario Bauza who piqued his interest in Afro-Cuban music. By 1940 Gillespie was participating in after-hours sessions with other musicians—C...