Nat Adderley, 68, a jazz composer and cornetist who played on nearly 100 albums, many of which were recorded with his brother Julian “Cannonball” Adderley, has died. Born in Tampa, Fla., Adderley took up the trumpet as a teenager after World War II and began his career playing in local bands in Florida. He switched to coronet in 1950 and after playing in U.S. Army bands during his military service, Adderley got his first big professional break when he joined the Lionel Hampton group in 1954. In later years, he played in the influential small group led by his more famous saxophonist brother. After Cannonball Adderley’s death in 1975, Nat Adderley toured Europe as a bandleader and as a member of larger ensembles. A skilled composer, Adderley’s pieces include “Work Song” and “Jive Samba.” His musical about the folk hero John Henry, “Shout Up a Morning,” which began as a collaboration with his brother, was staged on Broadway in 1986. In 1997, Adderley joined Florida Southern College as artist in residence. On Sunday in Lakeland, Fla. of complications from diabetes.