McMurray was born and raised in Detroit, where he played in local clubs influenced by John Coltrane and Cannonball Adderley. In 198,1 he played with avant-garde jazz group Griot Galaxy, and alt-disco funk group Was (Not Was), establishing his trademark cross-genre approach. McMurray has gone on to play with a wide array of artists, from Bob Dylan and Iggy Pop to Bob James and Randy Crawford. In 2013, McMurray featured on pianist Geri Allen’s celebration of Detroit “Grand River Crossings”. As well as eight albums as bandleader, McMurray has recorded two albums of Grateful Dead versions for Blue Note.