Born in Lima, Ohio, Henderson was one of five sisters and nine brothers. He was encouraged by his parents Dennis and Irene (née Farley) and older brother James T. to study music. He dedicated his first album to them "for being so understanding and tolerant" during his formative years. Early musical interests included drums, piano, saxophone and composition. According to Kenny Dorham, two local piano teachers who went to school with Henderson's brothers and sisters, Richard Patterson and Don Hurless, gave him a knowledge of the piano. He was particularly enamored of his brother's record collection. It seems that a hometown drummer, John Jarette, advised Henderson to listen to musicians like Lester Young, Stan Getz, Dexter Gordon and Charlie Parker. He also liked Flip Phillips, Lee Konitz and the Jazz at the Philharmonic recordings. However, Parker became his greatest inspiration. His first approach to the saxophone was under the tutelage of Herbert Murphy in high school. In this period of time, he wrote several scores for the school band.