Reed was raised in rural Odessa, Missouri, where his first exposure to music was his father's playing of the old-time fiddle (accompanied by his mother at the piano).
In 1937 he enrolled at the Eastman School of Music (studying composition with Howard Hanson and Bernard Rogers, conducting with Paul White, musicology with Howard Gleason, and music theory with Allen I. McHose), receiving a Ph.D. in composition in 1939.