Rivers plays with remarkable technical precision and a manifest knowledge of his materials. His sound is hard and extraordinarily well-centered, his articulation sharp, and his command of the tenor saxophone complete. It might be said that Rivers' playing exhibits little in the way of lyricism or humor. As a consequence, his playing has an unremitting seriousness that can be extremely demanding, even off-putting. Nevertheless, the depth of his artistry is considerable.
Rivers is as substantial a player as the jazz avant-garde has produced.
Rivers' father was a church musician, touring with a gospel quartet. Rivers was raised in Chicago and then Little Rock, Arkansas, where his mother taught music and sociology at Shorter College. He began taking piano and violin lessons at about the age of five. He later played trombone, before finally settling on the tenor. Early favorites were Don Byas, Coleman Hawkins, Lester Young, and Buddy Tate.