Turney began his career in the Midwest, playing in territory bands such as the Jeter-Pillars Orchestra.[1] He played with Tiny Bradshaw in Chicago before moving to New York City, where he performed with the Billy Eckstine Orchestra in 1945–1946.[1] Turney had little luck in New York, however, and returned to Ohio to play in local ensembles through the 1950s.[1] He toured with Ray Charles in 1967 traveling to the Far East and Australia, then was hired by Duke Ellington, in whose orchestra he played from 1969 to 1973.[1] He was hired to play alto saxophone as an "insurance policy" due to the declining health of Johnny Hodges.[1] He was the first flute soloist to ever play in Ellington's orchestra. He also played tenor saxophone in the band. Amongst his own compositions was "Chequered Hat", written in tribute to Hodges.[1]
Following his tenure with Ellington, he played with the Savoy Sultans and the Newport All-Stars, as well as in several pit orchestras.[1] In the 1980s, he toured and recorded as a member of the Oliver Jackson Quintet, with Ali Jackson, Irvin Stokes, and Claude Black.[3]
Turney recorded as a leader between 1975 and 1978, and released the CD, Big, Sweet 'n Blue in 1993. He died of kidney failure in 2001, at the age of 79.[2]