Turney began his career in the Midwest, playing in territory bands such as the Jeter-Pillars Orchestra. He played with Tiny Bradshaw in Chicago before moving to New York City, where he played with the Billy Eckstine Orchestra in 1945-46. Turney had little luck in New York, however, and returned to Ohio to play in local ensembles through the 1950s. He toured with Ray Charles in 1967, then was hired by Duke Ellington, in whose orchestra he played from 1969 to 1973. He was hired to play alto saxophone as an "insurance policy" due to the failing health of Johnny Hodges. He was the first flute soloist to ever play in Ellington's orchestra. He also played tenor saxophone in the band.
Following his tenure with Ellington, he played with the Savoy Sultans and the Newport All-Stars, as well as in several pit orchestras. In the 1980s, he toured and recorded as a member of the Oliver Jackson Quintet, with Ali Jackson, Irvin Stokes, and Claude Black.
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.
- 1978: I Let a Song with Booty Wood, Aaron Bell, Sam Woodyard, Raymond Fol
- 1993: Big, Sweet 'n Blue with Larry Willis, Walter Booker, and Jimmy Cobb (Mapleshade)
With Roy Eldridge
- What It's All About (Pablo, 1976)
With Oliver Jackson
- 1984: Billy's Bounce by Oliver Jackson Quintet (Black & Blue)
With Red Richards
- In a Mellow Tone (West 54)
With Randy Weston
- Jazz in Yverdon 1984 Concert: Oliver Jackson Quintet Archived 2013-09-09 at the Wayback Machine Retrieved 10 July 2013.