Abney studied piano and french horn at the Manhattan School of Music, and he played the latter in an Army band during military service. After returning he played in ensembles with Wilbur de Paris, Bill Harris, Kai Winding, Chuck Wayne, Sy Oliver, and Louis Bellson. He had a sustained career as a session musician, playing on recordings for Louis Armstrong, Benny Carter, Oscar Pettiford, Ella Fitzgerald, Carmen McRae, Sarah Vaughan, Eartha Kitt, and Pearl Bailey. He also played on a large number of recordings for more minor musicians and on R&B, pop, rock, and doo wop releases.
After moving to Hollywood, he worked as musical director for Universal Studios/MCA. He appeared as a pianist in the film Peter Kelly's Blues behind Ella Fitzgerald. Additional credits include recording and arrangements for the film "Lady Sings The Blues." He toured with Anita O'Day in the 1980s. Early in the 1990s he moved to Japan and toured there with considerable success, playing weekly at the Sanno Hotel in Tokyo. Upon his return to the United States in 2000, he died of complications from kidney dialysis. He was interred at Forest Lawn Cemetery, in Burbank, CA. He is survived by 5 children.