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Moore initially played piano but switched to bass in 1959. He played and recorded with Archie Shepp and Bill Dixon in Europe in 1962. In 1963 he was a member of the New York Contemporary Five, and while the ensemble was in Copenhagen, Moore recorded with Roland Kirk. In the fall of that same year, he played brefly with Thelonious Monk. Later in the 1960s Moore worked with Sonny Rollins, Jackie McLean, Frank Foster, and Lee Morgan. He recorded with Elvin Jones in 1966 and Clifford Thornton in 1967, but receded from view toward the end of the 1960s. Don Moore is currently active in the New York area.
With Elvin Jones
- Midnight Walk (Atlantic, 1966)
With Jackie McLean
- Jacknife (Blue Note, 1966)
With Archie Shepp
- Archie Shepp & the New York Contemporary Five (Storyville, 1963)
With Clifford Thornton
- Freedom & Unity (Third World Records, 1967)
- "Don Moore". The New Grove Dictionary of Jazz.