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Hirshfield studied under Ed Soph. He worked for the Joffrey Ballet in 1976-77 and then played with Mose Allison (1977-79). During the 1980s he worked with Red Rodney and Ira Sullivan (1981-85), Toshiko Akiyoshi (1986-89), and Bennie Wallace (1987-90). Alongside Fred Hersch and Steve LaSpina, he was a member of the trio Etc. during 1988-91. During this time he also played in a trio with Hersch and Michael Formanek. From 1990 he played with Harold Danko, played in Formanek's Wide Open Spaces project, and played again with LaSpina in a quartet setting. He also worked in a quartet with John Abercrombie and Andy LaVerne early in the 1990s. In the mid-1990s he played in a trio with Marc Copland and Dieter Ilg (1992-95), another trio with Tim Berne and Formanek (1993-94), and the Lan Xang ensemble with Dave Binney, Donny McCaslin, and Scott Colley (after 1995).
Hirshfield has also played with a number of other leaders, including Bob Belden, Marc Copland, Vic Juris, Steve Slagle, Dave Stryker, Jim Snidero, Warren Bernhardt, Jay Anderson, and Paul Bley.