Sauter studied music at Columbia University and the Juilliard School.[3] He began as a drummer and then played trumpet professionally, including with Red Norvo's orchestra. Eventually he became a full-time arranger for Norvo. He arranged and composed for Artie Shaw, Tommy Dorsey, Woody Herman, and especially Benny Goodman, earning a reputation for intricate work such as "Benny Rides Again", "Moonlight on the Ganges", and "Clarinet a la King".[4] A bout of tuberculosis contracted in 1942, however, forced a stay at the Summit Park Sanatorium in Pomona, New York, and stalled his musical career for some time.[5]
From 1952 to 1958, Sauter was co-leader of the Sauter-Finegan Orchestra. Between 1957 and 1959, he was Kurt Edelhagen's successor as leader of the SWF orchestra in Baden-Baden, Germany.[4] In 1961, he worked with tenor saxophonist Stan Getz on the album Focus,[4] a collaboration for which Sauter at Getz's commission wrote a suite of string compositions without primary melodies. This allowed Getz to improvise them in his customary style. Roy Haynes, the jazz drummer, appeared on "I'm Late, I'm Late", the only selection to use a non-string instrument other than Getz.
Although Sauter is best known for jazz, he also orchestrated Broadway musicals such as 1776, The Apple Tree, and It's a Bird...It's a Plane...It's Superman. Orchestrator Jonathan Tunick said of Sauter's Broadway work: "Eddie did these marvelous things, always theatrical, always effective. And completely unlike anybody else."[6] His composition "World Without Time" is used as the theme music for the public affairs show The Open Mind, originally hosted by Richard Heffner.
^Katz, Jamie (June 2009). "The Jazzman Testifies". Columbia College Today. Archived from the original on September 16, 2016. Retrieved December 12, 2020.