Born in New York City in 1940, Edward Cohen played piano and trumpet and attended the High School of Music and Art in Manhattan. While writing music in a classical vein, he was inspired by jazz and improvisation. As a teenager he worked as a jazz pianist at resorts in the Catskills, and he retained an avid interest in jazz throughout his life. He frequently entertained family and friends with sparkling and original renditions of jazz standards.

His formal musical training was entirely classical. He received a B.A. with honors in music from Brandeis University in 1961 and an M.A. in 1965 from the University of California at Berkeley, where he won the Ladd Prix de Paris, which sponsored two years of composing in Paris. Before coming to MIT, he taught at Brandeis University for thirteen years. He also taught at Harvard.

Although he was strongly focused on the creation of new music, Cohen found time for other pursuits. He spoke French fluently and had a lifelong interest in French literature and film. He was a determined distance runner who ran the Boston Marathon four times in the 1970s.