Spiegel attended Shimer and Brooklyn Colleges, Oxford University and the Julliard School. She studied composition with Jacob Druckman and computer music with Emmanuel Ghent and Max Mathews. Spiegel draws on a wide variety of musical roots, and her instrumental background includes banjo, folk and classical guitar, and renaissance and baroque lute. She is best known, however, for her work with electronic media, an activity in which she has been involved since the late 1960s. After several years of instrumental and analog composition, she began to compose with computers at Bell Telephone Labs in 1973. Her music has been heard widely in festivals, with video, film and dance. She has received commissions to compose works for chamber orchestra and other instrumental media.