Son of Bernice Douglass and Harry Reinhard Marshall, Sr, Marshall's early interest in music was the result of encouragement provided by his mother, herself an accomplished pianist and vocalist. As a youth, he performed as a soprano in the Boy's Choir at the Mt. Vernon Community Church, and during his high school years was influenced early by noted music instructor, Victor Laslo. After graduating from the Fox Lane High School in 1960, he pursued musical studies at Lake Forest College and Columbia University. In 1970 he became graduate assistant to Morton Subotnik at Cal Arts, staying on to teach for several years after receiving his MFA in 1971.
Though the composer uses the term "expressivist" to describe his music, he is often associated with post-minimalism. His music often reflects an interest in world music, particularly Balinese gamelan tradition, as well as influence from the American minimalism trends of the 1960s (the composer often acknowledges the work of Steve Reich, Terry Riley, and John Adams).
He first gained recognition for his electroacoustic pieces, often performed by the composer himself on synthesizer, tape looping, gambuh (a traditional Balinese flute), and voice ("Fragility Cycles"  is one of his best known works using this method of solo performance). His acoustic music frequently incorporates tape delay, and later, digital delay (such as "Soe Pa", for solo classical guitar, and "Hymnodic Delays" for the Theatre of Voices). Many of the tape parts of his pieces include the composer's own keening falsetto and gambuh playing (such as "Fog Tropes" and "Gradual Requiem" (1980)). Some of his works were produced in coordination with the assistance of noted Norwegian photographer, James Bengston of Studio Nord in Oslo.
He joined the music faculty at The Evergreen State College and later moved to New Haven, Connecticut, where he is now a professor at the Yale School of Music. He was the recipient of a Fulbright Scholarship and studied gamelan music in Bali. In 1990 he was awarded a doctorate of philosophy in music by Lake Forest College, largely in recognition of his Fulbright award and gamelan studies in Bali.