Born in Chicago, Cook served in the army during World War II and then studied at the University of Rochester and the Eastman School of Music.
Annie Carpenter Hayashi, Carpenter's niece, described him spending his evenings in his basement in a suburb of Chicago with the massive Mahler work spread out on several tables. "I think he had a vision for the completion," she told the Tribune. "He saw a fullness in Mahler that other people didn't see."