Glasgow studied at the Eastman School of Music with Harold Gleason and Catharine Crozier, receiving both his bachelor's and his master's degrees there.
He taught at MacMurray College for eleven years, then became Professor of Music (organ) at the University of Michigan-Ann Arbor in 1962, serving on the faculty until his retirement in 2005.
Annually, he appeared as a featured performer, lecturer and clinician at national and regional conventions of the American Guild of Organists.
He gave a recital, a lecture, and a master class at the International Congress of Organists at Cambridge University, and was a featured recitalist and lecturer at the American Classic Organ Symposium in the Mormon Tabernacle, marking the renovation of its historic organ.
Glasgow was named International Performer of the Year in 1997 by the American Guild of Organists.