Frederick William Rimmer (1914-1998) was Gardiner Professor of Music at the University from 1966 to 1980.

Rimmer was a graduate of The University of Durham (BMus 1939) and Selwyn College, Cambridge (BA 1948, MA 1954), and served with the 11th Battalion of the Lancashire Fusiliers in the Middle East during the Second World War. He was Senior Lecturer in Music at Homerton College Cambridge from 1948 until he came to Glasgow in 1951 as Cramb Lecturer in Music. He was appointed Organist in 1954 and Senior Lecturer in 1956.

Among many offices, Rimmer was a director of Scottish Opera, 1966 to 1980, and served on the BBC's Scottish Music Advisory Committee. He was Director of Scottish Music Archive, 1968-1980, and was awarded a CBE in 1980.