Born in 1947 in Stuttgart, Riethmüller studied musicology, philosophy and modern German literature at the Albert-Ludwigs-Universität Freiburg, where he received his doctorate in 1974 from Hans Heinrich Eggebrecht with the dissertation "Die Musik als Abbild der Realität", and habilitated in 1984 with his study on "Ferruccio Busoni's Poetik".