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.
Riethmüller held additional teaching positions at the Hochschule für Musik Freiburg (1985–87) and at the Martin Luther University of Halle-Wittenberg (1994).
[1] In 1999 he received the John G. Diefenbaker Award from the Canada Council for the Arts in Ottawa, and since 2002 he has been an Affiliated Faculty Member of the Canadian Centre for German and European Studies at York University in Toronto.
He participated in the academic self-administration and scientific organization as Dean and Vice Dean of the Department of Classical Philology and Art Studies at the Goethe University Frankfurt (1988-1991), the Department of Classical Studies at the Freie Universität Berlin (1995-1999), the Deutsche Forschungsgemeinschaft in Bonn (1992-2000), the Austrian Science Fund in Vienna (1993-2004), and the Chair of the Senate Commission for Research and Young Academics at the Freie Universität Berlin (1997-1999).
Since 2000 Riethmüller is editor of the journal Archiv für Musikwissenschaft including supplements.