Born in Herford, Sponheuer studied musicology from 1969 to 1976, from 1970 as a scholarship holder of the Studienstiftung des deutschen Volkes, (among others with Anna Amalie Abert, Kurt Gudewill and Walter Salmen), German Studies and philosophy at the Christian-Albrechts-Universität zu Kiel.
In 1976 he received his doctorate in musicology under Kurt Gudewill with a study on the history of the genre and aesthetics of the symphony.
In 1984 he received his habilitation in musicology with a thesis on Musik als Kunst und Nicht-Kunst.
Untersuchungen zur ästhetischen Dichotomie von 'hoher' and 'niederer' Musik im musikästhetischen Denken zwischen Kant und Hanslick“.
From 1994 to 1997 he was editor of the journal Die Musikforschung and from 1996 to 1998 vice dean of the faculty of philosophy.