Traditional recommendation systems represent user preferences in dense representations obtained through black-box encoder models. While these models often provide strong recommendation performance, they lack interpretability for users, leaving users unable to understand or control the system's modeling of their preferences. This limitation is especially challenging in music recommendation, where user preferences are highly personal and often evolve based on nuanced qualities like mood, genre, tempo, or instrumentation. In this paper, we propose an audio prototypical network for controllable music recommendation. This network expresses user preferences in terms of prototypes representative of semantically meaningful features pertaining to musical qualities. We show that the model obtains competitive recommendation performance compared to popular baseline models while also providing interpretable and controllable user profiles.