Performance with interactive computer systems offers compelling opportunities for new paradigms of music-making, in particular through novel interfaces which can facilitate expanded physical, cognitive, and social interactions with sound. But novelty presents challenges. Designs are frequently motivated by a sensing technique, a set of gestures, or a physical object, requiring the designer to create a sound world suited to the new interface and to define the interface’s relationship to it—a process we call mapping. Although this approach can be effective, it can suggest a deeper challenge: without the familiar context provided by musical conventions, creators of new musical interfaces are forced to effectively invent a performance practice for every new design. A consequence of the notion of the “composed instrument” is that interactive music suffers from a lack of a repertoire. Beyond merely a set of compositions available to performers, a repertoire provides a landscape of aesthetic reference points, a shared map among performers, composers, and audiences, on which individual performances can be situated. Through examples of recent performances of works by John Cage, I offer an approach to making new musical instruments and interfaces that is responsive to a repertoire of compositions and styles. Whereas our field is typically portrayed as an interdisciplinary synthesis of art and science, I suggest an opportunity for an alternative interdisciplinary approach to interactive music that incorporates humanistic inquiry into the aesthetics of past and contemporary music practices. Such an approach can serve as an antidote to the imperative for technical evaluation as a measure of value and legitimacy, while prompting composers to consider ways of describing or specifying new musical instruments and interfaces in scores—a practice through which the field can begin to develop a repertoire.