Throughout the short history of interactive digital music, there have been frequent calls for a new language of interaction that incorporates and acknowledges the unique capabilities of the computational medium. In this paper we suggest that a conceptualisation of possible modes of performance–time interaction can only be sensibly approached in light of the ways that computers alter the social–artistic interactions that are precursive to performance. This conceptualisation hinges upon a consideration of the changing roles of composition, performer and instrument in contemporary practice. We introduce the term behavioural object to refer to software that has the capacity to act as the musical and social focus of interaction in digital systems. Whilst formative, this term points to a new framework for understanding the role of software in musical culture. We discuss the potential for behavioural objects to contribute actively to musical culture through two types of agency: performative agency and memetic agency.