New Interfaces for Musical Expression must speak to the nature of ‘instrument’, that is, it must always be understood that the interface binds to a complex musical phenomenon. This paper explores the nature of engagement, the point of performance that occurs when a human being engages with a computer based instrument. It asks questions about the nature of the instrument in computer music and offers some conceptual models for the mapping of gesture to sonic outcomes. Keywords Interaction, Music, Mind, Gesture, Mapping, Dynamic Orchestration, Dynamic Morphology, Spectral Morphology.