Tremendous strides have been made in recent decades in our understanding of how composers in the European classical tradition learned their craft. That new understanding bears little resemblance to the ahistorical chord-centered simplifications taught in collegiate harmony classes. Because a significant gap exists between the complex mental representations learned by European composers and the simplistic harmony-class assumptions often underlying experiments in music cognition, this chapter seeks to bridge that gap by sketching a historically defensible outline of musical structure as it was understood by its “native speakers.” Aside from a tantalizing study by Meyer and Rosner (1982), hardly any investigations of “historically informed” listening have been undertaken. This chapter presents a number of ideas to stimulate such studies in the future.