Key Structure in “Das alte Jahr vergangen ist”

My discussion of Bach's chorale prelude “Das alte Jahr vergangen ist” centers on its key structure: the hierarchical arrangement of keys in the piece and the relationships between them. In the course of this discussion, I make a number of observations about the nature of key structure and the factors that govern our perception of it. I begin by considering one of Bach's four-part harmonizations of the chorale and then turn to the chorale prelude itself.