In attempting to determine how Johann Sebastian Bach taught composition, this article draws on recent archival discoveries to claim that it was not the ornamented, vocal Choralgesänge, but the simpler, thoroughbass-centered Choralbuch style that played a central role in Bach's pedagogy. Fascinatingly, many newly-rediscovered chorale books from Bach's milieu contain multiple basses under each melody, suggesting that Bach too may have employed this technique. What theoretical perspectives shall we bring to bear on this long-lost multiple-bass chorale tradition? This article asserts that it is a fallacy to assume that any pattern-yielding methodology offers a valid window into Bach's teaching. Rather, an attempt is made to recover modes of music-theoretical understanding that existed contemporaneously with Bach. Such a coterminous theoretical "paratext" potentially offers more insight into Bach's pedagogy because it establishes a horizon of possibilities from which we can draw when examining multiple-bass composition. Foremost within this paratextual horizon is the centrality of thoroughbass for Bach's understanding of composition. In particular, Bach was immersed in the pre-Rameau thoroughbass tradition as represented by the writings of Johann David Heinichen. In contrast to many modern harmonic perspectives, chordal roots and root progressions played little to no role in the pre-Rameau thoroughbass tradition. Dissonance was understood not harmonically, but dyadically in terms of syncopatio (suspension) and transitus (passing and neighbor) figures. Drawing from a variety of sources from Bach's circle, particularly those of his pupil, Johann Christian Kittel, this article posits that Bach may have understood multiple-bass chorale harmonization in terms of interlocking clausulae -that is, as a series of overlapping cadential modules. In sum, this article contributes to an ongoing revisionist project of recent years that aims to elevate early eighteenth-century thoroughbass from mere "pre-theoretical" accompaniment practice to its true place as the theoretical and practical basis of compositional understanding in Bach's day.