The objects of this study are the thirty-four gigues of J. S. Bach. This corpus of pieces represents one musician's encounter with the most engrossing dance genre of his time, and by coming to terms with this repertory I develop analytical perspectives with wide relevance to music of Europe in the early eighteenth century. The dissertation has a clear analytical focus but it also speaks to methodological issues of the relationship between theory and analysis, and the problem of reading a creative practice out of fixed works. Its main theoretical commitment is to middle-out perspectives on musical process. The dissertation's main themes are form, hypermeter, and schema. Its primary contribution to music theory lies in setting out an original position on the analysis of hypermeter, and advancing approaches to form and schema that are consistent with that position. "Form" and "schema" refer to compositional formulas that associate with hypermeter on the larger and smaller scales respectively, with observational windows as wide as the first half of a binary movement and as narrow as a couple of bars. Chapter 2 addresses the form of Bach's cello gigues. I arrive at a complete model of formal functions and phrase rhythm by first considering the turning points in the rhetoric of Fortspinnung. Chapter 4 addresses the chain of fifths sequence in Bach's harpsichord gigues. I analyze over fifty sequence passages, develop a typology of their contrapuntal frameworks, and consider the connections from sequence passages to subsequent events. These substantive analytical case studies flank the discussion of hypermeter. Chapter 3 includes analyses of Bach's orchestral gigue and two chamber-sonata gigues but is the most purely theoretical chapter. Its arguments are relevant to the study of meter and hypermeter across the whole "common practice" period. Since Chapters 2-4 address subsets of the corpus, a comprehensive overview is entrusted to Chapter 1, which also introduces the dissertation. Chapter 1's overview anchors the more specialized chapters in a wider reflection on the ability of compositional technique to inflect different styles, idioms, genres, and affects. / Music