The Art of Gigue Perspectives on Genre and Formula in J. S. Bach’s Compositional Practice

Rowland Moseley

PH.D. DISSERTATION Department of Music HARVARD UNIVERSITY · SEPTEMBER 2014

Revised and reformatted NOVEMBER 2018 © 2014–2018 by Rowland Moseley All rights reserved

Please cite this document as follows when using the Chicago notes style. In bibliographies: Rowland Moseley. The Art of Gigue: Perspectives on Genre and Formula in J. S. Bach’s Compositional Practice. Printed by the author, 2018. Revised edition of doctoral dissertation (PhD diss., Harvard University, 2014). In notes: Rowland Moseley, The Art of Gigue: Perspectives on Genre and Formula in J. S. Bach’s Compositional Practice (author, 2018; revised edition of PhD diss., Harvard University, 2014).

Abstract

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 study 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 study’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 study. 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. Contents

List of Examples vii

List of Tables xv

Preface to this Revised Edition xvii

Acknowledgments xix

1 Genre: “The Bach Gigue” as Corpus and Creative Practice 1 Introduction to this Study ...... 1 An Overview of Bach’s Gigues ...... 8 Repertoire and Chronology ...... 9 Distinctions of Style and Texture ...... 13 French and Italian ...... 13 Quick and Moderate ...... 16 Fugal and Lyrical ...... 19 Parameters of Form and Design ...... 22 Proportion ...... 22 Duration ...... 26 Tonal Palette and Cadence Schemes ...... 29 Corpus and Creative Practice ...... 32

2 Form: Bach’s “Cello Gigue” 39 Introduction ...... 39 How did Bach structure a gigue for cello? ...... 40 What makes a gigue tick? ...... 51 Quintessential Gestures of the Cello Gigue ...... 51 One, Two, Three ...... 52 Four ...... 53 Three Moments: Highlights from Gigues 1, 3, and 6 ...... 56 The G major Gigue ...... 57 The C major Gigue ...... 60 The D major Gigue ...... 65 Outlining a Phraseology ...... 70 The Four Modules ...... 72 Opening Complex ...... 74 iv The Art of Gigue

Answering Complex ...... 75 Interior Phrase ...... 76 Closing Complex ...... 77 Temporal Scale ...... 78 Written Length of Strains and Periods ...... 78 Tempo ...... 80 Proportions Reconsidered ...... 87 Finding a Level with Period II ...... 88 Hypermeter ...... 94 Finding a Level with the Answering Complex ...... 96 Three More Moments: Selections from Gigues 2, 5, and 4 . . . 97 The D minor Gigue ...... 97 The C minor Gigue ...... 102 The E ’ major Gigue ...... 110 Considering Form and Function ...... 114

3 Hypermeter 117 Introduction ...... 117 Theorizing Hypermeter in Bach’s Orchestral Gigue ...... 117 Situating the Analyst ...... 118 Progress Already Made ...... 119 The Temporalist View of Pulse ...... 122 An Illustration: BWV 1068 ...... 127 Frame of Reference ...... 127 Dot Diagrams ...... 128 Continuity and Change in Metric Levels ...... 128 Metrical Deletion and Well-Formedness ...... 131 Metrical Well-Formedness and Formal Design . . . . . 133 Metric Grids, Overlaps, and Elisions ...... 135 Contrast With “Accent” Theories ...... 142 Accent and Duration ...... 142 Realization, Expectation, Prediction ...... 146 Challenges to Metric Analysis Premised on Pulse ...... 149 The First-Pulse Problem ...... 149 The One-Pulse Problem ...... 150 The Last-Pulse Problem ...... 151 A Temporalist View of Hypermeter ...... 152 Revising Hierarchy, Re-Evaluating Continuation . . . . 152 Metric Projection, Prosaic Projection ...... 157 Projections “Acute” and “Obtuse” ...... 158 Projection Diagrams ...... 161 Diagramming Acute and Obtuse Projections ...... 162 Contents v

Idioms of Triple Hypermeter ...... 163 The Many-Pulse Problem ...... 167 Toward Rhythmic Reduction ...... 168 Analyzing Hypermeter in Bach’s Chamber-Sonata Gigues . . . . . 169 Pulse and Meter in Bach’s Gigue for Flute and Harpsichord . . 170 Flux and Containment Bach’s Gigue for Violin and Continuo . 177 Conclusion ...... 180

4 Schema: The Fifths Chain in Bach’s Keyboard Gigues 183 Existing Schema Studies ...... 185 A Typology of the Chain of Fifths in Bach’s Keyboard Gigues . . . . 191 Repertoire for this Case Study ...... 191 Contrapuntal Methods ...... 192 Analytical Approach ...... 196 Uses of the “Sixths and Sevenths Above” Type ...... 204 The E minor Partita as Essay in the Chain of Fifths ...... 215 Uses of the “Sixths and Sevenths Below” Type ...... 227 Uses of the “Fourths and Fifths” Type ...... 235 Peripheral Cases ...... 254 Connections to Other Analytical Studies and Repertories ...... 264 The Chain of Fifths in Bach’s Aria Introductions ...... 265 The Chain of Fifths in Corelli ...... 274 Conclusion ...... 278

Appendix A: Citations to Scores Reproduced in the Supplement 279

Appendix B: Corpus List and Chronology 283

Bibliography 289

Score Supplement (Separate Volume) 301

List of Examples

2.1 Formal outline generalized from Bach’s thirty-four gigues. . . . 40

2.2 Formal outline generalized from Bach’s six cello gigues. . . . . 41

2.3 Formal schema for Bach’s cello gigues...... 42

2.4 The Answering Complex in Bach’s cello gigues...... 43

2.5 The Opening Complex in Bach’s cello gigues...... 44

2.6 Period I in Bach’s cello gigues...... 45

2.7 Projection in the Opening Complex...... 46

2.8 Conspicuous metric departures in period I...... 46

2.9 Fortspinnung types in period I...... 47

2.10 Period II in Bach’s cello gigues...... 48

2.11 Period III in Bach’s cello gigues...... 49

2.12 Period III in the D minor cello gigue...... 49

2.13 Fleshed-out formal schema for Bach’s cello gigues...... 50

2.14 Pastiche of a Bach cello gigue...... 52

2.15 Analysis of periods and formal cruxes in the pastiche...... 54

2.16 Bach’s G major cello gigue (BWV 1007). Annotated...... 57

2.17 Thematic and motivic relations in the G major cello gigue. . . . 59

2.18 Bach’s C major cello gigue (BWV 1009). Annotated...... 61

2.19 Motivic relations in the C major cello gigue...... 63

2.20 Bach’s D major cello gigue (BWV 1012)...... 66 viii The Art of Gigue

2.21 Form-functional analysis of Bach’s G major cello gigue...... 71

2.22 Form-functional analysis of the pastiche...... 71

2.23 Map of phraseological modules within the three periods of Bach’s six cello gigues...... 73

2.24 Recomposition of period III in the pastiche...... 74

2.25 The final cadence in each of Bach’s six cello gigues...... 84

2.26 The opening Vordersatz in each of Bach’s six cello gigues. . . . . 86

2.27 Period II in Bach’s G major, D minor, and C minor cello gigues. 89

2.28 Period II in Bach’s C major cello gigue...... 90

2.29 Period II in Bach’s E ’ major cello gigue...... 91

2.30 Bach’s D minor cello gigue (BWV 1008)...... 99

2.31 Hypothetical ending for Bach’s D minor cello gigue...... 100

2.32 The final subphrase of Bach’s C minor cello gigue...... 103

2.33 Hypothetical ending for Bach’s C minor cello gigue...... 103

2.34 The end-rhyme in Bach’s C minor gigue...... 104

2.35 Bach’s C minor cello gigue (BWV 1011). Annotated...... 107

2.36 Chains of descending and ascending thirds in Bach’s C minor cello gigue...... 110

2.37 Bach’s E ’ major cello gigue (BWV 1010). Annotated...... 112

2.38 Recomposed opening of the E ’ major cello gigue...... 113

3.1 Example of projection in Bach’s orchestral gigue (BWV 1068), mm. 1–8...... 123

3.2 A metric dot diagram of the orchestral gigue...... 129

3.3 Recomposition of the orchestral gigue, mm. 18–24...... 140

3.4 Recompositions of the orchestral gigue, mm. 9–16...... 142 List of Examples ix

3.5 Diagram of prosaic projection...... 161

3.6 Diagram of metric projection...... 162

3.7 Diagram of acute metric projection...... 162

3.8 Diagram of obtuse metric projection...... 163

3.9 Diagram of obtuse prosaic projection...... 163

3.10 Diagram of ordinary triple hypermeter...... 164

3.11 Diagram of triple organization of the “1, 2, 2” idiom...... 165

3.12 Diagram of triple organization of the “1, 2—and” idiom. . . . . 165

3.13 Reconstruction of a non-modulating period as the basis of Bach’s gigue for flute and harpsichord, BWV 1030...... 171

3.14 Metric analysis of the opening theme (repeated) in Bach’s gigue for flute and harpsichord, mm. 1–8...... 173

3.15 Metric analysis of the “ideal” period in Bach’s gigue for flute and harpsichord...... 175

3.16 Contrapuntal framework for mm. 6–9 of Bach’s gigue for violin and continuo, BWV 1023...... 177

3.17 Metric analysis of mm. 6–9 of Bach’s gigue for violin and continuo.178

3.18 More detailed metric analysis of mm. 6–9 of Bach’s gigue for violin and continuo...... 178

3.19 Recomposed opening for Bach’s gigue for violin and continuo. . 179

4.1 Galant schemas according to Robert Gjerdingen’s analysis. . . . 188

4.2 Chain of fifths schema in which the upper voices form fourths and fifths...... 193

4.3 Chain of fifths schema in which the upper voices form sixths and sevenths, with the cantus in the soprano and the fourth-species counterpoint below. Sevenths occur on the weak beats...... 194 x The Art of Gigue

4.4 The same trio schema as Example 4.3 but with the second- species counterpoint registered differently. The bass tracks the onsets of new notes in the upper voices by similar motion. . . . 194

4.5 The same upper-voice schema as Example 4.3 with an alternative second-species counterpoint in the bass...... 195

4.6 Chain of fifths schema in which the upper voices form sixths and sevenths, with the cantus in the alto and the fourth-species counterpoint above. Sevenths occur on the strong beats. . . . . 196

4.7 The same upper-voice schema as Example 4.6 with an alternative second-species counterpoint in the bass...... 196

4.8 Abstraction of the trio texture basic to fifths chains...... 198

4.9 One of Roger North’s fifths chain schemas...... 200

4.10 Reduction of BWV 814, mm. 1–16...... 201

4.11 Another of Roger North’s fifths chain schemas...... 201

4.12 Score of BWV 809, mm. 14–201/2 (Romanesca)...... 206

4.13 Score of BWV 808, mm. 61/2–11 (Romanesca)...... 206

4.14 Reduction of BWV 808, mm. 8–11 (Romanesca)...... 207

4.15 Left hand of BWV 808, mm. 35–44...... 208

4.16 Score of BWV 808, m. 1 and m. 21: the opening salvo of the fugal subject in its original and inverted forms...... 208

4.17 Reduction of BWV 809, mm. 44–481/2...... 209

4.18 Further reduction of BWV 809, mm. 44–481/2 (with metric expansion removed)...... 209

4.19 Reductions of BWV 818, mm. 40–47...... 210

4.20 Reduction of BWV 810, mm. 73–80...... 210

4.21 Reductions of BWV 806, mm. 36–39...... 211

4.22 Initial reduction of BWV 818, mm. 40–48...... 212

4.23 Initial reduction of BWV 806, mm. 36–40...... 212 List of Examples xi

4.24 Initial reduction of BWV 810, mm. 73–96...... 213

4.25 Right hand of BWV 810, mm. 61–73...... 214

4.26 Reductions from BWV 830...... 216

4.27 Initial reduction of BWV 830, mm. 9–10...... 217

4.28 Initial reduction of BWV 830, mm. 151/2–171/2...... 217

4.29 Initial reduction of BWV 830, mm. 33–34...... 218

4.30 Initial reduction of BWV 830, mm. 411/2–431/2...... 218

4.31 Reduction of BWV 830, mm. 29–30 and 47–48...... 219

4.32 Initial reduction of BWV 830, mm. 29–32...... 219

4.33 Initial reduction of BWV 830, mm. 47–50...... 220

4.34 Reduction of BWV 830, mm. 5–6 and 22–24...... 220

4.35 Initial reduction of BWV 830, mm. 5–8...... 221

4.36 Initial reduction of BWV 830, mm. 22–24...... 221

4.37 Reduction of BWV 830, mm. 11–151/2...... 223

4.38 Reduction of BWV 830, mm. 171/2–21...... 224

4.39 Reduction of BWV 830, mm. 35–411/2...... 225

4.40 Reduction of BWV 830, mm. 43–46...... 226

4.41 Reductions from BWV 806 and BWV 815...... 227

4.42 Initial reduction of BWV 806, mm. 71/2–121/2...... 228

4.43 Initial reduction of BWV 807, mm. 21–34...... 228

4.44 Initial reduction of BWV 815, mm. 7–22...... 228

4.45 Reductions of BWV 807, mm. 61–74...... 229

4.46 Reductions of BWV 818, mm. 7–14...... 230

4.47 Reductions of BWV 828, mm. 25–48...... 231

4.48 Reductions of BWV 828, mm. 70–96...... 233 xii The Art of Gigue

4.49 Further reduction of BWV 828, mm. 70–85...... 234

4.50 Reduction of BWV 815, mm. 35–45...... 236

4.51 Further reductions of BWV 815, mm. 35–42...... 236

4.52 Reduction of BWV 817, mm. 9–16...... 237

4.53 Further reductions of BWV 817, mm. 9–12...... 237

4.54 Reduction of BWV 812, mm. 17–22...... 239

4.55 Further reductions of BWV 812, mm. 17–20...... 239

4.56 Reduction of BWV 831, mm. 9–16...... 240

4.57 Further reduction of BWV 831, mm. 9–12...... 240

4.58 Reductions of BWV 814, mm. 53–60...... 241

4.59 Initial reduction of BWV 814, mm. 53–68...... 241

4.60 Reductions of BWV 827, mm. 22–24...... 243

4.61 Initial reduction of BWV 827, mm. 22–24...... 243

4.62 Reduction of BWV 827, mm. 18–21...... 244

4.63 Further reduction of BWV 827, mm. 18–19...... 244

4.64 Reductions of BWV 831, mm. 37–40...... 245

4.65 Initial reduction of BWV 831, mm. 37–41...... 245

4.66 Reduction of BWV 831, mm. 42–48...... 246

4.67 Further reduction of BWV 831, mm. 42–46...... 247

4.68 (a) Descending tetrachord schema with bass of la–so–fa–mi as 1ˆ –7–ˆ 6–ˆ 5ˆ in minor. (b) Descending tetrachord schema with bass of re–do–ti–la as 4–ˆ 3–ˆ 2–ˆ 1ˆ in minor...... 247

4.69 Left hand of BWV 831, mm. 45–48...... 249

4.70 Overview of BWV 827, second strain...... 250

4.71 Further reductions from BWV 827...... 251 List of Examples xiii

4.72 BWV 827, m. 29, m. 36, and m. 39...... 253

4.73 Reduction of BWV 818, mm. 14–21...... 253

4.74 Initial reduction of BWV 818, mm. 14–24...... 254

4.75 A common harmonic progression...... 254

4.76 Reduction of BWV 807, mm. 35–47. “Conservative” reading. . 255

4.77 Reduction of BWV 807, mm. 35–47. “Radical” reading...... 255

4.78 Further reduction of BWV 807, mm. 35–47. “Radical” reading. 256

4.79 Reduction of BWV 827, mm. 151/2–181/2...... 257

4.80 Reduction of BWV 829, mm. 13–26...... 257

4.81 Alternative renderings of BWV 829, mm. 141/2–18...... 258

4.82 Reductions of BWV 827, mm. 101/2–151/2...... 258

4.83 Reductions of BWV 806, mm. 27–36...... 259

4.84 Reductions of BWV 818 (and BWV 818a), mm. 281/2–33. . . . . 260

4.85 Reduction of BWV 825, mm. 1–16...... 260

4.86 Further reduction of BWV 825, mm. 1–16...... 260

4.87 Reductions of BWV 832, mm. 23–28...... 261

4.88 Reductions of BWV 816, mm. 30–39...... 262

4.89 Reductions of BWV 823, mm. 9–24...... 263

4.90 Reductions of BWV 813, mm. 57–76...... 263

4.91 Riitta Rautio’s fifths chain schemas for Bach’s minor-mode aria introductions...... 266

4.92 As Example 4.91 but with chromatic major triads on the tonic and subdominant...... 266

4.93 Introduction to Bach’s aria, “Ich will dich nicht hören,” BWV 213/9...... 271

4.94 A subcategory of “a1” fifths chain as described by Rautio. . . . 271 xiv The Art of Gigue

4.95 Introduction to Bach’s aria, “Sein’ Allmacht zu ergründen,” BWV 128/4...... 273

4.96 Schemas of the Corellian fifths chain according to Daniel Harri- son...... 275

4.97 Alternative forms, from Harrison, of the fifths-chain schemas in Example 4.96...... 276

4.98 From Harrison, another schema of descending sequence credited to Corelli...... 277 List of Tables

1.1 Proportions of strains and periods...... 24

1.2 Generic proportions of three-period movements in which two periods belong to strain 2...... 25

1.3 Subject length and strain length in the fugal gigues...... 27

1.4 Tempos and durations: a provisional assessment...... 30

1.5 Tonal palette of Bach’s gigues...... 31

1.6 Similar formal modules to the cello gigues in Bach’s other gigues. 35

2.1 Ratios of periods in five of Bach’s six cello gigues...... 41

2.2 Phraseological analysis of Bach’s G major cello gigue and the pastiche...... 72

2.3 Phraseological outline of “the Bach cello gigue.” ...... 77

2.4 Bar and beat counts of periods in Bach’s six cello gigues. . . . . 79

2.5 Tempos from four recorded interpretations of Bach’s cello gigues. 81

2.6 Ranking of tempos shown in Table 2.5...... 82

2.7 Four-beat unit counts of periods in Bach’s six cello gigues. . . . 87

2.8 Summary of the ratios between periods in Bach’s six cello gigues. 91

2.9 Memory aid to fifteenth-century mensural rhythmic values. . . 93

2.10 The “basic lengths” as inscribed by period II in Bach’s six cello gigues, and the arrangement of periods by relative sizes of small, medium, and large...... 93

2.11 Exceptions to “semibrevis” hypermeter in Bach’s six cello gigues. 94

2.12 Exceptions to “brevis” hypermeter in Bach’s six cello gigues. . . 95 xvi The Art of Gigue

2.13 Durations of the four modules in Bach’s six cello gigues. . . . . 96

2.14 Durations of all subphrases in Bach’s six cello gigues...... 96

2.15 End rhymes between strains 1 and 2 in Bach’s six cello gigues. . 105

4.1 The pace of chain of fifths sequences in Bach’s keyboard gigues. 203

4.2 A subset of Riitta Rautio’s tabulation of attributes for fifths chains of schema “a1”...... 269

B.1 List and working chronology of Bach’s gigues...... 284

B.2 Selected authorities for the chronology in Table B.1...... 286 Preface to this Revised Edition

This “edition” of my doctoral dissertation is reformatted for a better reading experience and incorporates modest improvements to the clarity of the prose as well as the correction of a few errors that went undetected in previous proofreading. I have made some changes to my compositional pastiche of a Bachian cello gigue (still a long way off equaling Bach but better than before) and a number of cosmetic improvements to the figures. I have also removed a confusing application of the term “tenor” throughout chapter 4 in favor of the term “cantus.” It took some restraint not to rework the text more thoroughly, but the main purpose of the document is to improve upon the typographical format required of the Ph.D. dissertation. It was satisfying for me to prepare this version and I hope others benefit from it too. Throughout this text, I often refer to Bach’s suites and sonatas by their BWV numbers. I advise readers to keep at hand the list of BWV numbers and common titles supplied in the supplementary volume of scores. This list is also reproduced on the reverse of this page.

New York, New York November 2018 xviii The Art of Gigue

BWV Common Title of Work 806 “English” Suite No. 1 in A major 807 “English” Suite No. 2 in A minor 808 “English” Suite No. 3 in G minor 809 “English” Suite No. 4 in F major 810 “English” Suite No. 5 in E minor 811 “English” Suite No. 6 in D minor 812 “French” Suite No. 1 in D minor 813 “French” Suite No. 2 in C minor 814 “French” Suite No. 3 in B minor 815 “French” Suite No. 4 in E ’ major 816 “French” Suite No. 5 in G major 817 “French” Suite No. 6 in E major 818 Partita in A minor (original version) 818a Partita in A minor (revised version) 823 Suite in F minor 825 Partita No. 1 in B ’ major (Clavier-Übung I) 827 Partita No. 3 in A minor (Clavier-Übung I) 828 Partita No. 4 in D major (Clavier-Übung I) 829 Partita No. 5 in G major (Clavier-Übung I) 830 Partita No. 6 in E minor (Clavier-Übung I) 831 Ouverture in the French Style in B minor (Clavier-Übung II) 832 Partita in A major 996 Lute Suite in E minor 997 Lute Suite in C minor 1004 Violin Partita No. 2 in D minor 1006 Violin Partita No. 3 in E major 1006a Lute Suite in E major (arrangement of BWV 1006) 1007 Cello Suite No. 1 in G major 1008 Cello Suite No. 2 in D minor 1009 Cello Suite No. 3 in C major 1010 Cello Suite No. 4 in E ’ major 1011 Cello Suite No. 5 in C minor 1012 Cello Suite No. 6 in D major 1023 Sonata for Violin and Continuo in E minor 1030 Sonata for Flute and Harpsichord in B minor 1068 Orchestral Suite No. 3 in D major Acknowledgments

My most heartfelt thanks go to Christopher Hasty, whose advising of this project was judicious and unfailingly generous. His love of music and deep curiosity about it sustained my fascination with Bach’s gigues throughout the dissertation process. Meter as Rhythm first caught my interest while I was an undergraduate and it became a major point of departure for the ideas contained here. This project also owes much to my two readers, Suzannah Clark and Thomas Forrest Kelly. Between them, they spurred me to sharpen my arguments and broaden my thought, and they inspired me with their extraordinary knowledge of Bach’s music and music theory. I have been fortunate at Harvard to have numerous friends, colleagues, and mentors who lent me personal support and intellectual nourishment in this project and throughout the doctoral program. I am especially grateful to Alexander Rehding and Frank Lehman, whose mentorship and comradery, respectively, added so much to my life as a music theorist at Harvard. I also wish to record my thanks to Kofi Agawu, Fred Lerdahl, Christoph Wolff; to Andy Friedman, Johanna Frymoyer, John Z. McKay, Andrew Robbie, David Sullivan; to Jamie Blasina, Andrea Bohlman, Christopher Chrowrimootoo, Elisabeth T. Craft, William Cheng, David Kim, Luci Mok, Michael Uy, Gavin Williams; to Richard Beaudoin, Christian Lane; and to all my classmates, teaching colleagues, and students. My doctoral studies were enriched by a visit to Yale University under the Exchange Scholar Program in Spring 2008, and I wish to acknowledge here the warm welcome I received from faculty and classmates. My thanks go especially to David Clampitt, Richard Cohn, James Hepokoski; to Christo- pher Brody, Julia Doe, Joseph Salem, Christopher William White; and to Chelsea Chen. I am also deeply grateful to William Rothstein for allowing me to audit his seminar in the history of theory at CUNY Graduate Center in Spring 2011. And for friendship and interest in my work, thanks to Edward Klorman. For financial support, I thank Paul Buttenweiser and Oscar S. Schafer, the donors of Harvard scholarships which I received for three semesters in 2012 and 2013. I have also benefited from Harvard’s Presidential Scholar- ship and various summer awards from GSAS and the Department of Music. For permission to reproduce the scores of Bach’s gigues contained in Appendix A, I am indebted to Bärenreiter Verlag. For proofreading the music examples in chapter 4, I thank Evan Fein. xx The Art of Gigue

Lastly, I wish to name the people whose gifts to me I cannot begin to fathom: my parents, Margaret and David; my sister, Heather; and my spouse, Ryan. All of them are musicians by profession and have an abiding love of music which sustains mine. In this context, I would add to a list of special influences all my former lecturers, supervisors, and fellow students at the University of Cambridge. I am profoundly grateful for the remarkable education I received as an undergraduate at Cambridge, especially from Martin Ennis and Nicholas Marston. The excitement that was sowed with the first analysis assignment has stayed with me a long time. It amuses me to recall that when I visited King’s College for interviews, I performed the Capriccio from the Partita in C minor for John Butt. On that occasion, I linked my fortunes to Bach’s most famous non-gigue. Now, I give the gigue its due! 1 Genre “The Bach Gigue” as Corpus and Creative Practice

A dizzying variety of styles, metric structures, textures, types of upbeat, affects, and time signatures confronts the one who would understand Bach’s gigues.

Meredith Little and Natalie Jenne, Dance and the Music of J. S. Bach

Introduction to this Study

n the surviving compositions of J. S. Bach, no genre distills the I richness of early eighteenth-century music better than the gigue. A single movement title, albeit with various spellings, is the umbrella for a world of musical contrast, in which the notable opposition of French and Italian gigues is just one factor among many.1 Social and stylistic resonances are abundant enough that historical narrative falters; musical origins and influences, together with etymologies, are hard to recover.2 As scholars

1. The distinction between between French and Italian gigues is summarized in Meredith Ellis Little, “Gigue (i),” in The New Grove Dictionary of Music and Musicians, 2nd ed., vol. 9, ed. Stanley Sadie (London: Macmillan, 2001), 849–852; Carol G. Marsh, “Gigue,” in Die Musik in Geschichte und Gegenwart: Allgemeine Enzyklopädie der Musik, 2nd ed., vol. 3 (Sachteil), ed. Ludwig Finscher and Friedrich Blume, trans. Stephanie Schroedter (Kassel: Bärenreiter, 1995), cols. 1323–1329; Wolfgang Ruf, ed., “Gigue,” in Riemann Musik Lexicon, 13th ed. (Mainz: Schott, 2012), 237–238. Important eighteenth-century sources that also discuss the French–Italian distinction include Johann Gottfried Walther, “Giga (ital.) Gigue (gall.) oder Gicque,” in Musicalisches Lexicon (Leipzig: Wolffgang Deer, 1732), 281; Jean le Rond d’Alembert, “Gigue,” in Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers, ed. Denis Diderot and Jean le Rond d’Alembert, vol. 7 (Paris, 1757), 661. The most substantial survey of the history of the gigue is Werner Danckert, Geschichte der Gigue (Leipzig: F. Kistner & C. F. W. Siegel, 1924). Besides the dictionary and encyclopedia entries already cited, another significant one is Antoine Furetière, Dictionnaire Universel (Rotterdam, 1690).

2. Two separate etymologies have been claimed for “gigue,” one deriving from the name of a medieval stringed instrument (whence the German word Geige) and another deriving 2 The Art of Gigue observe, Bach’s gigues are the most diverse of his compositions in any dance type.3 Outside the orbit of the dance suite, it may be that Bach’s fugues, for instance, are equally multifaceted, yet there the corpus is much larger.4 And although Bach is regularly credited with applying every form and technique in ambitious, even extreme ways,5 the flamboyant variety of the gigues is rarely exceeded. The gigue punches above its weight. Some thirty-four gigues certainly by Bach survive today, mainly as the last movements of “suites,” “partitas” or “ouvertures.”6 There are twenty- one suite movements for harpsichord, two for lute, six for cello, two for violin, and one for orchestra. There are also two binary-form gigues in Bach’s chamber sonatas: one for violin and continuo, and one for flute and harpsichord. Not least for the variety of their instrumentations, the gigues are a superb repertory for studying important questions about Bach’s music and the multifarious musical practices it embodies. Analyzing these thirty-four movements, seeing what they share and where they differ, and reconstructing a past musical practice from them is difficult, and fruitful. Encapsulated here are all the challenges of reading creative practice out of fixed works, of generalizing, and of explaining specifics without denying the essential spontaneity of music-making. And whereas such challenges stalk the whole field of music theory and analysis, they become especially

from the Middle French verb giguer, meaning to dance or leap, along with similar words that refer to the legs or leaping motions.

3. See, for instance, the epigraph to this chapter: Meredith Little and Natalie Jenne, Dance and the Music of J. S. Bach, exp. ed. (Bloomington: Indiana University Press, 2001), p. 143. Little and Jenne add, of the Italian gigues, that “[t]he Baroque love of complexity is nowhere more joyously and enthusiastically expressed . . . ” (p. 153). According to Charles Rosen’s assessment of Bach’s keyboard suites: “The gigues take on a completely novel brilliance and weight, and are often fugues as rich and serious as any that Bach wrote. Some of these virtuoso gigues are also harmonically among his most daring essays, with dissonances that reach anything else his century attempted, and they have a rhythmic fury that is almost unique is his work.” Charles Rosen, “Keyboard Music of Bach and Handel,” chap. 3 in Critical Entertainments: Music Old and New (Cambridge, MA: Harvard University Press, 2000), 25–53, p. 42.

4. For a recent discussion of the genre variations within Bach’s fugues, see David Ledbetter, Bach’s Well-tempered Clavier: The 48 Preludes and Fugues (New Haven and London: Yale University Press, 2002).

5. Two of the most eloquent exponents of this view are Laurence Dreyfus and David Yearsley. See Laurence Dreyfus, Bach and the Patterns of Invention (Cambridge, MA: Harvard University Press, 1996) and David Yearsley, Bach and the Meanings of Counterpoint (Cambridge: Cambridge University Press, 2002), especially chap. 3.

6. Regarding Bach’s use of terms including “partita” and “partia,” see Malcolm Boyd, Bach, 3rd ed., The Master Musicians, ed. Stanley Sadie (New York: Oxford University Press, 2000), p. 94. Genre 3 poignant in a study of close to three dozen movements. The sample is large enough that individuated analyses cannot be the aim, but small enough that an intimate knowledge of musical detail presses on the formation of general theories. To hear the whole repertory of this study (with repeats) takes all of ninety minutes, yet exposes the listener to an extraordinary cross-section of Bach’s musical practice. Movements united under a single title, and from the hand of one composer, are heard to contain fascinating inflections of style, genre, and instrumental idiom. For the music analyst, this becomes a rare opportunity to probe deeply into compositional technique from a narrowly delimited standpoint. This study is about the Bach gigue, as a corpus of pieces and as a once- vivid encounter of one musician with the most engrossing dance genre of his time. But this study also takes the phenomenon of the Bach gigue as a form of discipline, using it to develop analytical perspectives that are widely relevant to music of Europe in the early eighteenth century. Given its special association with imitative procedures, the gigue is unequalled as a reflection on the intersection of counterpoint with dance music, which musicologists have long seen as a hallmark of Bach and his contemporaries. The themes of this study are spelled out in the titles of chapters 2–4. Each chapter focuses on a subset of Bach’s gigues by instrumentation—those for cello; then orchestra and melody instrument with accompaniment; and finally harpsichord—yet each chapter also makes connections to other works and my thinking on each topic is informed by close study across the entire corpus. A comprehensive overview of all thirty-four gigues is entrusted to the current chapter, where I map out the repertory by several means. Here, I build on the collected wisdom of Bach scholars including Christoph Wolff, David Schulenberg, Malcolm Boyd, Richard P. D. Jones, and especially Meredith Little and Natalie Jenne, whose Dance and the Music of J. S. Bach pays great attention to the gigues and Bach’s uses of the gigue topic in non-dance movements.7 My survey will address the following parameters:

7. Christoph Wolff, Bach: Essays on His Life and Music (Cambridge, MA: Harvard University Press, 1991); Christoph Wolff, Johann Sebastian Bach: The Learned Musician (New York: Norton, 2000); David Schulenberg, The Keyboard Music of J. S. Bach, 2nd ed. (New York: Routledge, 2006); Boyd, Bach; Richard D. P. Jones, The Creative Development of Johann Sebastian Bach, 2 vols. (New York: Oxford University Press, 2007, 2013); Little and Jenne, Dance and the Music of J. S. Bach. Much of Little’s and Jenne’s work on the gigue topic in non-dance movements was added in the second edition of Dance and the Music of J. S. Bach. On dance characters in Bach’s vocal music, his fugues, and his cantatas see respectively Doris Finke-Hecklinger, Tanzcharacter in Johann Sebastian Bachs Vokalmusik, vol. 6, Tübinger Bach Studien, ed. Walter Geisterberg (Trossingen: Hohner-Verlag, 1970); Natalie Jenne, “Bach’s Use of Dance Rhythms in Fugues,” BACH 4, no. 4 (1973): 18–26; Natalie Jenne, “Dancing Before the Lord: Dance Rhythms in Bach Cantatas,” in Thine the Amen: Essays on Lutheran 4 The Art of Gigue important distinctions of genre and style; tempo; Bach’s approach to binary form vis-à-vis division into “periods,” cadence schemes, proportion, even clock duration; and, not least, the chronology of composition and Bach’s evident modeling of some gigues on previous ones. This overview anchors the more specialized chapters in what becomes an ongoing reflection on the ability of compositional technique to inflect different styles, idioms, genres, affects—everything that the Bach gigue had abundantly in microcosm of Baroque music as a whole. My primary contribution to music theory lies in setting out an origi- nal position on the analysis of hypermeter, and advancing approaches to “form” and “schema” that are consistent with that hypermetrical perspective. “Form” and “schema” will refer to compositional formulas that associate with hypermeter on the larger and smaller scales respectively, with observational windows that can be as wide as the first half of a binary movement and as narrow as a couple of bars. Chapter 2 is about the form of Bach’s cello gigues, and the internal structures of their three main “periods.” Chapter 4 is about the chain of fifths sequence as Bach uses it in his gigues for harpsichord. These substantive analytical case studies flank the discussion of hypermeter in a logical progression from concrete analysis to more abstract theorizing and back again. On the side of form, important precedents for this study include Wilhelm Fischer on the Fortspinnungstypus, William E. Caplin on formal functions in Haydn onward, William Rothstein on phrase rhythm, and James Hepokoski and Warren Darcy on the “plots” and “trajectories” of sonata form; also notable are Heinrich Christoph Koch, Leonard G. Ratner, Wayne C. Petty, and Samuel Ng.8 On the side of schema, I have been influenced by Leonard B. Meyer, Robert O. Gjerdingen, Giorgio Sanguinetti,

Church Music in Honor of Carl Schalk, ed. Carlos Messerli (Minneapolis: Lutheran University, 2005), 123–138. A comparable treatment of Handel’s vocal music is offered in Karina Telle, “Tanzrhythmen in der Vokalmusik Georg Friedrich Händels” (PhD diss., Ruprecht-Karls-Universität Heidelberg, 1973).

8. Wilhelm Fischer, “Zur Entwicklungsgeschichte des Wiener klassichen Stils,” Studien zur Musikwissenschaft 3 (1915): 24–84; William E. Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven (New York: Oxford University Press, 1998); William Rothstein, Phrase Rhythm in Tonal Music (New York: Schirmer Books, 1989); James Hepokoski and Warren Darcy, Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata (New York: Oxford University Press, 2006); Heinrich Christoph Koch, Versuch einer Anleitung zur Composition, (Leipzig: A. F. Böhme, 1782–1793); Leonard Ratner, “Two-Reprise Form,” in Harmony: Structure and Style (New York: McGraw-Hill, 1962), 232–248; Wayne C. Petty, “Compositional Techniques in the Keyboard Sonatas of Carl Philipp Emanuel Bach: Reimagining the Foundations of a Musical Style” (PhD diss., Yale University, 1995). Genre 5 and Vasili Byros;9 and, still more deeply, this study bears the imprint of Kofi Agawu’s work on “prolonged counterpoint” and Laurence Dreyfus’s seminal monograph, Bach and the Patterns of Invention.10 The parts of this study devoted to formal and schematic analysis are not cantankerous toward any of these luminous precedents. But no existing scholarship comes close to giving hypermetrical analysis the leading role which I envisage. And in many ways, a weightier consideration of meter answers the challenge posed by the early eighteenth century to interpretive frameworks honed on the music of later decades. Channan Willner has in recent years demonstrated this with studies, based in the Schenkerian tradition, of Handel’s music in particular.11 My intentions for hypermetric analysis are for it to draw together ideas of content and design; for it to mediate the parsing of musical process into distinct sections and strands; and for it to take a leading role in situating observations about compositional material at particular moments in a listener’s or performer’s experience of that material, even the composer’s experience of it. Chapter 3 presents my ideas on hypermeter in two unequal parts: first, a theoretical argument that includes some analysis, and second, a brief illustrative analysis that accumulates some more theory. Chapter 3 is the most purely theoretical chapter, and is relevant to the study of meter

9. Leonard B. Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956); Leonard B. Meyer, Style and Music: History, Theory, and Ideology (Chicago: University of Chicago Press, 1989); Robert O. Gjerdingen, A Classic Turn of Phrase: Music and the Psychology of Convention (Philadelphia: University of Pennsylvania Press, 1988); Robert O. Gjerdingen, Music in the Galant Style (New York: Oxford University Press, 2007); Giorgio Sanguinetti, “The Realization of Partimenti: An Introduction,” Journal of Music Theory 51, no. 1 (2007): 51–83; Giorgio Sanguinetti, The Art of Partimento: History, Theory, and Practice (New York: Oxford University Press, 2012); Vasili Byros, “Foundations of Tonality as Situated Cognition, 1730–1830: an Enquiry into the Culture and Cognition of Eighteenth-Century Tonality, with Beethoven’s Eroica Symphony as a Case Study” (PhD diss., Yale University, 2009); Vasili Byros, “Towards an ‘Archaeology’ of Hearing: Schemata and Eighteenth-Century Consciousness,” Musica Humana 1, no. 2 (Autumn 2009): 235–306; Vasili Byros, “Meyer’s Anvil: Revisiting the Schema Concept,” Music Analysis 31, no. 3 (2012): 273–346.

10. Kofi Agawu, Music as Discourse: Semiotic Adventures in Romantic Music (New York: Oxford University Press, 2009); Dreyfus, Bach and the Patterns of Invention.

11. Channan Willner, “Stress and Counterstress: Accentual Conflict and Reconciliation in J. S. Bach’s Instrumental Works,” Music Theory Spectrum 20, no. 2 (1998); Channan Willner, “Sequential Expansion and Handelian Phrase Rhythm,” in Schenker Studies 2, ed. Carl Schachter and Hedi Siegel (Cambridge: Cambridge University Press, 1999), 192–221; Channan Willner, “Durational Pacing in Handel’s Instrumental Works: The Nature of Temporality in the Music of the High Baroque” (PhD diss., The City University of New York, 2005); Channan Willner, “Metrical Displacement and Metrically Dissonant Hemiolas,” Journal of Music Theory 57, no. 1 (Spring 2013): 87–118. 6 The Art of Gigue and hypermeter in the whole “common practice” period. My argument explicitly engages the prior work of Fred Lerdahl and Ray Jackendoff, Carl Schachter, Danuta Mirka, Justin London, and particularly Christopher F. Hasty,12 though it has been influenced by a wide circle of meter scholars including Maury Yeston, Andrew Imbrie, Joel Lester, Jonathan D. Kramer, Harald Krebs, Walter Frisch, William Rothstein, Richard Cohn, and John Paul Ito.13 The analysis at the end of chapter 3, though continuous with the theoretical discussion, is meant as a practical demonstration of my approach which can be read separately; it emphasizes the aesthetic implications of my ideas about hypermetric analysis, and it uses hypermetric analysis to illuminate the stylistic distinction of duo and trio idioms between a Corelli- inspired sonata for violin with continuo and a much more galant sonata, in “concerted” style, for flute with obbligato harpsichord. The pivotal finding of chapter 3, and the point of departure for its concluding analysis, is essentially the observation Ralph Kirkpatrick made of metric performance as follows:

By and large, those parts of the measure which are active and which control the establishment and maintenance of a tempo are the upbeats and offbeats. There is very little that can be done with a downbeat. The downbeat is a result, not a cause. But there is a great deal that

12. Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA: MIT Press, 1983); Carl Schachter, Unfoldings: Essays in Schenkerian Theory and Analysis, ed. Joseph N. Straus (New York and Oxford: Oxford University Press, 1999); Danuta Mirka, Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791 (New York: Oxford University Press, 2009); Justin London, Hearing in Time: Psychological Aspects of Musical Meter, 2nd ed. (New York: Oxford University Press, 2012); Christopher F. Hasty, Meter as Rhythm (New York: Oxford University Press, 1997).

13. Maury Yeston, The Stratification of Musical Rhythm (New Haven: Yale University Press, 1976); Andrew Imbrie, “Extra Measures and Metrical Ambiguity in Beethoven,” in Beethoven Studies, ed. Alan Tyson (New York: Norton, 1973), 45–66; Joel Lester, The Rhythms of Tonal Music (Carbondale: Southern Illinois University Press, 1986); Jonathan D. Kramer, The Time of Music: New Meanings, New Temporalities, New Listening Strategies (New York: Schirmer Books, 1988); Harald Krebs, “Some Extensions of the Concepts of Metrical Consonance and Dissonance,” Journal of Music Theory 31 (1987): 99–120; Harald Krebs, Fantasy Pieces: Metrical Dissonance in the Music of Robert Schumann (Oxford: Oxford University Press, 1999); Walter Frisch, ed., Brahms and the Principle of Developing Variation (Berkeley: University of California Press, 1984); Walter Frisch, “The Shifting Barline: Metrical Displacement in Brahms,” in Brahms Studies: Analytical and Historical Perspectives, ed. George S. Bozarth (Oxford: Clarendon Press, 1990), 139–163; Rothstein, Phrase Rhythm in Tonal Music; Richard Cohn, “Complex Hemiolas, Ski-Hill Graphs, and Metric Spaces,” Music Analysis 20, no. 3 (October 2001): 295–326; John Paul Ito, “Hypermetrical Schemas, Metrical Orientation, and the Prototype Category,” Journal of Music Theory 57, no. 1 (2013): 47–85. Genre 7

can be done to manipulate the causes represented in the rest of the measure.14

In my view, musical participants of all kinds have an experience of hy- permeter that hinges on articulative and connective qualities. To follow hypermeter is ideally to be in the position of the improviser who—in a sense—knows most about what they are creating when they are in the middle of creating it. By the lights of virtually all prior metric theories, the analyst of hypermeter is the one person who is lifted out of this situation, but I develop a methodology that insists on the opposite. The result is a vision of hypermeter in which metric boundaries—beginnings and ends—cede all their intensity to the connective moments which articulate musical time and metric hierarchy from the inside. And not too figuratively, this might be a vision of the whole study. While the outlines of Bach’s binary form might seem thoroughly under- stood already, chapter 2 uses the cello gigues to build a deeper knowledge of the major turning points that occur in each large section. These are the articulations where the internal rhetorics of Fischer’s Fortspinnungstypus and Liedtypus are navigated.15 Similarly, on the smaller scale, chapter 4 approaches the formula of the chain of fifths sequence with an overriding interest in the transition out of stepwise repetition that is usually interior to the “sequence passage,” and I also devote enormous attention to connections from the sequence passage to subsequent events. These are middle-out perspectives on musical process. Meanwhile, the present study makes an implicit argument for comparative analysis and the power of connections among multiple works to illuminate a shared creative practice. In the end, it is less important to etch the boundaries of what would and would not be a Bach gigue, than to follow the competing musical trends which animate the genre internally. And this essentially connective attitude softens the imperative to establish a knowledge base of contexts and categories prior

14. Ralph Kirkpatrick, Interpreting Bach’s Well-Tempered Clavier: A Performer’s Discourse of Method (New Haven: Yale University Press, 1984), p. 67.

15. Fischer, “Zur Entwicklungsgeschichte des Wiener klassichen Stils.” For a brief synopsis of Fortspinnung definitions by Fischer, Ernst Kurth, and Friedrich Blume, see Petty, “Compositional Techniques in the Keyboard Sonatas of Carl Philipp Emanuel Bach: Reimagining the Foundations of a Musical Style,” pp. 152–154. The sources for Kurth’s and Blume’s notions of Fortspinnung are Ernst Kurth, Grundlagen des linearen Kontrapunkts: Bachs melodische Polyphonie, 2 vols. (Berlin: Hesse, 1917); Friedrich Blume, “Fortspinnung und Entwicklung,” in Syntagma Musicologicum, ed. Martin Ruhnke (Kassel: Bärenreiter, [1929] 1963), 504–525. Per Petty’s citations, see, for modern commentaries on Kurth and Blume, Lee Rothfarb, Ernst Kurth as Theorist and Analyst (Philadelphia: University of Pennsylvania Press, 1988); Carl Dahlhaus, “Zur Theorie der musikalischen Form,” Archiv für Musikwissenschaft 34, no. 1 (1977): 20–37. 8 The Art of Gigue to interpretation of local material, which can stifle attempts at probing analysis. Music analysis in a “comparative” vein commits to understanding creative practices more than fixed works, and it always begins with compari- son of similar musical objects, thus deferring wider, implicit comparisons between generals and particulars, or texts and contexts. Consistent with a vision of middle-out discovery, comparative analysis emulates any musician’s experience getting to know the always-myriad practices current in composi- tion and performance: connections are made first, and their significance—if it can ever be fully known—is learned second. To take an example, our curiosity might be aroused by the fact that Bach only wrote French gigues in minor keys. It is tempting to explain this fact or to establish how rigid the alignment really was in Bach’s imaginative world. But, especially with only a handful of movements, robust historical conclusions are not possible. Instead, the insight into past practice remains provisional and invites wider forays into the musical creations of Bach, his associates, and contemporaries across Europe. We could ask what the modal bias of the French gigue was for other German composers of the same generation or earlier—and in this process, richer analytical opportunities might supplant the initial inability to account for the modality of Bach’s French gigues with narratives of origin, context, or influence. I see the present study as a possible opening for many analytical projects, a foothold for grappling with the compositional record not only of Bach’s practice but of compositional practice Europe-wide during the early 1700s. This study is tightly focused but what makes that concentration worthwhile is the special position that Bach’s gigues have as a confluence of things French and Italian; high and low; contrapuntal and harmonic; provincial and cosmopolitan.

An Overview of Bach’s Gigues

The rest of this chapter introduces “the Bach gigue” as a corpus and as a genre.16 My aim, here, is to answer a series of basic analytical questions, and to be comprehensive in a way that subsequent chapters are not. I favor intensive case studies in chapters 2–4, and the following overview will give a context to those later analyses. In particular, the rest of this chapter will prepare my turn to the cello suites in chapter 2 for addressing Bach’s approach to form.

16. Genre, in this sense, refers to compositional practice rather than reception, since “the Bach gigue” was clearly too specialized for its own conversant audience, and contractual notions of genre are anyway more applicable later in the eighteenth century, with the emergence of musical “publics” in centers such as Vienna. Genre 9

Repertoire and Chronology In this study, I count thirty-four original compositions by Bach in the form of binary gigue. Since other scholars have numbered Bach’s gigues at forty and forty-two,17 my own defining of the corpus requires explanation. I omit a number of gigues that appear in the modern Bach catalogue as follows.18 (1) A keyboard ouverture in G minor, BWV 822, is considered an early work of Bach’s by some scholars but generally it is not accepted to be one of his compositions.19 Musical features of the ouverture’s French gigue are quite inconsistent with Bach’s verified work: the first strain is composed as a parallel 8-bar period which cadences in the tonic and is reprised verbatim in the second strain to create a rounded binary form.20 (2) The keyboard ouverture in F major, BWV 820, has a securer position in the Bach catalogue but the gigue, specifically, is hard to take seriously: it is extremely repetitive, wayward in phrase rhythm, and it ends abruptly, without any let-up of eighth-note motion in the upper part. If the gigue is an original composition and accurately transmitted, it is certainly not on a par with the ouverture’s other movements and would have to pre- date them. Since it is beyond the scope of this study to come to terms with the oddities of BWV 820’s gigue in consultation with the primary sources, I have chosen to exclude this piece from my analyses. (3) Three keyboard arrangements by Bach of ensemble music by other composers are also excluded from this study. BWV 977 is a concerto arrangement, source unknown, featuring a gigue as the third movement; BWV 975 is an arrangement of the Vivaldi concerto written in 1712–1713 that was published as Op. 4, No. 6 in 1716, at that point with a different third movement from the binary gigue Bach had arranged. BWV 965—the most interesting case—is Bach’s arrangement from Reincken’s Hortus Musicus. As

17. Little and Jenne count forty whereas Marsh counts forty-two. Little and Jenne, Dance and the Music of J. S. Bach; Marsh, “Gigue.”

18. See Appendix A for citations for these movements in the Neue Bach Ausgabe.

19. David Schulenberg is sympathetic to the case for Bach authorship of BWV 822 but the Neue Bach Ausgabe presents it as “a probable arrangement of a work by a foreign composer.” See Schulenberg, The Keyboard Music of J. S. Bach, p. 46.

20. Schulenberg writes of this movement as follows (Schulenberg, The Keyboard Music of J. S. Bach, p. 48): “Like the gigue of BWV 820, this is in da capo form, but the symmetry of this movement is not an asset. It lacks the subtle rhythmic irregulaties that give interest to d’Angelbert’s gigues of the same type, and the second half falls into Italian-inspired sequences too routine to be interesting despite the stylistic contrast that they introduce ...” 10 The Art of Gigue

Richard Taruskin has observed, this arrangement amplifies its model,21 and in ways the other arrangements presumably did not, if Bach’s treatment of the first two movements in Vivaldi’s concerto is any indication. Though this work offers fascinating insights, it cannot count among Bach’s gigues for the purposes of understanding his own approach to the genre. (4) Lastly, my list of thirty-four gigues omits the lute versions of the D minor cello suite, BWV 1011, and the E major violin partita, BWV 1006. (The lute versions are catalogued as BWV 995 and BWV 1006a.) These distinct versions are counted as one with the string works when itemizing the corpus. By these omissions, the forty gigues cited by Little and Jenne are reduced to thirty-three. However, I add to my list the finale of the B minor Sonata for flute and harpsichord, BWV 1030 (actually the second part, titled 12 “Presto,” of a hybrid  and 16 movement). This is the one movement listed by Little and Jenne as “gigue-like” which is, in fact, a binary form, and thus a gigue in all but name.22 The “gigue” label is used by Bach in the finale of the sonata for violin and continuo, BWV 1023, and would have been equally appropriate here. Defining the corpus of Bach’s gigues also has a chronological compo- nent, since changes and developments in Bach’s practice over time are as much part of “the Bach gigue” as variations occuring between different styles or instrumentations. For compositions whose dates are uncertain, the relationship of analytical perspectives to chronology is reciprocal: analysis is premised on any available evidence and the consensus of music historians concerning chronology, but analysis can also inform chronology. A study such as this, deeply involved in one movement type and select technical aspects, can make small contributions to understanding not only how but when certain works were composed. In some cases, it is important to consider that the movements of one suite may have been composed at different times. Two movements of the keyboard partita in A major, BWV 832, for instance, are found in the Möller Manuscript (1703–1707), but the gigue—though short—is more assured in technique and more modern in style than either the aforementioned movements (Allemande, Air) or the two movements that fill out the suite

21. Richard Taruskin, Music in the Seventeenth and Eighteenth Centuries, The Oxford History of Western Music, vol. II. (New York: Oxford University Press, 2005), p. 242. See pp. 243–247 for scores of Bach’s arrangement and Reincken’s original, each of which is reproduced as far as the start of the second strain.

22. See Little and Jenne, Dance and the Music of J. S. Bach, pp. 303–306 in Appendix B for lists of pieces in gigue rhythm; and pp. 294–296 in Appendix A for lists of gigues. (Unfortunately, the page numbers are not printed.) Genre 11 in complete sources (Sarabande, Bourrée).23 The gigue alone is consistent with the more mature date of 1708–1714 attributed to BWV 832 in the first edition of New Grove.24 The most plausible explanation of musical conditions in BWV 832 is that Bach added the gigue some years after writing the other movements, perhaps to extend and modernize the suite at a time when new copies were made for pupils, patrons, or peer musicians. In its limited size and high level of technical control, the gigue of BWV 832 could well be contemporary with the F minor Suite, BWV 823, which scholars agree was written at Weimar, 1708–1714. As I explain below, BWV 832 and BWV 823 epitomize Italian gigue and French gigue respectively—from the tonal extremes of A major and F minor, at that. It is not impossible that Bach contrived these movements as a pair, at a time when he was absorbing lessons from better established composers, refining his own technique, and presumably preparing to write the large, ambitious suites he soon did. Another early work whose date analysis illuminates is the keyboard suite in A minor, BWV 818. Modern scholars tend to see BWV 818 as the earliest of Bach’s more substantial suite compositions, pre-dating not only the French Suites, with which it came to be transmitted, but also the English Suites. Analysis, at least of the gigues, strongly confirms that view. Although BWV 818’s gigue commits to a fugal procedure that is superficially similar to the strict, three-part gigues of the English Suites in E and D minors, several factors indicate a much earlier date. Not least is Bach’s treatment of the chain of fifths sequence, to be discussed in chapter 4. Another, cited by Schulenberg, is a sweeping scalar gesture which occurs during one of the sequence passages and recalls similar scales in Bach’s early fugues.25 The date of ca. 1705 named in New Grove II would, rightly, make this movement Bach’s earliest surviving gigue.26 A working chronology of all Bach’s gigues is given in Table B.1 (see p. 284). The chronological order, in particular, becomes important when I consider what may have changed in Bach’s thinking or what he may have learned over time. Mostly, the table synthesizes uncontroversial information that is needed for understanding what pieces are contemporaneous and what pieces are modeled on earlier ones. Regarding the more contentious dates (including of BWV 832’s and BWV 818’s gigues), the table represents

23. On the sources, see Schulenberg, The Keyboard Music of J. S. Bach, p. 11.

24. Stanley Sadie, ed., The New Grove Dictionary of Music and Musicians, 1st ed. (London: Macmillan, 1980).

25. Schulenberg, The Keyboard Music of J. S. Bach, p. 304.

26. Stanley Sadie, ed., The New Grove Dictionary of Music and Musicians, 2nd ed. (London: Macmillan, 2001). 12 The Art of Gigue my tentative conclusions after consulting secondary sources and considering aspects of musical style. Table B.2 (see p. 286) reproduces information gathered from just three widely used and well-established authorities of modern times.27 From the cello suites onward, only the two chamber sonatas, BWV 1023 and BWV 1030, have caused modern scholars difficulty over their date and conception. BWV 1030 is now dated to around 1730 and generally thought to have originated in G minor, given that the earliest source is a keyboard part in that key.28 Although there are reasons to doubt a G minor origin,29 1730 seems a reliable date—stylistically, the gigue could hardly be much earlier. The date of BWV 1023 remains uncertain, but recent revisions toward a Leipzig date from a Weimar one would be corroborated by the sophisticated and confident technique of the gigue as regards melody and phrase rhythm. Prior to the cello suites, I draw attention to my suggested dates for the gigues of BWV 996 and the English Suites. I assign the gigue, at least, of BWV 996 to an earlier date than the gigues of BWV 832 and BWV 823, due to the looseness of its phrase rhythm, especially around the beginning and end of sequence passages. On the evidence of sources, BWV 996’s date is “between 1710 and 1717, with a slight possibility of an earlier date of origin,” but on musical grounds, the gigue must substantially pre-date the English Suites and belong fairly early in the cited date range.30 (The gigue of BWV 811 offers a useful comparison since that plays with some similar chromatic ideas.) As for the “English” Suites (the early collection of keyboard suites with prelude), the internal chronology of this collection is uncertain because Bach probably organized the collection out of compositional order into the stepwise descent of keynotes (A–a–g–F–e–d); musicians and scholars

27. Sadie, The New Grove Dictionary of Music and Musicians, 1st ed.; Sadie, The New Grove Dictionary of Music and Musicians, 2nd ed.; Little and Jenne, Dance and the Music of J. S. Bach.

28. On the dating of BWV 1030, see Boyd, Bach, pp. 99–100; and Robert L. Marshall, “J. S. Bach’s Compositions for Solo Flute: A Reconsideration of Their Authenticity and Chronology,” Journal of the American Musicological Society 32, no. 2 (1979): 463–498.

29. The gigue of BWV 1030 has an unusual form, which appears to have been modeled on the gigue of the third French Suite, BWV 814. If this was the case, it seems likely BWV 1030 was conceived in the same B minor tonality as BWV 814, and that the 1730 source represents a transposed version, so that the extant B minor manuscript would not have been the earliest Bach produced. Another reason to doubt that BWV 1030 was originally conceived in G minor is the awkward placement of the main theme for the fingers of the harpsichord right-hand.

30. Christoph Öhm Kühnle, “Heinrich Nikolaus Gerber’s Rediscovered Manuscript of Johann Sebastian Bach’s Suite in E Minor (BWV 996): A Copy of Bach’s Hitherto Unknown Revised Version,” Bach 38, no. 1 (2007): 45–66, p. 47. Genre 13 have long speculated that this was a deliberate reference to one of Bach’s favorite chorales, “Jesu, meine Freude.” Schulenberg’s assessment is that “all six suites may contain individual movements that were composed at various dates.”31 However, so far as the gigues are concerned, analysis bears out the source evidence that BWV 806—in the form of BWV 806a—was conceived first and separately from the other suites; it also confirms Schulenberg’s observation that the A minor suite is “simpler in style and sparer in texture,” and presumably earlier, than Suites 3–6. I would point particularly to Bach’s treatment of sequences and their connection to what follows, discussed in chapter 4. Among the remaining gigues, the G minor and F major are close in style. Contrary to the order of presentation, I would argue that the G minor was probably written second, and the evidence of Bach’s modeling one gigue on the other is, again, discussed in chapter 4. Certainly the most mature of the gigues in the English Suites are those in E minor and D minor, which reach a new level of expressive intensity and strictness in fugal procedure. It is plausible, if the English Suites were written one at a time, that Bach decided after completing Suites 1–4, in the order 1, 2, 4, 3, what the keys of the two further suites and the presentational order of the whole set would be. By contrast, the “French” Suites (the collection of keyboard suites without prelude) give no reason to suppose that their presentation order is any different from their order of composition, and it is known that the E major suite was written last; Table B.1 shows a likely distribution of dates within the well-attested time window of 1722–1725. Stepping back from the detail of Table B.1, the bigger picture is one of thirty-four gigues written over roughly as many years, though not at a steady rate. Bach averaged about one a year during the 1710s and his first decade or so at Leipzig (1723–1733), but his later years at Cöthen (1720– 1722) witnessed a higher concentration with the composition of the cello suites and the French Suites. No more than two or three gigues survive from outside the period 1710–1733.

Distinctions of Style and Texture French and Italian The existence of distinct French and Italian forms of gigue, like the co- existence of “courante” and “corrente,” was a routine observation of music theorists and lexicographers from across Europe during Bach’s lifetime.

31. Schulenberg, The Keyboard Music of J. S. Bach, p. 280. 14 The Art of Gigue

J. G. Walther and Mattheson both mention it;32 so do Furetière, Brossard, Rameau, and d’Alembert. Occasionally, the French vs. Italian distinction is also made explicit by composers, including Michel Montéclair whose Cinquième Concert is cited by Little and Jenne for its two gigues, “à la manière Françoise” and “à la manière Italienne.”33 Bach maintains the musical contrast of French and Italian types as firmly as anyone, though his spellings of the movement title (“gigue” or “gique” vs. “giga”) do not denote this. The Italian title “giga,” used just twice,34 signals a virtuosic display of instrumental technique which displaces lyrical dance style or fugal style. Hence it is probably inappropriate to apply the term “giga” generally to non-French gigues by Bach or other composers in the German context, as Little and Jenne do. The non-French gigues are quite varied, and even if Germans of Bach’s generation recognized them all as “Italian” in some sense, the title “giga” evidently had a more specialized meaning, to judge not only from Bach’s usage but also from Walther’s and Mattheson’s descriptions. Just four of the thirty-one gigues autographed or otherwise transmit- ted under the title “gigue” or “gique” are French gigues. Their defining characteristic is the rhythmic figure known as the sautillant, Z Z Z , and this is pervasive. Eloquent illustration of the French and Italian types is found in two of Bach’s earliest and shortest gigues, in the individually transmitted keyboard suites in F minor, BWV 823, and A major, BWV 832 (see the supplementary volume for the scores). In BWV 823, the sautillant is present almost constantly, and abates only at the three authentic cadences to allow a momentary rest on the second beat of tonic harmony. This movement ff © only di ers from classic usage by maintaining an upbeat pattern of , not q q .35 In Bach’s three French gigues besides BWV 823, all longer and more sophisticated compositions, the sautillant is almost as ubiquitous. (Chapter 2 will say more about this.) By contrast, Italian gigues rarely include even isolated examples of this figure, especially in their composite rhythm. The 6 composite rhythm in BWV 832 consists of regular eighth notes in 8 ; again,

32. On Walther’s relationship to Bach, see Wolff, Johann Sebastian Bach: The Learned Musician, 332–334.

33. Little and Jenne, Dance and the Music of J. S. Bach, pp. 158–159. Less directly, the gigue of BWV 831 also carries an explicit label of “French” in the form of the title of the whole suite, “Ouvertüre nach Französischer Art.” It is worth stating that French composers of Bach’s generation regularly wrote Italian gigues, hence the thorough representation of the French–Italian distinction in French sources.

34. Namely in the B ’ major keyboard Partita, BWV 825, and the D minor violin Partita, BWV 1004.

35. The “classic” upbeat pattern, which prevails in the music of Lully and Rameau, is used in BWV 813 and BWV 831, Bach’s more mature French gigues for keyboard. Genre 15 this motion only pauses during the second beat of tonic harmony at each authentic cadence. Although the presence or absence of sautillant sets the French and Italian gigues apart, the two idioms are also distinct in ways other than their surface rhythm. Whereas the so-called “Italian gigue” can be one of several things, the French gigue has rather a limited stylistic scope for Bach. This is evident in the parameters of modality, tempo, and phrase rhythm. First, as mentioned, all Bach’s French gigues are in the minor mode, and all were conceived in flat keys. BWV 823 is in F minor. Its immediate antecedent, the one French gigue for cello, is in C minor but possibly originated in G minor as a lute piece,36 and the two remaining French gigues for keyboard were both conceived in C minor, with the second being transposed to B minor for publication. When a dance idiom is represented in such small numbers, it would be wrong to infer that Bach was only capable of imagining a French gigue in minor; after all, the Goldberg Variations draw a French-gigue topic into the sphere of G major. But a bias such as this might prove a useful departure for mapping the wider transmission and evolution of musical styles and genres. For German composers of Bach’s generation, the French gigue possibly had aristocratic associations that predisposed it to the minor mode. A second limitation of Bach’s French gigues is their likely tempo, 3 6 which I would place in the range of Œ = 68–80 in 8 or 8 . This is close to

Wendy Heller’s assessment that C = 88 is typically a comfortable tempo of 6 French gigues in 4 , and it can be expected for un-danced suite movements to be musically denser and steadier than social dances.37 Bach’s Italian gigues demand a contrastingly wide range of tempos. By any standards, BWV 832 has a quicker tempo than any French gigue, and no French gigue will have as slow a tempo as Bach’s other A major gigue, found in BWV 806, which has fairly continuous sixteenth notes. Finally, as a rule, the French gigues have a more conservative phrase rhythm than Bach’s Italian gigues. This state of affairs flatly contradicts the general situation as described by both Carol G. Marsh and Meredith Little; that in the French gigue “[p]hrase lengths became ambitious and irregular” whereas the rhythm of Italian gigues tended to be more balanced.38 The relative regularity of hypermeter in the French gigues indicates the extent

36. See Boyd, Bach, p. 95.

37. Wendy Hilton, Dance of Court and Theater: The French Noble Style 1690–1725 (Princeton: Princeton Book Co., 1981), p. 266.

38. See Marsh, “Gigue” and Little, “Gigue (i)” (quotation from p. 850). On phrase structure in the gigues of Lully, see Rebecca Harris-Warrick, “The Phrase Structure of Lully’s Dance Music,” in Lully Studies, ed. John Hajdu Heyer (Cambridge: Cambridge University Press, 2000), 32–56. 16 The Art of Gigue to which the French–Italian distinction is, for Bach, skewed towards actual dance traditions on the French side. Little and Jenne report that there are no extant choreographies associated with music of the Italian gigue 3 6 idiom.39 A cornerstone of Bach’s French gigues, in 8 and 8 alike, is a firm

, periodicity, grouping the Πbeats into fours. This clearly presents as a norm which is only abandoned briefly during the C minor cello suite, as discussed in chapter 2.

Quick and Moderate Among Italian gigues, whether imposing fugal movements or short pieces like in BWV 832, a division between faster and slower triplet motions has been observed by modern scholars, both in Bach’s music and more widely. Little and Jenne deploy the terms “giga I” when triplet motion is fast, without subdivision; and “giga II” when triplet motion is steadier, but with subdivision. BWV 832 illustrates the “giga I” category, whereas “giga II” can be seen in BWV 806, Bach’s other A major suite. Stylistic features that attend the difference of metric type are as follows: ornamentation is generally lighter in giga I, slurs more uniformly span triplet groups, and harmonic À 40 change is impossible at the triplet level (e.g. ). Little and Jenne also attribute a slower harmonic rhythm to giga I, which creates a foil to the speed of triplet motion. Because giga I can be felt as both faster and slower than giga II on different critera, this study will characterize Little’s and Jenne’s two types of Italian gigue as quick (giga I) and moderate (giga II). For

39. The relevant paragraph from Little and Jenne is worth quoting in full: “One difficulty in studying gigas is that they do not appear to have any choreographic associations. The gigas in Baroque musical suites have not yet been associated by scholars with a particular dance. It seems likely that gigas in Italy were originally a spin-off from the jigs of English country dance fame, but by the late seventeenth century gigas have a life quite apart from dance steps, as the works of Corelli and other Italian composers abundantly demonstrate. Even through English country dancing was popular in Germany throughout the eighteenth century, during Bach’s life and afterward, any connection between these dances and the gigas in his suites has yet to be established. Gigas appear to be more of a purely instrumental excursion than does any other Baroque dance except the allemande.” Little and Jenne, Dance and the Music of J. S. Bach, p. 157 (emphasis mine). By contrast, the choreography of French gigues is quite well understood. The chassé de gigue is one of the dance steps discussed in Sandra Noll Hammond, “Steps Through Time: Selected Dance Vocabulary of the Eighteenth and Nineteenth Centuries,” Dance Research 10, no. 2 (Fall, 1992): 93–108.

40. Here, I draw upon the tabulation of attributes of French gigue, giga I, and giga II in Little and Jenne, Dance and the Music of J. S. Bach, p. 145. Their table is rather a complicated way of stating what are the typical features of (a) all gigues, (b) giga I as against giga II or French gigue, and (c) French gigue as against Italian gigue (both giga I and giga II). Genre 17 the reasons given above, I will also amend Little’s and Jenne’s terminology by not using the word “giga” as a general term for Italian gigues. Although the eighteenth century’s theorists and lexicographers often highlighted the gigue’s varieties of tempo and affect, they did not organize quick and moderate Italian gigues into separate categories. Arguably, this is a distortion that occurs in Little’s and Jenne’s analysis because they choose to express the metric disposition of each dance type in Bach’s music in terms of a three-part hierarchy of “beat,” “pulse,” and “tap.” The usual “metric structures” of their French gigue, giga I, and giga II are recorded as II–3–2, II–2–3, and II–3–2, where the Roman numeral expresses the number of beats per measure, and the following numbers, pulses-per-beat and taps-per-pulse.

Sometimes the measure length is nominal, so, for example, II–3–2 includes 6 3 uses of 8 with regular sixteenth notes or of 8 , similarly, if organized into two-bar units. Under this analytical regimen, the giga I vs. giga II distinction is given priority over other distinctions of style and texture among non- French gigues. But the reading of metric structure raises questions. Little and Jenne credit giga I with a “slower tempo” that has the “illusion of fast,” whereas giga II and the French gigue have a “moderate tempo.” Thus the faster speed of triplet motion in giga I is, for Little and Jenne, a matter of affect rather than tempo because they situate the “beat” a certain distance 12 from the quickest rhythmic divisions in general operation. In a 8 movement whose fastest common rhythmic value is the eighth note, the “beat” is not Œ , as commonly understood, but C . On the one hand, this is an important insight: no metric theorists of the eighteenth-century or since have really acknowledged that the primary 12 12 beat, or Taktteil, of 8 can be C (not unless regarding 8 as a composite 6 of 8 is the same thing).41 Yet early eighteenth-century composers had no better way to notate music conceived with a primary beat that subdivided in two then three. The gigues of Bach’s G minor and D minor English Suites, BWV 808 and BWV 811, illustrate “12” signatures whose primary beats most performers are bound to feel at the half-bar, and melodic analysis can be marshalled to support this claim since emphasizing quarter-bars dramatically increases the incidence of dissonant intervals from beat to 42 beat. On the other hand, plenty of Bach’s “12” signatures are best inter- 12 preted conventionally, as expressing quadruple meter. The 8 signature to the gigue finale of Bach’s E minor Sonata for violin and continuo is a case in point. It is telling that Little and Jenne categorize this movement as

41. See Mirka, Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787– 1791.

42. I also place the gigues of the F major English Suite, BWV 809, and the B ’ Partita, BWV 825, in this category. 18 The Art of Gigue giga II although the triplet motion is subject to only occasional, decorative subdivision:43 giga I is clearly the most appropriate interpretation in every way except that C cannot be the felt (i.e. the danceable) beat.44 Very close in terms of appropriate tempo is the gigue of the A minor keyboard Partita, BWV 827, which arguably has four beats to the measure as well, contrary to the implication of Little’s and Jenne’s giga I categorization. The giga I vs. giga II distinction is more appealing if the “fastness” of giga I—i.e. the speed of its triplet motion—is not confined to being an “illusion” against an ostensible “beat” of triplet pairs. If “beat” means anything at all in terms of gesture, then Bach’s giga I movements should include metric structures of not only II–2–3, but also “2–II–3” (I freely adapt Little’s and Jenne’s notation here to reposition the “beat” on the metric level adjoining the fastest prevalent rhythmic denomination).45 In sum, the separating of quick and moderate Italian gigues is a questionable priority.46 Little and Jenne reveal in a footnote that “[w]e have not found Giga II pieces by Italian composers.”47 Though this suggests

43. These occasional subdivisions in BWV 1023 are similar to the quickest rhythm values in BWV 831, which, rightly, do not factor into Little’s and Jenne’s analysis of metric type.

44. In chapter 15, which is new to the expanded edition of their book, Little and Jenne comment of BWV 1023—and BWV 965, Bach’s Reincken arrangement—as follows (p. 277): “We discuss these as Giga II pieces because of the frequent harmonic changes within the ternary figures, but except for this feature, they could easily be considered as Giga I pieces.” However, this defense is much less appropriate to BWV 1023 than to BWV 965, which includes unusually fast harmonic rhythms. The main obstacle to categorizing BWV 1023 as a moderate gigue within Little’s and Jenne’s framework is surely the placement of the “beat.” In any case, this comment from the expanded edition highlights the friction involved in applying the quick–moderate distinction as Little and Jenne conceive it.

45. As Little and Jenne acknowledge, the giga I category also includes, with BWV 828, one instance of the highly unusual metric structure, I–3–3. They remark that “[e]ven though Kirnberger speaks of three beats to the measure [in 9/16], it is fair to say that most performers will feel the measure as one beat.” (Little and Jenne, Dance and the Music of J. S. Bach, p. 163.) Personally, I find a one-in-a-bar interpretation of this gigue a little facile, and Little and Jenne are perhaps inclined to this analysis because, again, their conception of metric structure does not accommodate the alternative. A three-in-a-bar reading would have to be expressed 1–III–3, upsetting their hierarchical placement of the “beat” at two metric levels’ remove from the fastest prevalent rhythmic denomination.

46. With the gigue of BWV 815, for example, Little and Jenne arrive at a classification of giga II where I see a quick Italian gigue (giga I), but how much is at stake in this interpretation is unclear. Although Bach’s Italian gigues tend to feature subdivision of the triplets either pervasively or not at all, it remains to be shown that distinct subgenres are really at work when the rhythmic idiom appears ambiguous.

47. Little and Jenne, Dance and the Music of J. S. Bach, p. 276. Genre 19 the distinction is meaningful in some way, it does also undermine the specifically Italianate designation “giga II.” More importantly, Little’s and Jenne’s categories of giga I and giga II are far from robust, and important questions concerning metric theory and metric performance are left unre- solved. Granted, a pared-down distinction remains valuable, between Italian gigues that have faster and slower triplets, the latter subject to subdivision. And especially for understanding how gigue topics are active in non-dance movements, a traditional concern for rhythmic idioms must be retained. However, other distinctions of style and texture in the non-French gigues should arguably take priority. In particular, placing too much stock in the French–Italian distinction risks overlooking a German specialty (begun by Froberger) of fugal gigue movements in suites for keyboard or ensemble.

Fugal and Lyrical The written textures of Bach’s gigues range widely, with some movements keeping to a particular number of voices while others exercise varying amounts of freedom, especially around beginnings and endings. The gigues for solo stringed instruments are split between movements written in an unbroken single line and movements which feature double or multiple stops; none of these solo works includes written rests. The strictly monophonic movements are the violin gigues, BWV 1004 and BWV 1006, and two of the cello gigues, BWV 1010 and BWV 1011.48 The rhetorical and formal sides to Bach’s use of multiple stops is considered during chapter 2 in connection with an analysis of the D major cello suite, BWV 1012. Like the gigues for solo strings, the two chamber-sonata gigues also present a mixed picture. On the one hand, BWV 1023 is written as a unbroken single line for the violin above the continuo bass, creating a strict two-part composition that envelops the unwritten element. (The continuo bass does use short written rests after stressed long notes.) On the other hand, BWV 1030, in trio texture, necessarily assigns one line—with rests—to the flute, but features a harpsichord part that steps outside a two-part remit to put chords to the flute’s opening thematic statement and its equivalent in the second strain.49 As for the orchestral gigue, BWV 1068, textural freedom

48. Two of these monophonic works, BWV 1006 and BWV 1011, are the solo-strings movements that Bach also arranged for lute (or Lautenwerck); I revisit this point later in the current chapter.

49. The following comment from Malcolm Boyd addresses Bach’s use of trio and duo textures in chamber sonatas: “In accompanied sonatas for violin, flute, or bass viol Bach preferred a fully composed harpsichord part to the continuo accompaniment that was then the norm. His sonatas for these instruments are therefore mostly in the nature of trio sonatas, with one of the ‘solo’ parts given to the right hand of the keyboard player. 20 The Art of Gigue of course applies in other ways: the fanfares for three trumpets and timpani interact with the core counterpoint of the strings on a spectrum between heterophony and independent polyphony. Still, the orchestral texture is anchored in a robust duet of melody (oboes doubling violins) and continuo bass, each an unbroken line. In the gigues for harpischord and for lute (or perhaps Lautenwerck), the number of written voices shifts between two and three at a basic level, with occasional thickening of the texture as far as four-part counterpoint and six-part chords. Three-part textures are basically exclusive to fugal movements, but those movements may also operate in two parts for long stretches or even most of the time. Two-part textures populate a variety of contexts. Nine movements for harpischord or lute are fundamentally duets. To begin with, the three French gigues of BWV 823, BWV 813, and BWV 831 are two-part pieces; only the last 8 bars of BWV 831 (the major, published work) feature some harmonic filling-in. Also strictly two-part, as written, are the lyrically conceived gigues of BWV 832, BWV 817, and BWV 997, and the gigues close in style to Bach’s two-part inventions, BWV 806,50 BWV 807, and BWV 814. Across the two-part pieces as a whole, the role of canonic or imitative technique varies. Some movements, more popular, lyrical, or galant in style, feature melody–bass duets with little or no canonic interaction: BWV 832, BWV 823, BWV 831, and BWV 997.51 It is worth noting that, contrary to wider tradition, Bach’s few French gigues are not especially inclined to imitation. Other movements are more contrapuntal to various extents. BWV 806, BWV 813, BWV 814, and BWV 817 begin each strain with a point of imitation and weave in canonic elements later; the opening imitations come at a delay of one or two Œ beats and persist for three or four Œ beats, and are cast at the lower octave or lower twelfth. Except in BWV 813, the first imitation is at the octave whereas the second is at the twelfth. The latest of the imitative pieces, BWV 817, strikes the most popular tone and combines canonic writing with passages of distinct melody–bass duet, in some ways exemplifying Bach’s stated aspiration to-

An important manuscript source of the six violin sonatas (BWV 1014–19), in the hand of Bach’s pupil and son-in-law Altnickol, actually has the title Sechs Trios für Clavier und die Violine.” Boyd, Bach, p. 97.

50. BWV 806 includes a sustaining notation for the arpeggiation of each strain’s final chord, which may reflect a general performance practice. Essentially, however, the composition is fully constrained to two parts.

51. BWV 832 has no canonic writing but does feature some contrapuntal artifice at the start of the second strain, where the material from the first strain is swapped between the hands. Genre 21 ward a “cantabile” style of keyboard performance and composition. Finally, BWV 807 is contrapuntal but not imitative: this movement opens with a four- bar theme in duet form whose upper and lower parts return separately later. Midway through the first strain (starting at m. 17), the upper part is reprised in the relative major with a free accompaniment, and the ensuing sequence passage delivers the corresponding reprise of the lower part (starting at m. 25) to cement a move to the new dominant. Bach wrote fugal gigues alongside other more lyrical or dance-like forms at all stages of his career. Ten harpischord gigues are fugal, and another two apply fugal practice in a lighter vein.52 Each strain of every fugal gigue begins with a three-part exposition, except the second strains of the two movements just identified as lighter in style. Otherwise, either a two-part or a three-part texture may predominate. The one work to strictly maintain three parts is the Partita in A minor, BWV 827. Also firmly in three parts, but with some thickening of texture are BWV 830, in which the written texture is amplified during the last six bars; and BWV 818, BWV 811, and BWV 812, in which only the final tonic chord of each strain is amplified. On the opposite end of the spectrum, the F major English Suite, BWV 809, is the one work limited to two parts following the first-strain exposition. Increasing use of three-part (over two-part) texture can be observed first in BWV 815, then BWV 808, BWV 810, and lastly BWV 816.53 In BWV 816, duet texture remains important, but the switches in and out of trio texture are conceived polyphonically, whereas in BWV 810, a voice is sometimes lost or gained without the melodic termination or initiation that would be expected in an ensemble piece. As for the late major-mode fugal gigues of the Partitas in D and G majors, BWV 828 and BWV 829, these represent similar textural conceptions to BWV 810 and BWV 816 respectively, but the contrast is exaggerated. Texturally, BWV 828 is the most flexible and sophisticated of Bach’s gigues, combining contrapuntal duets and trios with style brisé passages, fleshed-out chords, and a violinstic cadenza passage. On the other hand, BWV 829 is the most fastidious of Bach’s fugal conceptions in the major mode, without any liberties beyond three written parts. Apart from its continued use of duet passages within a well-defined trio framework, this movement is akin to the three-part rigor of the late minor-mode fugal gigues mentioned above (BWV 827 and BWV 830).

52. Again, see Ledbetter, Bach’s Well-tempered Clavier: The 48 Preludes and Fugues on the different sub-genres of fugal practice evident in Bach’s Das Wohltemperierte Clavier.

53. The texture is thickened in BWV 816 at the final tonic chord of each strain, and in BWV 815—more unusually—during the second-strain exposition, where full chords bolster the soprano entry (see m. 33). 22 The Art of Gigue

Parameters of Form and Design Proportion One of the most productive ways to map the structure and style of Bach’s gigues is to examine the proportions of their two strains and—where applicable—their three periods (or four, in one case). In this study, I use the term “strain” for each half of the binary form, rather than “reprise,” though the latter is standard among music theorists in North America today.54 I use the term “period” as understood by eighteenth-century, especially German, writers, notably Heinrich Koch.55 A period is therefore any section of a movement, necessarily quite substantial, that concludes with an authentic cadence, and that begins with the onset of the movement (if it is the first period) or following the previous authentic cadence. Nearly always, the first period and the first strain are one and the same. The second strain, however, tends to comprise two periods. Both BWV 823 and BWV 832 illustrate the typical three-period form, which, of course, is prevalent in binary forms throughout the eighteenth century and was clearly described by Koch, among others. One nuance that must be added to the Kochian definition of a period is that a half cadence must occasionally be recognized as a defining event, equal to an authentic cadence;56 this is unavoidable and uncontentious when the first strain is ended by a half cadence, and sometimes, the second strain has an interior half cadence of similar stature, sufficient to inflect two periods within the strain. Careful consideration of the strains and periods in Bach’s gigues—their bar counts, relative proportions, and internal phrase rhythm—suggests that Bach was capable both of planning the length of one or more sections in a movement, and of allowing a section’s length to be determined by intrinsic musical needs only (often, in that case, the needs of fugal procedure). The one universal constraint is that the second strain matches or exceeds the

54. I prefer “reprise” to mean a passage of music which repeats an earlier passage, following common English usage. The specialized use of “reprise” by scholars of form, to mean a section of music which is indicated to be repeated, takes its cue from French Baroque composers’ use of the term and has been standard since the 1960s. See Ratner, “Two- Reprise Form.”

55. Koch, Versuch einer Anleitung zur Composition. Koch’s term for the three main sections of a movement in rounded binary form or sonata form is Hauptperiode (main period).

56. Koch, Versuch einer Anleitung zur Composition. As Joel Lester notes: “This cadence [the ending of a period] is always, by Koch’s definition, a full close on the tonic of some key, but not necessarily the principal key of the movement.” Joel Lester, Compositional Theory in the Eighteenth Century (Cambridge, MA: Harvard University Press, 1992), p. 294. See also Scott Burnham, “Form,” chap. 28 in The Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge University Press, 2002), 880–906. Genre 23 length of the first strain; it is never shorter. Several approaches to the sizing of strains and periods can be discerned. (1) Bach appears, in some movements, to have engineered the first strain to fill out a “round number” of measures, then entrusted the exact length of the second strain to musical process (i.e. the procedures of a second strain running parallel to, and introducing variations relative to, the first strain). (2) Elsewhere, a simple ratio governs the length of the second strain relative to the first strain (which, again, fills a round number of measures). Depending on when and in what circumstances a movement was composed, it is conceivable that a 1 : 1 ratio occurs “accidentally” (without any specific intention in that direction, consistent with the first approach described). But most of the time, 1 : 1 and 1 : 2 ratios undoubtedly indicate Bach’s commitment to a specific number of measures in the second strain as well as the first. (3) When there is no obvious order to the ratio of strains, a movement in three periods is often straightforwardly proportioned on those terms instead. This approach has been the most easily overlooked by writers on Bach’s binary forms. For the most part, a simple ratio of the three periods is closely reflected in their phrase rhythm (e.g. the integers correspond to 4-bar units which are musically palpable). Specific ratios aside, the sizing of the three periods is important to the formal aesthetic of Bach’s gigues. Post-Weimar, Bach always put the shortest of three differently sized periods in second place. And for the most part, he was disinclined to have any two periods be equal: this occurs only in around one in four of his movements with three periods. (4) The last and most expressly logical approach to the sizing of formal units is the rational scaling of both strains and periods (when there are more than two). This approach is characteristic of Bach’s later gigues, and applies to movements in three periods whose strains relate by 1 : 1 or 1 : 2. Either the second strain is evenly divided into two periods,57 or is unevenly divided to produce a still-simple ratio. In two later compositions in relatively popular styles, for example, Bach unevenly divided the second strain of a 1 : 2 arrangement, such that the periods form a superparticular ratio, 4 : 3 : 5. Table 1.1 and Table 1.2 give a comprehensive overview of the pro- portions of strains and periods in Bach’s gigues. The works are listed in chronological order, as in Table B.1. Consistent with the interpretation of Bach’s procedures outlined above, I separate the ratios into “planned” and “unplanned”; alternative terms might be “instrumental” and “incidental.” This distinction is not a function of the ratios’ numerical simplicity; a number of simple, superparticular ratios appear in the “unplanned” category.

57. In the unusual case of BWV 1030, as discussed elsewhere, the first strain is divided in halves. 24 The Art of Gigue

Table 1.1: Proportions of strains and periods.

Planned ratios Unplanned ratios S2 / S1 BWV Key Fugal Strains Periods Strains Periods low–high 818 a ( ✔ ) 1 : 1 8 : 5 : 3 1= 996 e 1 : 1 1= 832 A 4 : 7 : 6 4 : 13 16 823 f 1 : 1 9 : 5 : 4 1= 806 A 2 : 3 11= 807 a 17 : 20 17 : 13 : 7 4 809 F ( ✔ ) 6 : 7 24 : 19 : 9 3= 808 g ✔ 5 : 6 5 810 e ✔ 1 : 1 1= 811 d ✔ 3 : 4 8= 1007 G 6 : 4 : 7 6 : 11 13 1008 d 8 : 4 : 7 8 : 11 9 1009 C 4 : 2 : 3 4 : 5 6 1010 E ’ 5 : 8 : 8 5 : 16 15 1011 c 3 : 2 : 4 1 : 2 14= 1012 D 7 : 4 : 6 7 : 10 10 1004 d 1 : 1 2 : 1 : 1 1= 1006 E 1 : 1 2 : 1 : 1 1= 812 d ✔ 3 : 4 12 : 9 : 7 † 8= 813 c 8 : 6 : 7 8 : 13 12 814 b 1 : 1 8 : 9 : 9 : 8 1= 815 E ’ ✔ 13 : 17 26 : 17 : 17 † 7 816 G ✔ 3 : 4 24 : 19 : 13 † 8= 817 E 1 : 1 12 : 5 : 7 1= 1023 e 2 : 3 16 : 7 : 17 11= 827 a ✔ 12 : 13 2 830 e ✔ 6 : 7 3= 825 B ’ 1 : 2 4 : 3 : 5 14= 828 D ✔ 1 : 1 1= 829 G ✔ 1 : 1 1= 1030 b 1 : 1 1 : 1 : 2 ‡ 1= 1068 D 1 : 2 1 : 1 : 1 14= 831 b 1 : 2 4 : 3 : 5 14= 997 c 1 : 2 1 : 1 : 1 14=

† Other parsings of the division of the second strain are possible in these movements due to an elision of the internal cadence. / ‡ More precisely, the first strain is composed of two 14-bar periods with a 4-bar linking passage between them. Genre 25

Table 1.2: Generic proportions of three-period movements in which two periods belong to strain 2.

BWV Key Periods L:M:S S:L:M M:S:L L:S:M S:L:L L:S:S 1 : 1 : 1 818 a 8 : 5 : 3 ✔ 832 A 4 : 7 : 6 ✔ 823 f 9 : 5 : 4 ✔ 807 a 17 : 13 : 7 ✔ 809 F 24 : 19 : 9 ✔ 1007 G 6 : 4 : 7 ✔ 1008 d 8 : 4 : 7 ✔ 1009 C 4 : 2 : 3 ✔ 1010 E ’ 5 : 8 : 8 ✔ 1011 c 3 : 2 : 4 ✔ 1012 D 7 : 4 : 6 ✔ 1004 d 2 : 1 : 1 ✔ 1006 E 2 : 1 : 1 ✔ 812 d 12 : 9 : 7 † ✔ 813 c 8 : 6 : 7 ✔ 815 E ’ 26 : 17 : 17 † ✔ 816 G 24 : 19 : 13 † ✔ 817 E 12 : 5 : 7 ✔ 1023 e 16 : 7 : 17 ✔ 825 B ’ 4 : 3 : 5 ✔ 1068 D 1 : 1 : 1 ✔ 831 b 4 : 3 : 5 ✔ 997 c 1 : 1 : 1 ✔

† Other parsings of the division of the second strain are possible in these movements due to an elision of the internal cadence. 26 The Art of Gigue

Rather, the table reflects a musical assessment of the conditions in each piece. With all six cello gigues, for instance, the proportions of the periods appear planned: the length of these sections is under direct control of phrase rhythm. In this context, one movement’s 1 : 2 ratio of strains is only incidental. Using Table 1.1, several trends can be identified that associate particular approaches to proportion with stylistic categories and with different phrases in Bach’s career. First, there is a strong correlation between the fugal idiom, used by many non-French gigues for keyboard, and the appearance of a continuous second strain. The interior cadences or harmonic articulations that do occur in fugal gigues become weaker as Bach’s career progresses. A second trend is Bach’s inclination to simplicity in later compositions, which may well reflect an aesthetic of published works or public genres. After 1725 (starting with BWV 825), strains are related by 1 : 1 or 1 : 2 and are scaled in multiples of sixteen or twenty-four bars. Bach’s specific commitment to these dimensions is evident when the internal phrase rhythm of a strain or period is irregular. In BWV 825, for instance, the second strain is metrically complex yet it fills thirty-two bars: away from the simpler construction of the first strain, the objective of filling a round number of measures is no longer continuous with the intrinsics of phrase rhythm. Another trend, relevant to precisely half the sample, concerns the layout of three differently sized periods (small, medium, and large). The arrangement L : M : S occurs in four early works but falls from favor; in the middle of Bach’s career, L : S : M is preferred, and later, M : S : L. As time progressed, Bach became more willing—or technically better equipped—to write a relatively long third period. Appropriately, chapter 2 finds this part of the form to be the most flexible and open to compositional artistry.

Duration Specific durations are, by definition, omitted from the question of pro- portions. But when movements are grouped in terms of proportions and associated stylistic parameters, some surprisingly specific conclusions can be drawn about the length of a gigue. A few examples deserve special mention, initially using compositional metrics only. Concerning the fugal keyboard gigues, first, a connection can be drawn between the lengths of first strains and their fugal subjects. As a rule, the first strain is twelve times the length of the fugal subject (thus, three times the length of a typical exposition containing three entries and a codetta). Table 1.3 isolates the relevant data. The outlying factor of 24 helps to explain the lighter style of BWV 818. The cello gigues, meanwhile, allow a number of insights into temporal scale which are explored fully in chapter 2. One key lesson is that the realization of some—but not all—formal functions can operate on two distinct scales. The “regular” and “large” scales are epitomized in Genre 27

Table 1.3: Subject length and strain length in the fugal gigues.

Duration in bars BWV Key Fugal Time sig. of subject of first strain Factor

6 818 a ( ✔ ) 8 1 24 24

12 809 F ( ✔ ) 8 2 † 24 12

12 808 g ✔ 8 2 20 10

3 810 e ✔ 8 4 48 12

12 811 d ✔ 16 2 24 12

812 d ✔  1 12 12

6 815 E ’ ✔ 8 2 26 13

12 816 G ✔ 16 3 24 8

12 827 a ✔ 8 2 24 12

830 e ✔ W 2 24 12

9 828 D ✔ 16 6 48 8

6 829 G ✔ 8 2 32 16

† The opening soprano entry is accompanied in stretto at the half-bar but the length of the subject is two full bars. 28 The Art of Gigue

6 the gigues of the first and last cello suites, which fill 34 and 68 bars of 8 respectively. Analysis of Bach’s uses of the chain of fifths in chapter 4 also yields observations about the speed and scale of specific musical elements which could be the springboard for much more wide-ranging theories of temporal scale in Bach’s practice and associated early eighteenth-century practices. Besides counting beats and measures, one can also map Bach’s gigues by their likely clock durations, given a set of reasonable tempo estimates.58 For instance, the four late 1 : 2 gigues coalesce around a performed length 1 2 1 2 of 2 15 –2 35 (with repeats). In three of these movements (BWV 825,

BWV 831, and BWV 997), the bar counts are identical and the tempos similar 6 ( C in  or Œ in 8 = ca. 76–84), while the remaining movement (BWV 1068) 6 achieves the same length with more bars at a faster tempo ( Œ in 8 = ca. 116). Of course, such observations remain quite provisional, since these tempo assessments are offered without support. Yet it is clear that different sub- categories of the Bach gigue tend toward different performed lengths, even allowing for the wide tempo variations that occur among interpreters. When, in chapter 2, I consider the tempos chosen for the cello gigues by four recording artists, I find their tempo choices across the six gigues to be surprisingly consistent in relative terms. This lends some credibility to relativized conclusions based on one musician’s choices, even if no-one’s specific tempo choices command general approval. Certainly the shortest of Bach’s gigues is that of BWV 832, cited above to illustrate the quick Italian gigue, whereas the longest is the fugal gigue 1 2 1 of the E minor Partita, BWV 830: these movements last ca. 1 15 and ca. 6 (with repeats). Between those extremes, however, the remainder of the 1 2 1 2 sample clocks at ca. 1 45 –4 30 , and the normal range could be defined 1 2 1 2 1 2 more narrowly as ca. 1 45 –3 45 . The upper range, from ca. 3 45 , is dominated by the fugal gigues composed at Leipzig but it also includes two especially ambitious earlier works—the fugal gigue of the last English Suite, BWV 811, and the giga in the D minor violin Partita, BWV 1004, which

58. I do not address historical sources concerning the tempo of gigues in this section because the evidence is not detailed enough to give reliable estimates concerning the performance tempo of Bach’s individual gigues close to the time of composition. While scholars have been able to reconstruct plausible tempo ranges for danced gigues based on theoretical treatises and composers’ notations, these still represent large margins of uncertainty. A classic study of meter and tempo is George Houle, Meter in Music, 1600–1800: Performance, Perception, and Notation (Bloomington: Indiana University Press, 1987). Besides scholarship already cited, work on tempo in Baroque dance music includes Jan van Biezen, “The Tempo of French Baroque Dances,” in Rhythm, Metre and Tempo in Early Music: Collected Articles (Diemen, Netherlands: Uitgeverij AMB, 2013). Genre 29 precedes the monumental chaconne.59 In Table 1.4, I list the data behind the preceding comments. Though provisional, this assessment offers a point of departure for considering issues of temporal scale that are too easily neglected. Chapter 2 shows, with the cello suites, how a more rigorous theoretical treatment can be begun.

Tonal Palette and Cadence Schemes Bach’s gigues, and the suites they are part of, use the standard tonal palette of the early-eighteenth century. Table 1.5 shows the incidence of major and minor keys up to four flats or sharps. The more lightly used keys are those that place to the flat side of D minor and G major, except for the related pair, C minor and E ’ major. Bach’s bias toward sharper keys could be ascribed to not only instrumental concerns, but also to temperament, since in these keys, a modulation to the dominant involves a real increase in dissonance. In the following paragraphs, I describe the cadence schemes employed in first major-mode, then minor-mode gigues. In major, the first strain always ends with an authentic cadence in the dominant. (Bach’s gigues, unlike some other dance movements, always meet a minimum of length and complexity beyond which a non-modulating first strain is not an option.60) The variety among major-mode cadence schemes belongs to the interior cadence of the second strain (assuming there is one). The norm is clearly an authentic cadence in the relative minor. However, in the two pieces that commence period III with a return of the movement’s opening phrase or head-motive, the authentic cadence of period II uses the key of the mediant instead; that way, the tonic pitch of period III’s melodic anacrusis is absent from the preceding Vv–i resolution.61 The full return of tonic harmony has greater impact after iii than it would after vi. A second exception to the norm occurs with the two gigues in the notably sharp key of E major: BWV 1006 substitutes the subdominant—which becomes the

59. By my assessment, the first strains of these movements all last 50 seconds or more (once through), a length which is not attained in other gigues. The length of the first strain is actually a stronger indicator than the overall length of a movement for the stylistic and generic distinctions cited.

60. From the cello suites, an example of a binary dance without modulation is Bourrée II of Suite no. 4, in which the first strain ends on the tonic. Further movements whose first strains only are non-modulating are Menuet I of Suite no. 1, Menuets I and II of Suite no. 2, and Gavotte II of Suite no. 5.

61. I introduce the symbol Vv in place of “V” or “V~” to indicate the major triad on 5ˆ in the minor mode. Thus, “V” is reserved for the dominant chord in the major mode, extending the usual ability of case-inflected Roman numerals to communicate a normal modal context as well as chord structure. 30 The Art of Gigue

Table 1.4: Tempos and durations: a provisional assessment.

˚ ˚ BWV Key Bar count Time sig. Est. tempo Est. duration, nearest second 1 2 818 a 48 (24 + 15 + 9) 6/8 Œ = 90 2 08 (32 + 20 + 12) 1 2 996 e 20 (10 + 10) 12/8 Œ = 56 2 51 (43 + 43) 1 2 832 A 34 (8 + 14 + 12) 6/8 Œ = 106 1 17 ( 9 + 16 + 14) 1 2 823 f 72 (36 + 20 + 16) 3/8 Œ = 80 1 48 (27 + 15 + 12) 1 2 806 A 40 (16 + 24) 6/8 Œ = 58 2 46 (33 + 50) 1 2 807 a 74 (34 + 26 + 14) 6/8 Œ = 128 3 28 (32 + 24 + 13) ‡ 1 2 809 F 52 (24 + 19 + 9) 12/8 C = 60 † 3 28 (48 + 38 + 18) 1 2 808 g 44 (20 + 24) 12/8 C = 66 † 2 40 (36 + 44) 1 2 810 e 96 (48 + 48) 3/8 Œ = 70 2 45 (41 + 41) 1 2 811 d 56 (24 + 32) 12/16 Œ = 58 † 3 52 (50 + 66) 1 2 1007 G 34 (12 + 8 + 14) 6/8 Œ = 80 1 42 (18 + 12 + 21) 1 2 1008 d 76 (32 + 16 + 28) 3/8 Œ = 66 2 18 (29 + 15 + 25) 1 2 1009 C 108 (48 + 24 + 36) 3/8 Œ = 72 3 00 (40 + 20 + 30) 1 2 1010 E ’ 42 (10 + 16 + 16) 12/8 Œ = 116 2 54 (21 + 33 + 33) 1 2 1011 c 72 (24 + 16 + 32) 3/8 Œ = 70 2 03 (21 + 14 + 27) 1 2 1012 D 68 (28 + 16 + 24) 6/8 Œ = 72 3 47 (47 + 27 + 40) 1 2 1004 d 40 (20 + 10 + 10) 12/8 Œ = 72 4 27 (67 + 33 + 33) 1 2 1006 E 32 (16 + 8 + 8) 6/8 Œ = 64 2 00 (30 + 15 + 15) 1 2 812 d 28 (12 + 9 + 7)  Z = 74 3 02 (39 + 29 + 23) 1 2 813 c 84 (32 + 24 + 28) 3/8 Œ = 68 2 28 (28 + 21 + 25) 1 2 814 b 68 (16 + 18 + 18 + 16) 3/8 Œ = 56 2 26 (17 + 19 + 19 + 17) 1 2 815 E ’ 60 (26 + 17 + 17) 6/8 Œ = 100 2 24 (31 + 20 + 20) 1 2 816 G 56 (24 + 19 + 13) 12/16 © = 112 4 00 (51 + 41 + 23)
1 2 817 E 48 (24 + 10 + 14) 6/8 Œ = 68 2 49 (42 + 18 + 25) 1 2 1023 e 40 (16 + 7 + 17) 12/8 Œ = 104 3 05 (37 + 16 + 39) Œ 1 2 827 a 50 (24 + 26) 12/8 = 106 3 46 (54 + 59) 1 2 830 e 52 (24 + 28) W C = 68 6 07 (85 + 99) 1 2 825 B ’ 48 (16 + 12 + 20)  C = 84 † 2 17 (23 + 17 + 29) 1 2 828 D 96 (48 + 48) 9/16 © = 142 4 03 (61 + 61)
1 2 829 G 64 (32 + 32) 6/8 Œ = 58 4 25 (66 + 66) 1 2 1030 b 64 (32 + 32) 12/16 © = 120 4 16 (64 + 64)
1 2 1068 D 72 (24 + 24 + 24) 6/8 Π= 116 2 29 (25 + 25 + 25) 1 2 831 b 48 (16 + 12 + 20) 6/8 Π= 80 2 24 (24 + 18 + 30) 1 2 997 c 48 (16 + 16 + 16) 6/8 Π= 76 2 32 (25 + 25 + 25)

˚ The breakdowns give the lengths of each period (for the movements listed in Table 1.2) or else the lengths of each strain. / † For these movements, the primary beat is defined as by Little and Jenne, contrary to the usual pedagogy of time signatures since ca. 1800. / ‡ The total estimated duration of BWV 807’s gigue takes account of the unusual da capo direction. Genre 31 only major key used at this location in a major movement—and BWV 817 substitutes the supertonic.62 Among minor-mode gigues, there are almost as many cadence schemes as movements. To address general trends, it is helpful to deal with each strain separately, with the proviso that the tonal stations of cadences are not duplicated between the strains. (Bach comes closest to revisiting a tonal station in BWV 812 and BWV 813, where the first strain ends in the dominant and the second strain has an interior half cadence on the dominant.63) Like in major, the first strain of most minor-mode gigues ends with an authentic cadence in the dominant. Here, the third of the closing harmony is always raised, thus preparing the return to the tonic key at the repeat. The less common cadence options are a half cadence in the tonic and an authentic cadence in the relative major. In a limited way, these choices may reflect significant factors of genre and chronology. Bach’s use of the half cadence is restricted to four consecutive minor-mode compositions of ca. 1722–1725, namely BWV 814, BWV 1023, BWV 827, and BWV 830. The relative-major

Table 1.5: Tonal palette of Bach’s gigues.

Minor keys Frequency Major keys Frequency

f 1 c 3 E ’ 2 g 1 B ’ 1 d 4 F 1 a 3 C 1 e 4 G 3 b 3 D 3 A 2 E 2 Total 19 Total 15

62. An apter description for the supertonic key is the “subdominant relative” since the latter term translates into minor-mode usage as well. After the relative, subdominant, and dominant, ii in major and VI in minor are the next most common secondary keys. The term “subdominant relative” originates with Hugo Riemann.

63. Also, in BWV 818 and BWV 996, Bach’s earliest minor-mode gigues, both strains modulate to the relative major and feature an elided cadence or some other significant articulation in that key. Yet these tonal positions are secondary to each movement’s two or three primary cadences. 32 The Art of Gigue option, meanwhile, applies in two of the four French gigues, though only in two of the fifteen non-French gigues. Given that the remaining French gigues also feature prominent cadences to the relative elsewhere in the form, a creative association seems likely. As for events earlier in the first strain, a handful of movements modulate to the relative major ahead of an eventual move to the dominant. Elided cadences to the relative occur in Bach’s earliest gigues, BWV 818 and BWV 996, and recur in BWV 813, ahead of modulation to the dominant, as well as in BWV 1023, ahead of modulation to the tonic for a half cadence. Yet more weight is allotted to the relative major in BWV 814 and BWV 1030, where the cadence bisects the first strain, and is no longer presented as only a first pass at closing the strain. In BWV 1030, the cadence is not even elided, so that, uniquely, the first strain has two periods: the first period modulates from i to III and the second period modulates from III to v, reproducing the previous material measure-for-measure. The same options are available for the interior cadence of the second strain (if there is one) as for the main cadence of the first strain, with the added option of an authentic cadence in the subdominant. One important difference, however, is the absence of a raised third at cadences in the dominant. The four options for an interior cadence are illustrated in the four French gigues, all of them very clearly in three periods. In the non- French gigues, the subdominant is narrowly the favorite option for a period- defining cadence within the second strain, but this preference does not apply to weaker forms of harmonic articulation at a similar stage. As to the end of the second strain, a minor-mode gigue may feature a raised third at the final authentic cadence, but usually it does not. A raised third occurs in an overall minority of movements, specifically in Bach’s two earliest gigues, BWV 818 and BWV 996, and in all the fugal gigues except BWV 808. Having outlined Bach’s cadence schemes in major and minor, an inter- esting example of modal mixture can now be mentioned in two major-mode gigues, BWV 1007 and BWV 825. In the first strain of each movement, the entire modulation to the dominant is inflected in the parallel minor. Only the resolution of the authentic cadence presents the dominant as a major triad, so that the whole passage could function equally well in a minor- mode movement. In a less extreme form, modal mixture is also a feature of BWV 1009.

Corpus and Creative Practice

Studying Bach’s gigues in isolation yields particular insights into the extent of two related practices in Bach’s work: self-modeling and pairing. Self- modeling involves the recall of strategies used in a prior composition and Genre 33 their application to a new work in the same genre. Years can elapse between the writing of two movements that are clearly connected, so it is likely Bach sometimes looked explicitly at an earlier gigue when tasked with writing a new one; I will argue that this happens on a few occasions. Meanwhile, pairing involves the exploration of similar strategies in two compositions produced around the same time. It is striking that some materially similar works were written in chronological proximity and Bach likely approached such works as mutual explorations of a similar concept; a few examples of this practice can also be identified. To unearth Bach’s acts of self-modeling and pairing—or to trace more informal affinities between movements—is, perhaps, to uncover the finest gradations of “genre” that exist. As far as comparative analysis is concerned, these compositional impulses open a window on genre that nuances conceptions of the individual work, general frameworks, and compositional typology. We are reminded not to equate “the Bach gigue” with the sum or abstraction of its known instances. At the level of movement-on-movement comparisons, one can tap into the compositional concerns that animate the Bach gigue as a creative prospect, without fixating on the issue of what is acceptable or unacceptable as a compositional outcome. Two examples of self-modeling in the French Suites, drawing on prior compositions for solo strings, revolve around shared tonalities: the C minor French Suite, BWV 813, appears to draw inspiration from the C minor cello suite, BWV 1011, while the E major French Suite, BWV 817, recalls the E major Violin Partita, BWV 1006. In these examples, as Little and Jenne briefly observe, similar melodic materials recur in the context of a shared key as well as shared rhythmic idiom: the C minor gigues are French gigues 3 6 in 8 and the E major gigues are moderate Italian gigues in 8 (with frequent sixteenth notes). BWV 1006 and BWV 1011 happen to be the two solo-strings suites that also exist in arrangements for lute or Lautenwerck, suggesting that BWV 817 and BWV 813 might be read as more ambitious attempts by Bach to “translate” musical ideas that were already untethered from their original instrumentation. The affinity of the two C minor gigues is discussed in chapter 2. The two E major gigues both have equal strains (16 bars each in BWV 1006, 24 bars each in BWV 817) and begin with a downward arpeggiation of the tonic triad. Furthermore, the sequences in strain 1 feature descents from a5 in the top voice, and following the sequences, the melodic climaxes of strain 1 are reached with identical downward scales from b5 (m. 121/2 in BWV 1006, m. 14 in BWV 817). Lastly, even though BWV 817 drives to IV instead of ii for the authentic cadence of period II, the first half of period II in both movements finds repose on Vv/ii with quite similar melodic elaborations (see m. 20 in BWV 1006 and m. 28 in BWV 817). 34 The Art of Gigue

Two further examples of movement-to-movement modeling also in- volve French Suites, either as the new work or the old one. In the fugal gigue of the G major French Suite, BWV 816, Bach adopts a similar design 12 to the fugal gigue of the D minor English Suite, BWV 811, also in 16 . Both movements are cast in strains of 24 and 32 bars, and are essays in perpetual sixteenth-note motion. The gigue of the B minor French Suite, BWV 814, on the other hand, becomes the model for the B minor Flute and Harpsichord Sonata, BWV 1030, written some years later. In all the examples of self- modeling cited here, keys and time signatures emerge as imaginative spaces in which “the gigue” is specially inflected. A final, perhaps deeper, example of modeling can be observed by marshaling some of the findings of chapter 2. Table 1.6 shows the prevalence, across all thirty-four gigues, of the formal schemas which chapter 2 finds essential to Bach’s cello gigues. Just one non-cello movement ascribes un- equivocally to the same formal concept: Bach’s orchestral gigue in BWV 1068. This movement is compiled of the same routines of phrase rhythm and formal function, with period I forged from an “Opening Complex” and “Answering Complex,” period II taking the form of an “Interior Phrase,” and period III consisting of a “Closing Complex” preceded by some other material (which is also typical for the cello gigues). I would argue that, with BWV 1068, Bach turned to a formal concept honed in the cello gigues in order to guide his composition of an orchestral gigue. Although orchestral gigues were fairly common in the works of Bach’s contemporaries, within orchestral ouvertures or as operatic numbers, this subgenre was new to Bach when he wrote BWV 1068 ca. 1731. The gigues for cello were appropriate models because of their relatively popular style and their affiliation to concerto style, which set them apart from most keyboard gigues and from movements with a more fluid phrase rhythm like the “giga” of the D minor Violin Partita. As chapter 3 shows, BWV 1068 includes a manipulation of hypermeter which is unheard of in the cello gigues, but the operative formal schemas are the same. This connection offers an insight into what sort of creative possibility an orchestral gigue was for Bach, even though there are not two examples in the corpus to extrapolate from. The practice of pairing—which is on a continuum with self-modeling— is evident especially in the fugal keyboard gigues, where three pairs of consecutive movements in the gigue chronology each exhibit a similar mind- set. These three pairs of movements do not share a key or (except one) a time signature; rather they explore different affects from a similar design concept. 12 Two English Suites, BWV 808 and BWV 809, present gigues in 8 that are largely conducted in two-part texture; these are the most Italianate of Bach’s fugal gigues and, as chapter 4 discusses, they monopolize the descending thirds sequence (elsewhere absent in Bach’s keyboard gigues). A second Genre 35

Table 1.6: Similar formal modules to the cello gigues in Bach’s other gigues.

BWV Key Opening Answering Interior Phr. Closing 818 a ( ✔ ) 996 e 832 A ( ✔ ) 823 f ( ✔ ) ✔ ( ✔ ) ✔ 806 A 807 a 809 F ✔ ✔ 808 g ( ✔ ) 810 e 811 d 1007 G ✔ ✔ ✔ ✔ 1008 d ✔ ✔ ✔ ✔ 1009 C ✔ ✔ ✔ ✔ 1010 E ’ ( ✔ ) ✔ ( ✔ ) ✔ 1011 c ✔ ✔ ✔ ✔ 1012 D ✔ ✔ ✔ ✔ 1004 d ( ✔ ) 1006 E ✔ ✔ ✔ 812 d 813 c ( ✔ ) ✔ ( ✔ ) 814 b ( ✔ ) ✔ ✔ 815 E ’ ✔ ( ✔ ) 816 G ✔ 817 E ( ✔ )( ✔ )( ✔ ) 1023 e 827 a 830 e 825 B ’ ( ✔ )( ✔ ) 828 D ✔ ✔ 829 G 1030 b ✔ ✔ Ñ 1068 D ✔ ✔ ✔ ✔ 831 b ( ✔ ) ✔ 997 c ( ✔ ) ✔ ✔ ✔ 36 The Art of Gigue compositional pair comprises the two large, minor-mode gigues that were entered in the Anna Magdalena notebook of 1725 and destined for Clavier- Übung I, BWV 827 and BWV 830. These movements both present a first strain of 24 bars, built on a fugal subject that lasts 2 bars, and both conclude the first strain with a half cadence. A third and final pair comprises the two large, major-mode gigues that were written specifically for Clavier-Übung I, BWV 828 and BWV 829. Even as these movements adopt markedly different attitudes to the rigors of fugal practice and experiment with different designs (the subject of BWV 828 is relatively long while that of BWV 829 is short), they both commit to a 1 : 1 ratio of strains and both use subjects of the 6–ˆ 5–ˆ 4–ˆ 3ˆ type.64 Here, in the heightened context of publication, the interplay of similarity and contrast is especially vibrant and would not have been lost on the purchasers of Bach’s originally serialized partitas when they acquired the D major and G major partitas in 1728 and 1730. The first three partitas of Clavier-Übung I had already presented maximum contrast in their final movements: an unusual hand-crossing “giga” in No. 1, no gigue at all in No. 2, and a strict three-part fugal gigue in No. 3. But for an astute subscriber, the fourth and fifth partitas shifted attention to what Bach was capable of within the established German tradition of the fugal gigue. Significantly, both movements introduce contrapuntal innovations in the second strain, and both infuse the fugal form with definite gestures toward galant style, of which BWV 829’s final cadence is the most striking. The various instances of self-modeling and pairing in Bach’s gigues underscore the value of a close reading of specific affinities between the individual instances of a given musical genre. Another kind of study on “the Bach gigue” might have set out—very usefully—to determine the genre’s origins and influences, and define parameters for identifying a gigue by Bach, as against the work of another composer or the work of Bach in other dance types. But the Bach gigue—if it is just one thing—is not very amenable to generalization of its compositional outcomes. It presents as a tangle of musical habits and aspirations that must be met on their own terms. By tracing the inner contours of the repertory, it becomes possible to look past the vexing diversity of thirty-four movements in Bach’s hand and approach an understanding of common compositional practice. Genre has an innate multiplicity which comparative analysis is well-placed to explore. Chapters 2 and 4 will offer two case studies that illuminate what kinds of creative prospect the gigue was in Bach’s practice, but both also resonate beyond the confines of the Bach gigue. Whereas theory and analysis usually trade on

64. On the voice-leading patterns of Bach’s fugue subjects and expositions, see the excellent study by William Renwick, Analyzing Fugue: A Schenkerian Approach (Hillsdale, NY: Pendragon Press, 1995). Genre 37 an economy of scale where individual works meet general models head-on, this study narrows the frame to a point where theory and analysis engage each other and their objects of study in a constant negotiation. I argue that in this approach concepts of the individual work and the individual genre are softened, and the horizon of knowledge reaches beyond the corpus of familiar works. In what follows, my hope is that we can learn about Bach’s compositional practice in such a way that repertoire familiarity enlarges rather than inhibits our sense of creative possibility within and around the genre.65

65. This aim, with respect to the corpus of Bach’s gigues, is inspired in part by the analytical methodology of Laurence Dreyfus. In setting out his approach to Bach’s techniques of invention and “disposition,” Dreyfus writes as follows: “To embark on this kind of analysis is to imagine the piece of music not so much as a static object but as a residue of human thoughts and actions.” Dreyfus, Bach and the Patterns of Invention, p. 10.

2 Form Bach’s “Cello Gigue”

ach’s approach to the gigue was far from uniform. Yet in the six B cello suites, penned mid-career, Bach operated a robust conception of form and phrase rhythm which is the topic of this chapter.1 To discover the form of a Bach cello gigue is to understand Bach’s practice at a point of relative stability that opens general insights on form and aesthetics. Lessons from this small repertory are useful for understanding how Bach and his contemporaries wrote gigues and other kinds of binary dance movement. The current chapter begins with a concise answer to the question, “how did Bach structure a gigue for cello?” then starts over with an extended essay on much the same topic. The essay is structured as an antiphony of analysis and theory that probes the internal dynamics of the genre: six analyses, each attuned to the peculiar musical conditions of one gigue, alternate with more theoretical sections that develop general observations and reflect on method. In these pages, Bach’s gigues for cello become a musicological laboratory for studying form. My objective is to explain formal function and phrase rhythm in “the Bach cello gigue” and to do it without just saying what happens in each or all of the six gigues Bach wrote. When working on the late keyboard Partitas, Bach originally planned—but did not produce—a seventh, and one might productively imagine a similar situation with the cello suites. The unwritten cello gigue can be the object we effectively seek to describe, steering our

1. The most detailed analytical exploration of the cello suites to date is Allen Winold, Bach’s Cello Suites : Analyses and Explorations (Bloomington: Indiana University Press, 2007). On the gigues, see pp. 77–82. In several ways, Winold’s formal analysis complements mine, though our analyses have different priorities and draw their own conclusions. Another notable, though brief, analysis of Bach’s C major cello gigue is contained in Donald Francis Tovey, “Sonata Forms,” in Musical Articles from the Encyclopaedia Britannica (London: Oxford University Press, 1944), 208–232, pp. 210–211. Tovey discusses the movement in the context of the history of binary and sonata forms, writing that “[s]ome of Sebastian Bach’s most typical gigues have at least two distinct themes, while more than one of Haydn’s ripest sonata movements derive everything from their first themes” (p. 210). 40 The Art of Gigue

Example 2.1: Formal outline generalized from Bach’s thirty-four gigues. examination of finished works to the reconstruction of a way of working. An open potential for creative activity is ultimately the definition of all genres and the following analysis aims to treat “the Bach cello gigue” as a creative prospect, not just a generalization of the existing outcomes. As far as possible, this means extrapolating from the individuality of each of Bach’s six cello gigues, to appreciate that a seventh would have been exceptional in its own way. An analyst could learn everything about the six gigues Bach wrote and carve out a kind of “omniscience” of the finished forms. But it does not follow that they would be ready to comprehend a new instance of the genre, let alone compose one. Scrupulous analysis can unfortunately box us into an ossified sort of appreciation of the extant texts; press on us a sense of the “inevitable” in their realization of the supposed archetype; prevent us, actually, from being able to think that the corpus is anything other than closed, the genre, anything other than fully incorporated in the surviving examples. These obstacles to a thorough yet luminous analysis are stubborn. Yet in countless small ways, this chapter battles those analytical demons. My goal is to take a deep dive into the musical detail of six fascinating pieces and bring to light simple, vibrant principles of Bach’s approach to form.

How did Bach structure a gigue for cello?

Bach’s gigues for solo cello, written ca. 1720 in the middle of Bach’s compos- ing career, present the most stable genre concept of any subset of his thirty- four gigues. They stand out for consistency of form. Whereas Example 2.1 shows the design that holds true across all thirty-four of Bach’s gigues, Example 2.2 gives the common design of the cello gigues, which is more specific. These movements follow the prevalent design of three periods— Form 41

Example 2.2: Formal outline generalized from Bach’s six cello gigues.

“periods” in Koch’s sense of sections articulated by authentic cadences.2 The internal cadences are accomplished in a variety of keys, with certain options reserved for pieces in the minor mode. Regarding the temporal proportions of the periods, it holds true in five of the six cello gigues that the three periods are different lengths and period II is shortest. Specifically, periods I and III relate to period II in ratios of 6, 7, or 8, to 4. Table 2.1 records these ratios for the cello gigues in G major, D minor, C major, C minor, and D major. The odd one out is the E ’ major gigue; this stands slightly apart from the others for several reasons, not least for being a rounded binary form. The ratio of this movement’s periods is 5 : 8 : 8. Moving beyond these initial observations, it is within the context of phrase rhythm that particularly intriguing consistencies emerge in Bach’s technique. A set of recurring compositional schemas operate at or below the level of the periods. I identify four such schemas or “modules” (as I will call them here). These are the Opening Complex, Answering Complex, Interior

Table 2.1: Ratios of periods in five of Bach’s six cello gigues.

BWV Key Ratio of periods 1007 G 6 : 4 : 7 1008 d 8 : 4 : 7 1009 C 8 : 4 : 6 1011 c 6 : 4 : 8 1012 D 7 : 4 : 6

2. Heinrich Christoph Koch, Versuch einer Anleitung zur Composition, (Leipzig: A. F. Böhme, 1782–1793). 42 The Art of Gigue

Example 2.3: Formal schema for Bach’s cello gigues.

Phrase, and Closing Complex. Example 2.3 offers an overview. Immediately, it should be noted that the four modules are not all equivalent in terms of phraseology. According to standard criteria, the third module is the only coherent phrase. By contrast, modules one and two are best described as subphrase complexes, lacking the closure or coherence of a phrase.3 Module four is likewise, except that in this case the schema is not even always present on the musical surface: it can stand behind a more complicated realization. Another point of general interest is the asymmetry of four modules within three periods, not unlike the initial asymmetry of three periods within two strains. In period I, the Opening Complex and Answering Complex collaborate. How, is most simply expressed in terms of Wilhelm Fischer’s idea of the Fortspinnungstypus.4 The Opening Complex that I observe spans the Vordersatz and the Fortspinnung; the Answering Complex spans the Fortspinnung and the Schlußsatz (also called the Epilog). As is well known, Fischer coined these terms in 1915 to describe a style of construction in Baroque music that applies to concerto ritornellos and often to the first half of binary dance movements. The general concept is that the music begins with a thematic statement and then spins that material out in sequences and other patterns until it is time to make a cadence.

3. I follow William Rothstein’s usage of “subphrase” here. See William Rothstein, Phrase Rhythm in Tonal Music (New York: Schirmer Books, 1989), pp. 30–32.

4. Wilhelm Fischer, “Zur Entwicklungsgeschichte des Wiener klassichen Stils,” Studien zur Musikwissenschaft 3 (1915): 24–84. Form 43

Example 2.4: The Answering Complex in Bach’s cello gigues.

Of the four modules basic to phrase rhythm and formal function in Bach’s cello gigues, the Answering Complex is the most consistent. This means that the end of strain 1 is the most tightly constrained area of the binary form. As shown in Example 2.4, the Answering Complex consists of three subphrases, which I label here as “Fortspinnung,” “Schlußsatz 1,” and “Schlußsatz 2.” Schlußsatz 2 is the cadence of the strain, whereas Schlußsatz 1 is a set-up for the cadence based on a melodic pattern of ascending steps or descending thirds. The Answering Complex, uniquely, always takes the same number of beats. If beats are defined as the focal pulse, which Justin London calls “tactus,” the beat structure is consistently 8 + 4 + 4. Some slight blurring of boundaries is apparent in the last two examples, but overall, the consistency of the set is striking. In Example 2.4, the hatched boxes highlight where these extracts belong in period I. The Opening Complex, the Answering Complex’s opposite number in period I, also has three subphrases: “Vordersatz 1,” “Vordersatz 2,” and “Fortspinnung.” Vordersatz 1 is a tonic prolongation, whereas, under normal conditions, Vordersatz 2 presents a move to the dominant. The Fortspinnung element is a sequence, missing in one case, but more must be said about this separately. The beat structure of the Opening Complex is most often 4 + 4 + 8, but longer subphrases are possible, as shown in Example 2.5. In 44 The Art of Gigue

Example 2.5: The Opening Complex in Bach’s cello gigues. the C major gigue, the Fortspinnung runs to 12 beats; in the D major, the whole module is double length. Before looking further at the Fortspinnung function, the interaction of the Opening and Answering Complexes should be understood. There are various options for relating the two modules, as illustrated in Example 2.6. In the D minor gigue, the second module simply follows the first. In the C major and D major gigues, other material intervenes. And in the G major and C minor gigues, I show the two modules overlapping, with a single Fortspinnung subphrase doing double duty. This latter option raises important questions, which I reflect on at the very end of this chapter. The issue for now is how the compositional modules I identify translate into musical experience. A brief theoretical diversion takes us to the topic of chapter 3. I would describe all occurrences of the Opening and Answering Complexes as hypermetrical entities. What I mean by this can be explained with reference to Christopher Hasty’s “projection” theory of meter.5 Simply speaking, projection is the process of reproducing metric durations. For example, one

5. Christopher F. Hasty, Meter as Rhythm (New York: Oxford University Press, 1997). Form 45

Example 2.6: Period I in Bach’s cello gigues. would say that Vordersatz 1 is “projective for” Vordersatz 2. This means that Vordersatz 2 proceeds as a sort of repetition of Vordersatz 1. Crucially, metric projection is anchored in the start of the second duration. And I would add to Hasty’s theory, that this is where, under certain conditions, we feel a larger duration emerge. In an Opening Complex, we experience Vordersatz 2 as a projection of Vordersatz 1 and in the process become aware (intra-actively) of a single metric span across both. Similarly, we experience the Fortspinnung subphrase as a projection of the complete Vordersatz and become aware of a metric duration spanning the whole module. (See Example 2.7.) Metric theory explains the musical integrity of each module, despite the two modules’ contradictory implications for how period I should be parsed as a formal structure. Along the lines of a processual theory of hypermeter, the moments of articulation central to each module should be emphasized over the ostensible boundaries of “hypermeasures.” Under normal circumstances, period I hinges on two essential turning points: the turn to Fortspinnung and the turn to Schlußsatz. (See the stars containing “1” and “2” in Example 2.8.) These turning points are the main accomplishments of the Opening Complex and Answering Complex as compositional schemas. Although other junctures may occur during period I, and very salient ones, these are not as fundamental to the genre. The D major gigue even includes 46 The Art of Gigue

Example 2.7: Projection in the Opening Complex.

Example 2.8: Conspicuous metric departures in period I, including projections in the Opening Complex and Answering Complex. Form 47

Example 2.9: Fortspinnung types in period I. a return of the opening theme in the dominant. But it is not of the same importance as the subsequent, much less salient, turn to the Schlußsatz. The last essential fact about period I concerns the content associated with Fortspinnung. As shown in Example 2.9, all Fortspinnung subphrases in the Opening Complex, marked “A” or “AB,” are sequential, whereas subphrases in the Answering Complex alone, marked “B,” have a static behavior—meaning that they sustain a bass pedal on 5ˆ or 4,ˆ or arpeggiate a dominant seventh chord. In the C major gigue, there is extra Fortspinnung material of the static kind between the two modules. Period II is much easier to generalize than period I. In five of the six cello gigues, the whole period is spoken for by the schema of a single phrase, parsing into a forephrase and an afterphrase. Most often, its beat structure is 8 + 8. Once again, however, the module runs longer in the C major gigue and the D major gigue. Example 2.10 offers a visual summary. It is worth noting how the structure of large-scale afterphrases compares to the generic Answering Complex of period I: although the large-scale afterphrases in the C major and D major gigues divide into subphrases of 8 + 4 + 4 and form structures similar to an Answering Complex, the subphrase corresponding to Schlußsatz 1 does not meet the melodic and rhythmic requirements of that function. 48 The Art of Gigue

Example 2.10: Period II in Bach’s cello gigues.

Period III and the schema of Closing Complex restore a level of complex- ity to the formal process. In some but not all respects, the Closing Complex is a re-run of the Answering Complex—not least because it actually reprises part or sometimes all of it during the familiar “end rhyme.” There are, like before, three subphrases, which I call “Fortspinnung C,” “Schlußsatz 1,” and “Schlußsatz 2.” As shown in Example 2.11, the favored beat structure is also 8 + 4 + 4. However, these dimensions are subject to expansion, unlike before. The C minor gigue features a wonderful recomposition of the previous Schlußsatz where each four-beat subphrase expands to six beats. And in the D major gigue, the large-sized sequence from the Opening Complex is grafted onto the regular-sized cadence, reconciling the disparity we saw in the movement’s first two modules. In an important distinction with the Answering Complex, the Closing Complex’s Fortspinnung element is sequential in all cases except the C major gigue, where it is part of a long end-rhyme. The Closing Complex is not necessarily present on the musical surface, as mentioned above. In this part of the form, Bach sometimes plays with the expectations a listener will have acquired during the Answering Complex. The actual succession of subphrases may be clearly related to that schema in a non-linear way. In the G major gigue, the rhyming cadence is aborted at the Form 49

Example 2.11: Period III in Bach’s cello gigues.

Example 2.12: Period III in the D minor cello gigue. 50 The Art of Gigue

Example 2.13: Fleshed-out formal schema for Bach’s cello gigues. last moment and the functions of Schlußsatz 1 and Schlußsatz 2 are repeated. The D minor gigue is more complicated still. The turn from Fortspinnung to Schlußsatz (marked by stars in Example 2.11) is altogether represented three times. Example 2.12 itemizes the successive subphrases of period III in the D minor gigue as they are heard relative to the Closing Complex schema. Example 2.13 summarizes the formal model of four large compositional schemas in “the Bach cello gigue.” The parentheses on the staff highlight the place of so-to-speak “extra-curricular” passages during periods I and III, which occur in two and four of the six giguesrespectively. In terms of phrase rhythm and formal function, the four modules represent the essentials of binary form as it is represented in the cello gigues. I suggest that the moments of articulation central to each module are extremely important, and taking a broad view of the form, we can finally appreciate how each of these moments articulates a different temporal perspective. The two articulations in period I represent the basic dichotomy of beginning and ending. The articulation in period II has the affect of balance or equilibrium. And the articulation in period III is oriented to ending and to the act of reprise; it marks the turn to cadence and the return of familiar materials. Form 51

What makes a gigue tick?

I now begin a lengthier treatment of the form of Bach’s cello gigues, which alternates between analysis and theory to answer more fully the question of what makes a gigue tick. I start by mapping the essential gestures of Bach’s cello-gigue form, arguing that the binary form is populated by four pivotal moments or “turning points.” In the next section, I explore one of these turning points in each of three cello suites (the G major, C major, and D major). With every analysis, events that span the whole gigue are related to the moment under discussion. Once these key moments in form function are introduced, I then unpack a full phraseology of the Bach cello gigue, with each turning point becoming the central articulation in a formal “module.” The theory of form pursued in this chapter is fundamentally a theory of crucial actions, and phraseological objects are tethered to the initial description of experiential moments. Together, the four modules express a scheme that recurs in changing configurations across Bach’s six suites. How these formal elements are scaled in time becomes the topic of the fourth section of this essay, which navigates issues of tempo and phrase length. We will see that Bach’s cello gigues draw on two distinct temporal scales for realizing generic ideas and that there is considerable creative mileage in the dialogue between them. The fifth and final section revisits the key turning points of the cello-gigue form by way of the three suites not yet discussed in detail (the D minor, E ’ major, and C minor). In this second round of analyses, we see special examples of formal moments and formal strategies where a phraseological schema has a life of its own, where it structures experience in a special way, and where the succession of formal functions is not straightforwardly realized.

Quintessential Gestures of the Cello Gigue Example 2.14 shows an original essay in the Bach cello gigue. This pastiche is a modest attempt to apply the formal model introduced above. Its numerous limitations signal how remote the ideal of creative empathy with Bach’s original texts really is. But, on a basic level, genre and form are recognizable, and it is worth understanding what basic requirements are fulfilled by this pastiche before getting into finer analysis of Bach’s own half-dozen essays. One advantage of starting with an example not by Bach is that the success of this unfamiliar form cannot be taken for granted. Analysts of form are, of course, challenged not to take the formedness of Bach’s music for granted either. After all, a knowledge of form is nothing without the force of a living conviction that a composition is capable in performance of beginning and sustaining itself and ending effectively. 52 The Art of Gigue

q q q q q q q q q
q 3 q q qq q q q q q q q q q q q q q q q q q q q q  8  q q q q q q q q q q

14  q q q  q q q q q q q q q q q q  q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q p f 27   q 
q q q q q q q q q q q q q q q q q q q q  q   q q q q q q q q q q q q q q q q q q q 40 q q q q q q q q q  qq q q q q q q q q q q q q q qq q q q
 q q q q q q q q q q q q q q q q q p 53     q q q q q  q q  q q q  q q q q q q q q q q q q q q q q q q q q q q q q q q q q  q q q q q q q q q q q  f  67

 q q   q q Example 2.14: Pastiche of a Bach cello gigue.

One, Two, Three In step with innumerable eighteenth-century dance movements, the basic framework for a Bach cello gigue can be expressed in a rule of “one, two, three”: one gigue consists of two repeated strains that together present three periods.6 The three periods are distributed unevenly between the two strains, such that the first period is synonymous with the first strain, and in the cello gigues—not the violin gigues, though—this distribution translates into a second strain always being longer than the first. To reference strains and periods, this chapter will use Arabic and Roman numerals respectively, as in “strain 1” and “period I.” Periods are demarcated by authentic cadences: one in the tonic at the end of period III and two in related keys (never the same one) at the ends of period I and period II; there are no others. Inside the periods, lesser moments of harmonic repose are situated on dominant harmony and some (a minority) merit the term “half cadence.” Apart from division into three

6. Of the countless writings to describe this form, two classics are Douglass M. Green, Form in Tonal Music: An Introduction to Analysis (New York: Holt, Rinehart, and Winston, 1965) and Ian Spink, An Historical Approach to Musical Form (London: Bell, 1967) (pt. III, chap. 1). Form 53 periods, two techniques that are well-documented in eighteenth-century dance movements and which apply to Bach’s cello gigues are beginning strain 2 with a variation of the very opening material, and ending strain 2 with a transposition of the cadence from strain 1, creating an end-rhyme. At the local level, another source of shape is the use of brief motives. These often describe the length of the notated bars, either aligned to the barlines or in anacrusic form. Proceeding top-down from the basics of a formal outline, it soon becomes valuable to modify to bottom-up or middle-out perspectives on formal function and phrase rhythm. (A motivic analysis would be an example of a bottom-up inquiry.) Formal rubrics or design concepts like the “one, two, three” rule gave Bach his bearings and allow us to picture the temporal expanse of a piece, but they only go so far. Very few statements could apply to the outward design of all six of Bach’s cello gigues, and to make inroads into Bach’s compositional practice on the level of the periods, analysis must change tack. Well-documented though the basics of binary form are, the finer details of how a period is put together are more elusive. In this area, the current chapter ventures an “articulative” model of form and seeks to supplant the empty time of a plan with an account of musical actions that not only fill time but need time because they embody specific desires for form and for sound. I will now introduce a way of looking at Bach’s binary forms that prioritizes key moments of articulation and aims to illuminate Bach’s individual movements as dynamic entities.

Four In Example 2.15 (reproducing the musical text of Example 2.14), four moments are highlighted by the symbol ↷. It is important to appreciate that these moments are not meant as instantaneous transitions from one subphrase to the next, but as short experiences of form-building that happen while a new subphrase is getting started. The four moments highlighted here are crucial to the musical argument of their respective periods; they are turning points, dynamic cruxes in the form. I will refer to these moments as “Crux 1” (↷1) and so on. Period I (i.e. strain 1) has two such moments and periods II and III, one each. These moments and the arc of their collaboration are the backbone of an effective gigue.7 For strain 1, which is not only the first half but a microcosm of the whole, the moments marked ↷1 and ↷2 realize the dichotomy of beginning

7. Note I am not using “crux” in the same sense that Ralph Kirkpatrick uses it. Ralph Kirkpatrick, “The Anatomy of the Scarlatti Sonata,” chap. 11 in Domenico Scarlatti (Princeton: Princeton University Press, 1953), 251–279. 54 The Art of Gigue

Period I ↷ 1 Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë  3 Ë Ë ËËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  8  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë

2 14 ↷  Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë p f 3 27 Period II ↷
 Ë Ë  Ë Ë Ë Ë Ë Ë    Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë   Ë Ë Ë Ë Ë Ë Ë Ë Ë 40 Period III Ë Ë Ë Ë Ë  ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËËË Ë ËË Ë Ë Ë Ë
 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë p 4 53 ↷    Ë Ë   Ë  Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  f  67

 Ë Ë   Ë Ë Example 2.15: Analysis of periods and formal cruxes in the pastiche.

and ending. These two cruxes are mutually supportive and they emerge as palpable accomplishments of the strain’s “earlier” and “later” music. Of all the three periods in Bach’s cello gigues, period I is most like a complete form, since, prior to becoming part of something larger, it must be able to stand on its own. By contrast, periods II and III can be somewhat simpler because they join themselves to the musical activity already underway. Crux 1 is the embodiment or emblem of beginning. It marks the transition out of an initial escalation of thematic content into the self-confident stride of a sequential passage. It thus anchors the process whereby musical space is opened up or “disclosed.” Conversely, Crux 2 stands for ending. Here, we witness a turn away from a broad demonstration of pattern to the focused energies of cadential preparation and cadence. This turning point anchors the closing-down or wrapping-up of musical space. If Crux 1 was the end of the beginning, Crux 2 is the beginning of the end. In Example 2.15, the broad, patterned element just referred to consists of the sequence that was ushered in at Crux 1, plus the prolongation of dominant harmony which grew out of it. To make a general contention, two sizeable articulations like these are arguably the minimum requirement for creating a sense of form: a single swift turn from “earlier” music to “later” music would, I suggest, not be enough to express the fundamental actions of beginning and ending. Form 55

Periods II and III each survive on a single crux, yet neither of these moments is really isolated; each plays into an ongoing “narrative” that joins the separate periods together. That said, Crux 3 is the epitome of a formal middle: the pivot from a tidy antecedent to a tidy consequent. At this juncture, dead center of period II, it seems that the problems of beginning and ending have neutralized each other and we can enjoy the impression that form comes easily. Relative to period I, Crux 3 takes the place of both Crux 1 and Crux 2: that means, in Example 2.15, that it comes eight bars into the period as well as eight bars before the end of the period. In its temporal outlook, Crux 3 pretends or aspires to a sort of serene independence, and period II emerges as a play universe of symmetry and charm. But the almost carefree character of the period and its primary articulation are tied to a palpable interiority. Much as it feigns a state of perfect balance, period II leans on the “narrative” that unfolds from period I’s turning points and it looks forward to period III. A move beyond the relative stability of strain 1, period II stands in consummate tidiness as a curious provocation to what follows. Period III then provides the satisfying conclusion that was lacking before. Centrally, it does so by reprising the end of period I and reclaiming for the tonic what was in a secondary key. Crux 4 harks back to Crux 2 and represents the final turn to closure. In the current example, it is also the “crux” in the usage coined by Ralph Kirkpatrick, that is, the moment in a binary form that strain 2 starts to match strain 1 in its approach to the final barline.8 Since strain 1 has been heard twice, recognition comes quickly and the moment of formal articulation is itself felt as a reprise. In Bach’s six gigues, the close of period I following Crux 2 is always reproduced in period III, subject to transposition and possible reworking. The “end-rhyme” is, of course, a compositional ploy which prevails (to varying degrees) in dance movements in binary form far and wide from the Bach cello gigue. Bach’s six gigues represent various treatments of the end-rhyme: examples where the rhymed endings differ in only minuscule ways; examples where extra subphrases are inserted or appended; and one example where the corresponding cadences are in opposite modes and the rhyme comes in especially subtle form. These are examined during the analysis of Bach’s C minor gigue below. In all cases, the end-rhyme engenders a special kind of listening in which details are put in relief at the same time as the overall form looms large. Long-range and short-range processes both come into focus, lessening the momentum of mid-range phrase rhythm. In this context, the articulation at Crux 4 announces the

8. Kirkpatrick, “The Anatomy of the Scarlatti Sonata.” 56 The Art of Gigue return of familiar, cadential material and invites listeners to follow closely the last events of the piece. The above scheme relates to Wilhelm Fischer’s notion of the Fortspin- nungstypus and perhaps also his Liedtypus.9 Essentially, I concur with many of Fischer’s analyses by interpreting strain 1 of all Bach’s cello gigues as a Fortspinnung type structure, consisting of Vordersatz, Fortspinnung, and Schlußsatz (or Epilog). Crux 1 is the onset of the Fortspinnung while Crux 2 is the onset of the Schlußsatz. Fischer’s tripartite concept, however, is nuanced in my formal scheme. To begin with, I parse the three elements into two pairs: Vordersatz–Fortspinnung and Fortspinnung–Schlußsatz. The “early” and “late” musics of strain 1 are conceived in separate spheres around the two focal articulations. For Bach’s cello gigues, at least, there are good aesthetic and metric arguments for avoiding a notion of the Fortspinnungstypus in which the three elements are simply strung together as beginning–middle–end. On a more practical note, my model of strain 1 will also specify divisions of the Vordersatz and the Schlußsatz. I regard the Vordersatz and the Schlußsatz as each divided into two segments with distinct formal functions and I rarely find it helpful to overlook these divisions.

Three Moments: Highlights from Gigues 1, 3, and 6 In three analytical vignettes, I will now explore the four cruxes of the cello-gigue form. The following analyses do not offer “mere examples” of a general idea and are not necessarily “typical”: the moments chosen for discussion are, instead, representative and illustrative because of their very uniqueness. I wish to demonstrate the character and vivacity that is possible at the generic articulations. The first crux of Bach’s cello-gigue form, the moment of “opening out,” is examined with Bach’s D major gigue (Suite No. 6). The second crux and especially the fourth crux, the final turn to cadence, are examined with the C major gigue (No. 3). And the third crux, the central articulation of period II, is examined with the G major gigue (No. 1); this is where I begin.10

9. Fischer, “Zur Entwicklungsgeschichte des Wiener klassichen Stils.”

10. I have prepared the editions that appear in this chapter myself, using the “scholarly critical performing edition” of Bach’s cello suites published by Bärenreiter in 2000, edited by Bettina Schwemer and Douglas Woodfull-Harris. This publication is valuable for including fascimiles of the five sources for the edition. These are [A] the manuscript (1727–1731) in the hand of Anna Magdalena Bach; [B] the manuscript (1726) in the hand of Johann Peter Kellner; [C] an anonymous copyist’s manuscript (second half of the eighteenth century); [D] another anonymous copyist’s manuscript (late eighteenth century); and [E] the first printed edition (Paris, 1824). For the C minor suite, the editors also consulted the autograph of Bach’s arrangement of that work for lute (not Form 57

BWV 1007 1 Period I  ↷   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë   6 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 8 Ë Ë Ë Ë
Ë 2 Period II 8 ↷ Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë
Ë Ë Ë Ë ↷ 3 Period III 15 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
↷ 4 22 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë extension 29 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Example 2.16: Bach’s G major cello gigue (BWV 1007). Annotated.

The G major Gigue Bach’s G major gigue is the most compact of the six, and the nearest prece- dent for my own pastiche. Example 2.16 reproduces the score.11 Little

included as a fascimile here). As to the printed Urtext volume of the current publication, Schwemer and Woodfull-Harris do not include slurs (bowing): this is left to performers to decide, with the aid of the fascimiles. The sources vary widely in this respect, and are often hard to make out. (Of course, some critical knowledge of early eighteenth-century bowing style helps, and some excellent guidance is given in the edition’s text volume.) To prepare my own editions, I have also sometimes referred to Volume VI/2 of the old Neue Bach Ausgabe, edited by Hans Eppstein (see Appendix A); the continuing value of this source lies in its reading of the slurs. The NBA provides two alternative texts for all the cello suites; the first is based on the Anna Magdalena Bach manuscript with some reference to the Kellner manuscript. The scores of the NBA were published in 1988; the critical commentary in 1990. In the absence of an autograph of the cello suites, editorial decisions are difficult, and the sources do not always agree, even regarding fundamentals of pitch and rhythm, and especially regarding bowing and articulation. I will explain the editorial choices represented in each score as it appears. In general, I follow the manuscript in the hand of Anna Magdalena Bach [source A]. However, comparison of the sources for the solo violin works (including the Bach autograph) shows that, unfortunately, Anna Magdalena Bach’s copying of J. S. Bach’s slurring is not only unclear but ridden with errors. Thus, any expert editing of the bowing in the cello suites is very welcome, and where I have been uncertain of my own readings, I have deferred to the authority of the NBA. 58 The Art of Gigue explanation is needed to connect this movement with the understanding of “Bach’s cello gigue” that I have begun to describe. The G major gigue exemplifies the form. Here, the idea of four cruxes is readily inferred by analysis without reference to other works. As far as m. 28, the separate periods are parsed into four-bar units by the articulations marked ↷ in Example 2.16. And it is clear that mm. 29–34 are in a sense ancillary: these are appended to the end rhyme and they function, in part, to reverse the unusual inflection of parallel minor in the main closing material. In the following analysis, I single out Crux 3 and address the issue of what motivic material Bach puts in play at major new departures within a movement, namely at the four cruxes and the start of periods II and III. As shown in Example 2.17, most major departures in the movement present materials that correspond to the opening, and specifically the bar- length motive that extends from the downbeat of m. 1 to the downbeat of m. 2. In particular, [O] and [Q] are close to [N]: both Crux 1 and the start of strain 2 are moments that answer directly to the movement’s opening. The variation at [T] goes a little further by re-working [Q]’s descending third,

11. The score of the G major gigue in Example 2.16 follows the Anna Magdalena Bach manuscript [A] and was prepared with reference to the Bärenreiter “critical performing edition” as well as the NBA. I have adopted the reading of slurs from the NBA. However, I will stress that all slurs shown here as grouping entire beats are not to be trusted; the manuscript is very ambiguous about where these should fall. Thankfully, no questions hang over the briefer slurs as shown here. Note that (unlike the NBA) I have not used any special stroke for the few slurs which are absent from the manuscript but are obviously implied. The supplementary volume may be consulted for this information. The combined evidence of the sources [A–E] leaves no doubts about the pitch content of the G major gigue: the isolated discrepancies from the content of the Example 2.16, which the critical performing edition highlights, are clearly scribal mistakes or slight musical corruptions of the original composition. The differences between my score and the two Bärenreiter editions consulted concern stemming and cautionary accidentals. The direction of stems here agrees with [A] and [B], save for one small difference; that in [A], the second e3 of m. 22 is stemmed up. The potential significance of stem direction can be observed in mm. 4 and 28. In m. 4, I stem g2 upward, and in m. 28, I stem b2 upward, creating a diagonal beam. This is the practice in all the eighteenth-century manuscripts [A–D]. Good typographical practice normally prevents the stemming of handwritten notations from being reproduced, but in the case of this movement, it is possible. It could be argued that the stemming of the two bass notes in m. 4 reflects an important difference in the harmonic and contrapuntal status of those notes, while the stemming of m. 28 expresses the elision of the authentic cadence visually. Concerning cautionaries, I do not show sharps in mm. 12 and 24 for f~3 and f~2. Regrettably, both the NBA and the newer edition print sharps here, without showing in the score—or mentioning in the critical report—that such cautionaries are absent from all four of the eighteenth-century manuscripts. F6 is unthinkable in these places and to specify the sharp is to inflect the score with the musical values of a later time, in which the stylistic literacy of performers could not be counted on. Form 59

N O BWV 1007
↷ 1  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  6 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 8 Ë Ë Ë  Ë P Q 8 ↷ 2 Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë  Ë Ë G E R ↷ 3 S T 15 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë ËË Ë Ë Ë ËË Ë Ë Ë Ë  G E U Ë ↷ 4 23 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë

30 Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Example 2.17: Thematic and motivic relations in the G major cello gigue. Brackets and slurs indicate motive forms. (Bowings and articulations are omitted.) A dashed stroke indicates an initial, “advance” presentation, prior to the repetition which isolates the motive as a distinct element. 60 The Art of Gigue g3–e3, as an ascending sixth, g3–e4, and interpolating the q q q figure. Even [P] and [U], at the two strains’ turns to cadence, recall [N] in a retrograde form. Yet Crux 3, the midway articulation of period II, does not parallel the movement’s opening in the same way. Although a3–d4–c4 is an inversion of g3–d3–e3 at [N] and b3–f3 ~–g3 at [O], the usual bar-long correspondence is missing. In context, the long-range motivic relation also is not conspicu- ous. Instead of recycling thematic materials from before, according to the established periodicity of four-measure spans, the afterphrase of period II is heard to seize on its own anacrusis. The shortest of motives, from [R], is rapidly pushed to the fore at [S]. One could say the afterphrase is “put up to it” by the Monte that forms period II’s forephrase. It is in the nature of such spacious sequences to precipitate a crisis in musical continuity at the end of their second units. Previous sequential repetitions at mm. 5–7 and 9–10 extend to a third iteration and acquit themselves by supplying a pre-dominant for the following move to V or I. Any continuation of the Monte, by contrast, would precipitate harmonic nonsense. Yet at the end of m. 14, the Monte’s first segment plants the motive that will serve as a way out. Across the barline at mm. 16–17, Bach makes a quick about-turn on the motive of the anacrusis. A seemingly ex tempore, unpremeditated use of pattern takes over. By stalling the smooth melodic motion that otherwise connects one beat to the next, the motivic process at Crux 3 creates the sense of a “watershed” movement which stands apart from the fluent, steady phrasing of the rest of the movement. The motivic process also reflects the symmetry, interiority, and paradoxical imbalance that characterizes period II overall.

The C major Gigue As in the G major gigue, so in the C major, Bach’s pointed use of a short motive inflects a formal crux with particular character. In this case, I analyze Crux 4 in period III. The score is given in Example 2.18.12 Despite the similar ilk of this discussion to the last, I will approach the interaction of large and

12. The score of the C major gigue in Example 2.18 follows the Anna Magdalena Bach manuscript [source A], except in mm. 19 and 105, where it is contradicted by the agreement of sources [B, C, D]. Unlike with the score of the G major gigue, it is not possible to reproduce eighteenth-century stemming practice. The bowings represent my own reading of source [A]; but note that the bowing in m. 19 follows source [B]. The bowing in m. 105 follows [A] even though the pitch d3 replaces c3. Uncontroversially, I understand slurs where none appear in mm. 25–27, 35–36, 93, 96–97, and 98–99. A performance following source [A], as here, would have to take the perhaps unusual step of starting on a down bow. Form 61

BWV 1009 Period I ↷ 1 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
3 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 8  Ë Ë

11 Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 

21
Ë Ë Ë Ë Ë Ë ËËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë   29 Ë   Ë Ë Ë Ë Ë   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë    2 39 ↷ Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Period II 49 ↷ 3 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë
 Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë  Ë 57 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Period III 66 Ë Ë   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë  Ë Ë Ë Ë 75  Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë

83 Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËËË Ë Ë Ë   91 Ë   Ë Ë Ë   Ë Ë Ë Ë Ë  
Ë ËËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 4     101 ↷ Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë ËË

Example 2.18: Bach’s C major cello gigue (BWV 1009). Annotated. 62 The Art of Gigue small differently, by starting with a very local observation and building an idea of its larger significance from there. The anacrusis to the main downbeat at Crux 4 is marked [Y] in Exam- ple 2.19. In a clever reversal, this harks back to mm. 1–2 and the movement’s Z Z Z 13 first presentation of the bar-length motive, Z Z , at [I]. Whereas [I] was responsible for the movement’s first, modest move to the dominant, [Y] is responsible for the movement’s climb-down from a large dominant pedal at the turn to cadence. The recollection at Crux 4 is clean because of the intervening absence of either C–D–E–F–G or G–F–E–D–C, in any octave. Even a non-scalar permutation of the same cluster of notes appears just once at [P] and a permutation that adds repetition of one pitch occurs just twice at [R] and [X]. The C–G pentachord is scarce and the recollection of [I] at [Y] is correspondingly direct. Though the C–G pentachord is used sparingly, the events at Crux 4 are enriched by the extensive role which is assigned to the scalar motive at secondary pitch levels. The scalar motive and a close variant occur at [J]–[O], [Q], [S]–[W], and [Z]. The selection criteria for these occurrences are first, a rhythm of Z Z Z Z Z , and second, a pitch contour of four steps in one direction then an additional step in the same or opposite direction. These figures are set apart from the rest of the piece, as the dashed slurs will illuminate. These slurs identify all segments of five notes that satisfy one but not both of the selection criteria, and such segments are few. Thus the bracketed segments make an impressively well-insulated motivic argument. A number of brilliant moments are created, even before the “clincher” at Crux 4. Given that Crux 4 is the focus of this analysis, I will trace the argument backward from its conclusion. Tellingly, the scalar motive is absent from period III prior to [Y]. The nearest precursors occur in period II, and here the emphasis is squarely on the ascending scale. In pitch space, period II’s three uses of the scalar motive loosely flank the position that will be taken at [Y]: [S]’s range of a3–e4 stands above, whereas [U]’s and [W]’s shared range of g2–d3 and f2–c3 lies below. As well as priming the pitch placement of [Y], period II’s scalar motives build up the figure into a thematic vehicle of expressive importance. The figure becomes important, in part, for extending the movement’s ambitus. First, [W] belongs to a reprise (mm. 57–64) of the sequence passage from period I (mm. 9–16) that takes the original passage one step lower, per the interval of the sequence itself. Thus [W] is both the transposition of [M]

13. g3–f3–e3–d3–c3 may be taken for an inversion of c3–d3–e3–f3–g3 about e3 within the diatonic scale, or it may be taken for the retrograde of the original motive (in which case, the diatonic scale need not be specified as the “space” of the transformation; the statement is consistent with serial analysis, for example). Form 63

J I ↷ 1 BWV 1009 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  3 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 8
Ë Ë L K M N O 11 Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
21  Ë Ë Ë Ë Ë Ë Ë Ë ËËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 29 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë


Q (P) ↷ 2 39 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 
S (R) ↷ 3 Ë 49 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë   Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë
Ë T V W U 57 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë AC  66 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë
Ë Ë Ë (X) Ë 75  Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
ËËË Ë Ë Ë

83 Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë

90 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Y


↷ 4 Z 100  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Example 2.19: Motivic relations in the C major cello gigue. As in Example 2.17, brackets and slurs indicate motive forms. 64 The Art of Gigue and its logical sequel, bringing the motive incrementally lower than it has been before.14 (So far, only the dramatic low c2 of m. 52 has opened up pitch space below g2.) Second, [S] brings the motive ecstatically higher than before, to sit at the upper octave of [K]. [S] picks up where [I] left off and, in Schenkerian terms, it reclaims the Kopfton 3ˆ of mm. 3–4. The descending form of the fully scalar motive, which period II does not cultivate, is introduced gradually in period I. [O], the closest cousin to [Y] and the first descending scale which bridges a perfect fifth, seems coaxed out of [I]. It appears as the outcome of a sequence that leads with the less assertive, returning form of the motive at [J] and [L]; its bold perfect-fifth span is prepared by the smaller diminished-fifth profile at [N] (expanding the motive’s range from a perfect fourth); and, in context, it is motivated by the generic pressure for resolution to V for concluding the sequence passage. In advance of the sequence passage, mm. 4–5 also supply an elegant transition away from the simple ascending form of [I] (see the unlabeled bracket in Example 2.19). By all these means, [O] is amply prepared. And by securing V of the dominant early in strain 1, it makes an appropriate opposite number to [Y], with its role of anchoring the turn to cadence late in strain 2. The motivic process of period I contains further subtleties. First, [Q] is the remote continuation of a pattern begun with [N] and [O]. Over a short distance, this pattern binds the move to V of the dominant to the promised cadence in the dominant that closes the strain. Second, [O] and [Q] carve out a place for the motive in pitch proximity to [Y]. Third, period I maximizes the expressivity of the scalar motive by exploring multiple species of the ascending or descending pentachord: major at [I], [M], and [O]; minor at [K]; diminished at [N]; and Phrygian at [Q]. Finally, looking ahead to the end-game at [Y], it is telling that [O] is quitted by a move from d3 to c3 as a new subphrase begins (see the dashed slur). At m. 21 and Crux 4, c3 recurs in equivalent metrical positions, on the downbeat of the four-bar hypermeter, and in each case, f~ 3 is used prominently two bars prior. At the same time as it winds up a long motivic argument, the scale at [Y] smooths over a contraction of registers in the movement’s end rhyme and discharges an important resolution of pent-up melodic dissonance in the rhymed Fortspinnung element. In strain 2, the dominant-based Fortspinnung element is reprised up a fourth from strain 1, whereas the tonic-based Schlußsatz element is reprised down a fifth. In the context of the new transition between those elements, [Y] helps to point up the arrival on c3 (where, in strain 1, g3 was sufficiently emphasized by register). Meanwhile, the resolution brought by [Y] operates on the melodic dissonance of the

14. Similarly, [Z] is the transposition as well as a logical sequel of [Q]. Form 65 preceding scalar motives in the rhythm of Z ZZZ Z . The rhythmic motive, Z ZZZ Z , or more inclusively, Z ZZZ Z ZZ , is a sophisticated reversal of the © original rhythm, Z Z Z Z Z . An exchange of rhythm values ( for À ) is Z ZZ Z © married, here, to a gestural reversal. Originally, led toward on a metric downbeat and filled the length of a bar, but Z ZZZ Z leads away from ZZ on a metric downbeat and fills two bars. The melodic dissonance pedaled by this opposite rhythm owes to the diminished species of pentachord, recalling [N], and the use of the minor-ninth interval—an upward extension of dominant harmony, which also recalls [N]. In strain 2, the anacrusis at [Y] resolves residual dissonance from the pitches a ’ 3 and e ’ 3 as well as f~ 3: g3 and d3 act as repercussions of the melodic resolutions that already apply directly and, by proceeding to c3 in line with typical bass and melodic motions, these notes relay the impact of resolution to the new downbeat at Crux 4. In strain 1, however, the stubborn dissonances of the Fortspinnung element—more strident for being higher—are less comprehensively dismissed. Another example of a dissonant note that requires more than the grammatical resolution, and that benefits from strain 2’s telescoping of registers, is b3 in mm. 95–96; this returns in m. 102 to be more fully resolved at a similar stage in the metric cycle of eight-bar units. Given that [Y] restores the original rhythmic figure ( Z Z Z Z Z ); that, for the first time, this figure arrives on the downbeat of a four-bar hypermeasure; and that [Y] therefore answers to the enlarged metric aspirations intro- duced by the motive’s rhythmic alter-ego ( Z ZZZ Z ZZ ), Crux 4 performs a rhythmic resolution too. At once a reprise and a resolution of strain 1’s widely spread turn to cadence, the special events at Crux 4 illustrate well the closural power that attaches to the important turning point of period III. The C major Suite, like no other, graces this moment in the form with the pithiest of summaries to a long musical argument.

The D major Gigue The subject of my third analysis is Crux 1 in the D major cello gigue, Bach’s largest and most ambitious. It is a moment of sheer exuberance; a display of gusto in which the opening of musical space and the promise of beginning are reveled in. Such treatment of the movement’s first major departure has a bearing on later events too. This analysis turns away from the intricacies of motivic analysis to examine both the power of Crux 1 as it occurs and the repercussions it has throughout the movement. The score is reproduced in Example 2.20. That Crux 1 is a weighty moment is already clear in the context of mm. 1–12. The downbeat of m. 9 has harmonic and timbral intensity because of the multiple stop and the sounding of a major seventh (d3 and c~ 4) for the first and only time in the 66 The Art of Gigue

BWV 1012 Period I
  6  8        1 7 ↷


      12
   
       16



 
          21            ↷ 2 25         Period II 29 Ë Ë            

34 ↷ 3       39       Period III 44 AC      

48       

Example 2.20: Bach’s D major cello gigue (BWV 1012). Annotated. Form 67

52 X Ë   Ë Ë Ë Ë Ë Ë ËË Ë   Ë Ë Ë Ë
Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Y 57 Ë  Ë Ë Ë Ë Ë   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËËË  61 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë   Ë  Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë

↷ 4 65 Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë
  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Example 2.20 continued: Bach’s D major cello gigue (BWV 1012). movement. (At the reprise in m. 57, the major seventh is omitted.) This sharp dissonance will be matched only by its inversion three-and-a-half bars later. The downbeat of m. 9 also has a thematic intensity because of its reversal of established melodic figures. While prior melodic motion across the barlines is downward, the anacrusis into m. 9 comes from below as e4– f~ 4. That change is reinforced by immediate repetition of the same upward step within the ensuing neighbor-note figure. Furthermore, events at Crux 1 rework the movement’s initial leap of a perfect fifth. The opening motive, a4–d4–e4, becomes e4–f~ 4 –b3, its retrograde-inversion, at m. 9. (Also, in mm. 9–10, the Œ outline e4–f~ 4–a4 from mm. 1–2 is loosely inverted to b3–g~ 3– e3.) The retrograde inversion of the emphatic opening motive contributes to the performance of an assertive and expansive character at Crux 1. One more reason a distinctive character can be performed at Crux 1 is the element of waiting for something to happen during the prior unit of mm. 5–8, a feeling that first arises because of the stationary harmony and that becomes poignant once the direct repetition starts. The sparsity of melodic invention presented here instills an expectant attitude vis-à-vis the departure which will come in m. 9. It is relatively unusual for a unit like mm. 5–8 to be a second, equal unit at the start of a movement or large section: more typically, it might form a “third quarter.” Come period II of the current gigue, the material of mm. 5–8 is indeed commuted to the metric “third quarter” of the period as mm. 37–40. In period I, the pedal harmony and direct repetition during mm. 5–8 place an unusual burden of expectation on the events at Crux 1, which these happily meet—and partly as a construct of the expectant attitude itself. 68 The Art of Gigue

How, then, does an especially emphatic Crux 1 bear upon the real- ization of the whole form? Crux 1 clearly has “consequences,” or—more circumspectly—it belongs to a wider experiment in formal balance that takes much of the movement to play out. Some caution is warranted here because the analyst who explains these factors is more like an engineer, who understands what balance of forces “animates” still objects, than a mechanic, who understands what objective motions are caused by changes in the application of force. This is not to say Bach’s gigues have an ideal “perfection” of form like the balance of forces in a functioning bridge or building. Rather, I mean to highlight the stability of the compositional text. Although, to some extent, I will “because” and “enable” into view the network of compositional factors that Crux 1 is engaged in, analytical narration is only a shorthand— one that idealizes composition as an unplanned improvisation. Really, formal dependencies operate both ways, and Crux 1 is as much constructed by subsequent events as subsequent events are constructed by it. The affect of Crux 1 relates first of all to issues of pacing in strain 1. Its elated rhetoric connects to the unsustainable scale—as it turns out—of the sequence in mm. 9–16. The sequence is too broad, its units too long, for being wound up in the way of Bach’s other cello gigues: it neither passes into a Schlußsatz via Crux 2, nor comes to a rest ahead of new Fortspinnung material. Instead, it stumbles into a reprise of the opening theme in the dominant. The untenably slow pace of the sequence is cemented around m. 14, when rather than continue the stately fifths chain at one root to every bar, the harmony of B minor expands to slow even more the move to E major (V of the dominant). Far from reinforcing the dominant, the extremely slow speed unsteadies it. The ambitious harmonic rhythm of the sequence passage is initially in line with the elated affect of Crux 1, but as events unfold, the timescale of the strain’s opening is revealed as a problem. Crux 1 threatens to make subsequent events pale by comparison. The opening and closing musics of strain 1 operate on different time- scales: the distance from the start of the strain to Crux 1 is twice the distance from Crux 2 to the end of the strain. In the G major and C major gigues this is not so, nor in the D minor and C minor gigues (nor, obliquely, in the E ’ major gigue). In the D major, the two cruxes are lopsided. This is a matter of local character as well as placement. Unlike in other movements, Crux 2, the start of the strain’s “end game,” cannot be clearly made out. Although m. 25 breaks four bars of dominant harmony with a turn to I6, the texture defines m. 24 as the cleaner break from the events begun at m. 21. Not until mm. 26–27 does m. 25 assume the function of a downbeat to a four-bar hypermeasure. By then, the time has passed for the kind of demonstrable departure we see elsewhere. Significantly, Crux 4 in strain 2 is much cleaner, allowing the turn to cadence to be more positively articulated at its reprise. Form 69

The lopsided musical forces in strain 1 continue to be felt in strain 2. At mm. 53–56, there is a remarkable departure into a four-bar passage with the assertive swagger of a unison, sul tasto passage of a sort found in Bach’s concertos. (See X in Example 2.20.) To imply an ensemble unison is an ironic accomplishment in a solo idiom touted for its implied polyphony. The passage is also unusual for having the quality of a contrasting thematic statement, though it is related to the movement’s opening. The effusive arpeggiation of tonic through mm. 53–56 is unlike anything else in Bach’s cello gigues. The relevance to Crux 1 is a matter of weight. One prominent moment in the business of opening or hitting a stride stands opposite another prominent moment in the spirit of summing-up or reigning-in. The brimming excitement of the downbeat at Crux 1, with its multiple stop and neighbor-note figure, and the collected strength of m. 52’s downbeat, amassed in one note, are mutually sustaining. Narratively, the “unison” passage answers the problem of an exaggerated opening-out gesture at Crux 1. Another balancing factor in strain 2 is the reprise of the sequence which Crux 1 introduced. (See Y in Example 2.20.) This recalls the ambitious scale of the movement’s opening within the sphere of the final cadence, and m. 59 is altered compared to m. 11, in order to appromixate the cadential gesture that follows at m. 67 and reduce the momentum of the first half of the sequence. A vein of musical argument that courses through these moments is the interaction of multiple-stopping with single-stopping. Of all Bach’s cello gigues, the D major uses multiple stops most extensively. The G major gigue features some lavish multiple-stopping in m. 4 but none afterward. The E ’ major and C minor gigues, meanwhile, are entirely monophonic. And the D minor and C major gigues, though they use multiple-stopping fairly liberally, do not make a feature of it so soon—essentially not until the closing music of strain 1. Nor do these other gigues use dense triple and quadruple stops so often. That the D major gigue was written for a five-stringed instrument certainly shows, and many of the multiple stops use the high e4-string. I argue that in this movement the dichotomy of multiple-stopping and simple melodic playing is an important compositional dynamic. One thing—the “vertical” amassing of sound—often leads to the other—the “horizontal” spinning-out of a single line. And moving between the two textural modes is valuable for articulating form. At cadences multiple-stopping tends to subside, with the last two bars of each strain becoming monophonic, and the same trend accompanies the arrival on I in m. 4 and the arrival on V in mm. 63–64. Multiple-stopping is, too, a large factor in the rapport between period I and period III, separating off period II as an enclave of lyricism (which begins with a solitary double stop on open strings but continues in a single line). This appears a generic 70 The Art of Gigue strategy. The D minor and C major gigues shun multiple-stopping entirely during period II, even as multiple stops are conspicuous in the textures of periods I and III. In both movements a smattering of double stops occurs at the very start of period III, as if agitating to recover a line of musical thought following strain 2’s internal cadence. In the D major gigue, however, the re-introduction of multiple-stops in period III is not so simple. Here, the marvelous “unison” topic serves as a rite of passage that must be completed before the thematic device of multiple-stopping can return. Not until after this melodic apogee, once the tonic triad has been melodized and a virtual continuo section has been subdued, are multiple stops reasserted with the reprise of the sequence. Thus the pointed use of multiple stops becomes the means for a musical argument that boldly intertwines our experience of special moments with our experience of form and line. This analysis shows how the visceral, “vertical” demonstration at Crux 1 is intimately connected with later events, and how it both indicates and constructs the movement’s expansive timescale.

Outlining a Phraseology Each of the formal cruxes just analyzed performs particular qualities or attitudes at a brief moment. These moments occur just as a new phrase or pattern is getting underway and are short and focused. Crux 1 in the D major gigue is an exuberant disclosure of broad musical ambitions. Crux 3 in the G major is a quick about-turn and an intimation of classical balance. Crux 4 in the C major is the pithy summation of an important musical argument at the threshold of closure. But these special moments are the sign of wide- ranging compositional technique. One critical dimension of such technique is phrase rhythm, and in this section, I develop a phraseology for “Bach’s cello gigue.” The phraseology is achieved by unpacking a compositional module from each formal crux. (“Module” is intended as the most neutral description possible.) My aim here is to explain how each period is put together, and explain what procedures of phrase rhythm are most stable in the genre of cello gigue. These explanations will reveal the arrangement of phrases and subphrases that is the setting for the formal scheme of four turning points. To outline the phraseology that emerges from comparative analysis of all six of Bach’s cello gigues, Example 2.21 and Example ?? label the larger modules and smaller subphrases in Bach’s G major gigue and my own pastiche. Table 2.2 presents the same information in a more explicit format. Form 71

BWV 1007 Vordersatz 1 Vordersatz 2 Fortspinnung AB
 q  q  q q q q q q q q q q q q q q q q q q q  6 q q q q q q q q q q q q q q q q q q q q 8 q q q  q Schlußsatz 1(1) Schlußsatz 2(1) Forephrase 8 q  q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q  q  q q Afterphrase Fortspinnung C 15 q q q q q q q q q q q q q q q q q q q q q q q q q q q q  q q q q q q q q q q q q q q q  Schlußsatz 1(2) Schlußsatz 2(2) 22 q q q q q q q q q q q q q q q q q  q q q q q q q q q q q q q q q q q q q q q q q q  q q q q Schlußsatz 1(2), second rotation Schlußsatz 2(2) 29 q q q q q q q q q q  q qq q q q q q q q q q q q q q q q q q q q q q q q q q q Example 2.21: Form-functional analysis of Bach’s G major cello gigue.

Fortspinnung A Vordersatz 1 Vordersatz 2

Fortspinnung B Schlußsatz 1(1) 12

Schlußsatz 2(2) Forephrase Afterphrase 25

Fortspinnung C 38

interpolation Schlußsatz 1(2) 50

Schlußsatz 2(2) 64

Example 2.22: Form-functional analysis of the pastiche. 72 The Art of Gigue

The Four Modules I will refer to the modules that house the four formal cruxes as the “Open- ing Complex” (containing Crux 1), the “Answering Complex” (containing Crux 2), the “Interior Phrase” (containing Crux 3), and the “Closing Com- plex” (containing Crux 4). Inside each module, the associated crux becomes the main articulation or departure. Note that the Interior Phrase is co- terminous with period II; the former term refers to the specific phraseologi- cal form, whereas the latter term refers to a formal container bounded by the start of strain 2 and its internal authentic cadence. My terms for the four modules reflect an important difference in status between the three “complexes” and the one “phrase.” The third module satisfies standard expectations for the harmonic, melodic, and rhythmic or metric closure of phrases. Its two halves fulfill the definition of a forephrase– afterphrase pair (though not a parallel period’s antecedent–consequent pair).15 This makes the third module markedly different from its peers. The remaining modules are collations of subphrases, hence “subphrase complexes.” The constituents of the Opening Complex, for instance, work together to perform a single formal function (fronted by Crux 1) but they do not make a phrase. This string of subphrases lacks the harmonic or metric closure of a true phrase: each subphrase is, in fact, better “closed” or more sensible as a phrasal unit than the whole series. The Opening Complex is open-ended, while the Answering and Closing Complexes begin in medias

Table 2.2: Phraseological analysis of Bach’s G major cello gigue and the pastiche.

Module Crux Subphrases G major Gigue Pastiche Opening Complex Vordersatz 1 mm. 1–2 mm. 1–4 Vordersatz 2 3–4 5–8 ↷1 Fortspinnung A 5–8 9–16 Answering Complex Fortspinnung B 5–8 13–20 ↷2 Schlußsatz 1(1) 9–10 21–24 Schlußsatz 2(1) 11–12 25–28 Interior Phrase Forephrase 13–16 29–36 ↷3 Afterphrase 17–20 37–44 Closing Complex Fortspinnung C 21–24 45–52 ↷4 Schlußsatz 1(2) 25–26, 29–32 61–64 Schlußsatz 2(2) 27–28, 33–34 65–68

15. I follow the use of these terms in Rothstein, Phrase Rhythm in Tonal Music, pp. 16–18. Form 73

Example 2.23: Map of phraseological modules within the three periods of Bach’s six cello gigues. The six gigues are horizontally aligned around the Answering Complex because this is the most consistent element from piece to piece, as discussed below. res. Although each subphrase complex divides into halves, these halves are far from being forephrase–afterphrase pairs. Thus the subphrase complexes are vital units of compositional thought without being units in a formalistic sense. In general, I suggest that Bach’s cello gigues sidestep the formation of phrases in the classic understanding. As a rule, periods I and III cannot be interpreted as phrases and nor can they be interpreted as consisting of phrases. How the four modules sit within the structure of three periods across Bach’s six gigues is represented graphically in Example 2.23. The horizontal extent of the light gray boxes represents the durational extent of the three periods; likewise, the black boxes show the reach of the four modules; and the white stars locate the formal cruxes. The graphic makes plain, in abstract 74 The Art of Gigue

Fortspinnung C 44  ~ 
Schlußsatz 1(2)    Schlußsatz 2(2)       Example 2.24: Recomposition of period III in the pastiche. form, the varied handling of periods I and III. It is, then, with regard to periods I and III of the standard binary form that the current phraseology is of greatest value for understanding Bach’s practice. These parts of the form challenge us to better understand how form and function relate, and how strong compositional schemas are made. The Closing Complex, in particular, can be un-straightforwardly realized. Unlike the corresponding Answering Complex of period I, the Closing Complex need not be flush with the end of period III, and in longer movements, it is not flush with the start of period III either. In Bach’s G major gigue, mm. 29–34 represent a repetition of the Closing Complex’s second half, a second take at the same formal functions. In my pastiche, the elements of the Closing Complex are effectively interleaved with an “extra-curricular” passage at mm. 53–60; a recomposition in Example 2.24 shows a pared-down version of period III that omits this. Later, we will see other methods for realizing the Closing Complex and performing its essential functions in an indirect way.

Opening Complex The Opening Complex launches strain 1 and consists of three subphrases which I will refer to as “Vordersatz 1,” “Vordersatz 2,” and “Fortspinnung A.” Vordersatz 1 is an expository statement, which takes four Œ beats in Bach’s G major gigue and also in my pastiche. It posits the key of the piece, sets a tempo, articulates a meter, and—in very little time—presents melodic and motivic mannerisms that will be central to the whole movement. It is a brief declamation, not a complete utterance. Vordersatz 2 is a follow-up subphrase which always matches the length of its predecessor. This does one of two things: either it maneuvers to an initial point of rest on the dominant or the relative major (minor-mode movements can do either) or it marks time on tonic or dominant harmony with a simple figuration that is heard twice. The first option is more typical, and represents the continuation of Fischerian Vordersatz, whereas the second option represents the tentative onset of Fortspinnung. This latter option can be understood as triggered by larger pressures, as explained later. Form 75

Fortspinnung A initiates Fischerian Fortspinnung in earnest, and is a response to the previous two subphrases. It invariably takes the form of a sequence passage. This matches or exceeds the combined length of Vordersatz 1 and Vordersatz 2. The start of this longer unit is precisely Crux 1 as introduced above: the moment that the thematic escalation of the opening gives way to a freer accumulation of musical duration. From here, there is some sense of “coasting” and expansive patterning represents a plateau in the period I’s emerging musical rhetoric. Crux 1 is therefore the crucial gesture amid what is a carefully organized series of events.

Answering Complex The Answering Complex, organized around Crux 2, draws strain 1 to a close. It consists of three elements like the Opening Complex but with the reverse arrangement of longer and shorter elements: a broad subphrase gives way to two conciser ones. I will refer to the three subphrases as “Fortspinnung B,” “Schlußsatz 1(1),” and “Schlußsatz 2(1).” Given the cadential thrust of the module, I will describe its three subphrases in reverse. Schlußsatz 2(1) is a short cadential progression that ends with a clear V– I motion, often leading from I6. The simple progression I6–V–I is common, recalling Caplin’s “expanded cadential progression” but without the pre- dominant (ii6 or IV). In Bach’s G major gigue and also in my pastiche, Schlußsatz 2(1) takes four Œ beats. The “set-up” for the cadential progres- sion is Schlußsatz 1(1). This second element of the Answering Complex features a simple melodic pattern that prepares the harmonic action to follow, outlining either a scale or an arpeggio. A pattern of descending thirds is typical; so too is an ascending stepwise tetrachord (especially from 3ˆ to 6).ˆ Schlußsatz 2(1) matches the length of Schlußsatz 1(1). The first element of the Answering Complex, Fortspinnung B, prepares the combination of Schlußsatz 1(1) and Schlußsatz 2(1). It is the broader subphrase from which emerge the variegated and carefully marshaled energies of closure. It is always equal to the length of the set-up and cadence routine. Fortspinnung B may be identical with Fortspinnung A or it may not. When it is, it shares the sequence form already described, though in the context of the Answering Complex, the same passage has a different function. When Fortspinnung B is distinct from Fortspinnung A, however, it tends to present “static” instead of “sequential” material, elaborating some kind of pedal tone. Either kind prepares the set-up and cadence routine of Schlußsatz 1(1) and Schlußsatz 2(1) by demonstrating an ample scope of musical pattern ahead of the turn to cadence. 76 The Art of Gigue

Interior Phrase The Interior Phrase, like Crux 3, stands out against its peers for its sense of equity between opening and closing and the “classical” balance of its elements. Its two subphrases merit the terms “Forephrase” and “Afterphrase” (which I will capitalize for this use) because of the powerful sense in which the second answers the first, often with the first having ended on dominant harmony. One of Bach’s gigues, the E ’ major, must be somewhat distanced from the notion of Interior Phrase introduced here, but even there, period II divides into equal halves (and somewhat resembles a parallel period structure). The Forephrase initially stands as a counterstatement to the opening of the gigue: some telling variation or transposition of Vordersatz 1 advances the Forephrase to halfway. There is also a strong tendency (not binding) to parallel Vordersatz 2, in which case any move to dominant harmony would usually correspond to the key of the coming authentic cadence. That the Interior Phrase has a bipartite rhythmic structure unlike the Opening Complex requires some explanation, since period II in Bach’s G major gigue or in my pastiche does, in fact, appear like a “sentence” structure with a basic short–short–long division. In these cases, I find that the central juncture is too pronounced for sentence rhetoric to assert itself. Granted, the Afterphrase is more continuous than the Forephrase in both examples. But compared to the Opening Complex in either movement, the Interior Phrase has a smoother connection between its first and second quarters: the Forephrase does not match the differentiation of Vordersatz 1 and Vordersatz 2. The Afterphrase rarely affects any particular relation to previous events; quite the opposite, in fact. As a rule, the Afterphrase leads with material that bears upon motives just heard more readily than it recalls its likely origins in strain 1. In Bach’s G major gigue, we saw an extemporizing instinct take over at this juncture. Quietly, as it were, both Bach’s gigue and my pastiche base the Afterphrase on the material of Fortspinnung A but the temporal affect obscures the long-range parallelism of strain 2 to strain 1. The Interior Phrase is permeated with the quality of answering. It begins as an answer on the large scale, strain 2 echoing strain 1, and ends by finding its own answer when Afterphrase is joined to Forephrase on the contained, medium scale. Thus the affect of symmetry belongs to both the Forephrase and the Afterphrase on two distinct scales, while an affect of interiority belongs to the Afterphrase alone. It is because of the split levels on which the Interior Phrase performs balancing actions that period II becomes an agitator for formal completion going into period III. In its hybrid temporality, the Interior Phrase models locally the very closure that it calls for globally. Form 77

Closing Complex Occupying period III, the Closing Complex draws strain 2 and the whole gigue to a close. It is to strain 2 as the Answering Complex is to strain 1, and it shares the tripartite, long–short–short design. I will refer to its three subphrases as “Fortspinnung C,” “Schlußsatz 1(2),” and “Schlußsatz 2(2).” Table 2.3 summarizes the phraseology as it now stands. As mentioned above, the Closing Complex is at least partly a reprise of the Answering Complex with the set-up and cadence routine recast in the tonic: the Schlußsatz subphrases always correspond whether or not Fortspinnung C is also the reprise of Fortspinnung B. Thus Crux 4—the start of Schlußsatz 1(2)—is the focal moment of recognition, even when the correspondence of strains (the “crux” in Kirkpatrick’s sense) begins earlier. Starting with Crux 4, the set-up and cadence routine from strain 1 is recast in the tonic.16 Generally, Bach changes little between the first and second presenta- tions of Schlußsatz 1 and Schlußsatz 2, though the changes may be telling, as in the C major gigue. The level of variation in my pastiche indeed far

Table 2.3: Phraseological outline of “the Bach cello gigue.”

Module Crux Subphrases Rhythmic type Opening Complex Vordersatz 1 Vordersatz 2 , S–S–L ↷1 Fortspinnung A ./ Answering Complex Fortspinnung B -/ ↷2 Schlußsatz 1(1) , L–S–S Schlußsatz 2(1) ./

Interior Phrase Forephrase -/ L–L ↷3 Afterphrase + Closing Complex Fortspinnung C ↷4 Schlußsatz 1(2) , L–S–S Schlußsatz 2(2) ./

-/

16. In my pastiche, mm. 60–68 are a somewhat varied reprise of mm. 21–28. The original outline of 5–ˆ 6–ˆ 5–ˆ 4–ˆ 3,ˆ downbeat-to-downbeat, is inexactly inverted to become 4–ˆ 2–ˆ 3–ˆ 4–ˆ 5.ˆ The inexactness here has to do with the different intervals being embellished, 5–ˆ 3ˆ and 4–ˆ 5,ˆ and these intervals can, in turn, be explained by the contrapuntal inversion of low and high elements in the melody, and the wider context of the bass progression from m. 53 to the end. 78 The Art of Gigue exceeds anything in Bach’s own major-mode gigues. However, in the C minor gigue, Bach went to some lengths to adapt the set-up and cadence routine from the major relative to the minor tonic; this is a topic of subsequent analysis. Fortspinnung C may or may not be a direct reprise of previous material. This does not affect the subphrase’s primary function as the gigue’s final demonstration of broader musical pattern ahead of the concluding cadence. Fortspinnung C may have a “sequential” or “static” character like Fortspin- nung B but has a stronger tendency to be sequential and is by no means expected to reprise that earlier subphrase. The option of “static” material, in the solitary case of Bach’s C major gigue, appears tied to the repetition of Fortspinnung B as part of a long end-rhyme. Whether or not Fortspinnung C is a reprise of some kind is connected to the length of period III. Of the gigue’s three periods, period III is the most flexible. While period I sometimes includes material that is “extra-curricular” to the phrase- ology of Opening and Answering Complexes, period III always includes extra-curricular passages or repetitions. Little in how period III realizes the Closing Complex, or adds to it, can be taken for granted. The Closing Complex is the necessary core of what period III does but it is never entirely sufficient—at least not in the simple guise of three subphrases strung together. Evidently, the model of Closing Complex does not fully account for the work that period III must do. Always, some of the complex is cycled through twice or other subphrases intervene at the start of the period. Example 2.24 shows a recomposition of period III from my pastiche that omits such extra-curricular elements and presents the Closing Complex simply. We see by this alteration that an effective third period can almost be made with just three subphrases in the archetypal long–short–short design.

Temporal Scale Written Length of Strains and Periods Now that the elements of a phraseology are outlined, the issue of temporal scale becomes critical. How should we judge or compare the size of phrase units—both within pieces and across different compositions? Regarding the successive modules or subphrases of a single piece, can standards be established for the “normal” relations between these entities? And how can we understand the temporal scale of things across multiple compositions? To make a clean start on this issue, I return to the basic rule of “one, two, three,” and attempt a first systematic comparison of Bach’s six cello gigues. What, initially, can be gleaned about the scaling of Bach’s cello gigue just from the written lengths of the two strains and the three periods? Form 79

Bach’s notations give us two ways to judge the length of a formal unit: counting bars or adding rhythm values. Compiled in the upper portion of Table 2.4 are the bar counts for each of Bach’s six gigues, with a break down into periods I, II, and III. (Note that the length of strain 1 is identical with the length of period I, whereas the length of strain 2 can be obtained by adding the lengths of periods II and III.) The lower portion of the table section gives the corresponding Œ beat counts. Both metrics will be useful for making comparisons from one movement to another. At the bottom of the table, the relative lengths of the three periods within each movement are expressed in numerical ratios (reduced to the simplest arithmetic terms). Needless to say, these hold precisely true only for the “composed length,” not the durations in performance, although most recorded interpretations are consistent enough with tempo that the duration of a given strain, as heard for the first and second times, usually differs by no more than a small fraction of a second. The lessons to draw from this data about all six gigues are fairly slim. It was mentioned previously that strain 2 is always longer than strain 1 in Bach’s gigues for cello. Regarding the three periods, it can only be added that period I is a different length to either of periods II and III and that period II’s length is matched or exceeded by period III. However, if one of Bach’s gigues is set aside, more can be said. It is a common problem, when trying to understand a genre by generalizing the finished forms of its corpus, that clear or powerful trends have a paradoxical tendency not to hold good

Table 2.4: Bar and beat counts of periods in Bach’s six cello gigues.

No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 Suite G d C E ’ c D

6 3 3 12 3 6 Time signature 8 8 8 8 8 8 Total bars 34 76 108 42 72 68 First period 12 32 48 10 24 28 Second period 8 16 24 16 16 16 Third period 14 28 36 16 32 24 Total Œ beats 68 76 108 168 72 136 First period 24 32 48 40 24 56 Second period 16 16 24 64 16 32 Third period 28 28 36 64 32 48 Ratio of periods 6 : 4 : 7 8 : 4 : 7 4 : 2 : 3 5 : 8 : 8 3 : 2 : 4 7 : 4 : 6 80 The Art of Gigue through every case. In the picture that Table 2.4 presents, the intransigent case is the E ’ major gigue (No. 4). For the five “synoptic” gigues, on matters of proportion, various con- straints can be identified: strain 2 is longer than strain 1 but does not exceed twice strain 1’s length; period III is longer than period II; period I is longer than period II; and, more specifically, periods I and III are each half as long again, three quarters as long again, or twice as long as period II. As a corollary to this last point, the difference in length between periods I and III is less pronounced than the difference in length between the shorter of these and period II. Each of these constraints is worth stating separately, since their generality varies among Bach’s other gigues and further afield. But here, all can be summarized in one simple rule: in a given movement, periods I and III relate to period II in dissimilar ratios of 6, 7, or 8 to 4. Before moving on, the corollary mentioned above deserves further explanation. With the D minor gigue (No. 2), the difference between periods I and III is expressed as 1 in the three-way ratio (8 : 4 : 7) whereas the difference between the shorter of these and period II is expressed as 3. In this gigue, the relative brevity of period II is most pronounced, making a stark contrast to the problematic case of the E ’ major gigue. With the G major and D major gigues (Nos. 1 and 6), the difference between periods I and III is again expressed as 1, whereas the difference between the shorter of these and period II is expressed as 2. Finally, with the C major and C minor gigues (Nos. 3 and 5), both differences are expressed as 1. However, the ratio 3 : 2 is wider than the ratio 4 : 3. In that sense, we can say the discrepancy in size among the three periods is always more pronounced between the shorter two

Tempo Tempo cannot but change to some extent with each performer, room, and instrument, with every style of performing and at every performance. Given how contingent the tempo “feeling” is on musical material, tempo lacks obvious standards for comparison, and it also is a complex phenomenon since musicians are always engaging in rhythmic activity at various levels with varying emphases. Yet analysts must reckon with tempo to understand the wider issue of temporal scale, where performance considerations interact with compositional factors. Knowing tempo is necessary for relating the “length” of a composed text to the “length” of a performance, but more than that, tempo is an important character trait. For getting an idea of temporal scale between different pieces, the core challenge lies in being able to use the data of the composed text and the data of tempo together in the service larger discoveries. Form 81

Perhaps the tidiest way to consider “the tempo” of Bach’s six cello gigues is to use recordings. Table 2.5 documents the tempos taken by four cellists, in what is a very small selection from the available recordings of the six complete suites.17 I only list as many recordings here as readers may reasonably explore with reference to the current discussion. My intention in turning to recordings is not to defer tempo judgments to “group wisdom” or to textual authority in a modern medium, but rather to draw some recorded interpretations into this chapter’s own musical deliberations. In Table 2.5 I have, in fact, included my own estimate of an appropriate tempo for each gigue.18 I suggest, for an analytical study such as this one, that the analyst’s thoughts on tempo should not be excluded from the frame: tempo is vital to

Table 2.5: Tempos from four recorded interpretations of Bach’s cello gigues. At the top of the table, I give my own estimate of tempo (see Table 1.4).

No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 Suite G d C E ’ c D Estimate Œ = 80 66 72 116 70 72 Starker 94 74 82 142 63 77 Ma (1983) 82 68 73 136 60 72 Kirshbaum 80 63 74 134 72 70 Arenas 86 68 75 119 52 75

17. These tempo readings were obtained as a function of the time elapsed between the downbeat of strain 1 (for the first time) and the downbeat of strain 2 (for the first time); all Strain-1 repeats were taken in these recordings, as one expects. My time measurements were as follows: for Starker, 30.6, 51.6, 70.3, 33.8, 45.9, and 87.0 seconds; for Ma, 35.1, 56.5, 79.2, 35.4, 48.1, and 93.9 seconds; for Kirshbaum, 36.1, 60.9, 77.4, 35.9, 40.1, and 96.1 seconds; for Arenas, 33.5, 56.5 (sic), 76.5, 40.3, 55.3, and 89.8 seconds. The tempos are rounded to the nearest one beat per minute.

18. The tempos come from a careful, one-time effort to estimate a suitable tempo for each of Bach’s thirty-four gigues, at a stage of being very familiar with them all. As with any actual performance, these tempos are not necessarily an ideal reflection of even my current and future opinion, but they were carefully determined. Refering to the scores, and being sure to consider the whole of each piece, the tempos were assessed according to a tempo scale in increments of two beats per minute. At the point of doing this, I had heard at least two or three, and in some cases many, recordings of each gigue, and had heard most in live performances. On the day of assessing my own tempos, however, I tried to separate myself from the memory of specific interpretations as much as possible, and I certainly did not refer to recordings at the time. Nor did I use an instrument to bring any of the gigues back to mind, to avoid exaggerating any inconsistencies between pieces I have learned to play and others I have never played. 82 The Art of Gigue questions of rhythm and meter, especially in a comparative analysis, and we cannot address these areas with maximum integrity if we write off tempo as something “subjective” or if we isolate it as an element of “performance” or “reception” distinct from “composition.” Table 2.5’s comparison of the tempos taken by Janos Starker, Yo-Yo Ma, Ralph Kirshbaum, and Adolfo Gutierrez Arenas reveals striking con- sistencies alongside pointed differences. The extrapolation of tempo rank in Table 2.6 helps to clarify these. I will note the similarities first. Always fastest by far, is the E ’ major gigue. The G major is always second fastest, and the C major, always next in line after that. Invariably, one of the minor-mode suites is slowest, and, in the middle of the pack, the D major is consistently close in tempo to the C major. On the other hand, there are certainly divergent interpretations or even schools of interpretation at work. Most pointedly, three cellists take the C minor gigue rather slow (Ma, even Starker, and especially Arenas) whereas Kirshbaum assigns a fairly brisk tempo. The slow tempos might signal a heightened consciousness of the French gigue idiom, for during the twentieth century, scholars tended to emphasize the “stately” bearing of this idiom against widely held connotations of the gigue as lively and fast (though the historical evidence is quite uncertain about definite tempo). Bucking the trend, Kirshbaum’s incisive C minor gigue does, at least, make a strong case for a quicker tempo; as Table 2.5 indicates, this is an approach I am personally sympathetic to. Among the four cellists, there is also a fairly wide range of tempos for the E ’ major gigue. Once more, one cellist (this time, Arenas) makes a good case for a more moderate tempo than the others choose. Arenas’s interpretation aside, the often very quick tempo of the E ’ major may reflect deliberate consideration of “clues” about 12 speed such as the 8 signature. (Such clues indicate what Meredith Little and Natalie Jenne call the “giga II” idiom, an ostensibly distinct subgenre

Table 2.6: For each interpretation shown in Table 2.5, the rank of tempos from fastest (1) to slowest (6).

No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 Suite G d C E ’ c D Estimate rank 2 6 3= 1 5 3= Starker 2 5 3 1 6 4 Ma (1983) 2 5 3 1 6 4 Kirshbaum 2 6 3 1 4 5 Arenas 2 5 3= 1 6 3= Form 83 of quick gigue, discussed in chapter 1.19) Needless to say, there is no right answer to whether such clues are read appropriately or are over-reacted to. Even as I suggest that some interpretations are on the slow or fast side, all such comparisons are relative. Any reader would want to consider their own thoughts on tempo and, I hope, sample the cited recordings. Although tempo decisions are personal and judgments about tempo are relative, it is, however, striking that variations operate within certain margins. Even with a more relaxed tempo, the E ’ major gigue is a clear outlier among the tempos of Table 2.5. This issue must be addressed if standards are sought for how a Bach cello gigue is scaled. As documented here, the E ’ major gigue’s Œ pulse is 116–142 beats per minute. That is appreciably faster than for any other gigue; these others have a Œ pulse of 52–94 beats per minute. We also know from Table 2.4 that the score of the E ’ major gigue has a lot more Œ beats. A total of 168 leaves even the grandiose D major gigue quite a bit behind at 136, and the other suites remain at 68–108. The question arises whether the written C of the E ’ major gigue is a better likeness to the written Œ elsewhere. Would this offer a better plane of comparison across multiple pieces, for asking how “big” is a phrase or subphrase, or how many “beats” a particular kind of recurring element has? Comparison of the final cadences of the six gigues, with Example 2.25, reveals that the written C in the E ’ major gigue is indeed a good equivalent to Œ elsewhere. The tonic usually arrives two Œ beats ahead of the final barline, but in the E ’ major gigue, the tonic is allotted four Œ beats. One might guess that Bach’s more generous rhythm values are related to his use 12 of 8 , but no such expansion is present in BWV 808, BWV 809, BWV 827, nor BWV 1023: in these movements, the final tonic arrives two Œ beats ahead 20 of the final barline, as usual. Of the twenty-seven of Bach’s thirty-four 3 6 12 gigues notated in 8 , 8 , or 8 , twenty-one clearly allot two Œ beats to the final tonic; this represents a little over 75% of the specified subset.21 The E ’ major cello gigue gets through its notated values more quickly than the other cello gigues, and it correspondingly does less—harmonically, at least— with each passing beat per the notation. This may not apply to Bach’s other

19. Meredith Little and Natalie Jenne, Dance and the Music of J. S. Bach, exp. ed. (Bloomington: Indiana University Press, 2001).

12 20. Two of Bach’s gigues in 8 , I have not mentioned here: those of BWV 996 and BWV 1004. The former would seem to allot four Œ beats to the final tonic (like the E ’ major cello gigue), whereas the latter would seem to allot the usual two beats. However, the harmonic rhythm is not altogether clear in either piece.

21. Other of the twenty-seven might be interpreted as alloting two Πbeats as well, whereas the remainder clearly do otherwise. 84 The Art of Gigue

BWV 1007 
ΠΠI BWV 1008
 Π  Πi BWV 1009
 Œ Œ I BWV 1010   Œ  Œ I BWV 1011  Œ
  Π ΠΠ ΠΠi BWV 1012      ΠI

Example 2.25: The final cadence in each of Bach’s six cello gigues. Roman numerals mark the arrival of the tonic. Form 85

12 8 notations, nor to his other pieces for which a fast tempo is appropriate, but with the E ’ major gigue, we will best understand issues of scaling if we count by C denominations what, elsewhere, we count by Œ . When, for comparative purposes, the beat counts and tempo readings for the E ’ major gigue are cut in half, the total written length becomes 84 beats—somewhere between the D minor and C major gigues—while the tempo range becomes 58–71 beats per minute. It is significant that the reduction of these values maximizes the coherence of each of the five lines of data in Table 2.5. No other arrangement of Œ or C tempo readings (one for each suite) is as tightly packed.22 That said, nothing about tempo is quite straightforward. Although we must interpret the E ’ major gigue under a “diminution” for comparison’s sake, it does not follow that it should be felt “in 2” when it is performed. Little and Jenne effectively say it should, by categorizing the movement as “giga II,” but, personally, I think that the written Œ ought to remain the primary beat (Taktteil) in performance. The range of tempos indicated by Table 2.5 suggests a range of opinions on this matter. Comparing tempos across Bach’s six cello gigues, the E ’ major is clearly “double speed” relative to the slower of its peers, but its relation to the fastest of its peers is indeed more ambivalent. Against the C major gigue, which lies in the middle of the field tempo-wise, a strict C = Œ relation is just about conceivable. Starker’s E ’ major gigue is almost expeditious enough to match Ma’s C major on those terms. But a strict Œ = Œ relation, say at 86 beats per minute, would be very hard to achieve convincingly. The E ’ major gigue becomes manic; the C major, too lethargic. Although we should regard the metric economy of the E ’ major gigue as a kind of “alla breve,” the point of these comparisons is never to erase the particular qualities of individual pieces. How the E ’ major gigue squares up to its peers on tempo can be explored further using the incipits in Example2.26. I will offer two com- ments here. First, I observe that the C of the E ’ major gigue can—if it is moderately quick—take the same speed as the Œ of the D minor (No. 2). We see this in Ma’s recordings: both denominations proceed at 68 beats per minute. Second, I suggest that the C and Œ pulses of the E ’ major gigue straddle an appropriate Œ pulse for the G major (No. 1). An extremely brisk performance of the E ’ major could maintain a strict C for Œ conversion with the G major gigue (say at 74 beats per minute), whereas an extremely brisk performance of the G major might match Œ for Œ with a steady

22. The appropriate metric for the standard distribution, here, is the logarithmic scale of base 2, but, as it happens, the same optimal ordering would be obtained by measuring the standard distribution in ordinary increments. I will not reproduce these calculations here since they are easily reproduced. 86 The Art of Gigue

BWV 1007  q q q q q q q q q q
q   6 q q q q q q q q q q q
q 8 q q q

BWV 1008 q q q q q q  q q q q q q q  q q q q q q q q q  83  q  q  q q q

BWV 1009 q q q q q q q q q q q q q q q q  3 q q q q q q q q q q 8  q q

BWV 1010  q q q q q q q q q q q q q q q q q q q q q q q q  12 q q q q q q q q q q q q q q q q q q q q  8  q
q 

BWV 1011  3 q 
q q q 
q q q q q
q q
q 8  q
q q q 
q q q
q q q q
q 

BWV 1012  q q q q q  q q q q q q q q q q q q q q q q q q q q   6  q
q q q q q q q q q  q qq q q qq q qq q q qq q 8 q
q q q     Example 2.26: The opening Vordersatz in each of Bach’s six cello gigues. Form 87

E ’ major gigue (say at 100 beats per minute). While the first comparison (to No. 2) offers straightforward support for interpreting the E ’ major gigue via rhythmic diminution, the second comparison (to No. 1) shows how it might be a challenge for the composer to calibrate generic procedures across the tempos of different compositions.

Proportions Reconsidered In light of tempo, we can now adjust the beat-count metrics for “composed length.” Table 2.7 amends the data from before by halving the values for the E ’ major gigue and reducing the beat counts to counts of , or fast  values.23 This table also includes an arithmetic resolution of the new values into their prime factors. When the rhythmic diminution in the E ’ major gigue is recognized, the comparison of composed lengths becomes clearer. No longer do the E ’ major’s periods II and III register beyond the measures attained by the D major gigue, which is appropriate given the D major’s greater length in performance and its status as a more ambitious composition. Also, the range of values belonging to period II and period III across Bach’s six gigues becomes more sensible. Period II takes 4–8 units (of , or fast  ), and period III takes 7–12 units. Only period I’s values are spread more widely than before, at 5–14 units. (Note that a range of 5–14 corresponds to a

Table 2.7: Four-beat unit counts of periods in Bach’s six cello gigues. Compare Table 2.4.

No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 Suite G d C E ’ c D

Total , (or fast  ) 17 19 27 42 21 18 34 First period 6 8 12 10 5 6 14 Second period 4 4 6 16 8 4 8 Third period 7 7 9 16 8 8 12 Or as prime factors First period 2 ¨ 3 23 22 ¨ 3 5 2 ¨ 3 2 ¨ 7 Second period 22 22 2 ¨ 3 23 22 23 Third period 7 7 32 23 23 22 ¨ 3

23. Counting dotted-half beats in BWV 1010 matches Little’s and Jenne’s definition of the “beat” in this and other of their “giga I” movements. See my discussion in chapter 1 and Little and Jenne, Dance and the Music of J. S. Bach. 88 The Art of Gigue spread of more than one on a logarithmic scale of base 2.) The adjustment of values suggests that the E ’ major gigue’s strain 1 is abnormally brief, which is confirmed by intrinsic musical factors, as discussed below. The composed length of a Bach cello gigue now stands at 17–34 units of , or fast  duration, with the low and high extremes differing by a factor of two. These extremes belong to the G major and D major gigues respectively (Nos. 1 and 6). At the mirrored ratios of 6 : 4 : 7 and 7 : 4 : 6 (mentioned earlier), the two structures point to two distinct orders of magnitude, two levels at which Bach explores similar phrase rhythms and formulaic devices. In the next section, I will start referring to these two orders of magnitude as regular and large. Seeing clearly the difference between them will prove important to managing effective comparisons of Bach’s six gigues. This issue was dealt with earlier during discussion of the D major gigue and its broad Opening Complex (around Crux 1). In that movement, Vordersatz 1 and Vordersatz 2 take twice as many Œ or fast C values as any other of Bach’s gigues, which is why Crux 1 occurs so far into strain 1. As seen in my earlier analysis, the larger of Bach’s two metric orders appears unsustainable and the “late” phase of strain 1 does not follow through on the same scale. Yet that grand scale is what Bach’s last cello gigue aspires to, and this ambition is neatly expressed in its doubling of the total length of the first cello gigue.

Finding a Level with Period II I turn now to tackle the issue of temporal scale from a phraseological angle, looking to intrinsic, musical measures for the size of periods, modules, and subphrases. The most fruitful analytical comparisons will come from discovering what are the points of relative stability first. Therefore I begin by addressing period II and its usual constitution as an Interior Phrase. Finding the areas of relative consistency and volatility in the temporal scaling is illuminating of Bach’s approach to the cello gigues’ binary form, and in the basic framework of strains and periods, the comparison of written lengths across Bach’s six gigues underscores the notion that period II is a site of particular symmetry. In the data of Table 2.7, the relative stability of period II is reflected as follows. First, there are fewer unique numerical counts for this period than its peers. Period II fills four, or six, or eight units; three unique lengths, to compare with four for period III, and five for period I. Second, consider what the resolution into prime factors reveals. Reading across the table, the roster of period II accumulates just one non-duple factor on the “bottom line” of metric organization: period II of the C major gigue appears triple in some way. But the rosters of period I and period III accumulate five non-duple factors each. Form 89

BWV 1007 Forephrase 13 q q q
q q q q q q q q q q q q q q q q q q q q q  q q q Afterphrase 17 q q q q q q q q q q
q q q q q q
q q q q q q

BWV 1008 Forephrase q 33 q q q q q q q q q q q q q q q q q    q   q q q q q q q q q q q q Afterphrase q q q q q q q q q q q q q
q q q q q q q q
q q
q q q q q   q q q q q q
q q q q q q q

BWV 1011 Forephrase 25 q q q q  q q q q q q q q q q
qq
q q   q q q q q  Afterphrase 32 q q q q q q q q q   q q q q q q q 
q q q q
q q q    q q q  Example 2.27: Period II in Bach’s G major, D minor, and C minor cello gigues.

An Interior Phrase, at the regular order of magnitude, essentially takes four , units. Three lucid examples of this scaling are reproduced in Example 2.27 from the G major, D minor, and C minor gigues; each takes sixteen Œ beats. In the C major gigue, where the triple factor arises, there is an expansion to this basic length, as shown in Example 2.28. Here, the Afterphrase grows to twice the Forephrase’s size, attaining the large order of magnitude under the pressure of a sequence that already runs as long as the whole Forephrase, where it should have acquitted itself in half the time. The “extra” length is added when the Afterphrase completes with a prolongation of pre-dominant harmony and the requisite cadence. Given that it transitions from sequential material into a set-up and cadence routine, the Afterphrase of the C major gigue resembles an Answering Complex. Thus the triple factor in the dimensions of the whole module arises in the hybrid scaling produced by a regular-sized Forephrase and a large-sized Afterphrase. Period II is longer still in the E ’ major and D major gigues, where the basic length of four , or fast  units is doubled to eight. In the D major (see again Example 2.20 on p. 66), period II is accomplished as a coherent 90 The Art of Gigue

BWV 1009 Forephrase 49

 Œ

Afterphrase 56       

65  





Example 2.28: Period II in Bach’s C major cello gigue.

phrase, divided symmetrically into halves and quarters; this realizes the notion of Interior Phrase on the large scale, reaching the upper limit of phrase length for Bach’s cello gigues. The passage represents one of only three phrases in all of Bach’s cello gigues that attain thirty-two Œ (or fast C ) beats, and in performance it is sustained for ca. 25 seconds. As re-imagined on the large scale, this Interior Phrase is articulated in quarters as well as halves and the types of material it contains are more comprehensive: the Afterphrase, like in the C major gigue, consists of sequential material followed by a set-up and cadence routine. In the E ’ major gigue, by contrast, period II does not stand as a coherent phrase. Rather, it divides into two parallel sections that fail to relate as halves of a larger unity (see Example 2.29). The midway articulation simply affects a starting-over instead of an answer or complement to the beginning of the period (which difference chapter 3 will express in terms of “prosaic” and “metric” species of rhythmic projection). Initiating what, elsewhere, would be Forephrase and Afterphrase, parallel thematic statements in the dominant and then the relative minor prove contradictory to the balanced rhetoric of an Interior Phrase. The second half is subject to considerable metric disturbance as well, which further undermines the affect of balance normally germane to period II. In this exceptional case, “Interior Phrase” becomes a misnomer. The parallel thematic statements signal that the normative length of period II is being almost rashly superseded, and Bach plays on the precarious boundary between the regular and large scalings presented with assurance in other movements. In the terms developed earlier, there is no Crux 3. Once the intrinsic musical “size” of period II across Bach’s six gigues is understood, one is equipped to revisit the question of temporal scale for entire movements. Table 2.8 reproduces the ratios from before in a form that expresses the simple rule stated earlier, that periods I and III relate to Form 91

BWV 1010 First half 11




 æ 
æ 

15




Second half 19

  



↑ strongest downbeats ↑

23

 
  
↑

Example 2.29: Period II in Bach’s E ’ major cello gigue.

Table 2.8: Summary of the ratios between periods in Bach’s six cello gigues.

Suite Ratio Further interpretation No. 1 G 6 : 4 : 7 No. 2 d 8 : 4 : 7 No. 3 C 8 : 4 : 6 No. 4 E ’ 5 : 8 : 8 (6 ´ 1) : (4 ` 4) : 8 No. 5 c 6 : 4 : 8 No. 6 D 7 : 4 : 6 92 The Art of Gigue period II in dissimilar ratios of 6, 7, or 8 to 4. The integers in Table 2.8 equate to a count of , values for the G major, D minor, and C minor gigues and a count of  values for the D major gigue. The three shortest of the cello gigues offer a compendium of outer-period lengths under the stated rule. Turning to the problematic E ’ major gigue, the integers equate to a count of fast  values, which is consistent with this gigue’s fast tempo. Analysis of period II now illuminates the unusual proportions of this movement by pointing to the intrinsic “double length” of period II, with its lacking Forephrase–Afterphrase relation. On its own terms, period II still points to a normative length of four fast  s, and against that yardstick, the relative size of periods I and III are not so unusual. Period III relates to the normal length of period II by 8 : 4, like in the C minor gigue. And though period I relates to period II by 5 : 4—falling short of the usual standard—there are also intrinsic factors of period I that point to a basic length of at least six fast  s. The “further interpretation” in Table 2.8 indicates how the movement’s outward ratio of 5 : 8 : 8 can be viewed as a transformation of a 6 : 4 : 8 design similar to those of the other gigues. All six suites—including the intransigent E ’ major—clearly set a standard in period II by which the scale of the outer periods can be understood. How the C major gigue fits in has already been touched on: as written, it is half as long again as the C minor. But before proceeding further, it will be useful to introduce a system for easily describing metric durations.

It is cumbersome to be describe units of “ , or fast  ,” for example, and factors of three in the metric organization prevent single durations being expressed in a single sign if dots are already needed to represent the notated beat. Moreover, it will be necessary to express durations beyond the ceiling of  . I will therefore adopt fifteenth-century mensural values to indicate standardized metric durations. The beat— Œ or fast C in the cello gigues—will be represented by the semiminima ( p ). Upward from there, the calibration of values through the maxima will be understood as duple throughout, per Table 2.9. Under this system, the duration of period II in the three shortest cello gigues will be represented by the longa ( ), with Forephrase and Afterphrase  each lasting one ( H ). And in the E ’ major gigue, the length of period II brevis will be represented by two longae (2 ˆ  ): because the period fails to cohere as one metric duration or phrase, it will not be represented as a . maxima Where period II does achieve the metric ceiling of the maxima ( Õ ) is in the D major gigue, where Forephrase and Afterphrase each last one longa (  ). With the C major gigue, finally, the total duration of period II can be represented by the longa perfectus, the union of three breves; this period is composed of a regular Forephrase ( H ) and a large Afterphrase (  ). Table 2.10 Form 93

Table 2.9: Memory aid to fifteenth-century mensural rhythmic values, calibrated by duple organization throughout (i.e. modus imperfectus, tempus imperfectum, prolatio minor).

Durations Õ  H B Y Contain 32 16 8 4 2 p 16 8 4 2 Y 8 4 2 B

4 2 H

2 

Table 2.10: The “basic lengths” as inscribed by period II in Bach’s six cello gigues, and the arrangement of periods by relative sizes of small, medium, and large. (I notate the longa perfectus with an anachronistic augmentation dot.)

Suite Second Period Basic shape

No. 1 G M:S:L  No. 2 d L:S:M  No. 3 C L:S:M £ No. 4 E ’ 2 ˆ [M:S:L]  No. 5 c M:S:L  No. 6 D Õ L:S:M 94 The Art of Gigue lays out the benchmark “basic lengths” inscribed in period II and records the arrangement of periods by relative size. We encounter a problem here, however. It is now unclear that the integers of the ratio 8 : 4 : 6 signify anything about the musical content of the C major gigue: “4” simply does not mesh with a phrase consisting of three breves. How can we reconcile the apparently simple ratio of period lengths with the movement’s phrase rhythm?

Hypermeter A proper assessment of hypermeter in Bach’s six gigues begins with the integers in Table 2.8. Where these numbers equate to a count of , or  or fast  vales, are such durations musically present through the course of a movement? The C major gigue presents the strong counterexample, in which a normative ratio 8 : 4 : 6 operates but these integers equate to a count of 6-bar units, which have no musical standing whatsoever. It cannot be taken for granted, therefore, that proportions are meaningfully connected to phrase rhythm, yet an attempt to connect these questions is essential to formal analysis. Returning to the data of Table 2.7, one finds that Bach’s cello gigues are almost entirely receptive to being parsed into four-beat units, whether 3 6 12 four-bar units in 8 , two-bar units in 8 , or two-bar units in a quick 8 .

Thus the G major gigue is composed of, and not only equates to, 17 , durations. Likewise, the C major gigue is composed of 27 , durations. The few exceptions to the pervasive periodicity of four-beat units—i.e. semibrevis hypermeter—are noted in Table 2.11. This table uses mensural values as detailed above, such that B =  in the E ’ major gigue, and B = , in the C minor gigue. In period II of the E ’ major gigue, B hypermeter is absent for some of the Afterphrase (mm. 19–26), whereas in period III of the C minor, B hypermeter is suspended during the Schlußsatz pair (mm. 61–72). Although Table 2.7 represents these periods with counts of “8,” neither period can be parsed into eight equal units. The relevant passage in the E ’ major gigue is reproduced above in Example 2.29, where the arrows

Table 2.11: Exceptions to “semibrevis” hypermeter in Bach’s six cello gigues.

Period Suite Bars I II III Actual Durations

No. 4 E ’ 19–26 ✔ B£ B B£ No. 5 c 61–72 ✔ B£ B£ Form 95 identify the hypermetrical downbeats. The clearest contradiction to an established two-bar hypermeter comes in mm. 22-23 when an ascending tetrachord device, 3–ˆ 4–ˆ 5–ˆ 6,ˆ is recalled from Schlußsatz 1(1). Given the pervasiveness of four-beat units in Bach’s cello gigues, it is not surprising that larger periodicities also occur. Periodicities of eight-beat units—i.e. brevis hypermeter—are used widely. The entire D major gigue can be so parsed. As for the others, Table 2.12 shows what passages do not conform to such parsing even as an underlying semibrevis hypermeter continues. It is worth noting that H hypermeter is most often negated, or simply absent, during period III. However, readers may prefer to digest this information later with Table 2.14. In this table, I use square brackets to invoke a certain duration (a certain number of p beats) absent any implica- tions about the internal metrical structure of the corresponding passage. At this point, it should be recognized that documenting “hypermeasures” is problematic, in that metrical processes are dynamic and are concerned with making connections rather than divisions. For the purposes of this chapter, conventional notions of metric “boundary” are not too disruptive, but there are underlying theoretical tensions here that chapter 3 addresses. To underscore what analytical judgments are encoded in the tables just presented, a second look at Table 2.10 is merited. Regarding the E ’ major gigue, the duration of period II would be rendered more accurately as “  + [  ].” As explained above, the square brackets are effectively a safeguard against forgetting local complexities of meter once analysis falls back to a higher level. Values not qualified by square brackets can then be totally trusted for their standard implications concerning internal metrical structure. By these means, my tables encode a comprehensive analysis of hypermeter in concise form.

Table 2.12: Exceptions to “brevis” hypermeter in Bach’s six cello gigues where the “semibrevis” hypermeter remains intact.

Period Suite Bars I II III Actual Durations

No. 1 G 29–34 ✔ [ H ] B

No. 2 d 49–60 ✔ [ H ] B

No. 3 C 9–32 ✔ H H

81–92 ✔ H

No. 4 E ’ 1–10 ✔ B [  ] 27–34 ✔ B B B B

No. 5 c 49–60 ✔ H B 96 The Art of Gigue

Finding a Level with the Answering Complex Table 2.13 gives the lengths of all four modules in the cello-gigue form. Further, Table 2.14 gives the lengths of all subphrases; a “middleground” hypermetrical analysis of each movement that also takes stock of “extra- curricular” passages which fall outside the recurring schemas I have iden- tified. The data in these tables allows the stability and variance in Bach’s temporal scaling to be mapped within explicitly phraseological territory. Square brackets have the meaning described above, while the arrows in Table 2.14 show when the Answering Complex begins at the same time as the previous recorded subphrase. Notice in Table 2.14 that in the G major

Table 2.13: Durations of the four modules in Bach’s six cello gigues.

Suite Opening Answering Interior Closing

No. 1 G “ ”     No. 2 d “ ”     No. 3 C £  £  No. 4 E ’ “ ” + [ ]      No. 5 c [ ]    £ No. 6 D Õ  Õ £

Table 2.14: Durations of all subphrases in Bach’s six cello gigues. “Extra” refers to material that falls outside the proposed formal model.

Suite Vordersatz 1 Vordersatz 2 Fortspinnung A Extra Fortspinnung B Schlußsatz 1(1) Schlußsatz 2(1) Forephrase Afterphrase Extra Fortspinnung C Schlußsatz 1(2) Schlußsatz 2(2)

No. 1 G B B H Ð H B B H H H B B H B B B H H B B H H p B B No. 2 d v B B

No. 3 C B B H H H B B H £ H B B  No. 4 E ’ B B Ð H B B [ ][ ] H B B    No. 5 c B B H Ð H B B H H H v p B£ B£

No. 6 D H H  H H B B   v  B B Form 97 and D minor gigues the functions of Schlußsatz 1(2) and Schlußsatz 2(2) are repeated—the record of durations wraps onto a second line—and in the E ’ major gigue the function of Fortspinnung A is omitted. The affected modules are assigned quotation marks in Table 2.13 to indicate that the recorded duration is notional rather than real due to the repetition or omission of those constituent functions. (The upcoming analyses of the C minor and E ’ major gigues address these issues.) According to the phraseology I have now laid out, the site of greatest consistency is clearly the Answering Complex. Its long–short–short pattern comprising Fortspinnung B, Schlußsatz 1(1), and Schlußsatz 2(1) always takes the durations “ H B B ” or, in other words, the beat count “8 + 4 + 4.” The last sixteen beats of strain 1 in a Bach cello gigue are thus extremely well defined. Pinpointing this invariance not only provides a benchmark for analytical comparisons but also offers an insight into the formal aesthetic of the genre. While period II is the most stable of the three periods in terms of scale, the Answering Complex is—even more clearly—the most stable of the four modules.

Three More Moments: Selections from Gigues 2, 5, and 4 Bach’s six scores have revealed certain formulas for structuring phrase elements, scaling them, and combining them. But it remains to be explained how phraseological schemas are themselves active in temporal experience. How do Bach’s cello gigues exploit the phraseological capacity of their per- formers and listeners? It may not be right to conceive of “competent” musical listening as a continuous stand-off between what we are perceiving and what we know already. Yet at special moments, there can be a palpable parting of ways between attention and expectation, a prying apart of “actual” phrase forms from “ideal” or “normal” ones. Two examples were mentioned earlier. In the D major gigue, the second quarter of the Opening Complex features stationary material that pushes against the usual behavior of Vordersatz 2 before it is normalized later as the third quarter of the Interior Phrase. In the C major gigue, the Interior Phrase begins on a regular scale but is pressured to complete on a larger scale by the Afterphrase’s reprise of the sequence from Fortspinnung A. The following analyses address a second selection of special moments, from the gigues in D minor, C minor, and E ’ major, in which Bach’s realization of a formal crux hinges on the phraseological “competence” of the listener.

The D minor Gigue Phraseology most tends to be “listener’s business” during period III. In this part of the binary form the operative schema of Closing Complex can 98 The Art of Gigue become detached from the actual course of events. The D minor gigue demonstrates it most strongly. Uniquely, this movement’s period I can be read as a single metric unit (one which attains the maximum duration of thirty-two beats),24 so period III undoes phraseological archetype against a background of previous solidity. The following analysis examines how Bach serializes the final turn to cadence (Crux 4) and directs his listener to follow the process. In the D minor gigue (see Example 2.30), period III unfolds as a complex negotiation with the schema of Closing Complex. The period opens with a Fonte—a slow, two-part chain of fifths sequence. Tonally, this passage marks an immediate return to the tonic key following the internal cadence in the subdominant, and the upper line of 6–ˆ 5–ˆ 4ˆ fronts a move toward dominant harmony. The harmonic rhythm is noticeably slower than previous sequential progressions in Fortspinnung A and the first half of Fortspinnung B. A faster version of Fortspinnung C might have resolved to Vv within an eight-bar span but here, Vv becomes a contrapuntal outcome extrinsic to the meter of the subphrase itself.25 At the new metrical departure starting on Vv (m. 57), an extemporizing spirit seems to take over, like in the G major gigue’s period II after the Monte. As annotations in Example 2.30 point out, the initial dyad g3–a2 arguably draws some potency from its connection to the cadences of both period I (on a2) and period II (on g3) and hence embodies a tussle between dominant and subdominant. Firmly framed to the dominant and situated ahead of a main cadence, the ensuing four-bar passage engages a cadenza topic and its onset offers the first intimation of Crux 4. With mm. 49–56 as Fortspinnung C, a Schlußsatz 1 function in mm. 57–60 would project a cadence (Schlußsatz 2) during the following four bars, as shown in Example 2.31. This hearing is supported by the emergence of a descending thirds pattern during the mooted Schlußsatz 1 subphrase and the arrival on 3ˆ (F) to start a possible Schlußsatz 2. Example 2.31 shows what Bach might have written if the arrival on 3ˆ had initiated a conventional i6–Vv–i cadence. Although the procedures illustrated in Example 2.31 have standing in the genre, they are not, however, the procedures prescribed by strain 1 of the gigue. (Refer again to Example 2.30.) Schlußsatz 2(1) features 3ˆ prominently in the bass but not until the second bar (m. 30), and Schlußsatz 1(1) is

24. This is one of three hypermeasures of Õ duration in all the cello gigues, along with period II of the D major gigue and period III of the E ’ major.

25. I introduce the symbol Vv in place of “V” or “V~” to indicate the major triad on 5ˆ in the minor mode. Thus, “V” is reserved for the dominant chord in the major mode, extending the usual ability of case-inflected Roman numerals to communicate a normal modal context as well as chord structure. Form 99

BWV 1008 Vordersatz 1 Vordersatz 2 Fortspinnung A Ë Ë Ë Ë Ë Ë   Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  83  Ë 
Ë  Ë Ë Ë  Ë
Ë Fortspinnung B

10  Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Schlußsatz 1(1) 19 Ë Ë Ë  Ë ËËË Ë Ë Ë Ë Ë Ë Ë Ë Ë   Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë  Schlußsatz 2(1) 

↓ A Forephrase 27 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë
Ë
Ë Ë Ë Ë Ë   Ë  Ë   Ë
Ë Ë       Ë Afterphrase 35 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë   Ë  Ë Ë Ë Ë Ë Ë Fortspinnung C ↓ G ^ 43 6 Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë
Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Schlußsatz 1? (no!) ^ 5 4^ 51 Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë
Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë  Ë ↑ G + A Schlußsatz 1(2) Schlußsatz 2(2) 59 Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë    Schlußsatz 1(3) Schlußsatz 2(3) † 66
Ë Ë Ë  Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë 
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 73 Ë  Ë Ë Ë Ë Ë Ë  Ë Ë
ËË Ë  Ë Ë Ë Ë Ë Ë Ë Example 2.30: Bach’s D minor cello gigue (BWV 1008). Annotated. 100 The Art of Gigue

Schlußsatz 1 Schlußsatz 2 
    æ    G E C♯ A F

Example 2.31: Hypothetical ending for Bach’s D minor cello gigue.

realized by a pattern of ascending steps (3–ˆ 4–ˆ 5–ˆ 6),ˆ not descending thirds. Indeed, a reprise of Schlußsatz 1(1) commencing at m. 61 quickly disabuses the listener of conceiving the prior mm. 57–60 as Schlußsatz material. From m. 61, the reprise proceeds at the lower fifth of strain 1’s Schlußsatz pair, with minimal adjustments to break a double stop and keep the lowest note on the cello. In itself, this passage satisfies perfectly the expectation for an end-rhyme. Nothing is intrinsically out of place and it would be logical to predict an ending in m. 68 (at † in Example 2.30). In the context of larger phrase rhythm, however, the conditions for closure are missing. On the metrical plane, the detour into “cadenza” material at mm. 57–60 disrupted the experience of Crux 4 that ought to have accompanied the start of the Schlußsatz reprise. Although mm. 61– 68 are right in themselves, the departure at m. 61 takes the listener by surprise and cannot fully embody Crux 4 as a demonstrative “beginning of the end.” Going into m. 61, one anticipates a Schlußsatz 2 subphrase, thus a metrical “fourth quarter” of the Closing Complex, but one negates that expectation when faced with the reprise of Schlußsatz 1—that is, when faced with material proper to a metrical “third quarter.” (Chapter 3 will explain the essential weakness of such metric elisions.) A positive feeling of metric complementation is therefore lacking at the start of Schlußsatz 1(2) and consequently, the ensuing cadence lacks the hypermetrical backing needed to end the movement. In the G major gigue, by contrast, the initial cadence had a sure hypermetrical footing and the postponement of closure hinged on a vaguer sense of period III’s appropriate length and level of commitment to the major mode. A second “rotation” of the Schlußsatz pair is thus begun at m. 69, introduced by continued sixteenth-note motion past the arrival on d2.26 This time, the start of Schlußsatz 1 plays into an established periodicity of B value (here,  ), consistent with the performance of Crux 4. The imminence of closure is thus strongly articulated and the formal departure

26. My use of the term “rotation” is similar to that of Hepokoski and Darcy, who generally apply the term to the thematic trajectory through a sonata exposition and its correlates in the form of development and recapitulation. See James Hepokoski and Warren Darcy, Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata (New York: Oxford University Press, 2006). Form 101 at m. 69 becomes the third and last gesture toward a strong crux for the Closing Complex. With the reprisal function of period III already fulfilled, however, it is worth asking what sorts of resolution remain for mm. 69–76 to accomplish. Schlußsatz 1(3) and Schlußsatz 2(3) do not simply ride out the metric correction; they also perform closural actions lacking in the previous Schlußsatz pair. One reason for a second rotation is that the Schlußsatz pair prescribed by strain 1 is overly fussy, with a crowded harmonic rhythm and a treatment of the final harmony that is more dissonant than in Bach’s other cello gigues. Compared to Schlußsatz 2(2), Schlußsatz 2(3) simplifies: it brings forward by one bar the descending scale from a3 to d2, it straightens the motives into an unbroken scale, it steadies the harmonic rhythm, and transforms the elaboration of tonic into a plain arpeggio. As if rectifying the elaboration of an already satisfactory harmonic resolution, this second rotation of the Schlußsatz pair has a primarily melodic character, despite its lucid harmonic progression. The stepwise resolution to 1ˆ in the low register, which also features in the C major gigue, exemplifies Bach’s attention to melodic resolution. In addition to simplifying the material of the first rotation, the second rotation functions as a reprise of significant materials originating outside the Schlußsatz context. Schlußsatz 1(3) reprises the second half of Fortspin- nung B, blending this double-stopped fixation on 4ˆ with the implication of Neapolitan-sixth harmony introduced during the Afterphrase at m. 45. In that this reprise involves prominent use of the open strings (d3 in strain 1, g2 in strain 2), a comparison may be drawn with the C major gigue and its return of Fortspinnung B as Fortspinnung C. The effect in the D minor gigue is that two potent ideas—one textural and motivic, one harmonic—are reproduced in the vicinity of the final cadence, so to intensify the cadence and forge a meaningful connection from earlier events to the niceties of closure. Fluency into the cadential progression, Schlußsatz 2(3), is assured by Bach’s change to the last eighth-note of m. 72 as against m. 24: resolution to i6 (the bass is implicit) now occurs within the metric orbit of Schlußsatz 1. In strain 1, 4ˆ had loomed larger for not being abandoned until the downbeat of Schlußsatz 2 and had contributed to the quality of half cadence that intruded at the end of the strain. By using material that originated prior to Crux 2, Schlußsatz 1(3) exag- gerates the gesture of falling back to approach the final cadence once more, and to some extent, this not only dramatizes the start of Schlußsatz 1(3) but also imparts rhetorical force to the start of Schlußsatz 2(3). (A similar effect in BWV 1068 is discussed in chapter 3.) The reprise from Fortspinnung B furthermore enacts a reversal of the stepwise descent that occurs in strain 1 between statements of the melodic ostinato over the 4ˆ pedal and over the 102 The Art of Gigue

3–ˆ 4–ˆ 5–ˆ 6ˆ tetrachord (mm. 21 and 25 trace b3–a3 whereas mm. 61 and 69 trace d3–e ’ 3). The ascent in strain 2 heightens the rhetoric of closure and the Phrygian inflection of 2ˆ only accentuates the palimpsest effect between Schlußsatz 1(2) and Schlußsatz 1(3). Finally, additional effects of the Phrygian 2ˆ deserve mention. In creating a minor sixth against the open string below, e ’ 3 invokes earlier, important uses of the same interval and double-stop structure (mm. 1 and 18) and it creates a link back to period II and its modulation to G minor. In sum, the chromatic inflection in Schlußsatz 1(3) activates a network of motivic restatement on the cusp of the final cadence, recalling ideas that have been vivid and sustaining earlier in the movement. Bach’s realization of the Closing Complex in the D minor gigue shows that resolution can take myriad forms, and that the turn to cadence in period III need not be concentrated at one point in time. The “moment” of Crux 4 is visited several times here, at mm. 57, 61, 69, and even 73. A picture emerges of the Closing Complex as a program for action which can be accomplished in varied and multifaceted ways. Arguably, closure is well- served by a self-effacing treatment of formal structures during period III, analogous to the techniques of “liquidation” in motivic process: resolution may be less about completing a musical structure than allowing listeners to extricate themselves from the particular ideas which have sustained a movement. With a clever and oblique application of phraseological archetype, the D minor gigue illustrates the general principle that in the end, temporal objects do not stand fully formed; they come undone.

The C minor Gigue Another approach to realization of the Closing Complex is witnessed in the C minor gigue, which presents the turn to cadence in especially pliable form. Of the two minor-mode gigues, the C minor is the one where Bach must adapt the relative major ending of strain 1 into minor for the ending of strain 2. The C minor gigue is unlike the G major and D minor gigues in that Bach does not cycle back over the Schlußsatz functions. Rather, he increases the one Schlußsatz pair beyond normal length, consistent with a similar lengthening of Fortspinnung C. The dimensions of the C minor gigue’s Closing Complex can be seen in Table 2.14 (refer back to p. 96). Although Table 2.14 reveals isolated subphrases of greater-than-normal extent in the Closing Complexes of other gigues, an across-the-board expansion is special to the C minor. Example 2.32 reproduces Schlußsatz 2(2), in which six Œ beats are assigned the cadential progression, i6–Vv–i; this is a unique case in the cello gigues and stylistically unusual. On all fronts, the present Closing Complex is similarly expanded. Fortspinnung C is elongated because it Form 103

BWV 1011 67   ΠΠ Π 
Œ
Œ Œ Œ Example 2.32: The final subphrase, Schlußsatz 2(2), of Bach’s C minor cello gigue. This takes six beats instead of the usual four.

Schlußsatz 1(2) Œ Schlußsatz 2(2) Œ

Π   ΠΠΠ 
Œ
Œ Œ Example 2.33: Hypothetical ending for Bach’s C minor cello gigue. However, the rapid descent from the high register in this re-composition prevents a fully satisfying close. accrues the length of an aborted Schlußsatz 1 subphrase, as in the D minor gigue. Just as before, an arrival on 3ˆ hints at an onset of Schlußsatz 2, per the recomposition in Example 2.33. However, a leap up to c4 rapidly withdraws that implication. A reprise of the proper Schlußsatz 1 material begins, and the onset of Schlußsatz 2(2) is pushed back to the arrival on a lower-register 3.ˆ Given the subsequent elongation of the Schlußsatz subphrases in addition to Fortspinnung C, the accustomed binary regularity of hypermeter in Bach’s cello gigues is brushed aside for the whole of the Closing Complex. Various factors inform the novel “perfection,” to adopt the vocabulary of mensural theory, in the temporal scaling of this module. Some are revealed by asking what, if anything, would have been amiss about simply transposing the Schlußsatz pair from strain 1. Why not exchange E ’ major for C minor, and close strain 2 with another Schlußsatz pair in the usual scaling? Example 2.34 reproduces the relevant passage from strain 1, and compares an exact transposition of that passage with Bach’s actual solution. The hypothetical Schlußsatz 1(2), which matches mm. 63–66 of Bach’s score, hardly arouses suspicion. However, the hypothetical Schlußsatz 2(2) does reveal some difficulties with the translation from major to minor. There may be nothing wrong with the harmonic progression or the melodic line: the hypothetical Schlußsatz 2(2) remains true to Bach’s style. But what is lost in translation is a degree of consonance and resolution. In the original, E ’ major rendition of the passage, I highlight two groups of notes that in aggregate form a bare fifth and a triad of G minor. These are not “harmonic” combinations since they straddle tonics and dominants. Yet their consonance matters, and the minor-mode recasting introduces a dissonant augmented fifth and augmented triad. In isolation the shape of the melody is strong enough to ride out these dissonant formations but the density of dissonance 104 The Art of Gigue

(a) Bach’s Schlußsatz 1(1) Bach’s Schlußsatz 2(1) 17 Œ  Œ Œ Œ

Œ Œ Œ
Πperfect fifth notes of a minor triad

(b) Hypothetical Schlußsatz 1(2) Hypothetical Schlußsatz 2(2) 
Œ  Œ Œ
Œ Œ

Π ΠΠΠaugmented fifth notes of an augmented triad

(c) Bach’s Schlußsatz 1(2) nested reprise of Schlußsatz 1(1) Bach’s Schlußsatz 2(2) 61 Œ
ΠΠΠ

Œ Œ

  Π

69 
Œ Œ

Π ΠΠnotes of augmented triad rearranged

Example 2.34: The end-rhyme in Bach’s C minor gigue: (a) the Schlußsatz pair of strain 1; (b) a hypothetical ending for strain 2 that transposes strain 1 (subject to chromatic inflection); (c) the end of strain 2 as Bach wrote it. Form 105 exceeds what is acceptable going into a final cadence. In the cracks of our usual notion of the succession and vertical composition of harmonies, big changes are wrought by the switch in mode. In Bach’s solution, the dissonances peculiar to the minor mode are variously alleviated and exploited. First, consider the group of notes marked in the locale of the cadential dominant (see mm. 69–70 in Example 2.34), where Bach retains characteristics of a literal major–minor translation but finds them a smoother form. With c3 interpolated and the rhythm changed, the hierarchical interplay of tonic and dominant is made more explicit and the augmented triad recedes from prominence. A similar smoothing of the major–minor translation is evident inthe prior realization of inverted tonic harmony in the melodic span from e ’ 2 to e ’ 3 (mm. 67–69).27 Altogether, Bach’s ending for strain 2 treats dissonance much more carefully than would a direct transposition from strain 1. It certainly makes sense to speak of Bach making “adjustments” here since direct transposition is so entrenched in the genre. Table 2.15 documents the end rhymes across Bach’s six cello gigues. And in all except the C minor we see literal transpositions of the

Table 2.15: End rhymes between strains 1 and 2 in Bach’s six cello gigues.

Rhymed elements Suite FA FB S1 S2 Changes Transp. S1 range Direction Mm.

No. 1 ✔ ✔ none V ñ I d2–b ’3 Ò 9–12 : 25–27, 34 No. 2 ✔ ✔ small a v ñ i c2–f4 Ó 25–32 : 61–68 g ✔ small b d3–e4 Ó 21–24 : 69–72 No. 3 ✔ ✔ ✔ small c V ñ I g2–g4 Ó Ò Ó 33–48 : 93–108 No. 4 ✔ ✔ none V ñ I f2–d4 Ó Ò Ó 7–10 : 39–42 No. 5 ✔ ✔ substantial d III ñ i e ’2–e ’4 Ó 15–24 : 61–72 e 2 4 No. 6 ✔ small V ñ I e –a Ó 9–16 : 57–64 ✔ ✔ small f c~2–a4 Ò 25–28 : 65–68 a. Double stop is broken in bar 65; f2 is 8va in bar 66. b. Scale degree 2ˆ is flattened in bars 69–71; altered in bar 72. c. Altered in bars 100 and 104. d. Expanded and altered in bars 67–70. e. Chord is adjusted in bar 57; altered in bar 59 and from last note of bar 64. f. Altered in bar 68 (a2Ña4 becomes d4Ñd2). g. Final barline is at bar 76. Otherwise all end rhymes are flush with the final barline.

27. BWV 995, the lute version of BWV 1011, makes explicit that mm. 67–69 are a prolongation of i6. 106 The Art of Gigue

Schlußsatz pair from one strain to the other, from dominant to tonic. Even if the hypothetical transposition in Example 2.34 is too dissonant for a compositionally viable ending, it reflects a pertinent expectation on the listener’s part. Dissonance treatment is not the only reason for the C minor gigue’s lengthening of Schlußsatz 2(2). Since it forms a phraseological pair with Schlußsatz 1(2), Schlußsatz 2(2) is also under pressure to match its prede- cessor’s own expansive initiative.28 Schlußsatz 1(2) is long because it offers a full reprise of precadential material that formerly extended back into the metric terrain of Fortspinnung B. The material in question is a chain of descending thirds, highlighted in the score in Example 2.35. As marked, the thirds chain begins concurrently with the tonic arrival of the ascending sequence that constitutes Fortspinnung AB and thus before Crux 2, which is consequently mitigated.29 But period III presents changed circumstances: Schlußsatz 1 follows a half cadence and the whole chain of descending thirds is repackaged as one metric entity. Why this material requires six, not four bars in the first place can be attributed to the number of notes traversed in the middleground. Carl Schachter and William Rothstein advance this as a recurring explanation for unusual phrase lengths.30 Here, six descending thirds are traversed from c4 (the point of departure) to e ’ 2 (the point of arrival at Crux 4). Quite plausibly, the prior descent of f4–d4–b3–g3 elicits an expectation of one descending third per bar that Schlußsatz 2(2) satisfies on some level, even though the internal distribution is irregular.31 The temporal expansion to the C minor gigue’s Closing Complex also connects, I would suggest, to subtle rhetorical concerns of the whole movement and to the rhythmic ethos of the French sautillant figure ( Z Z Z ). As discussed in chapter 1, four of Bach’s thirty-four gigues are French gigues and all are in minor. In these movements, the sautillant figure prevails to varying degrees. In BWV 823, it abates only at the three authentic cadences. In BWV 813, it is pervasive in all but six bars, and it even straddles

28. In period III of the G major gigue, the secondary Schlußsatz pair is metrically imbalanced, but this is an addendum to the primary Schlußsatz pair, which is balanced. This situation presents the one, weak exception to the rule of metrically balanced Schlußsatz pairs.

29. Concerning the approach to the high e ’4 in mm. 14–15, notice the brilliant motivic 3 3 ’3
3 4 ’4 connection back to mm. 1–2: f –d –e ( q q q ) becomes f –d –e . 30. See Rothstein, Phrase Rhythm in Tonal Music, p. 34.

31. Note that downward thirds are the appointed motion for Schlußsatz 1 in the D major gigue as well (whereas the others use upward steps). The D major gigue skips over 5ˆ in the approach to 3,ˆ so as not to pre-empt the dominant of the ensuing I6–V–I cadence. Form 107

BWV 1011 Vordersatz 1 Vordersatz 2 Fortspinnung AB q
q q q
q   3
q q q
q q q q
q q q q
q q
q q q q q
q q q   8  q q q
q q q
q q Schlußsatz 1(1) Schlußsatz 2(1) 11


q q
q q q q q q q
q

q   q
q q q q
q q q q q q q q q q q
q q
q   q q q q q q
q descending thirds Forephrase 23
q
q q
q qq
q qq
q q
q q qq  
q

q q q q q
q q
q q q q   q q q  q Afterphrase Period III: Fonte 33 q q
q q q q
q q q   q q
q q
q q  q q
q q
q q
q q   q q q q
Fortspinnung C 42 
q q q
q
q q
q
q   q q qq q
q q
q q q
q q q
qq q q q
q q q q q   q q q Schlußsatz 1?  Schlußsatz 1(2) 52 q q 
q
q
q q q q
q
q q
q q q q
q q q q
q q   q
q q q
q q q q q    Schlußsatz 2(2) 63
q    q q qq q
q
q q q
q q
q q
  q q
q q q
qq
q
q q q
q q q q Example 2.35: Bach’s C minor cello gigue (BWV 1011). Annotated. 108 The Art of Gigue the repeats since the upbeat pattern for strains and periods is q q . In BWV 831—which has the same upbeat pattern as BWV 813—the figure is again pervasive, occasionally in the form q q q q q q or q q q q q ); it eludes just three bars during period III. In the C minor cello gigue, the sautillant is less dominant though it remains the favorite bar-rhythm by a factor of three to two; include its close cousin, q q q q , and the prevalence rises to seven to one. Compared to the non-French cello gigues, therefore, the C minor gigue has a uniform rhythmic surface. (The D minor gigue offers an especially striking contrast.) The sautillant figure has a paradoxical quality. On the one hand, it is always moving forward, with an anacrusic aspect that is brought out especially in BWV 813 and BWV 831. On the other hand, there is something tenacious about this figure: the downbeats seem to hold on almost jealously to their afterbeats. This creates an ambiguity of thesic and anacrusic interpretations, that is, of parsings aligned or misaligned with the barlines. Affects of poise and agitation, or dignity and restlessness, are present at the same time, and the C minor cello gigue cultivates these qualities more widely in the phrase rhythm of period III as well. The dilute metricity of the expanded Schlußsatz subphrases makes them both stiller and more unsettled then their quadratic models. When the first note of the sautillant is lengthened, as in q q q q , the paradox of poise and agitation in the rhythmic figure is amplified. And as a whole, the Schlußsatz pair exaggerates the same quality. The same paradox percolates Fortspinnung C, where it is encapsulated by the use of trills. Trills accentuate the line e ’ 4–e6 4–f4, which culminates a melodic ascent begun at the start of period III. Concurrent with this ascent is a rhythmic narrowing from four-bar spans in the Fonte, to two-bar spans in the rising sequence of mm. 48–52, to bar-for-bar motivic repetition in mm. 53–54. The arrival on f4 represents the vanishing point of an exponential contraction. In an exaggerated retelling of m. 15 (mm. 49–56 are a variation of mm. 9–15), the trills at mm. 55–57 express the fraught condition of un- motion ahead of a move back to the safety of a conventional half cadence at m. 59.32 A valuable comparison to period III of the C minor cello gigue is found in period III of the gigue from the C minor French Suite, BWV 813, one of the French gigues just cited. The two periods begin in similar fashion but

32. The C minor cello gigue is a remarkable lesson in pitch retention between the two strains. Despite the transposition which applies to the reprise of the Answering Complex as the Closing Complex, many features of strain 1 return at pitch. The high e ’4 of mm. 15 and 55 is but one example. Also, c4 recurs in the hypermetrically strong positions of mm. 17 and 61; and the nexus a ’3–f3–g3 from mm. 21–22 recurs as f3–a ’3–g3 in mm. 68–69. Form 109 with a very different outcome. (See the supplementary volume for the score of BWV 813.) At the start of period III, the keyboard gigue closely parallels the form of the cello gigue by presenting first a Fonte in mm. 57–64 (with the typical harmonic progression for minor keys, Vv/iv–iv–V/III–III) and second an ascending sequence with a6 4 and b6 4 prominent in mm. 65–68. However, the events from m. 69 in the keyboard gigue and m. 53 in the cello gigue are starkly different. While the cello gigue follows A6 and B 6 with the upward scale toward F, the keyboard gigue outlines c5–d ’ 5–b6 4 6 4 in mm. 69–72, supported by the progression VI– ’II –Vv 2. Then, while the cello gigue moves to Vv, the keyboard gigue already makes a first attempt at Schlußsatz 2 in mm. 73–76. Parallel to the cello gigue’s forthcoming, elongated Schlußsatz pair, the keyboard gigue makes its second pass at the 3 4 same functions. On this attempt, the bass no longer gets stuck on f (c.f. Vv 2), and the melody rises to d 6 5 instead of d ’ 5, permitting a smooth approach to the cadential action of e ’ 5–d5–c5 (3–ˆ 2–ˆ 1ˆ ). The keyboard gigue represents the qualities of agitation and poise in a different way, playing on the frisson written into the Z Z Z figure by way of its snatched sixteenth-note. First, there is a rushed, premature cadence—notice the runs of sixteenth notes in anticipation—then a calmer attempt in which the piece regains its melodic and rhythmic composure. Bach’s use of triple hypermeter in the C minor cello gigue also invites a more systematic rationale. Little and Jenne suggest that the descending thirds material of Schlußsatz 1 represents the sautillant figure hypermetri- q q q q q q q
Z Z Z cally: they see in q q something like



 L , i.e. amplified.33 Although I disagree with some of Little’s and Jenne’s comments on the hypermeter of the C minor gigue (their comments are brief but raise contentious issues), the observation of a rhythmic augmentation is well taken. That observation adds another layer of explanation for the six-bar length of the descending thirds material of Schlußsatz 1, which in Little’s and Jenne’s reading comprises two triple hypermeasures. The factor of three is as vividly represented in the rhythmic organization as the interval of a third is in the pitch structure. Example 2.36 illustrates the C minor gigue’s reliance on melodic inter- vals of a descending third with a modest reduction of the movement’s outer periods. Brackets below the staff indicate chains of descending thirds and ascending sixths plus some isolated instances. The movement is preoccupied with the third in various ways. First, the beginning and ending pitches of the aforementioned descending lines in mm. 15–21 and 61–67 describe the root and mediant of each local tonic, spreadeagled between the extremes of register. Together, Schlußsatz 1(1) and Schlußsatz 1(2) therefore stake

33. Little and Jenne, Dance and the Music of J. S. Bach, pp. 152–153. 110 The Art of Gigue

BWV 1011 Period I: Fortspinnung q q  q q  q q q q q q  q q q q q q q q q 
q q

Schlußsatz 1(1) Schlußsatz 2(1) [Period II] 15 q q q q  q q  q q  q q q 
q q q

Period III: Fortspinnung 41 q

q q
q
q q q

q q q q q q q q q   q q q q q q  q q
q  



Schlußsatz 1(2) Schlußsatz 2(2) 57 q q  q q q q q q q   q q q q q  q q
q q   q q q q  q q

q q Example 2.36: Chains of descending and ascending thirds in periods I and III of Bach’s C minor cello gigue.

out both thirds in the C minor triad, given that the interval of transposition is itself a descending third. Turning from large to small musical events, the descending third also figures frequently as the interval between the offbeats of the sautillant motive. All such descending thirds are minor, since whenever the offbeats outline a descending major third, the interval is bridged by a passing tone and the basic sautillant figure is replaced by the rhythm, q q q q . For a movement dominated by descending thirds, it is significant, finally, that Schlußsatz 2(2) opens with a rapid accumulation of five ascending thirds from e ’ 2 through a ’ 3, outlining the most dissonant of tertian sonorities in Bach’s harmonic practice. This sallying dissonance inverts the accustomed cascade of descending thirds. It also encircles the tonic triad in its original, moderate register, preparing the terminal Vv–i progression. It is an agent of resolution in both respects, and a kind of escape mechanism from a melodic procedure that typically is available for Schlußsatz 1 function, but that permeates the whole of the C minor gigue.

The E ’ major Gigue Earlier, we saw how in the D major gigue special emphasis attaches to the act of beginning and the form of strain 1 is front-weighted. The moment of opening-out (Crux 1) is enormously assured but the turn to cadence (Crux 2) pales by comparison. In the E ’ major gigue the opposite imbalance applies and the emphasis is on ending: the opening-out never properly Form 111

transpires and the turn to cadence dominates. In fact, the E ’ major gigue contains the unique case of a formal crux being suppressed. Lacking a sequential passage altogether, period I omits the usual strong turn to Fortspinnung. Like in the D minor and C minor gigues, the negotiation of a vital “moment” is complicated, but now the act of articulation is not serialized or finessed but negated. The E ’ major gigue’s uniform rhythmic surface and unbroken monophony make an interesting environment for such an experiment in metric perception and formal comprehension. The following analysis examines the suppression of Crux 1 and its connection to later events during strain 2. The unusual turn of events occurs in mm. 3–6 (see Example 2.37). As soon as m. 4’s repetition of m. 3 takes hold, it becomes clear that mm. 3–4 are not going to contain a move to V and that Vordersatz 2 will not materialize in its usual form. Example 2.38 recomposes m. 4 to illustrate what might have been a more conventional approach. But as it is, m. 4 offers no harmonic repose, and mm. 5–6 join with mm. 3–4 as an elaboration on the same pedal tone of e ’ 3. On two counts, this undoes the generic articulation of Crux 1. First, the type of Fortspinnung material contradicts expectations of an Opening Complex. Not being sequential, mm. 3–6 obstruct the usual rhetoric of supplanting the Vordersatz with a harmonically mobile passage. Second, the emergence of a single subphrase through mm. 3–6 prevents an important metric articulation from taking place. Elsewhere, the onset of Vordersatz 2 is preparatory to a more striking departure twice as far into the movement. Here, however, m. 5 defers to m. 3, creating a four-bar hypermeasure at odds with a symmetrical unfolding from the movement’s opening. No later than the downbeat of m. 7, the function of mm. 3–6 as Fortspinnung B is apparent. The conventional opening routine is therefore overtaken by the events of a well-defined Answering Complex. One “answer” in the form of Vordersatz 2 is overwritten by a much larger “answer” that abruptly starts wrapping up a strain which scarcely began. Essentially, the turn to cadence at m. 7 constitutes the movement’s first significant move off tonic harmony, even though the key has by then shifted to the dominant. Nearly all the thematic and harmonic content of strain 1 belongs to the Answering Complex. The negation of the opening-out gesture is a uniquely unsettling departure from the formal scheme of the Bach cello gigue. In the E ’ major gigue, as much as the D major, events in strain 2 are complicit with the bias in strain 1. This movement presents the single case of a rounded binary form in Bach’s cello gigues. (Other gigues to include an element of rounding in period III are the orchestral gigue of BWV 1068 and the late lute gigue of BWV 997.) In part, the reprise that opens period III is recompense for the suppression of the Opening Complex 112 The Art of Gigue

BWV 1010 Vordersatz 1 Vordersatz 2 / latent Fortspinnung B q q q q q q q q q q q q q q q q q q q q q q q q 

12 q q q q q q q q q q q q q q q q q q q q
8 q q Schlußsatz 1(1) 5 q q q q q q q q q q q q 
q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q

q q q q q q Schlußsatz 2(1) Period II: first half 9 q q q q q q q q q q  q q 
q q q q q q q q q q   q q q q q q q q q

q q q q q q q q q   q q

13 q q q q q q q q q 
q q q q q q q q q q q q q q q q q q q q

q q q q q q q

16 q q q q q q q q q q q 
q q q q q q q q q q q q q q q

q q q q q q q q q q Second half 19 q q q q q q q q q q q q q q 
q qq q q q q q qq q qq q q q q q qq q q q q q q q

q q q q q q q

23 q q q q q q  q q q q q 
q q q q q q q q q q qq q q q q q q qq q q q q q q q q qq q q

q q q Period III: reprise  q q q q q q q q q q q q q q q q q q q q q q q q

q q q q q q q q q q q q q q q q q q q q
q q

31 q q q q
q q q q q q q q q
q q q q q q 
q q q q q
q q q q q q
q q q q q q

q q q qq q q q q qq q Fortspinnung C 35  q q q q q q

q q q q q q q
q q q q q q q q q q qq q q q
q q q q q q q q qq q q q q q q q q q q Schlußsatz 1(2) Schlußsatz 2(2) 39 q q q q q q q q q q q q q 

q q q q q q q q q q q q q q q q q q q q q 
q q q q q q q q q q

Example 2.37: Bach’s E ’ major cello gigue (BWV 1010). Annotated. Form 113

 q q q q q q q q q q q q q q q q q q q q

12 q q q q q q q q q q q q q q q q q q q q q q
8 q q

Example 2.38: Recomposed opening of the E ’ major cello gigue, with m. 4 changed to enact a resolution to V. in period I. Moreover, the onset of Fortspinnung C supplies the opening into a broad sequence which period I lacked, its Crux 1-like entrance dramatized by the prior propagation of additional modules in the mold of the faulty Vordersatz 2 (see mm. 31–34). Period II is also engaged in the act of recovery. Period II features returns of Vordersatz 1 in the dominant and the relative that reinforce the movement’s opening material. And the midway articulation of period II’s first half introduces another sequence passage whose onset supplies a surrogate for Crux 1. The two sequence passages in strain 2 are no ordinary examples, either. Sequential repetition is sustained through three full segments in the first passage and four full segments in the second. No other sequence passage in Bach’s gigues maintains its pattern as far as a fifth downbeat, as Fortspinnung C does here. The nearest contender occurs in Bach’s other E ’ major gigue—of the French Suite, BWV 815—where the pattern is broken at the anacrusis to the fifth downbeat. The cello gigue’s remarkably tenacious sequence offers a large prolongation of V that finally establishes a strong dominant position in dialogue with the tonic of mm. 27–28. (So far, Vordersatz 1’s tonic harmony has gone unanswered as part of the undermining of Vordersatz 2.) Late in the binary form, Fortspinnung C thus fulfills a similar function to Fortspinnung A elsewhere, culminating a particular formal narrative in which the “moment” of Crux 1 is initially suppressed but recovered later. Supporting both a commuted Crux 1 at m. 35 and the customary Crux 4 at m. 39, this sequence subphrase is oriented to opening as well as closing, similarly to Fortspinnung AB in the G major and C minor gigues. The formal irregularities of the E ’ major gigue are an appropriate topic on which to conclude an essay on the form of Bach’s cello gigue, since intrinsic factors in the movement are shown to explain its unusual outer dimensions. Since this movement poses a challenge to generalizing the proportions of a Bach cello gigue, for example, it is a significant achievement that the formal model not only accommodates the E ’ major gigue but gains credence through a meaningful engagement with its eccentric aspects. The E ’ major cello gigue is one of only two Bach gigues in which strain 2 is more than twice strain 1’s length—and by a wide margin. It is so because of a peculiar formal narrative, where, paradoxically, the posture of beginning 114 The Art of Gigue must be established with increasing confidence as the movement draws to a close.

Considering Form and Function I will finish this chapter with some thoughts regarding form and function in my model of “the Bach cello gigue.” The current essay began by introducing a notion of four cruxes—moments that articulate fundamental temporal attitudes. The phraseology was subsequently unpacked from these moments and to appreciate what difference that made we can recall Bach’s G major and C minor gigues. These are the movements where strain 1 has a tripartite layout in segments of eight Œ beats: Vordersatz, Fortspinnung, and Schlußsatz. In my reading, each strain consists of an Opening Complex that overlaps an Answering Complex, and thus a double formal function is claimed for the middle, sequential segment of the strain. By reflecting on that double function, the following comments address the musical status of three entities: the two subphrase complexes and the strain as a whole. The formal agency of Crux 1 and Crux 2 in strain 1 is the basis for identifying a double formal function in the subphrase “Fortspinnung AB.” Although the routines of Opening Complex and Answering Complex would be useful observations in any case, for purposes of comparison and ab- straction, the concept of formal cruxes assigns different qualities—not only a different time-frame—to the two modules. The notion of an overlap is therefore more than an analytical convenience. That two, distinct formal functions may be performed with one sequence passage is tied to the presence of two indisputably separate moments of formal articulation. What the sequence passage is to its “exit” juncture stands apart from what it is to its moment of inception. Crux 1 is about hitting a stride, whereas Crux 2 is about relinquishing broad patterns and triangulating closure. This contrary stance of the two junctures is passed to Fortspinnung AB, whose role changes between the two contexts. Crux 1 and Crux 2 are important events, distanced in time, which lay claim to the sequence passage in quite different ways. Coming at it from a metric perspective which chapter 3 elaborates, I suggest that the successive functions of Fortspinnung AB fail to harmonize. While Vordersatz and Fortspinnung are smoothly connected in Crux 1, and Fortspinnung and Schlußsatz are smoothly connected in Crux 2, the two junctures are in themselves incongruous. Strain 1 behaves as two large duple hypermeasures that overlap, not as one large triple hypermeasure. The decisive factor is the particular rapport of the two cruxes, rather than anything that is easy to observe about the content of the subphrases. As explained earlier, Crux 1 and Crux 2 represent the fundamental dichotomy of beginning and ending: they embody opposing attitudes in the formation of musical duration. Thus smooth succession obtains through Vordersatz– Form 115

Fortspinnung and Fortspinnung–Schlußsatz separately, but not all through Vordersatz–Fortspinnung–Schlußsatz. As the highest horizons of metric perception in strain 1 of Bach’s G major and C minor gigues, the overlapping durations of Opening Complex and Answering Complex each have a musical vitality which does not extend to the duration of the whole strain. I contend that to conceive a melodic and harmonic unity of Vordersatz–Fortspinnung–Schlußsatz, one would need to suppress the competition of temporal perspectives—i.e. beginning vs. ending—that makes sense of musical form in the first place. Unlike period II and possibly period III, which both join a formal process already underway, period I cannot be interpreted as a single phrase (or, more neutrally, a “phraseological unit”). The ultimate coherence of strain 1 is therefore experiential and rhythmic in my view; we do not grasp its melodic and harmonic content per se as a homogeneous whole. This is the sense in which I say the Opening Complex and Answering Complex have a more solid standing than the whole strain. The more we locate music’s formedness in the experience of perfor- mance, the more formal analysis is productively estranged from the premise of structural unity otherwise suggested by a “dimensional” concept of musical time. The analytical findings of this chapter demand some method- ological sophistication along these lines: how best can generic models for Bach’s temporal forms be conceived? The Opening Complex and Answering Complex are constituents of strain 1 only in a trivial sense, that they occupy a subset of strain 1’s time-span. Regarding more robust conceptions of musical structure, however, the two modules teeter at the limits of specific melodic and harmonic comprehension: as we consider longer spans of time, it becomes unclear what kinds of comprehension of musical content are available. Formal analysis must wrestle with the question of how our experience of a complete movement relates to our experience of its parts. In this regard, the G major and C minor gigues point us to an important realization. Though forms in themselves, the suphrase complexes of strain 1 are—with respect to the whole—not forms but functions. My suggested blueprint for a “Bach cello gigue” offers a middle-out perspective on compositional method, one that is innately open to being realized in different ways. There are formulaic elements—Bach certainly has a conception of ideal building blocks—but how these should be related and combined is unstable. Bach’s medium-sized structures have fundamental questions hanging over them about what sorts of compositionare possible or necessary in the making of a cello gigue. Formulas are played off against each other in order to problematize and empower creative acts of combi- nation. The collaboration of Opening Complex and Answering Complex, for instance, Bach achieves in at least five quite different solutions. My own 116 The Art of Gigue pastiche attempted yet another. Bach’s gigues for cello are more amenable than any other subset of the corpus to an analyst reconstructing a mold: the form can be defined in fairly specific terms. Nonetheless, we discover a scheme of compositional thought that is productively uncertain and unstable, a scheme in search of the musical coherence that only particular pieces can achieve—and achieve as a quality of embodied experience. By highlighting special moments and characteristic strategies in individual movements, this chapter has illuminated Bach’s creative practice of forming a cello gigue out of design elements whose collective success is anything but assured in advance. 3 Hypermeter

Bach’s gigues include some of the most rhythmically complex music that Bach wrote, and the following chapter is the fruit of grappling with the metrical process of movements ranging from the miniature French and Italian gigues of BWV 823 and BWV 832 to the complex fugal gigues of Clavier-Übung I. Here, I advance arguments about the nature of hypermeter and the nature of hypermetric analysis that are latent in chapter 2’s approach to form, that are also a guiding force behind chapter 4’s approach to schema, and that equip the analyst for important insights into metrical aspects of Bach’s practice. Although most of the chapter is dedicated to presenting theoretical ideas, these ideas originate in detailed study of all thirty-four of Bach’s gigues, and I engage three movements explicitly to demonstrate my ideas’ analytical potential. I divide the chapter into two parts. The first part, which is the majority of the chapter, presents my core argument toward a connective, “middle-out” understanding of metric process; here, I use Bach’s one orchestral gigue as an analytical case study. The second, much shorter part presents two brief analyses of Bach’s two chamber-sonata gigues.

Theorizing Hypermeter in Bach’s Orchestral Gigue

Carl Schachter put it succinctly when he wrote in 1987 that “[m]eter is a problem.”1 Appropriately, the last thirty years have witnessed great strides in the understanding of meter as well as hypermeter (metric organization beyond the level of the bar).2 Yet in this chapter, I argue that there remain fundamental obstacles to metric analysis, the practice of which often exposes

1. Carl Schachter, “Rhythm and Linear Analysis: Aspects of Meter,” ed. Felix Salzer and Carl Schachter, Music Forum VI, no. 1 (1987): 1–59. Quotation from p. 1.

2. Meter studies has developed as an important and self-reflective field of theoretical inquiry since the 1970s. An excellent overview of the literature, covering fifty-two carefully selected citations, is Justin London, “Recent Rhythmic Research in North American Musik Theory,” Zeitschrift der Gesellschaft für Musiktheorie 2, nos. 2–3 (2005): 163–168. Significant contributions to meter studies since 2005 include Justin London, Hearing in Time: Psychological Aspects of Musical Meter, 2nd ed. (New York: Oxford University Press, 2012); Mark J. Butler, Unlocking the Groove: Rhythm, Meter, and Musical 118 The Art of Gigue limitations in metric theory as a source of musical illumination. The main obstacle is that meter happens “in time” or temporally and that (at least partly) metric analysis must happen “in time” as well. Metric theory, for all its advances, has tended not to equip analysts for such a task.

Situating the Analyst Consider the odd predicament of metric analysis, which above all seeks to understand meter’s role in the formation of musical events by engaging critically with those events. Even though today’s theories usually situate meter in the listener (and, as such, are wise to meter’s subjugation to time), metrical “knowledge” is held to operate upon musical structures. In this formulation, the real domain of meter is a cognitive representation of musical content, not the temporal unfolding of music per se. But if metrical “knowledge” does not belong in time, where should an analyst of rhythmic phenomena expect to find it? It’s unclear how a thinking musician can access, introspectively, something that is already a structure of comprehension rather than something innately temporal and gestural. For this reason, the analytical “application” of many metric theories is at risk of a circular logic. The implicit function of many analyses is to establish, in specific cases, the relevance of a concept which is already described or prescribed by theory (and whose general relevance is assumed). This much is not wrong. It is legitimate for analysis to be subordinate to theory, and serve the role of assessing and improving theory by making its claims explicit for specific cases. Yet we should be cautious not to conflate another aim: to illuminate specific cases for the sake of our specific musical interest in them. If analysis is tasked with giving only correct or satisfactory “accounts” of specific cases, according to a chosen theory, it is not clear that analysis should be illuminating to us as musicians, as we hope or claim that it is.

Design in Electronic Dance Music (Bloomington: Indiana University Press, 2006); Scott Murphy, “On Metre in the Rondo of Brahms’s Op. 25,” Music Analysis 26, no. 3 (2007): 323–353; Samuel Ng, “Reinterpreting Metrical Reinterpretation,” Intégral 23 (2009): 121–161; Yonatan Malin, Songs in Motion: Rhythm and Meter in the German Lied, Oxford Studies in Music Theory (New York: Oxford University Press, 2010); Nicole Biamonte, “Formal Functions of Metric Dissonance in Rock Music,” Music Theory Online 20, no. 2 (2014); and, in particular, Danuta Mirka, Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791 (New York: Oxford University Press, 2009). For a concise bibliography of studies in the Schenkerian tradition of rhythm, meter, hypermeter, and phrase rhythm, see David Carson Berry, “Schenkerian Theory in the United States: A Review of Its Establishment and a Survey of Current Research Topics,” Zeitschrift der Gesellschaft für Musiktheorie 2, nos. 2–3 (2005): 101–137. Hypermeter 119

A theory that caters to metric analysis, and is subordinate to analysis, differs from a theory conceived to explain or define meter as a general phenomenon. Although one mode is not necessarily better than the other, there is a choice to be made here, which plays out especially in how time or temporality are conceived. To some extent, the choice has been obscured in scholarship of recent decades by co-opting into the theory-led approach ele- ments of an analysis-led approach (namely, the value placed on illuminating specific cases), but the opposing philosophies persist. Studies that offer a blend of perspectives, and rather successfully, may nonetheless harbor some significant contradictions of aim and approach. Perhaps because analytical traditions have been artfully co-opted into the dominant, theory-led paradigm of meter studies, the possibility for an analysis-led paradigm has escaped us. It is the object of this chapter to explore that possibility whatever the reasons for its neglect. For theory to become an instrument of analysis, the elements of “meter,” as traditionally understood, must be wrestled to the ground of a new intellectual framework. This would be the ground for acknowledging the “in time” or temporal condition of analysis itself. Metric analysis should be empowered by this, to become a genuine school of thought, as opposed to the annex for a given body of theory. Not all scholarship on meter should prioritize analysis, needless to say. But the ideas presented here will be of value to scholars with other priorities too. It is normal for theory-led approaches to meter to embrace spontaneous theoretical innovations in response to empirical observation, for instance, adding refinements that bring theoretical definitions better into line with metrical “intuition.” Scholars whose approach differs from that presented here may, then, be able to respond to some of the following ideas from within their own theories and models of meter, if they find themselves convinced of the musical wisdom of what follows. Both theory-led and analysis-led approaches to meter are “scientific” traditions of sorts, and thus rightly allow for gradual changes and accommodations in our very formulations of the phenomena we are dealing with. Although there is a basic difference between theory-led and analysis-led studies of meter, each may valuably inform the other.

Progress Already Made The kind of theory that would cater to metric analysis (and equip us for the “in time” nature of analysis) has, in part, existed for some years. Christopher F. Hasty’s Meter as Rhythm presents a “projection” theory of meter that, in 120 The Art of Gigue my view, is precisely that, at least so far as pulse is concerned.3 At base, Hasty presents a theory of pulse that is temporalist and that suits well an analysis-led stance on meter studies.4 Although Hasty engages questions of perception and juggles multiple perspectives, his main position stands in clear contrast to more cognitive approaches which typically subordinate analysis to theory. His theory implicitly empowers analysis by locating “the metrical” in the unfolding of musical actions themselves (rather than in a listener’s cognitive representations of sounding structure). And when metrical knowledge is situated in time—if “knowledge” is still the right word—then meter becomes something whose susceptibility to analysis we can readily understand. Meter becomes an aspect of rhythmic experience that we can get a handle on analytically, something different from an intu- ition of rhythmic structure that stands at arm’s length to music’s temporal condition. Yet by asserting that Meter as Rhythm already situates “the metrical” in the unfolding of musical actions, I get ahead of my argument, and use Hasty’s language rather than my own. To my mind, Meter as Rhythm offers a temporalist theory of pulse; not yet a temporalist theory of meter. But how can this be? The logic which Hasty sets in motion leads, I believe, to the repudiation of an entrenched thesis in modern metric theory, namely, the thesis that meter is adequately explained or described as a multiplicity of interlocking pulses. Meter is pulse in the plural; this is the reigning orthodoxy. But my findings, in pursuit of an analysis-led approach to meter, say otherwise. A temporalist theory of meter boils down to a theory of durational hierarchy that is different from that found either in traditional ontologies of meter or in Hasty’s “projection” theory. As I see it, Meter as Rhythm initiates a critique of the logical primacy of pulse in metric theory, yet still ascribes (implicitly) to that philosophy. If I am right that this residual traditional element presents significant obstacles to metric analysis, then, ironically, it may be the very axiom which Hasty shares with Justin London and other cognitively oriented theorists that has made Meter as Rhythm and its temporalist insights hard to digest for the field of meter studies.5

3. Christopher F. Hasty, Meter as Rhythm (New York: Oxford University Press, 1997).

4. The Merriam-Webster Dictionary defines temporalism as “a philosophical doctrine that emphasizes the ultimate reality of time and temporal things as contrasted with doctrines which reduce the temporal to a manifestation of the eternal.”

5. London, Hearing in Time: Psychological Aspects of Musical Meter is the pre-eminent modern study of meter from a cognitive and psychological perspective. For London’s review of Hasty and Hasty’s reply see Justin London, “Hasty’s Dichotomy,” Review of Christopher Hasty, Meter as Rhythm, Music Theory Spectrum 21, no. 2 (Autumn, Hypermeter 121

Some inkling of this chapter’s temporalist turn can be given as follows. In the context of analyzing metrical organization above the level of the bar, I find it largely untenable to theorize meter as consisting of the awareness of multiple pulse-periodicities; I find instead that metric theory must treat as foundational a class of rhythmic events that already embody the hierarchical principle. In other words, I conclude that simple pulse or pulse-periodicity has surprisingly poor credentials as a parameter for metric analysis, and I suggest that we direct our attention to more innately hierarchical or qualitative events. Metric analysis for analysis’ sake must, I think, mean attending to already-metric events. And in large part, the thrust of this logic is that we should be attending to various qualities of “continuation” (in Hasty’s language) or “weak beat,” in traditional terms.6 In a nutshell, this chapter sets out to achieve for traditional notions of meter what Hasty’s seminal exposition of “projection” theory achieves for the traditional notion of pulse, namely, formulating a theory that caters to analysis by locating meter in the unfolding of musical actions themselves. Given that Meter as Rhythm is known as a difficult book, however, it is worth mentioning that the following extension of Hasty’s work does not bring added difficulties. Rather, it simplifies matters by focusing on the theoretical core of Meter as Rhythm and working out some of the logical problems which the book’s arguments raise for metric analysis. Crucially, I shall be developing just one of Hasty’s objectives, the ontology of metric experience; I will not confuse that issue, as Meter as Rhythm certainly did for some readers and reviewers,7 by developing a body of observations about the likely metric perceptions occasioned by certain rhythmic events, or by addressing metric theory in terms of event formation.8 As a result, those ideas which are extended by the present

1999): 260–274; Christopher F. Hasty, “Just in Time for More Dichotomies—A Hasty Response,” Music Theory Spectrum 21, no. 2 (Autumn, 1999): 275–293.

6. It is worth mentioning that in some repertories (though not Bach’s gigues), the parsing of “strong” and “weak” beats at the level of meter is a complex issue. See William Rothstein, “National Metrical Types in Music of the Eighteenth and Early Nineteenth Centuries,” in Communication in Eighteenth-Century Music, ed. Danuta Mirka and Kofi Agawu (Cambridge: Cambridge University Press, 2008), 112–159.

7. Significant reviews of Meter as Rhythm are cited in the following paragraph.

8. The following illustrates Hasty’s interest in perception (Meter as Rhythm, 91): “My arguments thus far have been intended to support a claim that, given a relatively modest degree of attentiveness and in the absence of any competing durational relevancies, two immediately successive events begun with sound will necessarily result in projection if the first event is mensurally determinate and the duration of the second sound is not greater than that of the first event.” 122 The Art of Gigue work should be clarified. One might summarize the reception of Meter as Rhythm by saying that many readers have found the basic idea of “projection” compelling but the implications for metric analysis have proved perplexing.9 But a temporalist theory of meter need not involve impossible complexities. By teasing out the temporalist methodology at the core of Hasty’s work, and working out its logical ramifications, I hope to sketch a theoretical framework that supplies metric analysis with clear questions and ways of answering them.

The Temporalist View of Pulse Even though I argue that meter cannot be explained or described temporally as a multiplicity of interlocking pulses, a temporalist theory of pulse is nonetheless the appropriate springboard for a temporalist theory of meter. Hasty’s “projection” theory is precisely that theory of pulse, and in this section I introduce its most important features.10 Simply speaking, “projection” means the process of reproducing metri- cal durations. In Example 3.1, for instance, duration B reproduces duration A. Thus, in Hasty’s language, duration A is “projective for” B. This means that duration B proceeds as a sort of repetition of duration A. Borrowing from ordinary English, we might say that duration A “is the measure of” duration B. That said, this relationship is better expressed in more processual terms: duration A becomes projective for duration B, or duration A becomes the measure of B. It is important to appreciate that “projection” does not refer to an arrangement of consecutive durations in a sounding structure or in a lis- tener’s cognitive representation of a sounding structure; rather, it refers

9. Arnold Whittall writes that: “He [Hasty] is suggesting that an essential shift from reflection on something that has ‘become’ to something that is in the process of ‘becoming’ . . . is a valuable and desirable phenomenon—even though the problems this creates for the craft of writing about musical compositions in a theoretically informed manner are considerable.” Arnold Whittall, Review of Christopher Hasty, Meter as Rhythm, Journal of Music Theory 43, no. 2 (Autumn 1999): 359–371, p. 360.

10. The following are notable reviews of Hasty’s book: Nicholas Cook, Review of Christopher Hasty, Meter as Rhythm, Music & Letters 80, no. 4 (1999): 606–608; Gretchen Horlacher, Review of Christopher Hasty, Meter as Rhythm, Intégral 11 (1997): 181–190; London, “Hasty’s Dichotomy”; John Roeder, Review of Christopher Hasty, Meter as Rhythm, Music Theory Online 4, no. 4 (1998); Joseph P. Swain, “Shifting Metre,” Review of Christopher Hasty, Meter as Rhythm, Music Analysis 20, no. 1 (2001): 119–141; and Whittall, Review of Christopher Hasty, Meter as Rhythm. See also Hasty’s reply to London: Hasty, “Just in Time for More Dichotomies—A Hasty Response.” I do not make explicit reference to these reviews, for the most part, but all offer valuable perspectives on Hasty, some complementing and some contradicting the points made in this section. Hypermeter 123

BWV 1068  À  6 q q  q q q q q q q q  8 q  q q q q q q q q q q q q q q q q q q q 1   6 q q q q q q q 8


q Duration A

5 À  q   q q q q q q q q q q q q q q 
q q   q 1  q q q q q q q q q q q q q q q

q q q  Duration B

Example 3.1: Example of projection in Bach’s orchestral gigue (BWV 1068), mm. 1–8. to the act or conviction of repetition. Hence, duration A is “projective for” duration B only while the latter is current in musical performance. And so, in principle—that is, in the absence of complicating factors—the thing or event we describe as “the projection” does not exist before duration B begins nor after it ends. The theoretical consequences of this statement must be clearly spelled out. It means that “the projection” is an event whose temporal footprint is (though often similar to duration B) distinct from either or both of duration A and duration B. These durations are affiliated to what I will call the “projection-event” but are not its constituent parts. One possible misreading of statements about the temporal contingency of projection must be forestalled. To stress that projection-events do not exist “outside the moment” (so to speak) is not to say that analysis is hopeless and that we can only marvel at meter as it is happening. Projection theory presents no direct critique to comprehensive accounts of rhythmic structure. On the contrary, any projection—however fleeting—is written into a bigger picture, regardless of whether one paints the larger situation as “process” or “structure.” The important point is that the domain of meter (either metric process or metric structure) is temporal experience per se and not an objective timing of musical events or musical experiences. This needs to be said because the precise theoretical implications of the “projection” idea have sometimes got lost amid the reception of Meter as Rhythm as a book that champions the ineffable qualities of music (which, 124 The Art of Gigue admittedly, it does).11 Consider, for example, Justin London’s insisting that, “[t]emporal processes qua processes have a structure to them.” (London 1999, 271). London implies, here, that if Hasty’s intellectual preoccupation with music’s ineffable qualities were set aside, the “projection” idea would readily assimilate with structural paradigms much closer to London’s own cognitively oriented studies of meter. But “projection” theory is not just an impassioned retelling of traditional models, as the above distinction between the temporality of the “projection-event” and its pertinent durations makes clear. The claims concerning the temporality of projective process and its pertinent durations are, in fact, not always easy to discern in Hasty’s original telling and are worth reviewing. In places, Meter as Rhythm is substantially occupied with explaining or describing discrete projection-events in service of the general ontology of metric process. In that strand of Hasty’s argument, it is sometimes true that the elements of projection are examined in a kind of “frozen” state that recalls the same structural conceptions of rhythm that Hasty renounces. Yet it is critically important that we recognize for any given projection-event that the various “moments” are not attributed to the linear unfolding of time. Thus, the beginning of duration A is not being posited as an action that really happens prior to the beginning of duration B. These are, rather, elements of the projection-event that co-exist, “moments” that embody at once the distinct temporalities of past and present, or (in more complex situations) present and future. The whole point about projection is that a just-completed duration stands “behind” the current duration, or that a soon-to-be-completed duration is going to be superceded or “overwritten” by the coming duration. By definition, then, the beginning of A is made known at the same time as the beginning of B is made known. And we should be able to specify, in particular instances, when this occurs; perhaps most often, we become conscious of a projection-event at the point in time that duration B actually begins. It is, though, possible to examine what a projection-event is from a linear viewpoint too, and it is as well to realize that Hasty does this a fair amount. The various “moments” in a single projection-event may be subject to a kind of narration in that context. But any such narration must be received with caution, and, for current purposes, should not be taken literally. If I am right that a temporalist approach to meter must ultimately place theory in the service of analysis, then the “succession” in a projection-event is

11. See, in particular, Whittall, Review of Christopher Hasty, Meter as Rhythm. The following is an example of a passage from Meter as Rhythm (p. 12) which speaks to music’s ineffable qualities: “Rhythm is in this way evanescent: it can be ‘grasped’ but not held fast. As an aspect of experience, the rhythmic is not captured by analysis and measurement.” Hypermeter 125 unequivocally heuristic. The relation of Hasty’s “projective potential” to his “projected potential” is not a chronological relation. That said, it would misrepresent Meter as Rhythm—and ignore a major source of confusion for readers and reviewers—to characterize as purely heuristic Hasty’s own narrative treatments of the projection-event. As well as offering an ontology of meter in a fairly abstract and philosophical vein, Meter as Rhythm has another, quite different side to it, namely, a substantial exploration of metric perception. In line with prior work in the field of “rhythm and meter,” Hasty does attempt to explain how metric perceptions arise with respect to rhythmic events. And in this quite different strand of Hasty’s argument, the “succession” in a projection-event is altogether more real. For many readers, Hasty’s narratives of the formation of projective and projected potentials will have been a prominent aspect of Meter as Rhythm, regardless of whether they welcomed them or not. But it would be unfortunate if the logical core of the projection idea were eclipsed by Hasty’s parallel attempt to promote a temporalist perspective in the study of metric perception. Hasty’s ontology of meter is really not at all continuous with his discussion of how metric perceptions arise in response to rhythmic events; he may weave the two strands of argument together, but if we are going to pursue them further, they must be untangled. That two quite different arguments are going on concurrently is seen most vividly in Hasty’s notion of “indefinite projective potential,” an idea which only makes sense in the context of the rhythm–meter perception argument. “Indefinite projective potential” describes a listener’s awareness of the duration of an initial event. It points to their awareness of a duration whose specific size is not yet known but that promises to become specific and lend itself to reproduction. This notion would be a valuable element, to be sure, in a temporalist account of how durations are formed and how meter is created. Yet, “indefinite projective potential” is emphatically not consistent with the other strand to Hasty’s argument, the basic ontology of projection. This important distinction is worth rehearsing. In Hasty’s account of meter’s emergence in the rhythmic field, “indefinite projective potential” precedes chronologically the full emergence of projection. The notion makes a certain sense, not least because the emergence of definite potentials is a change in circumstances that does not happen instantaneously and cannot be cut off from is surroundings. However, for Hasty’s ontology of projection, where an “indefinite” potential is logically too, the notion of “indefinite projective potential” has no real merit. In logical terms, an “indefinite” duration might belong to a phenomenal world of which the “metrical” is a subset, but, as it stands, an “indefinite” duration is not metrical and should remain exterior to the basic ontology of meter. 126 The Art of Gigue

The sharp distinction I draw between Hasty’s basic ontology of meter and his account of metric experience does no violence to either philosophy, but allows us to isolate what the lessons of Meter as Rhythm are for the current purpose of theorizing meter with an eye to analysis. The conclusion of four paragraphs ago can therefore be restated, with the added acknowledg- ment that I am narrowing Hasty’s argument: although various “moments” can be distinguished within a single projection event—chiefly the beginnings of the two durations—these should not be attributed to successive points in time; not in the temporal experience of a listener nor in the chronology of sounding structure. If we commit to a stable philosophical or “scientific” position, it becomes clear how projection ought to be construed temporally. Since one’s choice of theoretical ends thoroughly affects what mechanisms, models, and philosophies are right to use, let me repeat what the aims of an analysis-led approach to theorizing meter are. The purpose here is to equip us with a deep understanding of meter for our own interpretive ends. For that reason, we will consider the nature of meter but set aside the issue of how meter emerges from the field of musical activity in general. Hence many questions central to the “rhythm and meter” literature can be sidelined; it is not the current task to explain or describe listeners’ perceptions of meter for a given (rhythmic) stimulus. In light of these commitments, the temporal implications of “pro- jection” can be settled in the following five key points. First: “the metrical” in a musical passage or movement is a projective process that can be resolved into multiple projection-events, which occur at various stages in time, both successively and concurrently with one another. Second: each projection-event embodies a temporal duality of, in Hasty’s language, the “projective” and the “projected.” This is a duality of adjacent temporal positions: past and present, or (this, the more complex situation) present and future. But the projection-event itself is not composed of two parts in succession: projection is the feeling—act or conviction—of reproducing a metric duration, and the time during which this feeling occurs is something else from the temporal span of either or both of the pertinent durations. Third: two similar durations or durational potentials are the focus of each projection-event, namely (in Hasty’s language) the “projective potential” and the “projected potential.” These are understood in direct relation to the sounding structure as it has unfolded, is unfolding, and may continue to unfold. But these durations are not inscribed in or related to us by the linear unfolding sound itself. The claim is not that we “hear” one and then the other. To put it curtly, projection is not a function of succession. Hypermeter 127

Fourth: we might, nonetheless, distinguish two phases for the projection-event: a “prospective phase,” during which the sounding music is that of the projective potential, and an “active phase,” during which the sounding music is that of the projected potential. (These terms are mine.) It is worth observing that projection-events routinely commence in the active phase, and do not include a prospective phase. Fifth and finally: it should be emphasized that projection essentially refers to a feeling of repetition or reproduction. Indeed, logic dictates that, in the abstract, a given projection emerges as the repetition or reproduction of a metric duration is initiated. In principle, therefore, it is normal for the projection-event to begin and end concurrently with what Hasty calls “the realization of projected potential.” Even when the situation is more complex, the focus of the projection-event is the becoming of the projected duration. And when we factor in the front-weighted nature of metric duration in musical experience, it becomes clear that projective process is anchored in our marking the onset of the projected duration. “Beginning again” or “starting over” is the basic fact of metric process as projection theory conceives it.

An Illustration: BWV 1068 I now offer an analysis of Bach’s sole orchestral gigue (from BWV 1068) to illustrate the temporalist view on pulsed phenomena. My frame of reference here and throughout the chapter will be levels of pulse and durational periodicity that extend upward from the “tactus” (as Justin London defines it) to periodicities of no more than sixteen tactus beats at a time.12 Hypermeter, in a word, is my core concern, although metric processes on a par with the notated meter are also of interest.

Frame of Reference At the upper limit of the metric hierarchy, the periodicities I discuss are always attested by analysis on a case-by-case basis, in line with both tempo- ralist theory and my commitment to an analysis-led approach to meter. I have not observed in Bach’s gigues periodicities of more than sixteen tactus beats, nor singular metric units of more than forty-eight tactus beats, so hypermeter stops there as far as I am concerned. Of course, periodicities of sixteen tactus beats may already sound improbably large, but I have yet to explain what my observations involve and what my claims about metric experience are. As for setting a lower limit on meter, my reasons for not

12. London, Hearing in Time: Psychological Aspects of Musical Meter, pp. 15–17. 128 The Art of Gigue addressing pulse levels smaller than the tactus are twofold. First, there is no significant need of new models or new methods to understand Bach’s rhythm at the sub-tactus level. Second, “projection” theory seems, to me, a poor match for understanding rapid patterns of regular accentuation given the sensitivity to durational qualities that it posits of the listener and demands of the analyst.

Dot Diagrams Adopting a method of representation that is not at all temporalist to begin with, the metric structure of BWV 1068’s gigue is laid out in Example 3.2. This is a dot diagram in the manner of Lerdahl and Jackendoff.13 Lerdahl and Jackendoff make explicit that such diagrams equip us to portray one “final-state analysis” of the relevant piece or passage. They are not used to convey anything about the experience, through time, of the music in question. Moreover, only by ad hoc annotations, such as brackets, are evolv- ing metric situations marshaled to an (almost) single view of the structure where contradictions such as overlaps occur. The interventions of brackets etc., effectively allow more than one “final-state analysis” to co-habit in one diagram, with the number of observation points being determined by the number of disruptions to the metric grid. Yet such remedies do not make for an account of metric process. Lerdahl and Jackendoff see these diagrams as representing a competent listener’s understanding or assimilation of what they have just heard in terms of a hierarchical metric concept. It is open to question whether each “final-state analysis” has a purview that extends back indefinitely, or only as far as the beginning of the current metric state. But if a dot diagram does no more than illustrate a succession of metric hierarchies with all the benefits of hindsight, and largely conflating the cognition of meter with the application of metric concepts to already completed musical events, it nonetheless is an efficient way to grasp the compositional profile of metric events.

Continuity and Change in Metric Levels

In the gigue of BWV 1068, the tactus is maintained throughout. The pe- 6 riodicity of the notated 8 bar is also consistently maintained (which it is 12 not in all 8 gigues, for example) and this is the lowest level of structure represented in Example 3.2. The metric structure becomes more interest- ing—from the dot diagram point of view—at the next largest level of pulse or pulse-periodicity, namely, the level of 2-bar hypermeasures. Regarding

13. Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA: MIT Press, 1983). The first dot diagram appears on p. 19. Hypermeter 129

Example 3.2: A metric dot diagram of the orchestral gigue. 130 The Art of Gigue terminology, this chapter adopts Hasty’s use of “bar” for the length of the notated measure, yet follows common practice by referring to units above the level of the bar as “hypermeasures.”14 My text will distinguish hypermeter two, three, or more levels superior to the notated meter by prefixing a superscript to the word “hypermeter,” so that 2hypermeter refers to second-order hypermeter, 3hypermeter to third-order hypermeter, and so on.15 Note that despite the described usage of “bar,” the abbreviations “m.” and “mm.” are retained for measure numbers. The basic hypermeter in BWV 1068 is the smallest level at which meter is in flux. Although a sense of 2-bar units is ubiquitous, the phase of this pulse-periodicity switches between “odd–even” groupings (in terms of bar numbers) and “even–odd” groupings. In connection with these switches of phase in the hypermeter, a concept of “metric scenes” becomes useful. The switches of phase just described articulate the onset and cessation of distinct metric scenes. A metric scene can be defined as the smooth unfolding of a single metric hierarchy or metric type. (This chapter usually avoids the prevalent term “metric state” as it can be confusing whether “state” refers directly to hierarchical structure or to a passage of music that demonstrates hierarchical structure.) The musical actions that take place during a metric scene will roughly have the property of metrical well-formedness as described by Lerdahl and Jackendoff. So what is the correlation of metric scenes and metric types? Whereas a change of metric type—e.g. to triple hypermeter from duple—will always imply a new metric scene, a new metric scene can be articulated without altering the metric type. In BWV 1068, the 1hypermeter is invariably duple, like the meter proper, but a succession of distinct metric scenes is created by switches of phase to “even–odd” grouping and back again. The gigue of BWV 1068 is cast in three periods, like the cello gigues, and it shares, in large part, those pieces’ approach to phrase rhythm. Both in period I and in period III, there is a shift to an even–odd phase of the duple hypermeter and back again. No such shift occurs in period II, however, underscoring the conclusion of chapter 2 that period II assumes an air of symmetry and balance. In period I, the shift to an even–odd phase is

14. The term “hypermeter” was apparently coined in Edward T. Cone, Musical Form and Musical Performance (New York: Norton, 1968), specifically in Cone’s third essay (the second essay introduces “hypermeasure”). One of the significant discussions of Cone’s ideas is David H. Smyth, “Patterning Beyond Hypermeter,” College Music Symposium 32 (1992): 79–98.

15. This shorthand is similar to one employed by Alan Dodson. See Alan Dodson, “Performance and Hypermetric Transformation: An Extension of the Lerdahl–Jackendoff Theory,” Music Theory Online 8, no. 1 (2002). Hypermeter 131 brief and applies to the subphrase previously referred to as Fortspinnung B. This is the eight-beat subphrase—here a sequence—that precedes the four- beat precadence and four-beat cadence. Unlike in any of the cello gigues, then, Fortspinnung B and Schlußsatz 1(1) can be said to overlap by one bar. Whereas m. 21 is initially felt as a “weak” bar in the context of the sequence (mm. 18–21), it becomes “strong” in the context of the precadential standing-on-the-dominant (mm. 21–22). This metrical sophistication impacts the larger form of the strain. In contrast to the cello gigues (except perhaps BWV 1012), BWV 1068 obscures the very transition from Fortspinnung to Schlußsatz that in the cello pieces was an important site of metric articulation. Even though the material of m. 21 serves quite well its new role as a “strong” bar, there is no feeling of a strong beat as m. 21 begins. As I explain below, that feeling is what is deleted according to Lerdahl’s and Jackendoff’s concept of “metrical deletion.” The overlap thus results in a transfer of articulative weight to the start of the cadence-proper, i.e. the transition from Schlußsatz 1(1) to Schlußsatz 2(1). Accordingly, the fanfare quality of the strain’s last two bars is accentuated, in complement to the opening of the gigue which is about to be repeated or (on the second pass) restated in the dominant. Bach also “ups the ante” for the cadence-proper by the types of material presented in Fortspinnung B and Schlußsatz 1(1). Whereas Fortspinnung B was, in the cello pieces, “static” if it did not double as Fortspinnung A, in BWV 1068 it is sequential. The task of building up tension on dominant harmony is, then, the work of Schlußsatz 1(1) instead, which arpeggiates V7 and does not (as in the cello gigues) outline a melodic pattern of descending thirds or ascending steps.

Metrical Deletion and Well-Formedness I now turn to the theoretical apparatus by which Lerdahl and Jackendoff account for overlaps and elisions in metric structure, and their methods for representing these phenomena in dot diagrams. In BWV 1068, the experience of mm. 18–22 is such that m. 21 and m. 22 are both felt as “weak” bars when they begin. In terms of “metrical irregularities at hypermeasure levels,” this would be an instance of Lerdahl’s and Jackendoff’s second kind of “metrical deletion,” namely “deletion of the strong position.”16 About this, they write: “A second and more rare kind of metrical deletion gives the intuitive effect of a retrospective awareness that a metrical shift has taken place. . . . [and in relation to a specific example, from Schumann] The effect in the analysis of the musical surface is a metrical structure containing two

16. Lerdahl and Jackendoff, A Generative Theory of Tonal Music, pp. 99–104 (section 4.5); p. 103. 132 The Art of Gigue weak beats in a row.”17 Such structures are designated as well-formed by the “Metrical Deletion” rule, which functions in a limited way to “[allow] for irregularity” within the generation of tonal music’s hypermetric aspect.18 Besides overlaps such as the one at m. 21, metrical deletion includes elisions or “deletion of the weak position.”19 Incidentally, although Lerdahl and Jackendoff state that elision is more prevalent than overlap, it should be said, this is not the case in Bach’s gigues, and the same reverse preference for overlap over elision might be true of much early eighteenth-century music. When applied at multiple places and on multiple levels of metric structure, the “Metrical Deletion” rule is sufficient to confer the status of well-formedness upon large tracts of Bach’s gigues, but rarely if ever a whole movement. In the case of BWV 1068, the obstacles to metrical well- formedness not finessed by this rule are one in each strain. Notice that the brackets in Example 3.2 respect the three periods as a basic division in the grouping structure but the metrical pattern is continuous across each period division.20 There are, thus, five well-formed segments to a performance of BWV 1068, if one includes the repeats and considers the metric structure up to the level of 8-bar hypermeasures (which Lerdahl and Jackendoff mention more than once as the largest of the common hypermeters). These passages are mm. 1a–17a, mm. 18a–17b, mm. 18b–52a, mm. 52a–52b, and mm. 52b–72b. Included in these passages are overlaps at mm. 21 and 69 (where deletions occur on the level of the bar), and an elision at mm. 58– 59 (where deletion occurs on the level of the 2-bar hypermeasure). Note that in the overlaps, the deleted strong positions would belong to the bars following those named. Arguably, this reading errs on the side of being overly synthetic, especially by hearing mm. 58–65 as an 8-bar hypermeasure, and by hearing at m. 16 the subsumption of a major 4hypermetric downbeat in order to accommodate m. 17 to the preceding passage.21 But the reading

17. Lerdahl and Jackendoff, A Generative Theory of Tonal Music, p. 101. The pertinent example is 4.49 on p. 102.

18. Lerdahl and Jackendoff, A Generative Theory of Tonal Music, pp. 103, 99.

19. Lerdahl and Jackendoff, A Generative Theory of Tonal Music, p. 103.

20. The bracketted dots at the start of period III indicate pulses which are determined not by the metric relationships within the period but which are instead the result of the opening bars’ continuity with period II. The dot on the fourth level indicates the downbeat of an 8-bar hypermeasure. The dot on the fifth level indicates what would be the downbeat of a 24-bar hypermeasure, if period III is initially thought to continue the very large triple hypermeter which, arguably, period II creates.

21. It may or may not be correct to regard m. 16 as an overlap; if it is, m. 17 presents as the second bar of a 16-bar 4hypermeasure whose initial downbeat has been subsumed. I posit this reading to avoid isolating m. 17 in the parsing of “well-formed” passages, but Hypermeter 133 demonstrates the value of Lerdahl’s and Jackendoff’s distinction between instances of metrical deletion and other, more striking transitions from one metric scene to another.

Metrical Well-Formedness and Formal Design According to Lerdahl’s and Jackendoff’s model of metrical well-formedness, BWV 1068 passes through a series of well-formed passages that tally closely with the formal concept this piece shares with the gigues for cello. Period II unfolds a single metric hierarchy, consistent with its constitution as the Interior Phrase, a coherent unit of melodic and harmonic activity in the middle of the movement.22 Period I, however, is more complex, and features a metrical adjustment around mm. 16–18 which does not conform to one of the “permissible” metrical deletions. As a whole, the period is not well- formed but falls into two main parts (mm. 1–16 and mm. 18–24) each of which are well-formed. These two parts correspond precisely to the schemas of Opening Complex and Answering Complex identified in the cello gigues. Period III is at once more complicated than period I and more fluent, there being no obvious “watershed” in the metric structure. And in both respects, this also accords with the difference of character observed between the three periods in the cello gigues context. Period III, with its one obligatory formal schema, does not have the same onus to convey distinct temporal attitudes of beginning and ending—hence there is no need for any major break in the metric process. Yet period III does tend toward irony or playfulness with the conventions of form and phrase rhythm, so metric sophistication is absolutely appropriate. Most of period III is spent with duple hypermeter in the opposite phase to the beginning of the period and its final cadence. The initial, dramatic departure occurs at m. 52, where the resolution of the period’s opening fanfare to G major is overwritten by the start of a broad cycle-of-fifths sequence. The fanfare (mm. 49–52) forms a clear 4-bar 2hypermeasure; the sequence begins with another clear 4-bar 2hypermeasure (mm. 52–55) which impinges on the fanfare. Since the very start of m. 52 is felt as a weak beat of the duple hypermeter (with g5 in the melody and g2 in the bass), the metric adjustment is best described as an overlap. That said, the material

it makes no difference to the overall interpretation, since period I still cannot be read as a well-formed whole. In Example 3.2, I represent the overlap at m. 16 only in the grouping brackets, not in the dots. (Note that the overlaps and elisions are depicted identically in the dot structure itself.)

22. This analysis of period II as a straightforward triple 4hypermeasure will be nuanced later. In the context of a temporalist analysis, there is more to say about the articulations at m. 37 and m. 41. 134 The Art of Gigue of m. 52 moves quickly to establish a strong-beat character, especially the new melodic motive that introduces b5. Therefore this particular overlap is closer to being an elision than, say, m. 18 or m. 21. In line with Lerdahl and Jackendoff, however, the adjustment at m. 52 is neither an overlap nor an elision, in the sense of one beat’s being “deleted” at some level of metric structure. The larger situation of the cited 4-bar units says otherwise. The sequence advances smoothly into a third 2-bar unit, which in my reading is the move into the third quarter of an 8-bar 3hypermeasure, but which (in any case) does not fit the 3hypermeter that the start of period III presumably continues from period II. Sensibly, Lerdahl’s and Jackendoff’s definition of “overlap” does not allow for five-eighths of a hypermeasure to be telescoped: the far-reaching adjustment at m. 52 is a full violation of metrical well- formedness. After that dramatic switch to an “even–odd” phase with the basic hypermeter—and with the 8-bar 3hypermeter too, effectively—the remain- der of period III traces a long arc toward stability. To begin with, the cycle-of-fifths sequence establishes its credentials as the point of farthest remove from the metric logic of three 8-bar units per 24-bar period, which period II followed to a T. The bass is particularly responsible for a sense of rhythmic abandon, with its arrivals on a3 in m. 53, then g3 and f~ 3, anticipating the harmonies of the following hypermetric downbeats. As it turns out, that feature of the bassline helps to convey the quadratic design of the sequence when, as I read it, the sequence’s fourth quarter is interrupted by the ascending sequence at m. 58.23 The interruption at m. 58 is, as noted above, an elision, and this brings the 8-bar 3hypermeter closer to its regular position. Once the new sequence begins in m. 58, the bass reverts to marking the notated meter and the pattern of chromatic ascent performs a purposeful rhetorical shift in the direction of closure. This sequence participates in the same correlation of ascending stepwise motion to precadential function that chapter 2 observed in the cello gigues, even though the character of Fortspinnung is prominent and the steps are paced too slowly for a Schlußsatz 1 function. Nonetheless, the 8-bar

23. In terms of voice leading, the quadratic design of this sequence is based on the standard archetype of descending tetrachords in parallel tenths, b5–a5–g5–f~5 in the melody, and g3–f~3–e3–d3 in the bass. This schema is conventionally organized into a large quadruple hypermeasure. It is conceiveable, though, that one would analyze mm. 52–57 as a triple 2hypermeasure. Hypermeter 135

3hypermeasure of the sequence (mm. 58–65, as read here) does incorporate a cadence of sorts in mm. 64–65.24 The next step toward metric stability and tonal closure is made in m. 66 when the unequivocal Fortspinnung element from the Answering Complex of period I is reprised. On the back of mm. 18–21, mm. 66–69 are a brilliant demonstration of invertible counterpoint in a gigue whose general demeanor is more galant than contrapuntally learnèd. The leaping sixths are re-assigned to the bass, while the melody takes on the smooth, sinuous figures. This exchange sees the bassline adjust to reinforce the regular rhythm of tactus beats and bars, somewhat in parallel to the change of heart observed at the start of the ascending sequence. Momentous as the reprise is, however, this third sequence of period III is unlike the others insofar as it does not introduce a major metric adjustment. Whereas in period I, the same passage began in metric obscurity, the 4-bar 2hypermeasure is now continuous with what precedes it. Thus, the 2hypermetric downbeat is actually articulated as such: changes on the macro level, and changes on the micro level—removing a syncopation from the bass—work together to create a more assertive beginning. At this point, both the 2-bar 1hypermeter and the 8-bar hypermeter are back in phase with a naïve division of period III’s 24 bars. A foregone conclusion, the final step toward metric stability occurs with the overlap at m. 69, reprising m. 21. Looking back, the period now includes two proper “metrical deletions,” such that, were the respective “positions” reinstated, the three sequences would each commence an equal 8-bar unit—squeezing out the opening fanfare. Earlier, I observed that the overlap between the generic Fortspinnung and Schlußsatz components means a shift of articulative weight in favor of Bach’s pithy cadence. On its return for the second strain, this cadence becomes a ringing endorsement of ambitious metric processes.

Metric Grids, Overlaps, and Elisions in Terms of Projection In moving to a temporalist perspective on meter and specifically to projec- tion theory, nothing that was said in connection with Example 3.2 will be contradicted. Rather, the departure from Lerdahl’s and Jackendoff’s notion of metric structure is initially a matter of emphasis. Under the formalisms of their Generative Theory, the unfolding of a single metric state, “deletions” aside, is intrinsically uninteresting. But projection theory invites much greater sensitivity to the metric possibilities within the “grid.” Rather than

24. This reading admittedly glosses over considerable subtleties in the passage, which has none of the assured Auftaktigkeit of the 8-bar units of period II or even of the first sequence in the current period. 136 The Art of Gigue assert that consecutive units of similar size necessarily constitute a pulse- periodicity, this approach demands that the connection of each unit to the last is established case-by-case. From the perspective of projection, no two metric “grids” are the same, and no single metric state is sustained simply by waiting for time to take its course; meter’s temporal condition goes deeper than that. Projection theory’s capacity for finding interest in the supposedly uniform “grid” has led Mark J. Butler to apply it to electronic dance music, and an analyst of Bach’s music may well turn to projection theory for similar reasons.25 Whereas the technology of the dot diagram and its associated theory invites us to ponder moments of obvious pattern-breaking—and perhaps to value these moments artistically—the first mark of a temporalist approach is its invitation to revisit the sites of metric regularity. In the crudest terms, projection theory asks us to confirm whether consecutive units or “measures” of similar size are indeed connected at all. Two 8-bar hypermeasures, such as Lerdahl and Jackendoff may observe, are not necessarily conjoined in musical experience by the requisite feeling that the second hypermeasure reproduces—is a projection of—the first. On the contrary: the kind of pulse-periodicity that appears “given” in a dot diagram may harbor substantial discontinuities in addition to the more likely continuities. We see this, for instance, in BWV 1068’s cases of metrical deletion. Regarding cases of metrical deletion, dot diagrams implicitly make the claim that we can separate the irregularity that arises on higher levels from the regularity that persists on lower levels. Consider, for example, the “deletion of the weak position” at mm. 58–59. The suppressed weak beat occurs on the level of alternately strong and weak 2-bar units, so that, in other words, the time interval is dramatically shortened between consecutive accents on the 4-bar level. Yet pulse-periodicities on the 2-bar level and smaller remain intact. Although the wording of the Metrical Deletion rule suggests some intuition of rupture on the 2-bar level, that would presumably be a matter of grouping or something other than the hard facts of metric structure.26 Since units of two bars, one bar, and one tactus beat are maintained throughout the passage including the “deletion” (mm. 52–69), Lerdahl’s and Jackendoff’s theory would see no disturbance in these metrical layers.

25. Butler, Unlocking the Groove: Rhythm, Meter, and Musical Design in Electronic Dance Music.

26. The dichotomy of “meter” and “grouping” has fielded a certain amount of criticism, not least from Hasty. See, for example, Frank Samarotto, “The Body that Beats,” Review of Harald Krebs, Fantasy Pieces, Music Theory Online 6, no. 4 (2000). Hypermeter 137

From the stance of projection theory, however, it is absolutely possi- ble that the integrity of these metrical layers is compromised. Indeed, a downbeat in the 4-bar 2hypermeter at m. 58 would strongly mitigate (if not prevent altogether) a 2-bar projection of mm. 56–57 into mm. 58–59. For Hasty, the hierarchical nature of meter is such that any (relatively large) projection subsumes smaller ones, meaning that a “new beginning” on the level of the 4-bar 2hypermeter cannot simultaneously be a new beginning on the level of the 2-bar 1hypermeter. In other words, the claim is that we cannot (or do not, as rule) feel that we are “starting over” on two scales concurrently. This principle, incidentally, is only as black-and-white as the presence of metric hierarchy in the first place, and this needs to be remembered to avoid unnecessary analytical dilemmas. But so long as there is hierarchy, the general observation goes that smaller pulse-periodicities are wrapped up within larger ones. Be it assumption or observation, this constraint on projection is critical among the ideas advanced by Meter as Rhythm. With a clear 8-bar hypermeasure such as mm. 1–8 of BWV 1068, there- fore, mm. 1–2 are “projective for” mm. 3–4 but mm. 3–4 are not “projective for” mm. 5–6. Rather, m. 5 brings a “new beginning” on the scale of 4-bar units, and the sense of an already primed 2-bar unit in mm. 5–6 must instead be attributed to the fact of their being a projection of mm. 1–2 as part of the larger projection of mm. 1–4 into mm. 5–8. This is precisely the phenomenon described by Hasty as “the inheritance of projective complexity.”27 If much later, at m. 58, we do experience the (unexpected) beginning of a 4-bar 2hypermeasure, it is therefore projection theory’s explicit claim that the 2-bar hypermeter is broken. Whereas the dot diagram shows a recalibration of the higher metric layers above a substratum of regularity, a projective analysis would also recognize disruption in the subordinate pulse levels. At first, it is not obvious that the “deletion of the weak position” in mm. 58–59 presents a good opportunity for distinguishing the perspective of projection theory. The dot diagram already shows a break in the metric pattern and it appears that projection theory just interprets this break as more acute, affecting all levels of the meter. But on closer inspection, there is a major reversal here. An accent theory points to a metric accent at m. 58 on the level of 4-bar units, an accent which is the assertive downbeat of a new metric scene. Projection theory is more circumspect. Though there is obviously a new beginning at m. 58, it cannot be assumed to have specific metrical value, neither in the sense of its durational import being clear nor in the attendant sense of its being “metrical” at all. Of course, it would be important to acknowledge that projective relationships soon accumulate

27. Hasty, Meter as Rhythm, pp. 149–152. 138 The Art of Gigue within the new metric scene. Specific metrical value certainly does accrue to that new beginning. But until m. 59 arrives, the new beginning conjures the proto-metrical dimension of Hasty’s “indefinite projective potential.” In simple language, m. 58 is not a downbeat like (say) the downbeat at m. 49, because there is no prior downbeat and therefore no definite pulse. Taken only so far, the argument is confusing and shows projection theory in a poor light. The theoretical basis for elision has been cast into doubt. The next step, therefore, is to recognize that projection theory will situate the metric rupture at m. 58 squarely at the feet of the 2-bar hypermeter, precisely the largest “pulse stream” which a dot diagram registers as continuing undisturbed. Elision—Lerdahl’s and Jackendoff’s “deletion of the weak position”—is primarily felt as a negation of the 2-bar pulse. Despite a regular structure of 2-bar units across the break, mm. 56–57 are patently not “projective for” mm. 58–59; that is the temporalist argument. Something about the new material does not allow us to hear a metric connection. We can pin a disconnective attitude on the second half of m. 58 and especially m. 59, where the ascending sequence breaks ranks with the cycle of fifths. The harmonic move to IV at m. 59 negates the cycle of fifths’ “fourth quarter” resolution to I, and a firm break in the melody occurs with the downward leap to b4. So whereas accent theories look to the positive assertion of a 2hypermetric strong beat at m. 58, projection theory identifies a negation of the continuity of 2hypermetric beats. On the one hand, there is the “objective” irregularity in the dot diagram’s third tier. On the other hand (says projection theory), there is a hidden discontinuity in the second tier, and this—rather than anything shown on the third tier—is responsible for articulating the change of metric scene. To someone familiar with the classic examples of “elision” from Haydn or Mozart, the reversal may seem peculiar. The typical illustration involves an authentic cadence (resolving to tonic in the fourth bar of a quadruple hypermeasure) which is “crashed” by a subito forte passage, bringing forward the phase of the hypermeter by one bar. The question would be, how that forte entrance can be interpreted as anything other than a hypermetric downbeat when it occurs. The answer, in the language of this study, is that such assertive rhythmic devices are not—at the time of their initial shock— “metrical” assertions.28 A metric theory based on projection must make a dis- tinction between recognizable projection-events and other rhythmic events which we may be conditioned to “hear as” beats in some more inclusive sense. Regarding the classic examples of elision, projection theory effectively calls

28. For an excellent recent re-appraisal of metric overlap, see Ng, “Reinterpreting Metrical Reinterpretation.” Ng revisits the theories of Lerdahl and Jackendoff, and Rothstein, and addresses the relationship of hypermeter and phrase. Hypermeter 139 for a slightly different configuration of “metric accent” and “phenomenal accent” as conceived by Lerdahl and Jackendoff.29 “Phenomenal accents” are often associated with volume or dynamic force, but need not be considered in such terms exclusively. In Bach’s gigues, elisions often happen when familiar thematic material returns, and these thematic assertions also have some of the quality of a strong beat. But, again, these thematic entries cannot be credited with much specific metric strength. The argument of this chapter supports, in fact, the aesthetically rich idea of an opposition between “the metrical” and “the thematic” for Bach’s music.30 In my readings of projective process, thematic returns frequently happen at moments where the metric slate has effectively been wiped clean. The use of familiar material with a strong character seems to carry the music forward at the moments where meter bows out. While projection theory is more circumspect about elision than ac- cent theories, the opposite is true of overlap. This follows from the two perspectives’ different attribution of “agency” to higher and lower pulse levels, with accent theory gravitating to the lowest level of irregular accent and projection theory, to the highest level of regular accent. The greater circumspection of accent theory in the context of overlap is evident in the wording of Lerdahl’s and Jackendoff’s Metrical Deletion rule. The rule cites the “retrospective” reinterpretation of a weak beat as strong. Thus, “deletion of the strong position” includes a category of metrical comprehension— retrospection—which the “deletion of the weak position” does not. And this indicates a fundamental inequality between the phenomena of elision and overlap which is not reflected in the technology of a dot diagram. Projection theory registers the inequality not in terms of retrospection but by how it sees the moment of rupture—as a surprising negation of projection or a surprising origination of projection. Elision is established by a negation. Overlap, however, is established more positively, by the occurrence of a small-scale projection where a larger one or none was anticipated. Because,

29. Lerdahl and Jackendoff, A Generative Theory of Tonal Music, p. 17. For discussion of metric and phenomenal accent, see London, Hearing in Time: Psychological Aspects of Musical Meter, pp. 18–19; and Richard N. W. Blom-Smith, “A Theory of Accent in Tonal Music with an Assessment of Selected Modern Accentologies” (PhD diss., King’s College London, 1994).

30. This partially contradicts Schoenberg’s notion (developed by William E. Caplin) of the opposition between tight-knit and loose-knit zones in later eighteenth- and nineteenth- century music, insofar as that notion implies that hypermeter is a stronger feature of thematic materials than of transitional or developmental areas. Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang (New York: St. Martin’s Press, 1967); William E. Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven (New York: Oxford University Press, 1998). 140 The Art of Gigue

Fortspinnung B q q q q q q q  q  q  q 
q  q 
q  q q q  q  q q q q q
q q q q q
q q q q q q q q q q q q  Schlußsatz 1(1) Schlußsatz 2(1) q q q q q q q q q q q q q q   q q q q q q q  q q    q  q  q q q q q     q q q Example 3.3: Recomposition of the orchestral gigue (Closing Complex), mm. 18–24. with projection theory, each new beginning is exclusive to one level of pulse, the origination of a smaller new beginning can be seen as carrying agency in the “deletion of the strong position.” A projective continuity of hypermetric beats actively prevents the start of a new hypermeasure; this occurs on the highest level of regular pulse.31 Accent theories, on the other hand, treat pulse streams as independent of each other, and so “deletion of the strong position” does indeed rest with an absence: an accent is understood to be present only in retrospect. This process belongs to the lowest level of irregular pulse. The clearest example of overlap in BWV 1068 occurs with m. 21. When m. 21 is first articulated, during the move from downbeat to upbeat and perhaps further, it takes the weak position in the duple hypermeter. There is a clear one-bar projection from m. 20 whose harmonic action is the resolution to V7. When m. 22 is articulated, however, another one-bar projection occurs, taking m. 21 for the projective potential, and contradicting the preceding 32 event. The harmonic action of the new projection is a prolongation of V7, a prolongation which feels tangential to the resolution that introduced it. The overlap has a knock-on effect described earlier as a “transfer of articulative weight” to m. 23. Example 3.3 recomposes Bach’s mm. 18–24 as a regular

31. It must be added to the theory that projective continuity between beats is not necessarily transitive. Otherwise, one could not distinguish a case of elision within a duple environment from the appearance of a triple measure. Given two successive projection- events whose respective projected and projective potentials are synchronous (are realized by the same content), the second projection-event may be smoothly grafted onto the first, or it may negate the first. The latter situation is the elision scenario.

32. An element of contradiction will be essential to overlap as seen by projection theory. Hypermeter 141

8-bar 3hypermeasure to show how a restored “strong position” four bars from the end would diminish the pithy character of the cadence.33 A close look at elision and overlap reveals projection theory’s sen- sitivity to the rhythmic convictions that animate an apparently regular “pulse stream.” According to a temporalist theory of pulse, connection and disconnection are both possible through a succession of equal durations, and in fact, the experience of “metrical deletion” is best explained by focusing on the highest level of regular accent, as it appears in a dot diagram. But there are, besides elision and overlap, phenomena which a dot diagram does not show that underscore more firmly the difference a temporalist approach to pulse makes. To conclude the analysis of BWV 1068, I will address mm. 13–16 to illustrate projection theory’s capacity for finding interest in the apparently uncomplicated “metric grid.” The 4-bar span of mm. 13–16 is a clear instance of quadruple hyper- meter (duple 2hypermeter grouping duple 1hypermeter). The content of these bars conveys the internal structure of a quadruple hypermeasure with absolute clarity. Moreover, this would be the fourth hypermeasure in an unbroken chain. These facts lead an accent theory—certainly a “generative” one—to regard mm. 13–16 as part of the smooth unfolding of a single “metric state” from m. 1. The dot diagram shows a grid extending across mm. 1–16 (refer to the lower three levels of accent for now) and this analysis of the beat structure cannot be faulted. There is, however, a vital feature of mm. 1–16 which this analysis ignores, namely, that the metric continuity of the gigue’s opening is disturbed well before m. 17 adds irregularity to the beat structure. Not later than the second beat of m. 14, the movement’s initial metric environment starts to be dismantled. As shown in Example 3.4, mm. 14–16 could be rewritten to make mm. 1–16 a cogent phrase. But as they are, mm. 14–16 seem to strike out on a different path from the prior sequence and the initial Vordersatz. The sense of pulling away from an established metric environment is sharpest with the second beat of m. 14, where the prospect of a cadence rapidly dissolves and the—rather late—modulation to the dominant takes hold. The projective continuity of mm. 13–16 with mm. 9–12 is significantly weakened at this point; the larger continuity of mm. 9–16 with mm. 1–8, even more so. To track metric process at moments like this, aforementioned distinctions about the temporality of projection-events and potentials all come into play. In spite of an unwavering beat structure,

33. The recomposition in Example 3.3 in some ways justifies, for the first strain of BWV 1068, the concept of underlying “8-bar phases” which is ubiquitous in Little’s and Jenne’s discussion of Bach’s dances. However, I do not claim that an 8-bar hypermetric norm is in any way actually present in the composition. Generally, the temporalist view on pulse is opposed to such analytical rationalizations. 142 The Art of Gigue

(a) Non-modulating with cadence on dominant q q q q q q q q q q q q q  qq q q q q q q q q q q q q q q q q q q q q q q q q q q q   q q q q q q q
q q

q
q q q q q q    q q q q q q q q q q q q q q q q q q q q q q (b) Non-modulating with cadence on tonic  q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q    qq q q q q q q q q q q q q  
q q
q
q q q q q q q
  q q q q q q q q q q q q q q q q q q q q Example 3.4: Recompositions of the orchestral gigue (Fortspinnung A), mm. 9–16.

enormous flexibility is possible in the rhythmic connections that are or are not made.

Contrast With “Accent” Theories Accent and Duration Key to our understanding of “projection” theory—and being able to build upon a temporalist view of pulse—is the realization that “projection” oper- ates on durations, not accents. However, in the response to Meter as Rhythm and its partial assimilation into meter studies, theorists have not always adequately distinguished between the conceptual underpinnings of projec- tion theory and more traditional, “accent theories” (as Hasty calls them). Among the ramifications of this are some confusions over the meaning of “projection” which give it connotations of prediction or expectation that do not really belong.34 To clarify the essential difference between projection theory and ac- cent theories, and their reliance on concepts of “duration” and “accent” respectively, I will contrast Hasty’s notion of projection with its (not unrea- sonable) repurposing by Danuta Mirka in Metric Manipulations in Haydn and

34. An important recent study which is concerned with expectation in metrical and other matters is David Huron, Sweet Anticipation: Music and the Psychology of Expectation (Cambridge, MA: MIT Press, 2006). Two illuminating reviews of Huron’s work are Eric Clarke, Review of David Huron: Sweet Anticipation, Music Analysis 27, nos. 2–3 (2008): 389–392; William Benjamin, Review of David Huron: Sweet Anticipation, Journal of Aesthetics and Art Criticism 65, no. 3 (Summer 2007): 333–335. Hypermeter 143

Mozart.35 Mirka draws on Hasty’s idea of projection, in tandem with some work of Ray Jackendoff that postdates his and Lerdahl’s Generative Theory, in order to adapt traditional notions of metric structure toward the analysis of a listener’s in-time experience of metric organization.36 Thus, Mirka invokes the idea of projection but repurposes it for a cognitive account of metric perception based on accent. One could say that Mirka clarifies the lessons of Meter as Rhythm in the direction of a theory-led approach to meter, choosing the opposite path from this study, which pursues an analysis-led approach. A brief look at Mirka’s study is valuable for highlighting the conceptual changes involved in moving between a temporalist theory of pulse and a psychologically sophisticated accent theory. In Hasty’s original and largely temporalist account, the objects of “projection” are durations. Projective process is the manifold reproducing of metric durations at different times and on different scales, and each “projection-event” (in my language) is a single act of reproduction, involving the two potentials—past and present, or present and future. For Hasty, a projection-event is completed when the projected potential is fully realized; in other words, the “aim” of projection is to string together two similar durations. By this account, the basis of any pulse or pulse-periodicity is durational projection. Despite what most readers and reviewers have noted, namely Hasty’s deep concern for the detail of musical surfaces, it is worth noting that Hasty’s analyses gravitate to the rhythmic middleground, where an emphasis on duration pays dividends. The application of projection theory in this study accentuates that bias, being nearly exclusive to hy- permeter and addressing pulse-periodicities of the order of the bar and larger. Significantly, that focus on hypermeter makes for a contrast with Mirka’s study of Haydn and Mozart, which is addressed to meter proper, and concerns processes which are (or might be heard as) operative at the level of the bar and smaller. In Mirka’s repurposing of the “projection” idea toward a more cogni- tivist understanding, projection’s objects are no longer durations, but accents instead. For Mirka, projective process would be the action, by musical participants, of attending to nascent and established pulse streams, and anticipating the forthcoming articulations in the rhythmic texture. Here, the completion of a projection-event would be imagined differently. It is barely justified, though, to conceive of discrete “projection-events” at all. The point is that, for Mirka, projection attains a kind of maturity once a third accent

35. Mirka, Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791.

36. Ray Jackendoff, “Musical Parsing and Musical Affect,” Music Perception 9, no. 2 (Winter 1991): 199–230. 144 The Art of Gigue has arrived. In succession to the two accents that are minimally necessary for a potential pulse stream to be extrapolated, a third accent confirms or validates the extrapolation. The third accent or “new beginning” (in Hasty’s language) is therefore the aim of the projection model as repurposed by Mirka. Figuratively, this takes us one step further than Hasty, for whom projection’s teleos is the full realization of the projected potential. Hasty’s basic projection-event brackets together two durational “potentials” and ends there, but Mirka’s leans forward into the implication, and the likely realization, of a third metric accent. Absolutely key to this essential difference between Hasty and Mirka is a stark contrast in how the two theories conceive of duration. From Mirka’s perspective, durations are simply quantities of time, as they are for “accent theories” in general. This is no indictment of course, for nobody and certainly not Mirka would isolate meter from other musical parameters having to do with harmony, melody, rhythmic gesture, and so on; the point is simply that this model of meter works with “empty” durations because it works with a dimensional concept of time. But from Hasty’s temporalist perspective, what we might call “pure duration” is anathema; a degree of abstraction at which Hasty’s theory falls apart and its statements become nonsensical. For projection is all about the feeling of rapport between a duration that is in progress and a prior duration that is projective for it or a further duration for which it is projective. Thus, the relationship between the two potentials, projective and projected, is implicitly a matter of quality as well as quantity. We must understand, though, that Hasty’s “projection” theory is not a hypothesis about what happens when a listener is presented with two equal durations in a sounding structure, regardless of how those two durations might be qualified. Hasty’s core claims are not so psychological, even though (a little confusingly) Hasty does argue questions of psychology too. We must also understand that Hasty’s theory is not a metaphysical assertion about the nature of pulse. It is instead a descriptive account of the metric relevance that can exist of one duration for another. And, in my view, it is worth emphasizing that “projection theory” does not claim to explain pulsed or periodic phenomena nearly so generally as the word “theory” might suggest. Hasty’s notion of projection is theoretical to the extent it is logical, but is nonetheless grounded in analytical observation. Nothing is assumed about what creates or causes projection, and when or where the phenomenon occurs is a question that lies outside the study’s basic remit. It therefore makes perfect sense for Hasty to see a succession of equal units in a score yet be open to observing a mix of continuous and discon- tinuous effects; it is not given that an “objective” succession of equal units is one pulse stream (or “state”). This is the point Hasty makes when he Hypermeter 145

firmly distances himself from “accent theories” for which duration, because it is quantity only, is unchanging in the face of repetition. For Hasty, an “objective” succession of equal units does not necessarily cohere as a projective process, and even if it does, there might be a gradual change in terms of quality. This latter possibility explains why the first and last units of a smooth series might, if juxtaposed out of context, fail to create a significant sense of periodicity or projective coherence. In summary, metric studies based on accent (including Mirka’s) operate with the ideal of “pure duration.” And for the purposes of studying the metrical in music cognition or in music’s sounding structures, this seems an irreproachable scientific device. But in Hasty’s temporalist study of meter, “pure duration” has a destructive twist: instead of being a solid concept upon which metric theory is built, it becomes the vanishing point, the abstraction too far which would negate the entire approach to looking at duration relationally. Connected to this, a hard dichotomy of continuity and discontinuity would be another vanishing point of Hasty’s theory. I invoked the question of continuity and discontinuity above when underlining the freedom under projection theory to determine whether or not “objective” successions of equal units translate into coherent projective processes. But to admit total continuity and total discontinuity as real options would also fatally undermine Hasty’s theory. From the standpoint of projection theory, then, the concept of empty duration is beyond the pale because by it “the metrical” would cut all ties with musical content and in so doing relinquish the observed relevance of one duration for another which is the very nature of projection. It is a critical underlying argument of Meter as Rhythm that “pure duration” is no duration because the traction of musical content is let go. “Pure duration” is beyond abstract, in the sense that abstraction should mean an (always particular) pulling away from specifics, but not a total evacuation of lived reality for some separate conceptual sphere. For Hasty, “pure duration” is anathema because it means the incursion of the timeline, the radical substitution of one kind of “science” for another, and the parting of ways for meter and rhythm. I underline the point about “pure duration” forcefully since, in my view, Meter as Rhythm underplays this important logical facet of the “projection” idea. Pertinent arguments are plentiful—for instance, when Hasty observes that “[as traditionally] understood, meter . . . marks durations but is external to the durations it marks.”37 But there is a danger that Hasty’s concern with duration’s qualitative aspect could be mistaken for a separate intellectual commitment—to ever-new experience, etc.—having little to do with the

37. Hasty, Meter as Rhythm, p. 19. 146 The Art of Gigue mechanics of the theory. We see, here, a major dividing line between the ontologies of meter that grow up around alternate ways of studying metrical phenomena.

Realization, Expectation, Prediction A questionable reading of Meter as Rhythm which is perhaps less apparent in the literature than in conference papers or private conversations, but which nevertheless has a certain amount of traction, is the notion that Hasty’s “projection” is essentially a mechanism of prediction or expectation. Although I will not brand this as a complete misreading, because elements of Meter as Rhythm support it, one must nevertheless appreciate that it does some violence to the core claims of projection theory. The feelings or convictions of projection described by Hasty are not really about predicting. Fundamentally, the claim is not that we are—in the sense of estimating— “projecting” when something is going to happen or how long something is going to be.38 At the core, the most basic projection is neither about predicting the start of a third unit (as for Mirka) nor anticipating the length of the second. Described in such terms, projection would indeed be venturing into the very realm of “pure duration” which we just established is inhospitable to it. Granted, Hasty accords some sense of prediction to projection on the psycho- logical side of the argument that deals with rhythm and meter perception. This stands in the same strand of Meter as Rhythm that “narrated” projection. On the ontological side of the argument, however, a firm line needs to be drawn. The metric feelings that projection theory aspires to describe are not about mapping durations in advance and waiting expectantly for these forecasts to be confirmed or denied. They are instead about tracing the contours of a presently unfolding rhythmic situation in the manifold “new beginnings” that bear it aloft, upon what Hasty might call its immediate musical pasts. Plainly speaking, projection theory is more concerned with past–present relations than present–future relations. As mentioned earlier, the currency of the projection-event in temporal experience tends to be limited to an “active phase” during which the sounding music is that of the

38. The following passage from Hasty speaks to the difference between projection and prediction (Meter as Rhythm, p. 69): “If we are to follow the event, our attention must be relatively continuous—if our attention is broken, we stop following and are no longer with the event. But to ‘follow’ is not to trail along behind the event or even to keep up with it ‘at every instant.’ It requires above all that we keep moving ahead, that we anticipate what is about to happen in order to follow what is happening. [But] . . . Anticipation in this sense is not the projection of a definite outcome but a readiness to interpret emerging novelty in the light of what has gone before.” Hypermeter 147 projected potential. In simple circumstances, the projective and projected potentials translate into “past” and “present,” since we are not even aware of projection—so there is not projection—before a repetition is actually initiated. A projection theory that resists notions of prediction, pure duration, and continuity vs. discontinuity, resists as well an understanding of “real- ization” that otherwise is almost ubiquitous in meter studies, and in music theory generally. As commonly understood, realization means “making good” on some design (or plan, prediction, intention etc.) which previously was abstract or prospective. Thus, with meter, a duration’s being realized means simply that it happens or “comes to pass”; prospects translate into events. Conventionally, we might say, for instance, that the listener expects the completion of a given hypermeasure and that their expectation is either confirmed or denied (or maybe both in distinct ways). Realization would mean, then, that the unfolded sound structure corresponds to what the listener had expected, or to what the listener was led to expect by the composer or the work itself. Amid this knot of tenses and agencies, the problem from a temporalist perspective appears as follows: if the seat of “the metrical” is temporal expe- rience itself—not the structure of a composition, nor a listener’s schematic understanding of a composition—then what does it mean to realize a duration? Can “the realization” of a durational potential be accomplished, so that the potential becomes somehow real and finished. Or is “realization” something that only exists as an active pursuit? The former interpretation allows us to conceive degrees of realization, in terms of how much of a prospective duration “comes to pass.” An expected duration might be partially realized; it might be fully realized. Yet a temporalist approach favors the other interpretation, that to realize a duration is simply to be occupied with it in present experience.39 From this standpoint, conventional theory appears stranger the more one considers it: metric predictions flock to a listener, who must shepherd good predictions into the fold of structure—events as they happened—while turning away bad predictions. Of course, entrenched music aesthetics have long allowed music theorists to commend both the confirmation and the subversion of expectation, so our frustrated predictions are ideally delightful rather than irritating, and our accurate predictions are ideally pleasing rather than tedious. But the basic idea in describing expectation, confirmation, and denial is that listening is about witnessing a work “take shape” and that good listening is active listening which means anticipating what shape the music might take before it is laid down. In the same vein,

39. For strong hints of this conclusion, see Meter as Rhythm, p. 82. 148 The Art of Gigue listening might be described as the acquisition of musical information through the medium of time, or the gradual revelation of musical structure to consciousness. This conception of listening can be described as cognitivist. Cognitivism puts a strange spin on “realization” from the temporalist point of view. From this vantage point, the idea of realization as prospects- becoming-events is suspect. As far as temporal experience is concerned, “outcomes” are less, not more, objective than processes, and no “outcome” of an active process can outlive active processes altogether. If we cannot identify the ways in which a fully “realized” duration plays into some new metric activity, we have no business objectifying it at all. Where would a “realized” duration have reality? In a mental chronicle of the sounding music’s structure? In the listener’s bodily memory? Or only in the mechanisms of music analysis itself? Questions are also raised vis-à- vis the possibility for degrees of realization. If a given projection-event is abandoned prematurely, in what sense has a part of the projected duration been realized? Is it sensible to conceive of realization as a progressive move toward meeting an expectation? As it happens, there is a certain amount of agreement between traditional and temporalist metric theories on this issue: it is generally recognized that an unfinished quadruple measure (say) is not just a duple or triple measure that we had expected to be longer. But at base, this is the same argument Hasty makes in Meter as Rhythm with respect to “beginning”: that, from a temporalist perspective, beginning cannot be defined as a starting-event that precedes the acquisition of duration. The temporalist view problematizes the whole idea that specifically metric duration is achieved gradually “through time” and it certainly is wary of conceiving listening as an effort to parse a sounding structure into durations. Meter studies have, again, not been helped toward a clear confrontation of the basic issue by the multiple strands of argument in Meter as Rhythm. Once more, a line must be drawn between the ontology of metric process— which is consistent with an analysis-led approach to meter—and the psy- chology of metric perception, which is not.40 Despite Hasty’s commitment to process philosophy, which would be averse to the notion of lasting results of metric process, Hasty nonetheless accounts various outcomes or (so to speak) “exit scenarios” for the generic projection event.41 The possible outcomes are, first, the full realization of projected potential; second, the

40. On the side of pyschology or a rhythm-and-meter argument, Hasty does (contrary to my argument in the previous paragraph) reinforce an understanding of realization as the progressive achievement of a durational product (Meter as Rhythm, p. 74): “Thus, what I earlier called the growing pastness of beginning is the progressive realization [i.e. creation] of a definite potential for duration.” See also pp. 93–94.

41. See “Process Philosophy” in Stanford Encyclopedia of Philosophy. Hypermeter 149 non-realization of projected potential following the realization of projective potential; and third (this is only encountered in complex circumstances), the non-realization of projective potential. But these outcomes belong with Hasty’s “narration” of projection: in the heuristic sphere. To think of them either as permanent outcomes or as the whole purpose of projection would be a mistake. Cognitivism is always looking forward to the surity of knowledge a listener has once that something has been heard in its entirety, but temporalism sees the end of a given process as the moment a listener lets go of whatever experiential “knowledge” it carried.42 Much more could be said to contrast a “projective” ontology of meter from accent theories of meter. For one thing, I have not distinguished a process philosopher’s concept of “musical experience” from a psychologist’s concept of the “experience of music.” However, for the purposes of this study, it will be enough to have contrasted projection theory’s durational premise with the accentual premise of other theories, and to have explained that projection is not a mechanism of prediction as commonly understood. To summarize, projection is not succession, projection is not prediction, and projection theory is not, at heart, a speculative theory of metric perception.

Challenges to Metric Analysis Premised on Pulse Returning to the gigue of BWV 1068, I will now detail the challenges which Hasty’s projection theory raises for metric analysis. This develops my argument that a projection theory of pulse is still inadequate to the analysis of meter, and that there is a general problem with defining meter as a function of multiple pulse-periodicities.

The First-Pulse Problem The first challenge concerns beginnings or what Justin London calls “en- trainment” and Mirka, “establishing meter”; our first exposure to a “metric state.”43 Projection theory has it that pulse kicks in at the moment of beginning-again or starting-over. Thus the tactus beat of BWV 1068 is not established until the second beat, where the bass is demonstrative. The duple meter is not established until m. 2, where the melody returns to A. And the duple hypermeter is not established until m. 3, where the harmony moves to I6. But as the metric scale increases, the pattern becomes less persuasive.

42. Incidentally, it is telling that on the temporalist side but not the cognitivist, the “listener” could equally be the performer, composer, or improviser.

43. London, Hearing in Time: Psychological Aspects of Musical Meter, p. 12; Mirka, Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791, pp. 31–32. 150 The Art of Gigue

Is the start of m. 5, where the opening fanfare repeats on B minor, really the first that we are aware of an emerging 4-bar 2hypermeter? And is the start of m. 9, the start of the sequence, our first glimpse of 8-bar 3hypermeter? Although this would stand to reason, as a matter of observation, it is not true in practice. One is, instead, aware of each level of meter before its first unit is over: by the middle of m. 3 at the latest, we become aware of duple, 4-bar 2hypermeter (mm. 1–4 as first unit) and likewise by the start of m. 6, we become aware of duple, 8-bar 3hypermeter (mm. 1–8 as first unit). Although, in projection theory’s defense, it does not deny that a projection event can begin in “prospective phase” (as defined above), the theory is silent on how it can happen outside the “inheritance of projective complexity”; that is before a larger periodicity has been “entrained.” The problem of when meter kicks in is perhaps even more severe for an accent theory. According to Mirka, three accents are needed to establish a pattern; two accents merely generate a hypothesis which will not be “de- livered to consciousness” if unconfirmed. To some extent, a metric analysis premised on accent can cover its tracks by simply claiming that BWV 1068’s m. 1 is “heard as” a hypermetric downbeat, without having to say how long it takes us to establish that interpretation. Hasty’s projection theory of (as I characterize it) pulse cannot make such a claim. But fundamentally, accent theories and Hasty’s pulse-bound projection theory have the same trouble modeling the pace of “entrainment” that can be observed with hypermeter. I will refer to these difficulties as metric theory’s first-pulse problem: the problem that relatively large periodicities can emerge prior to not only the third accent (or new beginning), but also the second. A theory of pulse is inadequate to explain the pace at which metric hierarchies emerge.

The One-Pulse Problem Closely related to metric theory’s first-pulse problem is its one-pulse problem. This is the problem that—by all modern theoretical accounts—there can be no such thing as a hypermeasure which is not preceded or succeeded by another; in other words, that stand-alone hypermeasures do not exist. Once again, the theory is reasonable (or at least, internally consistent) but musical observation contradicts it. From m. 9 of BWV 1068, until at least the start of m. 13, we are, I suggest, quite clearly aware of duple meter on the 16-bar scale. Although m. 17 is emphatically not the start of a second 16-bar 4hypermeasure, there is a palpable sense of the formation of a metrical unit of sixteen bars within what would be the first such unit. This feeling is strongest in the sequential passage, and would last through m. 16 if the passage were recomposed as shown in Example 3.4. As it is, our awareness of the cited 4hypermeter wanes as early as the second half of m. 13, which only reinforces the point that our sense of a 16-bar metric unit Hypermeter 151 hardly is attendant upon the imminent launch of a second unit. Whereas our awareness of the first 2-bar hypermeasure intensifies rapidly with the pickup to m. 3, and seems closely tied to the projection of a second 2-bar hypermeasure, the situation on the large scale is rather different. Neither a projection theory of pulse nor an accent theory can account for the fact of standalone hypermeasures; pulse levels at the apex of a metric scene containing only one duration or one accent. Yet, a metric scene in Bach’s gigues more often than not reaches its hierarchical limit with a hypermeter that is expressed in a single unit; it is less likely that the top-level hypermeter runs to a second unit. We have already seen this, without yet calling it meter, in the cello gigues, whose formal “modules” are hypermetric units.

The Last-Pulse Problem Another challenge to a metric theory premised on pulse concerns endings. It is telling that no end-oriented counterpart to the idea of “entraining” or “establishing” meter exists. And while Meter as Rhythm is critical of the inevitable, automatic character of the pulse stream in accent theories, projec- tion theory wrestles with a similar problem in that it ties the ending of one duration to the beginning of another. If a metric unit is properly completed— fully and cleanly realized—Meter as Rhythm more-or-less commits to saying that this projected potential is bound to become a projective potential too, meaning that a further projection event is incipient.44 However, this does little to account for the fact that metrical music can come to an end without abandoning its listeners to a soundless world of metric implication. Indeed, metrical music often arrives at a convincing conclusion by being more, not less, demonstrative in its meter than previously.45 Given that pulse is a pattern which is presumed to continue in the absence of signs to the contrary—and certainly in the presence of corroborat- ing factors—metric theory struggles to separate the ending of one pulse unit

44. The following passage is one of several in which Hasty ties ending and new-beginning together (Meter as Rhythm, p. 75): “There is, however, a potential that end does realize. This is the potential—always ‘present’ while the event is present—that this event will be succeeded by another, whereby the present event will be past.” Hasty also extends this line of argument, bringing him close to Mirka’s notion of projection (Meter as Rhythm, p. 82): “If end and beginning are inseparable as a realization of durational potential and a simultaneous making present and making past, we could say that the promise of a second beginning is also a promise for a third event and that the potential of the second beginning for a definite end is also felt as the expectation of an immediately successive event.”

45. Contrary to this claim, Hasty writes (Meter as Rhythm, p. 83, emphasis mine): “If there is no actual third beginning, the durational potential of the second beginning will still be realized, but the end of the second event will be somewhat indistinct.” 152 The Art of Gigue from the beginning of the next. How can a given movement end by laying down an unequivocal hypermeasure without leading the listener to expect or project another one? To explain ending is traditionally to trace the lines of melodic and harmonic closure, while metric theory exits consideration since meter is commonly thought to be a mechanism of getting started and keeping going. Metrical matters obviously play a large role in the forms of closure we currently ascribe to melody and harmony, though there is no indigenous concept of metric closure, only metric entropy. But some theory of metrical ending should have a place in our models and ontologies of meter, if by them we aspire to understand something important about rhythm and temporal forms.

A Temporalist View of Hypermeter Revising Hierarchy, Re-Evaluating Continuation Key to resolving the three problems outlined above is a rewriting of metric theory that makes hierarchy more fundamental to our model or ontology of meter. Hierarchy is a basic axiom of all metric models or ontologies. “[R]egular pulse grouped by another regular pulse” is how Samarotto de- scribes it.46 And invariably, meter is defined as temporal organization on at least two scales or levels. But has “hierarchy” been theorized appropriately for a metric theory in the service of metric analysis? Where does the traditional concept leave the analyst who needs to know not just what they are looking for but where they are looking for it? Convention has it that meter is multiplicity of pulse, such that whatever is necessary to a model or ontology of pulse will be sufficient to account for meter, if only those ele- ments are compounded subject to constraints that determine proper metric relations. Notions pertinent to pulse—of “accent,” “duration,” “regularity,” “projection” and so on—are not supplemented in any fundamental way to arrive at a theory of meter. Only the fact of multiplicity, of hierarchy itself, is new. But this continuity between pulse and meter will be challenged by a temporalist theory of meter that answers to the analytical problems cited above. Metrical theory’s existing reliance on the concept of pulse is equally visible in accent theories and Hasty’s projection theory. Accent theories hold the traditional idea of strong and weak beats to be the “intuition” which attends a metric structure that nonetheless is not configured of such

46. Frank Samarotto, “A Theory of Temporal Plasticity in Tonal Music: An Extension of the Schenkerian Approach to Rhythm with Special Reference to Beethoven’s Late Music” (PhD diss., CUNY Graduate Center, 1996), p. 48. This comment is cited in Mirka, Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791, p. 14. Hypermeter 153 qualities itself. Likewise, Hasty’s projection theory interprets strong and weak beats as instantiating “beginnings” which differ in scope but not in kind, at least so far as the basic ontology is concerned. Even though Meter as Rhythm disposes of the concept of independent pulse streams, and makes durational quality essential to the ontology of pulse, the distinction of strong and weak beats is settled on the interaction of smaller and larger (“dominant”) beginnings. Consistent across disparate methodologies, then, is a commitment to theorize meter in terms of pulse. This raises a subtle contradiction on the temporalist side: that “pure” hierarchy has ontological traction whereas “pure” duration does not. But this contradiction has gone unnoticed, and, in general, the definition of meter as multiplicity of pulse has not been questioned. Arguably, it has been challenged by people altogether skeptical of the value of “meter” for understanding and performing music, but there is no explicit critique to speak of. The logic of meter as multiplicity of pulse seems unassailable. There is no intrinsic problem with theorizing meter purely in terms of pulse hierarchy. Yet I do propose a change in approach specifically in connection with my aim of subordinating theory to analysis. The three problems cited above—the first-pulse, one-pulse, and last-pulse problems— are analytical problems which can be resolved by a temporalist theory of meter that acknowledges hierarchy at a deeper ontological level, making it something more than an addendum to a self-sufficient theory of pulse. This means re-evaluating the concepts and the experiences of strong beats and weak beats. A temporalist view of meter will take as its point of departure an apparently innocuous step in the standard argument about how meter is experienced or perceived. The starting contention, no-one disputes: that meter is “regular pulse grouped by another regular pulse,” as Samarotto says. Certainly, meter involves temporal organization on a minimum of two commensurate scales. Where the temporalist view parts company with the standard argument is in the latter’s move to break down the experience of meter into successive experiences of manifestly strong and weak beats or manifestly large and small beginnings in Hasty’s terms. Schachter states: “It is a truism that meter arises out of the interaction of strong and weak beats.”47 The key word here is “arises”; the idea, that meter is the product of patterns in accentuation or duration which have their own ways of being made, performed, experienced, or perceived. Meter arises as a synthetic capacity that operates upon separate strong-beat and weak-beat elements. It is hard not to agree with Schachter that meter proper, operating at the level of notated bars, is identical with an “interaction of strong and

47. Schachter, “Rhythm and Linear Analysis: Aspects of Meter,” p. 5. 154 The Art of Gigue weak beats.” However, in connection with hypermeter and specifically for analytical purposes, the “truism” is an under-interrogated assumption. Meter may be modelled as multiplicity of pulse. But that is not to say we can best explain metric perception or metric experience as consisting of pulse perceptions on multiple levels. This stage in the standard argument limits the scope of “meter” to our theory of pulse and our general concept of hierarchy (not even a specifically musical one). As indicated earlier, the abstract purity of hierarchy that enters here is a severe problem for a temporalist theory, since it inscribes—rather than merely enlists as a heuristic device—a vacancy of musical content which is detrimental to the whole notion of projection. The solution lies in a radical re-evaluation of hierarchy. Prolonged engagement with Bach’s gigues, and repeated encounters of the analytical problems cited above, prompt me to argue that Schachter’s “interaction” cannot be fruitfully understood in terms of separate experiences of “strong” and “weak” elements that are then synthesized into meter. If theory is to equip the analyst for the temporal condition of analysis itself, that position is untenable. The challenges of hypermetrical analysis are, as I have found in studying Bach’s gigues, well served by an ontology of meter that emphasizes the generic “weak beat” instead. I argue that it is more fruitful to situate metric “knowing” in the experience of weak beats alone than it is to attribute the generic “strong” and “weak” beats to separate perceptual or experiential moments. Under this conception—which is really a logical result of temporalism—the traditional concept of “two levels” is plowed into a single experiential category with a particular place in time vis-à-vis the projection event and its associated durations. This radical leap is, in fact, a short step from the rudiments of projection introduced earlier: that projection is anchored in the act of “beginning again” or “starting over”; and that out of this action, a structure of multiple pulses can be unpacked. The generic projection event thus involves successive durations, namely past and present during the privileged active phase. Yet projective process does not consist of experiencing one duration and then another. The same line of thought can be applied to meter, with the result that metric process does not consist of experiencing the onset of one, dominant duration and then the onset of another, subsidiary duration. Hierarchy can—must, for a temporalist approach—be regarded as embedded in the smaller-scale “beginning again,” which at the same time prolongs or revitalizes a durational “beginning” on the larger scale. It is a radical move to recognize the generic “weak beat” as so important. The temporalist ontology of meter which can be elaborated from this claim emphasizes the articulative nature of metric process and involves a complete re-negotiation of the importance of boundaries and “units” in the traditional sense. Hypermeter 155

An articulative ontology of meter disposes of the three analytical challenges cited earlier. Presaging the shared solution to those problems is the fact that an articulative ontology allows us to say the simplest metric object would be one duple measure. In contrast, strange as this sounds, two duple measures would have to be the simplest instance of meter for any theory that regards meter as multiplicity of pulse, even theories as different as Hasty’s and what is arguably the prototypical accent theory, Maury Yeston’s.48 By allowing the analyst to observe a sense of “weak beat” that combines a smaller “beginning again” with the prolongation of a larger “beginning,” an articulative theory does not insist that the assumed larger “beginning” corresponds to a “beginning again.” Rather, the theory recognizes that the smaller pulse can be experienced (or performed, perceived, etc.) in such a way that it already intimates the larger pulse which groups it; that is, even though the larger pulse has not yet advanced to a second duration. Thus, if we recall Samarotto’s phrase—“regular pulse grouped by another regular pulse”—we can observe an important asymmetry in what London called “entrainment” or Mirka “establishing meter.”49 According to an articulative ontology, the smaller pulse only emerges with the start of its second unit, but the larger pulse may emerge at precisely the same time, with the subdivision of its first unit. Both London and Mirka, in their own way, would recognize this possibility as a psychological result of our familiarity with certain schemas, such as the 8-bar parallel period. But under a temporalist and analytical agenda, metric theory must take it upon itself to account for this possibility, namely the capacity for a larger pulse-periodicity to become known at the moment of subdivision. “Weak beats” that originate awareness of beat and measure at the same time are, to state the central thesis of this chapter, the essential component of a temporalist ontology of meter, specifically an ontology of meter that empowers the analyst as a necessarily temporal agent. It is a simple innovation which radically destabilizes our notion of meter as hierarchy of pulse, but it solves at a single stroke the major problems for metric analysis outlined above (as well as smoothing other obstacles which this chapter does not spell out). The first-pulse problem was that we routinely become aware of moderate to large hypermeters before a second unit is hatched, let alone a third. Once the feeling of a “weak beat” is recognized by theory as a fundamental object, analysis is permitted to say that a hypermeter

48. Maury Yeston, The Stratification of Musical Rhythm (New Haven: Yale University Press, 1976).

49. See note 43 for citations to Mirka and London. 156 The Art of Gigue can emerge during its first cycle, and analysis is empowered to chart the patterns of emergence, which are patently connected to the articulation of “subdivisions.” Similarly, the one-pulse problem was that large hypermeters, in particular, can be felt without a second unit ever being begun at all. Again, to recognize that the feeling of a “weak beat” is very basic to meter is to empower so-called “intuitive” and probing analysis. The first-pulse and one-pulse problems reference the same conceptual limitation, in effect, at the left edge and top edge of a dot diagram. Overcoming the last-pulse problem is perhaps an even profounder achievement. If metric continuity is held to be a matter of “weak beats” more than neutral pulse streams, then metric theory can take ownership of ending in addition to the beginning and sustaining of musical forms. When metric ontology is reorganized around the feeling of “weak beats” as something fundamental, we can shed the implication of a purely pulse- based theory that indefinite repetition is the order of things and that ending is arbitrary with regard to metric structure. Recognizing “weak beats” at a basic level means recognizing the capacity for metric actions to triangulate closure, above and beyond acknowledging the potential for metric states to be perpetuated indefinitely. This is appropriate, given that simple repetition is ultimately much less prominent in the metric processes of tonal music than one might guess based on the theoretical accounts of meter. I have indicated already that Bach’s gigues comprise metric scenes which usually reach their ceiling with a hypermeter whose realization is limited to a single span. Hasty’s projection theory already distances itself from the idea of continuous “pulse streams” by its view on hierarchical interaction. To that extent, Hasty substantially deflates the connotations of pulse toward indefinite perpetuation.50 But only by granting “weak beats” special status can theory shake off the last-pulse problem and account for a feature of much tonal music: the finality of very metrical passages. A fully temporalist ontology of meter only overcomes these problems for analysis by making a radical departure from the traditional practice of theorizing meter as multiplicity of pulse, in the strong sense described earlier. That departure is a step beyond the already radical arguments of Hasty. Yet it stabilizes and decomplicates projection theory by removing the vestiges of an incompatible concept of hierarchy, a concept which creates untenable positions for the analyst of metric process. I argue that an analysis- led approach to meter requires a metric ontology not limited by the ontology of pulse.

50. Hasty is critical of this understanding of pulse (Meter as Rhythm, p. 5): “Once set in motion, meter can seem to run autonomously, driven by its own internal law and fated from the beginning to reproduce its preordained set of time divisions.” Hypermeter 157

According to a temporalist theory of meter, the “weak beat”—Hasty’s “continuation”—becomes the one leading moment in the making of a duple measure, the simplest metric object.51 Here, the smaller and larger pulse- periodicities of a given meter are made known all at once. Hierarchy is unpacked, metric “knowledge” conveyed, from a single temporal position. The weak beat is, then, not only a concept in metric structure, but an articulation which happens at a specific point in time,52 and which—broadly understood—has a monopoly on the formation of metric relationships. A special type of rhythmic moment, the weak beat is an irreducible element of metric process and the metric analyst’s most basic task should be to map its occurrences.

Metric Projection, Prosaic Projection Once the special capacity of weak beats to embody metric knowledge is recognized, a major distinction emerges between what I will call prosaic projection and metric projection. I use “prosaic projection” to mean simple pulse projection; projection by Hasty’s definition. The central act of prosaic projection (its central conviction or perception) is the act of starting-over: the feeling of another which accompanies the start of the second duration in the generic projection event. I use “metric projection,” on the other hand, to indicate a more dedicated feeling of the other. Hasty’s “continuation” is exactly what I mean here, only the ontology is differently construed to accommodate hierarchy as an irreducible quality rather than a function of multiplicity. The difference of metric from prosaic projection thus lies in the complementary character of the second unit, and the quality of prolonging a larger duration while simultaneously starting over on the smaller scale. Now that the concept of metric projection has been introduced, a term is needed for the larger duration involved in a metric projection-event, which is neither “projective” nor “projected” since repetition is not instrumental for its emergence. I will refer to the larger duration involved in a metric projection as the metric envelope. A clear case of prosaic projection would be a projection-event in which one 2-bar span is projective for another 2-bar span with zero implication of an encompassing 4-bar span. Examples of unambiguous prosaic projection are not plentiful in the hypermeter of Bach’s gigues. One of the few good

51. Given two “weak beats” this statement also applies to the making of a triple measure. Triple meter is addressed shortly. Note that my text will often use “meter” instead of the more cumbersome “hypermeter,” but hypermeter remains the topic of this chapter.

52. Though not a “durationless instant.” For a critique of that idea, see Meter as Rhythm, pp. 9–10 and 75–76. 158 The Art of Gigue illustrations occurs toward the end of BWV 827, mm. 42–47, where the inverted fugue subject is repeated in the dominant, tonic, and subdominant minors in 2-bar segments on the approach to the Schlußsatz, which comprises a descending thirds pattern (mm. 48–49) to prepare the cadence (m. 50). Examples of unambiguous metric projection are, by contrast, extremely plentiful. The beginning of BWV 1068, for one, features a strong metric projection on the level of 2-bar spans at the start of m. 3. Thus a duple structure of “strong” and “weak” beats may be read on the 2-bar level and we see the emergence of a metric envelope spanning 4 bars: a large duple 2hypermeter is now in play. In practice—especially with the analysis of elaborate fugal gigues—it is not always easy to tell “prosaic” and “metric” projection apart. These are ultimately observed qualities that could be part of a more fine-grained typology. However, in my study of Bach’s gigues, I have found this basic typology generally adequate to the comparisons and observations I wish to make. Only in rare situations does the prosaic–metric distinction seem inconsequential, tangential to the interests of musical interpretation and performance. To separate prosaic and metric qualities of projection is reasonably straightforward most of the time, and is almost always an illuminating exercise for understanding rhythmic process. Although one could recognize gradations of prosaic and metric projection, depending on how prominent the metric envelope is, I will skirt that complication here. There certainly are, however, more than two types of projection that must be recognized in this discussion. It is incumbent upon a temporalist ontology of meter to recognize as many types of “weak beat” or other continuative gesture as are necessary for the theory to cover all the basic strategies of metric structure; as many types as necessary to equip the analyst to discover not only triple meter, but also various structures that manifest the general idea of “a measure” in less orthodox ways, and structures that involve multiple “levels” of meter in sophisticated “interactions.”53

Projections “Acute” and “Obtuse” The phenomenon I will call acute metric projection is a logical extension of metric projection but comes to attention only through analytical practice, as a recurring observation concerning metric emergence. With plain metric projection, two levels of pulse became palpable at a single weak beat. With acute metric projection, however, a single weak beat bears the primary

53. I distance myself from the terms “levels” and “interactions” because the idea of pure hierarchy is anathema to the temporalist theory being elaborated here. Even within the conceptual limits of the theory, the notion of “levels” is an approximation to the real complexity of metric process. Hypermeter 159 responsibility for surfacing three levels of pulse, and two layers of metric hierarchy. At its simplest, this is the phenomenon of the spontaneous feeling of a fourth beat, one articulation that precipitates one’s whole sense of quadruple meter. Everything that was said of metric projection applies doubly. Here, the feeling of complementation can be described as “the other within a larger ‘the other’.” Even though the second and third beats of a generic quadruple measure might clearly define the tactus pulse, and perhaps the half-measure pulse, the fourth beat is where the complementary relations of duple meter on two levels snap into place. In this scenario, pulse is galvanized to a properly metric perception late in the unfolding of the “measure.” For projection theory, the novelty of acute metric projection is its recursive element. Just as the fourth beat of a generic quadruple measure assumes a dominant beginning of the third beat, so the two together—by affecting a larger continuation—assume a dominant beginning of the first beat. Still more so that with prosaic and plain metric projection alone, the analysis of metric processes is not clear cut where acute metric projection is involved. Acute metric projection is not a sudden rush of metric knowledge preceded by total ignorance; rather, it is a moment of metric conviction that significantly outshines previous intimations of meter. To be precise, it is the continuation of the larger projection (beat three in a generic quadruple measure) which pales in situations of acute metric projection. The initial smaller projection (at beat two) may be relatively strong and fully metric. The question is simply whether a certain hypermeasure is articulated pri- marily by its weak beat or, more remotely, by a weak beat of its weak beat. (In the analysis of Bach’s gigues, I have not been moved to observe further levels of recursion, and they seem implausible.) For an example of acute metric projection, consider mm. 25–28 of BWV 1068. It is possible to perform this opening to the second strain such that the 2-bar 1hypermeter and 4-bar 2hypermeter (each duple) both kick in in earnest with the downbeat of m. 28. In this case, m. 27 may clearly express the start of a second 2-bar unit, but the specific feeling of that unit’s complementing the prior unit, and combining with it, is not yet crystallized. Similarly, the bar units can be clearly articulated by m. 26 without there being much sense of complementation, which is the essence of duple hypermeter. These feelings of complementation large and small are saved for m. 28. The acute metric projection becomes even more dynamic if the sense of 2-bar units is suppressed altogether before m. 28, by performing m. 27 as “another” on the scale of bar units instead. (That option introduces an element of change which does not assimilate to the notion of “unfolding” a metric state.) To illustrate what is special about acute metric projection as an option in performance—and composition, before that—the interpretation 160 The Art of Gigue of mm. 25–28 just described can be contrasted with another, in which m. 27 would be performed as a metric projection that outshines the subsequent articulation at m. 28, dispelling the acute metric projection. The more m. 27 is felt as a complement of m. 25, the less m. 28 can do. And mm. 25–28 in themselves are perhaps none the worse for this. But the second 4-bar 2hypermeasure does, I argue, suffer by the weighting of m. 27 over m. 28. Come the corresponding articulations at mm. 31 and 32, the enlarged metric horizon of 8 bars and the use of an authentic cadence favor the former articulation. Only if m. 27 is not over-emphasized can m. 31 be really effective. In fact, part of m. 31’s importance lies in its own capacity for inflecting an acute articulation, binding mm. 29–32 firmly to mm. 25– 28 as their duple complement. Though m. 29’s downbeat was already another m. 25, metric rapport was lacking, perhaps because of the stepwise harmonic relation. Thus, I suggest that in mm. 25–32 of BWV 1068, the leading moments in the metric process occur around the downbeats of mm. 28, 29, and 31, and the first and last of these carry the greatest responsibility for intimating duple hypermeter on three levels. Like acute metric projection, what I call obtuse projection is a phe- nomenon that involves two layers of meter, and, at its simplest, can be understood as an option for articulating the fourth beat in a generic quadru- ple measure. But obtuse projection is opposite to acute metric projection in that it negates the—already active—larger projection that would bind the “measure” together. An obtuse projection is a projection that would be interior to the active phase of a larger projection-event, except that it casts off from the larger projection. It is a subdivision that is destructive, rather than creative or supportive, of its metric environment. Because obtuse projection is no disruption to the beat pattern, however, it is a form of metric discontinuity that eludes a dot diagram. The specific rapport of successive durations is key, and even more than other phenomena described in this chapter, obtuse projection comes to attention through analysis rather than as a logical extension of metric theory. For an example of obtuse projection, consider m. 15 in BWV 1068 and the metric projection on the level of 2-bar units which occurs there. The previous discussion of BWV 1068 ended by addressing this moment. Although m. 15 articulates a sturdy 4-bar 2hypermeasure across mm. 13–16, the specific rapport of mm. 15–16 with mm. 13–14 is not consistent with the already active projection-event in which mm. 13–16 are unfolding as the duple complement of mm. 9–12. Without breaking ranks with the 4-bar 2hypermeter (or the 2-bar 1hypermeter), m. 15 stops the 8-bar 3hypermeter in its tracks (the 16-bar 4hypermeter, too). Accent theories cannot credit such events to meter per se, but these are a vital ingredient of Bach’s metric technique. Note that obtuse projection may be either metric (as in the Hypermeter 161

Example 3.5: Diagram of prosaic projection. example given) or prosaic. The point is that a positive connection on some smaller scale is coupled to the negation of all projections on larger scales. Finally, concerning obtuse projection, it must be understood that no metric process is instantaneously discontinued at the onset of a beat, just as none is begun instantaneously either. With BWV 1068, the larger hypermeters are already slipping away with the second half of m. 14. But the negation of metric processes has the same kind of rhythmic profile as their origination, at least in Bach’s music. Metric processes are organized around a beat structure, and recognizing obtuse projections helps to rectify metric theory’s general neglect of how hypermeters are ended or abandoned.

Projection Diagrams Building on the simple diagrams introduced by Hasty in Meter as Rhythm I will now introduce a method for diagramming projective process. Hasty uses adjoining arcs to illustrate the two potentials—projective and projected—of a given projection event, and I shall do the same, albeit with changes and additions. The advantage of the method promised here is the ability to document complex metric processes in a single diagram, laid out along a timeline. Example 3.5 shows my symbol for a prosaic projection-event. Like in Hasty’s diagrams, the first arc represents the projective potential and the second arc, the projected potential. I have however inverted Hasty’s dashed and solid strokes, so that the solid stroke indicates (rather than the “determinacy” of the past) the greater vitality of the projection-event during its active phase. The general rule is for a given projection to emerge—or at least come through most strongly—at the point of starting-over. For that reason, I show the projective potential curving downward, like a reflection, but the projected potential arcs upward, suggesting something like the “surfacing to consciousness” which Mirka describes in her analysis of metric perception. Following the principle that projection-events tend to become “live” at the point of starting-over, and consistent with this chapter’s arguments about metric analysis, the downward and upward arcs of the diagram represent “past” and “present” temporalities. Effectively, the downward arcs are to be read backward and the upward arcs forward, with 162 The Art of Gigue

Example 3.6: Diagram of metric projection.

Example 3.7: Diagram of acute metric projection. the point at center representing the point at which we become aware of the entire projection. The thin line is a timeline (no temporalist gloss on this is necessary) and the intersection of the timeline by the projection’s S-curve represents—in an idealized fashion—the moment of rhythmic articulation or “accent.” Augmenting the symbol for prosaic projection, the symbol at Exam- ple 3.6 illustrates a metric projection-event. The diagonal stroke is Hasty’s symbol for “continuation”; the extra arc above, an innovation, represents the metric envelope. Note that this extra, wider-angled arc would meet the horizontal at the same point as the beginning of the projective potential if it were extended backward. As it is, the diagram makes plain the point I made earlier about the teleological basis for the coherence of the two pulse periodicities. For the metric envelope is drawn only within the window of time during which the projection-event is “live.” Every analytical diagram in this chapter subscribes to the admittedly simplistic view that projection- events always open directly into the generic active phase, without being intimated during the generic prospective phase. The way to impart greater subtlety to these diagrams would be to adjust the start of the wider-angled arc to show the projection event’s onset more precisely.

Diagramming Acute and Obtuse Projections The symbol for an acute metric projection-event is shown in Example 3.7. The diagonal stroke still indicates “continuation,” now made steeper to convey the acuteness of “continuation of continuation” and (this is the obvious visual difference) positioned so as to straddle the middle arc. The two solid arcs opening in mid-air represent the metric envelopes of the two layers Hypermeter 163

Example 3.8: Diagram of obtuse metric projection. (The large dot identifies which projection that is.)

Example 3.9: Diagram of obtuse prosaic projection. of meter; that is, in the generic quadruple measure, they represent the durations of the second half of the measure and of the entire measure. The dashed arc, representing projective potential, takes on a lopsided “w” shape in order to keep multiple symbols separate in complex diagrams. The right side of the “w” represents the immediate, smaller projective potential; the left side, the more remote and larger projective potential. (These correspond to the third beat and the first half of the quadruple measure.) An obtuse metric projection is diagrammed at Example 3.8. The novel element in this diagram is the symbol for negation of a projection, namely the early termination of the solid arcs, highlighted by short vertical lines. Regarding the projected potential which is negated and the envelope of the obtuse metric projection which precisely supplants it, the vertical line signals the discontinuity which would otherwise not be visible. For comparison, Example 3.9 shows an obtuse prosaic projection. Both these diagrams show an obtuse projection disrupting duple hypermeter, but obtuse projections may occur during the active phase of any pulse projection or metric projection.

Idioms of Triple Hypermeter Beyond the basics of prosaic and metric projection, I will now introduce the types of projection involved in forming non-duple hypermeters, specifically triple hypermeter of various sorts. Although the more advanced phenomena of duple hypermeter are in some ways more important than the options for non-duple hypermeter, some element of triple hypermeter is found in many of Bach’s gigues. 164 The Art of Gigue

Example 3.10: Diagram of ordinary triple hypermeter.

Meter as Rhythm ontologizes triple meter by way of the notion of “deferral.” The precise meaning of deferral is tied to the particular way continuation is conceived. Hasty theorizes continuation as a new-beginning which allows a previous—and consequently “dominant”—beginning to remain in force, and, in other words, allows a “dominant” duration to continue growing. Thus his “deferral” refers to the delay in concluding a measure that results from a secondary continuation. In simple language, the end of the measure is pushed back by one beat. One can detect in this formulation, incidentally, some recognition of the power of “continuation” on Hasty’s own terms. In progressing from a temporalist view of pulse to a fully temporalist view of meter, a shift occurs in what exactly is understood to be deferred. Meter as Rhythm situates deferral in a delay of the measure’s end or an extension to the life of the “dominant beginning.” But I suggest that deferral is experienced in the context of more positive rhythmic aspirations to completion and complementation; that is, within qualitative dimensions of metric projection. It cannot be understood extrinsically as an extension (under certain constraints) of the larger duration per se. Not the larger duration, but the act of metric projection is the subject of deferral: this would be the fully temporalist view. Thus the projection-event which defines meter from the inside is itself “projected.” Triple meter is illustrated by Example 3.10. The horizontal line is taken directly from Hasty and symbolizes deferral. The inclusion of a continuation sign in the lower, “projective” part of the diagram reflects the interpreta- tion of deferral as a projection of the continuation relationship itself.54 In practice, especially with larger hypermeters, it is typically not until half way through the second beat that the immediate sense of completion or complementation is attenuated, and we become aware of a triple as opposed to a duple formation. But the graphic does not attempt to trace our shifting sense of the metric envelope.

54. Under this meta-projection, the projective potential for the generic triple measure’s third beat includes the quality of a projected potential. Hypermeter 165

Example 3.11: Diagram of triple organization of the “1, 2, 2” idiom. (The large dot identifies the special “third” beat.)

Example 3.12: Diagram of triple organization of the “1, 2—and” idiom.

Another kind of deferral is illustrated in Example 3.11 which is not part of Hasty’s theory nor the standard accent theories. The phenomenon illustrated here would conventionally be regarded as a matter of grouping and not meter: a succession of three units where the third is felt as a repeat of the second. Against the basic schemas of duple and triple measures, one would count this not as “1, 2, 3” but “1, 2, 2.” Thus, the articulation highlighted by the large dot could be described as a “secondary second beat” or (adapting language I used earlier) “another ‘the other’.” Whereas in a triple measure, the first continuation is deferred for a second continuation, here, it is deferred for a simple reiteration: the third unit is articulated not by metric but rather prosaic projection. As the count of “1, 2, 2” implies, the third unit has a more emphatic than expansive rhetoric, and the extra projection does not, in a sense, expand the metric envelope beyond that of a duple measure. The z-shaped curve is meant to illustrate the extension of the measure as a function of reiterating the generic second beat. Rightly, this suggests that the initial metric projection is not fully completed or resolved with the second sounding unit. The vertical line takes Hasty’s symbol for beginning (which otherwise my diagrams do not use) to mark the shift in this kind of deferral from metric to prosaic projection. A third kind of deferral is illustrated in Example 3.12. This is not part of Hasty’s theory or the standard accent theories either. Here, the third of 166 The Art of Gigue three units is felt not as a repeat of the second, but as a duple complement of the second. Against the basic schema of duple and triple measures, one would count this not as “1, 2, 3” or “1, 2, 2” but “1, 2—and.” The articulation highlighted by the large dot has the feeling of an internal subdivision of the second beat, such that units 2 and 3 coalesce as an enlarged complement of unit 1. (The articulation at “and” in the count of “1, 2—and” is a sort of acute metric projection.) An articulative theory makes it possible to recognize this feeling as a metrical device, rather than a compositional deformation of metric archetypes. This is valuable if, as in this study, metric analysis is used as a point of entry for other forms of analysis, instead of appearing as a function of prior observations about melody, harmony, motivic technique, and so on. Within the current theoretical frame, this third form of deferral exhausts the possibilities for triple organization. As with all projective phenomena, the feelings of deferral in “1, 2, 2” and “1, 2—and” cannot be grasped in the abstract but only when real durational content is at hand. Forms of triple organization are pertinent to BWV 1068, since the three periods each consist of twenty-four bars and are all somewhat open to being read against a putative naïve design of 8-bar units. Period II is, indeed, formed of three 8-bar, duple 3hypermeasures. As I see it, these three segments also coalesce as a single metric entity— the chapter 2’s “Interior Phrase.” But how exactly do the three segments relate? A valuable comparison is available in periods II of BWV 1009, the C major cello suite, and BWV 825, the B ’ major keyboard Partita. Both comprise three units of 8 tactus beats each (fewer than BWV 1068’s sixteen). BWV 1009’s period II, though triple on first glance, clearly falls into two halves—one short, one long—corresponding to the form functions of Forephrase and Afterphrase. Recalling chapter 2, the Forephrase accords with the “regular scale” that applies to all of period II in BWV 1007, 1008, and 1011, whereas the Afterphrase accords with the “large scale” that applies to all of period II in BWV 1012. In BWV 1009, therefore, the start of the third unit is felt as an interior articulation of a now-enlarged second half: “1, 2— and.” The period is an asymmetric expression of duple meter. By contrast, BWV 825’s period II is formed of more equable units, the the description of “a triple hypermeasure” is apt. Although units 2 and 3 together resemble the large Afterphrases of BWV 1009 and 1012—and despite their being a direct parallel to BWV 825’s own Answering and Closing Complexes—the continuity of texture and melody between units 1 and 2 erodes the sense of a prevailing articulation at that juncture. The two moments of articulation are equivalent: “1, 2, 3.” Despite their apparently similar structure, the two passages from BWV 1009 and BWV 825 stand at distinct places on a spectrum of metric possibility. I would argue that BWV 1068’s period II falls somewhere between those feelings of “1, 2–and” and “1, 2, 3.” By Hypermeter 167 recognizing these qualities, we sharpen our vocabulary for metric process, and identify musical distinctions for the analysis of compositional technique to explain.

The Many-Pulse Problem A crucial difference between projective analyses and dot diagrams must now be explained, with reference to an analytical problem which I call the many-pulse problem. This was not discussed earlier because it is not an intrinsic problem of analyses based on accent theories, nor of analyses based on Hasty’s projection theory, but is a major challenge that arises in moving between the two approaches. It is a possible pitfall for the move to implement a temporalist theory of meter. The problem is that a single point of rhythmic articulation may implicate multiple (or “manifold”) acts of projection, thwarting the analyst’s ability to tease apart metric process into discrete “levels” and successive “actions.” For someone adhering to a conception of metric analysis as the uncovering of a grid or beat structure, accepting Hasty’s notion of “the inheritance of projective complexity” leads to a paradox. The generic “quadruple hypermeasure” is a simple case. Consider a simple rhythm “1, 2, 3, 4”: even if the fourth beat is not explicitly sounded, some sense of an articulation is inevitable because of the relationship between the two halves. To be explicit: if a 2-bar projection takes place at m. 3, then a 1-bar projection is already prescribed for m. 4 due to the inclusion in that 2-bar projection of the 1-bar projection from m. 2. Any “original” impetus for a 1-bar projection at m. 4 is thus intertwined with the “consequences” of the previous and ongoing projection-events. How can the analyst be sure whether the articulation they observe at m. 4 is really there? Does the feeling of a projection belong to m. 4 or should it be attributed to mm. 2 and 3? Such doubts speak to fearsome methodological issues having to do with the competing perspectives of psychology and process philosophy. The point is that the analytical quandary results from an untenable mix of perspectives. Moving to a fully temporalist theory of meter requires some loosening of the idea that metric process is composed of separate points of articulation and that these separate articulations “originate” meter. At the very least, it means no longer tasking metric analysis with isolating those origins. So the discrete projection-event is most of the time only an approximation to the truth of the situation, even within the conceptual orbit of projection theory. No projection-event which is subordinate to the active phase of another can be regarded as a truly independent rhythmic impulse, and most projection-events fall into this category. 168 The Art of Gigue

A temporalist conception of hierarchy, including the inheritance of projective complexity, is thus incompatible with dot diagramming and the aspiration to uncover a metric grid or structure that it represents. A basic premise of dot diagrams is that one “dot” is not merely another in disguise; that beats 2 and 4 of a quadruple measure have an equal footing and are independent, and that beat 4 is not to any degree a mere repercussion of beat 2. Once the projective model of pulse hierarchy comes into play, the “grid” ideal of metric structure thus becomes untenable. Hasty makes this quite plain in Meter as Rhythm, albeit not explicitly in the form of the many- pulse problem.55 The temporalist view is that well-formed “metric states” are a flawed ideal, even for describing the state of play at one moment in time. Hence, an animated dot diagram, however intricate, would never be a temporalist analysis. That simple statement needs to be underscored. If the many-pulse problem discredits the “grid” for a specifically temporalist analysis of meter, the question now arises what a metric analysis should be. If the seried ranks of regular articulations would be a façade in the context of a temporalist approach, what ought to replace them? What rhythmic articulations should the analyst aspire to describe?

Toward Rhythmic Reduction In that crucial question, the debate over the dichotomy of rhythm and meter looms large. Suffice it to say that approaches affiliated to process philosophy or temporalism are generally hostile to the dichotomy, whereas approaches affiliated to psychology or cognitivism are generally amenable to classifying “rhythm” and “meter” separately.56 For current purposes, however, the direction is clear: to skirt the paradox described above while still moving toward a temporalist theory of meter, we have to relinquish the ideal of the metric grid and accept a more flexible concept of metric states. To take an example, we may come to recognize multiple ways of making a quadruple hypermeasure; the regular, evenly weighted beat pattern of “1, 2, 3, 4” will no longer have a monopoly on being metrical. For want of a better term, “simple rhythms” are the objects which remain for metric analysis to discover, once the ramifications of the many-

55. See, for instance, Hasty, Meter as Rhythm, pp. 18–19.

56. This emphatically does not mean that cognitivists must necesarily regard the distinction between “rhythm” and “meter” as an objective reality in music or the experience of music. The point here is the willingness to enter a basic categorical separation between “rhythm” and “meter” in formulating ontologies, models, and theories. Even as I seek to characterize an opposition of “temporalist” and “cognitivist” perspectives, however, one must also recognize that there are many kinds of cognitivist perspective on music and non-musical phenomena which I am not at all qualified to discuss. Hypermeter 169 pulse problem have percolated through the ontological and methodological apparatus. Specifically for a temporalist approach, the idea falters, that a regular beat pattern is an uncomplicated background or substratum of metric articulations, though it remains true that any hypermeasure or “metric scene” can be translated into a regular beat pattern for heuristic ends (such as constructing typologies). After the impossible contingencies of regular beat patterns have been recognized, the question that remains is the question of relative weight. Metric analysis must turn to defining the articulative priorities of a given passage; this, instead of attempting to isolate all of the rhythmic impulses which “generate” the beat pattern or (more broadly) metric process—which is impossible.57Seen from the traditional angle, “meter” will encroach on the domain of “rhythm,” taking in simple rhythms such as those sanctioned by Fux for counterpoint in the fifth species.58 Metric analysis thus becomes synonymous with a kind of rhythmic reduction; a selective weighing of the articulations in a given passage and their assessment in terms of the projective types introduced above. Rather than isolate rhythmic activity at certain levels of pulse, the analyst must convey the rhythmic sense of a passage with a limited number of articulations, which may or may not be evenly distributed. The potential for metric analysis of this kind begins to be explored in the brief studies of Bach’s chamber sonata gigues which now follow.

Analyzing Hypermeter in Bach’s Chamber-Sonata Gigues

Meter may raise stringent challenges to theoretical understanding but, in closing this chapter, I hope to show that the concepts and diagrammatic tools introduced here are not unduly difficult to apply. In fact, I claim that a connective, “middle-out” perspective on hypermeter comes more easily than more established concepts, and opens up new possibilities for the inter- pretation of rhythmic technique, specifically in the challenging environment of Bach’s gigues. At this juncture, a comment of Ralph Kirkpatrick’s sums up the changed point of view that this chapter has championed:

By and large, those parts of the measure which are active and which control the establishment and maintenance of a tempo are the upbeats

57. The word “generate” appears in inverted commas to set apart the cognitivist paradigm which is at odds with the methodology being espoused here.

58. Johann Joseph Fux, Gradus ad Parnassum (Vienna: Johann Peter van Ghelen, 1725). See Schenker, Counterpoint, and William Rothstein, “Rhythm and the Theory of Structural Levels” (PhD diss., Yale University, 1981). 170 The Art of Gigue

and offbeats. There is very little that can be done with a downbeat. The downbeat is a result, not a cause. But there is a great deal that can be done to manipulate the causes represented in the rest of the measure.59

In the remaining pages, I present analyses of Bach’s two chamber-sonata gigues: the gigue for flute and harpsichord in BWV 1030, and the gigue for violin and continuo in BWV 1023. These movements make an interesting stylistic contrast. Where one inhabits a trio-sonata idiom and has clearly demarcated hypermeasures, the other is written in a leaner duo idiom and pursues a much more changeable course with hypermeter and phrase rhythm.

Pulse and Meter in Bach’s Gigue for Flute and Harpsichord Bach’s gigue for flute and harpsichord takes a relatively mechanistic ap- proach to form. Much of the movement is effectively spent unpacking a single, preconceived period through two-and-a-half “rotations” in the keys of the tonic, dominant, and relative major. An explicit reconstruction of the “ideal” period can be made by joining the movement’s first ten bars to its last four with the aid of a linking device (in the bass part) taken from a third location: Example 3.13 shows the result. This model completes a clear Vordersatz–Fortspinnung–Schlußsatz routine without leaving B minor. When, with BWV 1030, the beginning and end of the movement are brought together in the “ideal” period, an important connection comes to the fore between two passages whose pitch content and metric content I will now examine. The passages in question are the third quarter of the main theme and the first half of the closing material, both of which operate a counterpoint of 6–ˆ 5–ˆ 4–ˆ 3ˆ over 4–ˆ 3–ˆ 6–ˆ 5.ˆ In the artificial context of the ideal period, the later passage clearly recalls the earlier, subject to rhythmic expansion, and returns the flute to the same motivic and tessitural space. However, in the complete movement, the similarity of the passages is obscured at first by a modulation to the relative major: the last four bars of the ideal period are transposed up a third. One might say the whole movement is motivated by the eventual recovery of the connection that is only latent in the initial presentation. The purpose of the following analysis is to describe the metric character of the relevant passages, and explain their role in the movement’s larger metric process. As chapter 1 mentioned, it is quite unusual that strain 1 includes two equal periods. The first period of the movement, as is, transposes the closing

59. Ralph Kirkpatrick, Interpreting Bach’s Well-Tempered Clavier: A Performer’s Discourse of Method (New Haven: Yale University Press, 1984), p. 67. Hypermeter 171

^ ^ ^ Mm. 1–10 6 5 4^ 3 q q

 q q q q q q q q q q q q q  1216 q q q q q q
q q q
q q q q
q q q q q q q q  
q q q q   
12 q q q q qq q q q q q  16 q q q
q q q q q
q q        q q q q
q q   q q q q 1 

12 q   q q q 16    q  ^ ^ ^ 4 3^ 6 5 q q q

q q q q q q q q q q q q q q q q q q q q q q  q q q
q q q
q q    q

q q  q q q q q q q q q q q  q q
q  q q q q q q
q q
q q q q 
q q
q q q 1 
q q q q q q q q q q
q     q q  q q q  q q q
q q q q q
q q q q

q q q q q q q  q q q q  q  
q q q q q q q q q q  q q q q 

q q q q q q q q q q q q
q q q q  q q
q  q q   q 1 

q q q   q q    q q
q q    Mm. 61–64   q
q q
q q q q q q q q q q q q 
 q
q q q q q q q
q q q q q q q q q q  ^ ^ ^ 6 5 4^ 3  q q q
q q q q q q q q q q q q 
q  q q q q q q q q q  4^    q q  

q q q q q q q q q q q q q q q q q q q q q ^ ^  3^ 6 5 From mm. 28–29 q q q q q
q q q q q q q q q q

q q q
q   
q q 
q
q q q
q q q
q q q q  q q q q qq q   1 
q q  q q 
q 
q q q q q  q q Example 3.13: Reconstruction of a non-modulating period as the basis of Bach’s gigue for flute and harpsichord, BWV 1030. 172 The Art of Gigue material and makes an authentic cadence in D major, from where a short link leads to the start of the second period on F~ minor. The second period then proceeds as a measure-for-measure reprise of the first period, with flute and harpsichord right-hand exchanging roles. A modulation is not made here, so the period remains in the dominant and matches the tonal simplicity of the reconstructed ideal period. Yet the extent of recall between the two 6–ˆ 5–ˆ 4–ˆ 3ˆ passages is hindered by several factors. (Refer here to mm. 21, 25, and 29– 30 [104, 108, and 112–113]; the score is reproduced in the supplementary volume.) First, the melodic similarity is less prominent on the harpsichord, especially given that the high flute dominates the closing material. Second, the flute’s repeat of the main theme occurs an octave above the harpsichord’s presentation, so the specific register of the sixteenth-notes figure in the closing material is not reinforced. Third, the bass part switches registers too, and small changes partially erase the motive of 4–ˆ 3–ˆ 6–ˆ 5.ˆ Similar changes throughout the second period distance it from the clear melodic patterning of the reconstructed model, despite its non-modulating structure. The contrapuntal device of 6–ˆ 5–ˆ 4–ˆ 3ˆ over 4–ˆ 3–ˆ 6–ˆ 5ˆ is primed for impor- tance throughout the movement, even during the 32 out of 64 bars when the ideal period is not being relayed directly. For example, the ascending se- quence in strain 1, which links the two periods, features a high flute line that plays into the flute’s subsequent statements of 6–ˆ 5–ˆ 4–ˆ 3ˆ in F~ minor. Strain 2, however, is where the opportunities are extensive for developing a musical argument around the tetrachordal idea. Strain 2 is constructed—without an internal cadence—of two large sections that account for respectively 5/8 and 3/8 of the strain’s duration. Bookending the first section (see mm. 33–52 [116–135]) is a 2-bar hypermeasure, repeated both times, that realizes the progression Vv–i with a firm melodic outline of 4–ˆ 3–ˆ 2–ˆ 1ˆ . At the front end, the unit is heard in the tonic then subdominant, and vice versa at the back end; these modulations of the tetrachord reinforce the diatonic scale of B minor. Between these bookends, furthermore, occur two variations on the movement’s main theme that manipulate the 6–ˆ 5–ˆ 4–ˆ 3ˆ device. At the harpsichord’s presentation, the tetrachord’s resolution to g4 (in E minor) is delayed as part of a modulation to G major (see mm. 41–42 [124–125]). At the flute’s presentation, the tetrachord becomes Phrygian in line with the switch to major mode, and is subject to a chromatic continuation that pushes upward (see mm. 47–48 [130–131]). As for strain 2’s second section (see mm. 53–64 [136–147]), this opens with a varied reprise of the sequence from strain 1; an initial step toward the end-rhyme that later locks in with the movement’s last four bars. The upper line of the sequence is, again, essentially tetrachordal, in the form of 8–ˆ 7–ˆ 6–ˆ 5.ˆ Continuing the downward scale of the prior Vv–i unit (4–ˆ 3–ˆ 2–ˆ 1ˆ ), the sequence thus leads into the territory of the closing material’s now-imminent 6–ˆ 5–ˆ 4–ˆ 3ˆ descent. Hypermeter 173

1 2 3 4 5 6 7 8

Example 3.14: Metric analysis of the opening theme (repeated) in Bach’s gigue for flute and harpsichord, mm. 1–8. This reduces the theme to nine articulation-points including the beginning.

The 6–ˆ 5–ˆ 4–ˆ 3ˆ idea and its tetrachordal companions have a definite metric character and purpose, which turns out to be pivotal in a dynamic interplay of prosaic and metric kinds of projection. As defined above, prosaic projection is the articulation of “another”; a new beginning which does not assume weak-beat character and so does not imply metric hierarchy unilaterally. In the ideal period of BWV 1030, the penultimate 2-bar unit represents prosaic quality at its peak: the articulation of pulse more than meter. Although there are three layers of pulse which group in twos ( © ,
Œ , and C inside of , ), the insistence of each beat is the primary rhythmic affect, over and above any sense of binary completion. At the highest level, for instance, the onset of 4–ˆ 3ˆ is felt more as an emphatic sequel of 6–ˆ 5ˆ than a metric complement of it. The effect of this metric character on the following cadence is twofold. First, the clear beats lay a foundation for the cadence, prescribing what duration is available for the resolution to tonic, and projecting a rhythmic grid which the more varied material (and tempo) of the cadence can play against. Second, the suppression of metric projection maximizes the impact of continuative “bounce” both within the cadence unit and at its start, where a 4-bar hypermeasure is articulated that embraces the 6–ˆ 5–ˆ 4–ˆ 3ˆ unit. The emphasis on prosaic projection in the 6–ˆ 5–ˆ 4–ˆ 3ˆ idea has a larger strategic advantage. This is readily apparent in the third quarter of the movement’s opening theme—that initial, faster presentation of the 6–ˆ 5–ˆ 4–ˆ 3ˆ device. Example 3.14 shows a metric reduction of mm. 1–4 and mm. 5–8 (the repeat of the theme) to nine articulation-points each. In this analysis, the internal articulation of the theme’s third quarter and the onset of its fourth quarter are the “flattest,” most prosaic projections, and metrical 174 The Art of Gigue feeling is resurgent during the theme’s fourth quarter. A general principle is illustrated, in fact, by the resurgence of meter (i.e. of continuative feeling) in m. 4 following m. 3. To the extent an articulation is strong during the passive phase (the first half) of an enveloping projection, it is hard for a corresponding articulation during the active phase (the second half) to be impactful. For this reason, patterns of four regular beats tend to emphasize either the second or the fourth whenever the sense of binary completion is strong at the third beat. In the current example, not the weight but the quality of articulation is upgraded at the fourth ( Œ ) beat: the “flat” half-way articulation of m. 3 is a foil to the “bounce” that comes half-way through m. 4. The metric character of the third quarter thus facilitates an effective navigation from the theme’s midway articulation, where the metric horizon is set, to the eventual arrival on Vv. By redoubling the intensity of lower pulse levels, the material of m. 3 counters the tendency for metric process to pale in the second half of a large hypermeasure. Example 3.15 shows that in the ideal period, the expanded 6–ˆ 5–ˆ 4–ˆ 3ˆ unit performs a similar function. Accentuating pulse over meter at a penultimate phase in a formal unit is a procedure writ large in the use of a dominant pedal late in strain 2. Prior to the last four bars, which complete the ideal period, the pedal holds © Œ C forth for 51/2 bars. Pulses of
, , and are clearly articulated (with C first straddling, then aligned with the barlines) but a metrical rapport between the levels is lacking and hypermeter is suspended. Metrically as well as harmonically, the dominant pedal passage thus provides an effective foil to the closing material, where even the 6–ˆ 5–ˆ 4–ˆ 3ˆ unit feels relatively metrical. The pedal passage also fosters the sense of metric projection at the start of the closing material, to which it is more than equal in terms of duration, and which it groups with harmonically as a dominant–tonic pair. Here, the heavily pulsed passage is not a well-defined “third quarter” or even a coherent metric unit, so its preparatory role is no longer linked to stealing attention from a large-scale projection (the onset of a second half). However, the dominant pedal does begin as an extension of the chain of fifths sequence, which itself has “second half” connotations. In this frame, the heavily pulsed passage allows a metrical “fourth quarter” to be rescued not from the glare of a larger projection, but from a position of metric obscurity where the boundaries of rhetoric and rhythmic organization are blurred. I will end my analysis of BWV 1030 by asking what metric role the 2-bar 6–ˆ 5–ˆ 4–ˆ 3ˆ unit has in the ideal period. Whereas the initial 6–ˆ 5–ˆ 4–ˆ 3ˆ unit is the third quarter of the 4-bar opening theme, the place of the expanded form is less simple. To come to terms with the phrase rhythm of the ideal period, we can turn to chapter 2’s analysis of the cello gigues. The ideal period’s opening 8 bars present—twice over—a fairly typical Vordersatz Hypermeter 175

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Example 3.15: Metric analysis of the “ideal” 14-bar period in Bach’s gigue for flute and harpsichord (see Example 3.13). 176 The Art of Gigue pair; first led by the flute, then the harpsichord. Each four-bar rotation comprises two bars of tonic prolongation (Vordersatz 1) and two bars that navigate to an initial point of repose on Vv (Vordersatz 2). If the beat were 12 interpreted as Œ in 16 , each subphrase would be the typical four beats, but in any case—even if the density of melody and harmony suggests a felt © beat of
—the subphrases’ durations fall in the same range as in the cello gigues. The terms of chapter 2 relate less easily to the final four bars of the ideal period. On the one hand, the 6–ˆ 5–ˆ 4–ˆ 3ˆ unit—the period’s penultimate 2-bar hypermeasure—has something of a “static” Fortspinnung B character. On the other hand, it prolongs a pre-cadential progression from iv to i6 and features prominent stepwise motion, albeit downward, consistent with Schlußsatz 1 function. The 4 + 4-beat routine of set-up and cadence might, © ˆ ˆ then, be identified on two levels: by counting
s (so interpreting the 6–5– 4–ˆ 3ˆ unit as Fortspinnung B) or by counting Œ s (so interpreting the 6–ˆ 5–ˆ 4–ˆ 3ˆ unit as Schlußsatz 1). Where the period simply does not conform to the cello gigues’ model, however, is in the brevity of the sequence passage at mm. 9–10. At only two bars, not four, the sequence is unequal to the length of the larger Schlußsatz pair (as Fortspinnung B) or the length of the Vordersatz pair (as Fortspinnung A). To the extent the sequence and the remainder of the ideal period form an Answering Complex, BWV 1030 modifies the cello gigues’ consistent 8 + 4 + 4 design to a 4 + 4 + 4 design. By my analysis, the 6–ˆ 5–ˆ 4–ˆ 3ˆ unit is therefore the middle element of a triple hypermeasure spanning 6 bars. Its emphasis of pulse over meter, in this instance, allows a relatively quick transition from Fortspinnung to Schlußsatz and a convincing deferral of metric projection. Large triple hypermeasures, especially those that stand alone, typically erode the sense of projection from beat 1 during beat 2 in order to integrate and empower the deferred projection at the onset of beat 3. By directing attention to lower levels of pulse, the 6–ˆ 5–ˆ 4–ˆ 3ˆ unit permits precisely that switch of its own extrinsic function. At the same time, it is a transitional space for re-calibrating expectations of the length of the whole period. If a large metric projection is felt at the onset of the sequence, which is possible per Example 3.15, the expectation of a 16-bar period needs to be artfully forestalled. The lesson of BWV 1030, then, is that a relatively four-square structure can still be metrically sophisticated; that hypermeasures with identical beat structures can have different metrical meanings; and that a hypermeasure’s metrical profile is connected to its formal function. Moreover, the dichotomy of prosaic and metric projection can be vital in a movement’s rhythmic design. At a certain stage in a formal unit, of whatever scale, it becomes helpful to prioritize pulse over meter, and this is what Bach accomplishes with BWV 1030’s pivotal 6–ˆ 5–ˆ 4–ˆ 3ˆ idea. Once pointed out, this aspect of Bach’s Hypermeter 177


q
 q
q    q q q q
q Example 3.16: Contrapuntal framework for mm. 6–9 of Bach’s gigue for violin and continuo, BWV 1023. technique is not difficult to grasp, but only because of this chapter’s earlier theoretical innovations is it even possible to understand that meter is not reducible to pulse, and that pulse can be accentuated in opposition to the feelings of hierarchical and successional rapport that are proper to meter.

Flux and Containment Bach’s Gigue for Violin and Continuo The phrase rhythm of Bach’s gigue for violin and continuo is anything but mechanical in the style of the flute sonata. In this piece, complex issues of flux and containment come to the fore, notably in Bach’s persistent use of metric overlap. As explained earlier, an overlap occurs whenever a weak beat takes the place of an expected strong beat so that a new metric unit attaches tangentially to a previous weak beat and transforms it into a new beginning. According to the theory I have advanced, metric overlap is a fairly straightforward procedure based on the positive qualities of the weak beat; the surprise is not based on an impression of reduced accentual size or strength, and no “retroactive” modification of the feeling of the previous beat is necessary. Perhaps the clearest illustration of metric overlap in the violin and continuo gigue is found in the middle of strain 1. Mm. 6–9 feature two instances of metric overlap, even though the underlying counterpoint shown in Example 3.16 could make sense as a well-formed quadruple hyper- measure. As realized, the passage is composed of three elements: an ascending sequence at mm. 6–7, a faster descending sequence at mm. 71/2– 91/2, and a standing on V at m. 9. The resulting beat structure of C beats is depicted in Example 3.17, which demonstrates the accommodation for overlaps in my diagramming style. A more detailed metric analysis of the passage also reveals the preparation for each surprising turn at the C level. As Example 3.18 shows, oblique projections occur on the Œ level

first, disrupting the current projection on the level of , , but without yet straying from the established beat structure. These small articulations smooth the metric shifts and result from the changes of motivic pattern at each latent new beginning. More fundamentally, though, this passage is 178 The Art of Gigue

6 7 8 9

Example 3.17: Metric analysis of mm. 6–9 ( C beat structure) of Bach’s gigue for violin and continuo.

6 7 8 9

Example 3.18: More detailed metric analysis of mm. 6–9 of Bach’s gigue for violin and continuo. compelling because each new element is quicker to grasp than the previous one: the periodicity of motivic repetitions narrows from , to C to Œ . At the passage’s reprise in strain 2, the rhythmic intensification is exaggerated when the first element is changed into a descending sequence that runs to a third bar, making the successive elements span three, two, and one bars. In the movement’s three-period design, the passage just analyzed forms the middle of period I and the opening of period III, following strain 2’s interior cadence in the subdominant; as such, it is arguably the main block of Fortspinnung material. But in this movement, the flexible stringing-together of melodic and harmonic devices is not restricted to the Fortspinnung interior. At all stages, Bach’s violin and continuo gigue is metrically subtler than any of the cello gigues, the orchestral gigue, or the trio-textured gigue for flute and harpsichord. The opening and closing sections of each strain include metric overlaps too. Sometimes this is because a subphrase is drawn out to resolve on the downbeat of the next hypermeasure. The movement opens, for instance, with a prolongation of tonic that approximates the Vordersatz 1 function in the cello gigues. Although the subphrase is more substantive harmonically than the Vordersatz 1 function that chapter 2 described, the greater difference lies in the tonic resolution’s being pushed onto the start of the following hypermeasure—beyond the subphrase’s private metrical domain of four C s. To appreciate the expansive impulse at work here, Example 3.19 shows a recomposed opening in which the resolution is brought inside the span of  . The dual meaning of m. 3’s downbeat as written is clarified in strain 2 when the functions of resolution and departure Hypermeter 179

etc. q  12 q q q q qq q q q q q q  q q   8

q q q q q q q q q q q q  q  q q q q q q q q   12  q  q  q q
q
q q 8 q
q q
Example 3.19: Recomposed opening for Bach’s gigue for violin and continuo. are separated out at mm. 19 and 21 respectively. Metrical sophistication also applies through the remainder of strain 1’s opening events. While mm. 3–4 present a move to Vv in 4 C s, consistent with the Vordersatz 2 function 4 described in chapter 2, the arrival on Vv is twisted to Vv 2 and an extra bar is appended which reverts the harmony to i. At the start of m. 5, there is a strong metric projection from m. 4 which arguably defers to m. 3, creating a triple hypermeasure. Regardless of whether mm. 3–5 are interpreted as a triple hypermeasure or two duple hypermeasures overlapped, however, the metric process is not bound by the same rules as in the other gigues studied so far. An expansionary impulse, disruptive of hypermetrical formalism, is also evident in strain 1’s closing material. Once again, starting at m. 10, an initial resolution to tonic is pushed beyond the confines of a 2-bar hypermeasure onto the start of the next unit. In mm. 10–121/2, the attributes of a Schlußsatz pair of the cello gigues’ type can be identified: a heavily pulsed precadential element of four Œ beats and a cadential progression, I6–V–I, of another four Œ beats. However, the pre-cadential element is drawn out to a hiatus on V7 and the cadence is delayed. This means that the usual metric support for closure is lacking: the Schlußsatz 1 and 2 elements do not match and it is not clear whether the onset of I6 answers to the start of the precadential material or only the prior V7 chord. The tonic resolution is then elided with the start of a secondary Schlußsatz passage that culminates in a half cadence in the tonic to end the strain. Though quite different to the first, the second Schlußsatz passage repeats the insertion of a hiatus on dominant harmony (specifically vii 7) at the end of the cadential approach. In the final three bars of strain 1, the incursion of vii 7 dramatizes the “moment” of metric continuation which the whole movement explores in fluid and almost ad hoc ways. One major aesthetic implication of my earlier arguments is that meter always operates in a state of crisis. Metric horizons are continually expiring and creating a need for some form of continuation, which may be consistent with the existing beat structure or may not be. And at certain levels and in certain styles, metric overlap and other “sophisticated” devices are, in fact, favored by Bach over the use of regular repetition as a way of moving 180 The Art of Gigue beyond a given metric horizon. Thus the virtual fermata on vii 7 in the current example is emblematic of the creativity which is repeatedly asked of “weak beats.” In the rejoinder to vii 7 at mm. 151/2–16 (inclusive), metric projection returns with gusto to deliver a cadence that overcomes the impasse. Curiously, it is ambiguous whether the provisional resolution to i at m. 151/2 answers metrically to the vii 7 chord alone, or to the descent from VI begun at m. 14; either interpretation can dominate depending on the performance. I would argue that the continuation is initially felt on the larger level (as a metric projection of 11/2 bars forming a 3-bar hypermeasure), but is pulled to the smaller level (as a metric projection of C s forming a bar measure); the change occurs once Vv draws near at the end of m. 15 and once the resolution of c6 to b5 emerges as a significant element of the violin line. Following this interweaving of large and small continuations, I then interpret a medium-scale continuation overriding them both at the start of m. 16 (this, a metric projection of , s forming a 2-bar hypermeasure). What does not change through these closing bars is the emphasis on completion, which I have argued is the essence of hypermetric process. Perhaps more than any other of Bach’s gigues, the movement for violin and continuo speaks to the continuum of metric ingenuity that connects sophisticated and simple practices to each other, and that binds regular and irregular structures alike to the ongoing challenge for music to continue in rhythmically sensible ways.

Conclusion I began this chapter by arguing that metric theory is almost universally deficient in saying where, when, or how the analyst of music is meant to access or observe metrical processes. In its effort to say what meter is, and define what metrical things there are, theory takes for granted the modes of knowledge and discovery that analysts—and musicians, for that matter— must operate with. There is an implicit conflation of epistemology with ontology; an assumption that once one has a general theory or knowledge of metric phenomena, specific instances present themselves spontaneously and music becomes an open book. But meter’s essential temporality thwarts that assumption. The analyst of meter has no choice but to engage music in its own time and at its own pace, and modes of awareness and introspection have an essential importance. To conceive of meter as a pattern of strong and weak beats or a hierarchy of durations is not, actually, to be properly equipped for finding instances of hypermetrical phenomena. The aim of this chapter has been to improve the understanding of how hypermeter is anchored temporally, in terms of our ability to know it and recognize it in performance, and the aim has also been to better define the different sorts of metric insights that can be had—with prosaic projection, Hypermeter 181 metric projection, and so forth. Naturally, such advances in epistemology leave a mark on ontology too: the very nature of hypermeter seems different once we recognize what might be called the “epistemological privilege” of weak beats. But ultimately, an independent ontology is not the point once theory is in the service of analysis. When analytical practice takes the lead, the definitive claims of a single, coherent metric theory are scaled back in favor of the messier virtues of a school of thought. Even as I argue for a very limited set of analytical tools, there is a significant amount of leeway for the analyst to determine what important articulations there are, and what projective types these instantiate at various levels of detail. Metric analysis is not annexed to theory, for verifying or illustrating ideas, but rather stands alone as a musicological practice, capable of creating new knowledge and new forms of knowledge concerning musical experience. Yet the needed recognition (as I argue it) of analytical agency and of analysis’ profound temporal contingency does not mean that metric analysis becomes whimsical. It means that metric analysis begins to engage questions of effective performance that otherwise are kept at arms length by drawing a firm line between structure and execution. To an extent, this chapter has argued against the objective credentials of metrical phenomena and the idea that an impartial appraisal even ought to be possible. But if a metric analysis ultimately appears as a complex set of performance decisions, perhaps that is no bad thing.

4 Schema The Fifths Chain in Bach’s Keyboard Gigues

n the hands of early eighteenth-century musicians, the chain I of fifths sequence was a form of effusive individual expressions in a pan- European language. This formula, more than any other, could affirm the endlessly repeatable nature of tonality while, in the same breath, mustering a unique instance to meet every situation—every style, genre, vocal or instrumental affectation, and musical personality. The chain of fifths is thus the ideal subject for a chapter about the formulaic aspects of Bach’s gigues, and the various schemas which populate this impressive group of pieces. The present study is, in a sense, all about unwrapping one complex schema: the Bach gigue. But scholars of eighteenth-century music today mean something fairly specific by the term “schema,” and it is that particular notion of the schematic which this chapter addresses: the notion of tonal music’s constant engagement with various archetypal polyphonies of no more than a few bars’ scope.1 The chain of fifths stands in this chapter as a prime example of the basic contrapuntal devices that were tools of the trade for every modern European musician in the early decades of the eighteenth century.

1. Notable work in the field of schema studies includes: Robert O. Gjerdingen, A Classic Turn of Phrase: Music and the Psychology of Convention (Philadelphia: University of Pennsylvania Press, 1988); Robert O. Gjerdingen, Music in the Galant Style (New York: Oxford University Press, 2007); Giorgio Sanguinetti, “The Realization of Partimenti: An Introduction,” Journal of Music Theory 51, no. 1 (2007): 51–83; Giorgio Sanguinetti, The Art of Partimento: History, Theory, and Practice (New York: Oxford University Press, 2012); Vasili Byros, “Foundations of Tonality as Situated Cognition, 1730–1830: an Enquiry into the Culture and Cognition of Eighteenth-Century Tonality, with Beethoven’s Eroica Symphony as a Case Study” (PhD diss., Yale University, 2009); Vasili Byros, “Towards an ‘Archaeology’ of Hearing: Schemata and Eighteenth-Century Consciousness,” Musica Humana 1, no. 2 (Autumn 2009): 235–306; Vasili Byros, “Meyer’s Anvil: Revisiting the Schema Concept,” Music Analysis 31, no. 3 (2012): 273–346. A sympathetic music- analytical approach, from a somewhat different intellectual tradition, is Kofi Agawu, Music as Discourse: Semiotic Adventures in Romantic Music (New York: Oxford University Press, 2009). The schematic aspects of Bach’s music feature in Sanguinetti’s work and are treated exclusively in Dalia Cohen, “Bach: Forerunner of the Future through Exploration of the Potential of Learned and Natural Schemata,” Understanding Bach 3 (2008): 9–30. 184 The Art of Gigue

I offer here a detailed analysis of Bach’s use of the chain of fifths— organizing them into types, defining appropriate parameters for their in- terpretation, looking to them to make distinctions of style and genre, and finding in them clues to Bach’s changing priorities and growing expertise.2 Contrapuntal schemas other than the chain of fifths are not neglected in this chapter, though. One cannot become expert in any formula or device without appreciating how intimately it is connected with other devices. I will therefore explore connections between the chain of fifths and other sequential devices, such as the descending thirds sequence, which is rare in Bach’s gigues, and ascending sequences, which are frequent; and I will address closely related devices that we usually would not call sequential.3 Crucially, this chapter is as much concerned with what happens after a chain

2. As a reflection on Bach’s changing technique and stylistic range, this chapter contributes to existing more wide-ranging studies of Bach’s music. Perhaps the most substantive in analysis is Richard D. P. Jones, The Creative Development of Johann Sebastian Bach, 2 vols. (New York: Oxford University Press, 2007, 2013). Other important, indeed seminal, works are Christoph Wolff, Johann Sebastian Bach: The Learned Musician (New York: Norton, 2000) and the contributions to John Butt, ed., The Cambridge Companion to Bach (Cambridge: Cambridge University Press, 1997).

3. The sizeable theoretical literature on sequence includes Jairo Alberto Moreno Rojas, “Theoretical Reception of the Sequence and Its Conceptual Implications” (PhD diss., Yale University, 1996); Daniel Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence,” Journal of Music Theory 47, no. 2 (Fall 2003): 225–272; Adam Ricci, “A Theory of the Harmonic Sequence” (PhD diss., Eastman School of Music, University of Rochester, 2004); Adam Ricci, “Non-Coinciding Sequences,” Music Theory Spectrum 33, no. 2 (Fall 2011): 124–145; Ryan McClelland, “Sequence as Expressive Culmination in the Chamber Music of Brahms,” in Expressive Intersections in Brahms: Essays in Analysis and Meaning, ed. Heather Platt and Peter H. Smith (Bloomington: Indiana University Press, 2012), 147–185. On Bach’s uses of sequence in particular, see Georg Reichert, “Harmoniemodelle in Johann Sebastian Bachs Musik,” in Festschrift Friedrich Blume zum 70. Geburtstag, ed. Anna Amalie Abert and Wilhelm Pfannkuch (Kassel: Bärenreiter, 1963); Laurence Dreyfus, Bach and the Patterns of Invention (Cambridge, MA: Harvard University Press, 1996); Hartmuth Kinzler, “Vier Quintfallsequenzfälle und ein Beinahe- Quintparallelenfall: Notizen aus der musiktheoretischen Provinz zu Chopin, Bach, Brahms, Beethoven und Mozart,” in Musik und Leben: Freundesgabe für Sabine Giesbrecht zur Emeritierung (Osnabruck: Universität Osnabruck Fachbereich Erziehungs- und Kulturwissenschaften, 2003), 258–301. There have been numerous analytical studies of the sequence in nineteenth-century music, including David Damschroder, “Schubert, Chromaticism, and the Ascending 5–6 Sequence,” Journal of Music Theory 50, no. 2 (Fall 2006): 253–275; Rudolf Rasch, “Circular sequences in Mozart’s piano sonatas,” Tijdschrift voor muziektheorie 11, no. 3 (2006): 178–202; Eric Werner, “Nature and Function of the Sequence in Bruckner’s Symphonies,” in Essays in Musicology in Honor of Dragan Plamenac on His 70th Birthday, ed. Gustave Reese and Robert J. Snow (Cambridge, MA: Da Capo Press, 1997), 365–384. It is beyond the scope of the present chapter to offer a literature review. Moreno and Ricci each offer comprehensive overviews of writings on sequence from more historical and scientific standpoints respectively. Schema 185 of fifths as with the technique of the sequence itself. I mostly consider a sequence in isolation from what goes before, but how the sequence plays into subsequent events is of prime interest. This accentuates the particular circumstances of multiple works in the texture of their interaction with formulas and genres. Like chapter 2, this one explores that fundamental interaction, but the theoretical focus is crisper and the corpus of works more numerous. True to the paradox of the exemplary formula itself, this chapter is both absorbed in specifics—Bach, the gigue, the chain of fifths—and oriented to a very general understanding of the circulation and development of musical ideas through early eighteenth-century music.4

Existing Schema Studies

Scholars have recently made strides in understanding the patterns, the formulas, and the organizing devices which manifested themselves when music was made in the eighteenth century. As a prelude to this chapter’s schematology of the fifths chain in Bach’s gigues, I review one notable contribution to schema studies by Robert Gjerdingen.5 This chapter can be seen as part of a shared general trend—if not an argument, since it meets no real opposition—toward understanding eighteenth-century compositional practices in relatively practical terms, emphasizing pedagogy and impro- visation,6 and stressing the continuity between music’s different modes of production and consumption. A musical practice, rather than a fixed corpus of musical works, is the horizon of analytical value here, even if the analysis of a highly sophisticated musical practice requires quite a holistic view of compositions, far removed from any reactionary assertion of music’s modular or formulaic qualities. Robert Gjerdingen’s Music in the Galant Style eloquently demonstrates the debt of Italian court composers to a repertoire of “gambits” that came in and out of fashion or enjoyed persistent use during the middle decades of the eighteenth century. The relevant time period is ca. 1720 to 1790, with a center of gravity somewhere between the 1750s and 1770s. From ca. 1790,

4. For comments on the ubiquity of the chain of fifths sequence, see Richard Taruskin, Music in the Seventeenth and Eighteenth Centuries, The Oxford History of Western Music, vol. II. (New York: Oxford University Press, 2005), p. 185.

5. Gjerdingen, Music in the Galant Style.

6. Improvisation in eighteenth-century styles has recently been a subject of renewed music at the hands of Roger Moseley, among others. Roger Moseley, “Presenting the Past: The Experience of Historically Inspired Keyboard Improvisation,” Keyboard Perspectives 2 (2009): 83–102; Roger Moseley, “Mozart’s Harlequinade: Improvising Music alla commedia dell’arte,” Common Knowledge 17, no. 2 (2011): 335–347. 186 The Art of Gigue the galant style was on the wane (and its historical and social habitat was changing also),7 but its distinctive gambits were by now assimilated into European musical discourse in general. As Gjerdingen argues, the ingenuity of a Beethoven or a Rossini in the early nineteenth century owed much to the galant ways of their predecessors: having facility with the patterns of the previous century’s courtly music meant being able to compose fluently, fast, and with penetrating musical intelligence. Gjerdingen’s work is a remarkable contribution to the history of European musical composition, not least because it establishes the significance of composers and teachers whose music is little known, or unknown, today—composers such as Leonardo Leo, Giovanni Battista Somis, Baldassare Galuppi, Niccolò Jomelli, and Francesco Galeazzi. In teasing out a repertoire of common gambits, Gjerdingen’s study accomplishes something of a reconstruction of a forgotten musical language. The patterns which Gjerdingen isolates must have been familiar, quite consciously, to galant composers. Riepel gave names to some of them; the Fonte, Monte, and Ponte, those often used after the double bar of a minuet.8 But named or not, these patterns were essential units of musical thought to the majority of galant composers, on par with cadence formulas or clichés of fugal writing.9 We can assume that galant instrumentalists also were aware of such patterns: Quantz offers instruction in embellishment on a similar basis of compositional literacy.10 Gjerdingen makes a persuasive case that the courtly consumer of galant music knew its common patterns too, and drew a connoisseur’s pleasure from the composer’s fine presentation of an

7. Several of Gjerdingen’s examples are contemporaneous with the French Revolution, the event which sent shock waves through European court culture and set in motion a series of important historical changes in the social and financial situation of musicians.

8. On Riepel’s contributions to music theory, see chapter 10 of Joel Lester, Compositional Theory in the Eighteenth Century (Cambridge, MA: Harvard University Press, 1992).

9. For examples of and commentary on eighteenth-century approaches to fugue, including typical formulas of contrapuntal writing and fugal design, see Johann Joseph Fux, Gradus ad Parnassum (Vienna: Johann Peter van Ghelen, 1725) (modern translation: Alfred Mann, ed. and trans., The Study of Counterpoint: from Johann Joseph Fux’s Gradus ad Parnassum (New York: W. W. Norton & Company, 1965); Alfred Mann, The Study of Fugue, paperback ed. (New York: Dover, 1987); Paul Mark Walker, Theories of Fugue from the Age of Josquin to the Age of Bach (Rochester, NY: University of Rochester Press, 2000). For a Schenkerian perspective on the formulas of Bach’s fugal writing, see William Renwick, Analyzing Fugue: A Schenkerian Approach (Hillsdale, NY: Pendragon Press, 1995).

10. Johann Joachim Quantz, On Playing the Flute, 2nd ed., ed. and trans. Edward R. Reilly (New York: Schirmer Books, 1985). See, for example, the section on cadenzas in two parts, pp. 187–190. Schema 187 idea, or deft manipulation of stock phrases. That Gjerdingen is right about this seems beyond doubt, though the precise psychology of such listening remains a worthwhile topic of investigation, some several decades after Leonard Meyer first championed it within modern music theory.11 Gjerdingen’s common language of simple contrapuntal schemas, ad- duced from galant court music and pedagogical sources, is a magnificent contribution to understanding the methods of eighteenth-century composers. Example 4.1 gathers together his basic repertory of contrapuntal gambits: those he reviews in a dedicated appendix plus several other items which are addressed in the main text only. Gjerdingen organizes his appendix somewhat chronologically, according to the historical pre-eminence of the various schemas, but the method of organization used here follows Gjerdingen’s own knack for elucidating the kinship of different voice-leading paradigms. The schemas fall into four groups. I translate Gjerdingen’s diagrams into music notation, against his own judgment that this is too 12 problematic, so one key (F major) stands for all major and minor keys and one meter (  ) stands for all metric situations that preserve the same layout of strong and weak beats. The names which Gjerdingen gives to the schemas are printed underneath each example. The first group of schemas is a family of paired progressions (a–f), plus a more basic form of the oldest one (g), all of which begin and end on the same harmony. This is the largest and most flexible group, and they typically serve thematic functions. More detailed information about their usage over time and across different genres can be omitted here. The second group (h–i) consists of further paired progressions which tended to serve interior functions, typically following a cadence (h) or following modulation to the dominant (i). The second of these (i), in its various forms, is distinguished from the preceding ones by its inclination to either iambic or trochaic meter. The third group (j–k) consists of primarily thematic schemas which flourished early in the eighteenth century, and are metrically trochaic and relatively open as harmonic entities. The fourth group (l–n) consists of the three schemas named by Riepel in the 1750s: the two paired progressions by stepwise descent (Fonte) and ascent (Monte), and the dominant prolongation (Ponte). In the case of the Fonte

11. Leonard B. Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956). With the notion of “competent” listening—also germane to Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA: MIT Press, 1983) —the potential problem is that by idealizing the listener as connoisseur we tend to understand subconscious listening processes, or improvisation and composition, in terms of the rational structures familiar from conscious thought, and risk skewing our theory of schemas toward principles already established by music theory. For sensitive recent work in the psychology of listening see the work of Vasili Byros cited above.

12. Gjerdingen, Music in the Galant Style, p. 453. 188 The Art of Gigue

A B C Z Z 
Z Z Z Z Z Z Z Z Z Z Z Z Z Z 6 6 6 6 6 5 6 5 6 5 6 5  Z Z Z Z \
Z Z Z Z Z Z Z Z Z Z Z Z

Meyer Jupiter Pastorella

D E F 
Z Z Z Z Z Z Z Z Z Z Z  Z  Z Z 6 5 5 6   6 5 3 3 5 6 6 6 6 Z Z \ 
Z Z Z Z Z Z Z Z Z Z Z Z Z Z Aprile Sol–Fa–Mi Do–Re–Mi Adeste Fidelis

G H I

Z Z Z Z  Z Z Z Z Z Z 6 7 6 Z Z Z Z Z 6 ’7 4 2 5 6 6 6 6 6  Z Z Z  Z
Z Z Z Z Z Z Z Z Z Do–Re–Mi Quiescenza Fenaroli

J K L 
Z Z Z  Z Z Z Z Z Z Z Z Z Z  Z 6  4Z 6 6 5 2 6 6 6 6 7 5 5
 Z Z Z Z Z Z Z  Z Z Z Z
Z Z Z  Z Romanesca Prinner Fonte

M N O
    Z   Z Z Z Z Z Z 6 6  6 6Z Z 5 5 7 5 5 7 Z  Z  
Z Z Z    Z Z Monte Ponte Indugio

Example 4.1: Galant schemas according to Robert Gjerdingen’s analysis. Schema 189 and Monte, note that the translation from major to minor does not involve the preservation of scale degrees as previously: instead, Example 4.1 can typically be read in D minor without transposition. In his comments on these patterns, Gjerdingen emphasizes the modality of the five-three triads over any claims about an overarching tonality, observing that the two-part Fonte proceeds from minor to major (and the three-part, from minor to minor to major) whereas the Monte can be unpredictable. Finally, Example 4.1 includes, for completeness, one schema (o) which clearly post-dates Bach and his immediate contemporaries. A few more detailed observations, now, concerning the third group, which were historically early enough to have an important role in Bach’s practice alongside the Fonte: Gjerdingen’s “Do–Re–Mi” and some forms of Monte (if not that described by Riepel). What Gjerdingen calls the “Romanesca” (a name with some historical basis, unlike the others except Riepel’s) was a classic opening gesture of the early galant style, at its height in the 1720s and 1730s, and was most conspicuous in adagio movements. Gjerdingen demonstrates how the preferred galant bassline combined the stepwise and leaping Romanesca basses each common in seventeenth-cen- tury music.13 The soprano complements that bass motion and defines the key. The second schema grouped with the Romanesca in Example 4.1 often followed the Romanesca and was a common riposte to many kinds of thematic statement. It was also well-established in the 1720s but remained ubiquitous through the 1770s. To Italian music students, then well-versed in hexachordal solfeggio,14 this schema must have come easily. It clearly defined a key without being cadential, could take up the slack of an assertive or broad opening gesture, and was well-suited to drawing a line under a thematic area. Various options existed for articulation and rhythm, with the third, dissonant event in the tetrachordal design often being elongated. This schema’s possibilities for sophisticated integration into larger musical contexts were well-developed by galant composers, and the exploration of such is a particular virtue of Gjerdingen’s study. Indeed, Gjerdingen

13. Gjerdingen, Music in the Galant Style, pp. 25–44.

14. Hexachordal solmization was (to the ridicule of Mattheson) still practiced in German choir schools in the first quarter of the eighteenth century, and would have formed part of Bach’s own training. The role of the hexachord concept in Bach’s fugal practice is considered in Walter Schenkman, “The Influence of Hexachordal Thinking in the Organization of Bach’s Fugue Subjects,” Bach 7, no. 3 (1976): 7–16; David Ledbetter, Bach’s Well-tempered Clavier: The 48 Preludes and Fugues (New Haven and London: Yale University Press, 2002). 190 The Art of Gigue demonstrates how the interpolation of additional bass elements may result in a chain of fifths.15 The relevance of Gjerdingen’s study to this chapter ultimately extends to specific musical materials, specific musicological concerns, and questions of methodology. Firstly, Bach’s gigues contain clear applications of schemas that were central to galant practice. BWV 997, Bach’s last gigue, opens with a Romanesca that bears all the hallmarks of the prototype as defined by Gjerdingen, except for major tonality (see mm. 1–2, returning at mm. 37–38). BWV 1030, also a relatively late work and close to galant style, makes extensive use of the common riposte formula discussed above, with 6–ˆ 5–ˆ 4–ˆ 3ˆ in the soprano and, in the bass, the canonic option of 4–ˆ 3–ˆ 6–ˆ 5ˆ that Gjerdingen describes (see mm. 86, 94–95, and similar). BWV 816 also includes a passage (mm. 161/2–19) consisting of the 6–ˆ 5–ˆ 4–ˆ 3ˆ riposte, now with the prototypical bassline elaborated as a fast fifths chain, followed by the only instance in Bach’s gigues of what Gjerdingen calls the “Monte principale,” a harmonic progression of I–V–ii–vi. Outside the gigues, Bach’s music is also explicitly addressed by Gjerdingen more than once.16 The second area of relevance of Gjerdingen’s study lies in a number of its musicological concerns. Some of these are historical, including questions of the dissemination of musical ideas between the Italian centers of the galant movement and the geographical and cultural environs of Bach and his German peers. Gjerdingen briefly considers Bach’s knowledge of a Durante partimento and Pergolesi’s Stabat Mater, for instance.17 In the opposite direction, Gjerdingen also addresses the historical development of some schemas from the clausulae of Renaissance (and earlier) polyphony, something considered perhaps more fully by William Rothstein and Giorgio Sanguinetti.18 Other concerns of Gjerdingen’s correspond to theoretical issues raised by the analyses in this chapter. The uneasy relationship of some schemas to the concept of the tonic–dominant axis is addressed, and the difficulty sometimes of defining a key center, though the diatonic collection may be well-defined. There are also important insights into how sequential paradigms—notably the fifths chain—are embedded in simpler tonal devices, rather than operating as freely extendable iterative

15. Gjerdingen, Music in the Galant Style, pp. 58 and 455.

16. Gjerdingen, Music in the Galant Style, pp. 182, 226–227, and 443, among others.

17. Gjerdingen, Music in the Galant Style, pp. 226–227 and 442–443.

18. William Rothstein, “Transformations of Cadential Formulae in the Music of Corelli and His Successors,” in Essays from the Third International Schenker Symposium, ed. Allen Cadwallader (Hildesheim: Georg Olms Verlag, 2006), 245–278; Sanguinetti, “The Realization of Partimenti: An Introduction.” Schema 191 procedures of their own. Finally, Gjerdingen’s study is relevant to this chapter, and has influenced it, on methodological grounds. Although this chapter does not engage pedagogical sources—such as the partimenti so crucial to Gjerdingen’s project—the opposite impulse to also derive a schematology of compositional practice by analysis is well-established in the work of Gjerdingen, Sanguinetti, Byros, and others, and is continued here. In particular, this chapter is intended to connect with analyses such as Gjerdingen’s marvelous reading of Mozart’s G minor Symphony’s slow movement, where a schematic perspective deepens one’s understanding— and experiencing—of Mozart’s practice, and does much more than show that certain schemas are applicable.19

A Typology of the Chain of Fifths in Bach’s Keyboard Gigues

Repertoire for this Case Study This chapter is centered on an exhaustive treatment of Bach’s gigues for harpsichord. These are twenty-one in number not including BWV 965, Bach’s arrangement of Reincken’s Suite in A minor from Hortus Musicus, and BWV 820, Bach’s Suite in F major, whose ostensible gigue movement I doubt is authentic. Across the twenty-one movements considered here, I count around forty-five chains of fifths and analyze them all. However, this total includes a handful of examples that are somewhat peripheral to the sequence schema, either because they are fast-paced and have too much the character of an embellished scalar motion, or because they are relatively slow-paced and articulated in a way that indicates the category of Fonte, which is certainly continuous with the schema of fifths chain but can still be usefully distinguished from it. As a rough guide, a Bach gigue can be expected to include two fifths chains, which holds for non-keyboard movements as well, but the distribution across the gigues is not at all even. Some gigues contain many fifths chains. The schema seems more than usually forthcoming in movements in A minor or E minor, and also in violin works. Other gigues contain no chain of fifths sequence at all, sometimes despite pervasive sequential procedures based on fifth progression in the thematic material; this is the case with BWV 811. As to formal placement, the typical situation would be to see one chain of fifths in each strain of a gigue, but when the whole movement contains one or three, which is often, the more likely location is the second strain. One reason for this is the option of having one fifths chain in each period of a three-period form, as seen in

19. Gjerdingen, Music in the Galant Style, pp. 123–128. 192 The Art of Gigue the cello gigues BWV 1007 and BWV 1012. Generally, the expansive rhetoric of a chain of fifths sequence is deployed at a mature stage in the course of a movement, strain, or period.

Contrapuntal Methods This chapter demonstrates the possibility, through one or more layers of polyphonic reduction, of relating nearly all the chain of fifths sequences in Bach’s harpsichord gigues to one of three basic types of counterpoint and ultimately to one kind of texture. Whatever the actual disposition of a given passage—in two, three, or sometimes four parts—the operative schema is in trio texture. The primacy of trio thinking is never really in doubt with Bach’s harpsichord gigues; hence the upper part of two-part passages almost invariably juggles two lines of thought.20 Within the basic trio texture, one line—not normally the bass—takes a leading role, corresponding to the cantus firmus in Fuxian exercises.21 This line consists of stepwise descent, is metrically stable, and, in the passages we most readily identify as sequential, it tends to take the form of a descending tetrachord (a tendency which seems especially strong in Bach’s approach to the sequence by comparison with other composers). Alongside the “cantus,” a second line moves at the same, slow speed in regular syncopations, as in Fux’s fourth species. This syncopated element also belongs in one of the upper lines normally, though it seems more welcome in the bass position than the cantus. Finally, the third and nimblest element of the basic trio texture is what normally goes in the bass; a line moving at double the speed of the cantus, as in Fux’s second species.22 It transpires that in much two-part keyboard writing wherever the two hands present similar material, an important asymmetry can be observed.

20. In this chapter, I use the term “part” to refer to voices in the actual disposition of a given passage and the term “line” to refer to voices in the operative contrapuntal schemas (or underlying texture). “Voice” may refer to either phenomenon.

21. It is known that Bach read and valued Fux’s famous counterpoint treatise, and while Bach was still living, Lorenz Mizler issued a German edition in Leipzig. Fux, Gradus ad Parnassum; Johann Joseph Fux, Gradus ad Parnassum, ed. and trans. Lorenz Christoph Mizler (Leipzig: Mizlerischen Bücherverlag, 1742).

22. The polyphonic model described here is especially sympathetic with previous discussions of sequence advanced by Daniel Harrison and Ulrich Kaiser. Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence”; Ulrich Kaiser, “Lamentobass: Musik aus vier Jahrhunderten,” OpenBook (accessed April 2014 at http://www.musik-openbooks.de/lamento), 2013. Occasional examples of fifth chains in the described texture (especially of the “fourths and fifths” type; see below) are also found in pedagogical texts, especially in the thoroughbass tradition. Schema 193

  q q q q
q  q q q   q q q Example 4.2: Chain of fifths schema in which the upper voices form fourths and fifths. (The alto could just as well begin with a consonant a4 but the suspended c5 is given to underscore the main intervallic relationship.)

The right hand expresses the activity of two lines in the basic schema (soprano and alto, either of which may be the “cantus”), whereas the same motivic materials in the left hand reflect the genuinely melodic mobility of a single additional element, the bass. Unlike the slow-moving lines, that third line of the basic trio texture is not held to stepwise movement. Much of the time it will consist of leaps in the same intervals as describe the harmonic relation of those other two. It is in the nature of sequential passages, of course, that the “second-species” counterpoint will also trace a regular pattern, contrary to the stile antico aesthetic properly implied by references to Fux. The bass of the archetypal trio texture is, in a sense, the point of departure for all the motivic and repetitive aspects of the fully realized sequence. My first step in devising a typology of Bach’s chain of fifths sequences has been to distinguish three basic approaches to contrapuntal construction within the texture just described. Analysis of all the gigues reveals that the critical parameter, here, is the intervallic relationship of the fourth-species line to the cantus. The most flexible approach—and the one which would most exemplify the chain of fifths to many musicians—is characterized by an interplay of fourths and fifths. Example 4.2 offers a simple illustration. It is worth mentioning that the cantus depicted here, F–E–D–C or fa–mi–re–do,23 is one of the more common tetrachordal cantuses of sequential passages by Bach and other early eighteenth-century composers, although the diatonic orientation of the schema is not yet our concern. In this disposition of the upper voices, the bass is compelled—barring any marked deviations—to

23. My use of solmization syllables in this chapter follows the practice of movable do with the la form of minor. The diatonic collection in major or minor thus comprises do, re, mi, fa, so, la, and ti, and the chromatic scale in minor is solmized la–te–ti–do–di–re–ri– mi–fa–fi–so–si–la. 194 The Art of Gigue

  q q q q  q q
q   q q q Example 4.3: Chain of fifths schema in which the upper voices form sixths and sevenths, with the cantus in the soprano and the fourth-species counterpoint below. Sevenths occur on the weak beats.

 



  



6



Example 4.4: The same trio schema as Example 4.3 but with the second-species counterpoint registered differently. The bass now tracks the onsets of new notes in the upper voices by similar motion, not contrary motion. The chromatic c~3 is apparently Bach’s normal practice for this schema at this position in the diatonic scale. move in a zig-zag of fourths and fifths, spelling out the root progression and harmonizing at the lower tenth each new note of the fourth-species duet.24 The two remaining types of contrapuntal construction that I have identified involve an alternation of sixths and sevenths between the upper voices. Of these, the more prevalent is that which places the cantus in the soprano position, and the syncopated counterpoint in the alto. In this pattern, the consonant intervals fall on the strong beats, in spite of the metrical connotations the 7–6 pattern has when heard in isolation. Example 4.3 illustrates this approach, once again with a cantus of F–E–D–C. It is interesting to observe, here, Bach’s apparent preference for wide leaps in the bassline, where economical thirds and steps would suffice to spell out the same notes. One plausible reason for that preference is the use of low notes to define the meter. In addition, the leaping bassline achieves the same marriage of melodic motion (in the bass) to harmonic relationship (in the upper voices) that is habitual in the fourths-and-fifths pattern. The

24. I use the term “tenth” somewhat loosely here to mean either tenth or seventeenth, and maybe even third. It is important to note that in the pattern described here, Bach’s basslines favor contrary motion over parallel motion vis-à-vis the onsets of new notes in the upper voices. Thus the intervals of those new notes with the bass are most likely to alternate seventeenths and tenths. Schema 195

Z Z Z
 Z Z   

Example 4.5: The same upper-voice schema as Example 4.3 with an alternative second-species counterpoint in the bass. In practice, the alto can be expected to begin on c5 before commencing the sustained notes, but b4 is given here to underscore the main intervallic relationship.

more economical alternative is nonetheless used by Bach, especially in his earlier works, and so is another kind of second-species counterpoint. These are illustrated in Example 4.4 and Example 4.5, each with a cantus that begins G–F–E or so–fa–mi (a favored scalar position). The top voice of these examples differs from the simple tetrachord design of before: the completion of the “cantus” line in sequence passages of this length is, in many situations, not subject to any obvious norms following the arrival on the third note. The counterpoint of Example 4.5 harmonizes the dissonances of the upper voices not with six-five-three chords but with nine-five-three chords.25 Like in the given fourths-and-fifths pattern, the bass now accompanies the changes in the upper voices with a series of seventeenths and tenths. The least prevalent of the three contrapuntal types is, then, that which puts the cantus in the alto position and the syncopated counterpoint in the soprano. The dissonant sevenths assume the stronger metrical position in this case. Example 4.6 illustrates the pattern with a cantus that once again begins G–F–E or so–fa–mi. As before, two options are available for the second-species counterpoint normally assigned to the bass. The dissonances can be harmonized either as six-five chords or as nine-three chords, which Example 4.7 illustrates. It is worth observing that Example 4.6 differs from Example 4.7 and previous examples by its bass not matching the cantus in parallel tenths. Considering the general possibility for reducing chain of fifths schemas to yet simpler paradigms of descending motion, the approach of Example 4.6 places the designated cantus in a precarious contrapuntal situation: if a reduction to first-species were to be attempted, this middle

25. Since the suspended ninths are resolved concurrently with (not before) a change in the bass and the active root, these are “essential” dissonances according to Kirnberger’s classification. The same is, of course, true in the six-five-three scenario, where the essential dissonances make the interval of a fifth above the bass and represent the seventh above the root. Johann Philipp Kirnberger, Die Kunst des reinen Satzes in der Musik (Berlin and Königsberg: G. J. Decker / G. L. Hartung, 1771–1779). 196 The Art of Gigue

      ~~
    ~ 

Example 4.6: Chain of fifths schema in which the upper voices form sixths and sevenths, with the cantus in the alto and the fourth-species counterpoint above. Sevenths occur on the strong beats. (The soprano could just as well begin with a consonant d5 but the suspended f5 is given to underscore the main intervallic relationship.)

 q q  q q q     q q 
  q  q q q q q  Example 4.7: The same upper-voice schema as Example 4.6 with an alternative second-species counterpoint in the bass. voice might not stand. Though not the business of this chapter, it is an interesting question what exact status the named “cantuses” have in terms of tonal structure, the classification of formulas, or the actions of memory, improvisation, and instrumental performance. Lastly, for preliminaries, it should be recognized that sometimes a sequence passage switches from one of the main contrapuntal methods to another. See for instance the reductions in Example 4.18 and Example 4.20 (on p. 209).

Analytical Approach To benefit future studies that build on this one, I will detail how I came to conceive of, look for, and categorize fifths chains as I do. The most appropriate modes of analysis are not obvious, but instead emerge through analytical work. When an analysis project is ambitious enough that the tolerance for misunderstandings and inefficiencies is reduced, the concepts one has going into it are likely not the same concepts one takes away at the end. The very name, chain or “cycle” or “circle” of fifths sequence, dictates a certain conception of the phenomenon: that root motion is definitive. Textbooks and dictionaries of two centuries have drilled this conception Schema 197 deep into music pedagogy, and the overwhelming majority of such texts use simple four-part writing for illustration, often incorporating prepared sevenths, but otherwise cleaving to plain triads.26 The fifths chain is gener- ally treated as a “harmonic,” not “contrapuntal,” phenomenon, so the SATB format holds sway, and ultimately, the subject of any illustration is the root progression and the voice leading proper to it. To harmony instruction’s credit, the “chain of fifths sequence” is widely known about and recognized by musicians; it could be the envy of almost any category in music analysis. But that does not mean that what is being recognized, musically, are the attributes that pedagogy describes. This study—among others—offers a different view of the substance of the “chain of fifths” phenomenon, in which root motion takes a back seat. For one thing, it is not even true that a chain of fifths sequence will sustain a root motion by descending fifth. This chapter includes several counter-examples. Yet concrete melodic elements in stepwise descent are always present and their scalar orientation is easy to define. In the analysis of Bach’s sequences, Roman-numeral or movable-do analyses of root motions proved of negligible independent value in the emerging typology. (I refer to the la-minor form of movable do.) Much more reliable and informative, regarding a sequence’s tonal orientation and essential harmonic content, is the diatonic position of certain elements in the melodic skeleton. As already revealed, I locate the core of Bach’s sequence technique in a basic three-voice texture, and look to the “cantus” and fourth-species lines of that texture for the fundamentals of a typology. In the abstract texture of Example 4.8, the flagged notes are the cornerstones of an analysis: one almost never encounters in Bach a passage one would call a “chain of fifths” in which these three notes are hard to name or to locate diatonically. Where the root motion may be contentious, and the majority of melodic content relatively

26. For a number of examples, see chapter 1 of Ricci, “A Theory of the Harmonic Sequence.” Examples in commonly used college textbooks include Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 2nd ed. (Fort Worth: Harcourt Brace Jovanovich College Publishers, 1989), p. 251 and Stefan Kostka and Dorothy Payne, Tonal Harmony, 6th ed. (New York: McGraw–Hill, 2008), p. 115. The simplest illustrations of fifth chains are typically homorhythmic and proceed in regular time values. Heinrich Schenker criticizes the use of unrhythmic harmony exercises and illustrations in Heinrich Schenker, Harmony, ed. Oswald Jonas, trans. Elisabeth Mann Borgese (Chicago: University of Chicago Press, 1954), pp. 175–179. Schenker is disparaging of an example from Richter, against which he holds up an example from “Bach’s Generalbassbüchlein.” He praises the latter for the “rich rhythmical articulation” of its bassline. For a modern edition of the Generalbassbüchlein, which is based on Niedt and believed to have been dictated by Bach at Leipzig, see Pamela Poulin, J. S. Bach’s Precepts and Principles For Playing the Thorough-Bass or Accompanying in Four Parts, vol. 16, Early Music Series (Oxford: Clarendon Press, 1994). Chapter 9 of the Generalbassbüchlein commences with an illustration of a chain of fifths. 198 The Art of Gigue

↓ ↓
Ë Ë Ë Ë

↑ q
Ë Ë Ë Ë Ë Ë

Example 4.8: Abstraction of the trio texture basic to fifths chains. The three flagged notes are the cornerstones for the analysis of a sequence’s pitch content. changeable, those three melodic points are excellent footholds for the analyst. This insight about analysis is also an insight on the tangible profile of what is, after all, a musical schema. For the composer, improviser, performer, or listener, the melodic complexities of the Bachian fifths chain will be grounded in the sense of one voice’s slow stepwise descent, subdivided rhythmically by the intervention of a second voice at a certain interval above or below. The shift of focus from root motion toward concrete melodic motion is an adjustment between bottom-up and middle-out perspectives whose advantages extend beyond avoiding problems of root analysis. One major pitfall of a bottom-up perspective is the conflation of sequence forms that begin with the tonic triad in both strong and weak metrical positions. Analysts often make little of this difference, though it often expresses a fundamental distinction between passages that commence metrically on IV at the first strong beat, heading for I, and passages that commence on I, with V as the goal. Not only the idea of root motion by fifth, but the very idea of sequence is problematic in the analysis of chain of fifths passages too. In this chapter, I often emphasize the words “sequence passage” or “sequence schema.” My intention is to access a dimension of meter and phrasing that I suggest is strong in our appreciation and recognition of chain of fifths passages, but which has only meager representation in textbook or dictionary defi- nitions. Although stepwise “sequential” repetition is the hallmark of the phenomenon we call a chain of fifths passage, I do not equate “sequence”— as in, “a sequence passage”—with the extent of sequential repetition only. As the forthcoming analyses will show, Bach’s sequence passages fall into various metrical types, which can be enumerated by the number of units that correspond to sequence segments (usually 4, 2, or 3) and, where applicable, a label of “fast” or “slow”—this, in cases where the sequence proceeds at roughly double or half the usual pace. (The issue of tempo is explained below.) Meter is an important factor in the visual form of this chapter’s Schema 199 musical reductions, which can be seen, for instance, in Example 4.50 (on p. 236). All reductions in this chapter assign new rhythm values for the sake of a fair comparison between pieces, with Z as the usual pace of root motion and C as the usual pace of stepwise descent in the cantus. The dashed barline shows the metrical end of the sequence passage, in light of my assessment of this passage as metrically quadruple. The material beyond that barline is extraneous to the sequence—it is not underpinned by the basic contrapuntal schema—but, in a wider sense, it completes the momentum of the sequence harmonically and melodically. The change to small print, meanwhile, marks not a metrical or melodic termination but a motivic one: this is where the characteristic textural and thematic content of sequential repetition is abandoned. It is a major trope of the literature on sequences that a sequence might, in principle, go on indefinitely but, in practice, will be kept to a length that does not try the listener’s patience.27 But Bach’s music, at least, provides no real support for this idea. (Perhaps it is more often stated than believed, anyway.) In the rare case that one of Bach’s sequences is felt to break off prematurely, a contradictory expectation for the length of the sequence can always be defined. The fact that the sequence ends is not the issue. Yet because the phenomenon of the sequence passage has been identified with the idea of sequential repetition almost exclusively, there is nothing intrinsic to the usual definition that explains the formation of discrete entities. This chapter proposes that a “chain of fifths sequence” should be defined as a metrically coherent passage that commences with but is not restricted to sequential repetition. Although the chain of fifths sequence is not particularly well-served by most harmony theory, and is maybe too obvious or not learnèd enough to concern contrapuntal theorists in depth, three centuries of commentary have certainly not left music theory barren of insights. For the purposes of this chapter, with its necessarily limited scope, it is worth relaying a few points of interest from off the beaten track. One theoretical source contemporary with Bach, if ignorant of his music, is Roger North’s treatise, “The Musicall Grammarian,” a manuscript penned in England during 1728–1733 and notable for its concern with

27. Harrison characterizes this as “music-theory lore.” Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence,” p. 226. For a typical discussion of the competing claims of “variety” and “comprehensibility” in the use of sequence techniques, see Arnold Schoenberg, Structural Functions of Harmony, 2nd ed. (London: Faber, 1983), pp. 125–136. 200 The Art of Gigue

 q q   q q q q q  q q qq
 q q q q q q q q q q
é   q q q q q q q
 q q q q q q

Example 4.9: One of Roger North’s fifths chain schemas (sic: the antepenultimate chord).

“schematismes.”28 North explicitly commits himself to describing the com- positional fashions of his generation, distinguishing for instance between recent Italian developments and more longstanding practices of contempo- rary English composers. His approach is, indeed, schematic and analytical, with Corelli as a leading light. (North was born around 1651 and his musical tastes may have been a little old-fashioned at the time of writing.) For North, the “consort of cadencys,” the chain of fifths, has its origin in stepwise motion; it “shew[s] how the scale may be wrought to the porposes of musicall air.”29 In a section entitled “The manners of working upon the scale,” North introduces the fifths chain on the back of simple two- part illustrations of suspension chains of 7–6 and 2–3, which he dubs “tormenting the scale.” A plain suspension chain he says “tends to no elegance or rapture,” thus acknowledging the only proto-musical status of his contrapuntal demonstrations, whereas “masters disguise the matter with affected breakings and devisions.”30 Of the fully fleshed fifths chain, North illustrates three patterns. The first “scheme” is reproduced in Example 4.9, similar to Example 4.2 but with an additional voice. North’s next pattern (not reproduced here) is a simple two-part idiom of thirds and sixths, which is “much in use among composers and is a good help at need when better invention fails.”31 Though this pattern is simpler than the first, North is probably right to say, historically, that it is “spa[w]ned” by the other. Not much in evidence in Bach’s gigues for keyboard, this schema shines through in just one fifths chain in BWV 814. Shown in Example 4.10 (cf. mm. 5–8 of the score), this is the only purely triadic passage in the whole sample,

28. [Roger North], Roger North’s The Musicall Grammarian 1728, ed. Mary Chan and Jamie C. Kassler, Cambridge Studies in Music (Cambridge: Cambridge University Press, 1990), p. 159.

29. Ibid., p. 160.

30. Ibid., pp. 159–160.

31. Ibid., pp. 160–161. Schema 201

7 BWV 814 AC q  q q q q q  q q q q q q q q q q q
q q q  q q q q q q  q q q  q q q q q 1
 q q q q q q q q  q q q q q short fifths chain q

Example 4.10: Reduction of BWV 814, mm. 1–16.


Z Z Z  Z Z E  Z Z Z Z

Example 4.11: Another of Roger North’s fifths chain schemas. (In this case, North’s example breaks off without coming to a resolution.) and the only passage devoid of non-chordal tones. North’s third and final chain of fifths schema is reproduced in Example 4.11. This is an inversion of Example 4.6, and North attributes it to Corelli. Not least for his references to Corelli, North is a precedent for the most important modern influence on the present study, namely Daniel Harrison’s article, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence.” (Harrison’s article is addressed directly later in this chapter.) Several decades after Roger North was writing, Albrechtsberger in his program of thoroughbass instruction came as close as anyone to observing something else important about the chain of fifths, beyond its stylistic and schematic debt to simple suspension chains.32 This is the chain of fifths’ bias for the minor mode. At the end of a long section introducing various keyboard drills for learning harmonic progression, Albrechtsberger falls back to emphasizing simple patterns which must be perfected in all keys. And here, an important asymmetry occurs between the major and minor modes. Albrechtsberger’s drill for learning the common chords in major keys is an ascending sequence; his equivalent drill in minor is the chain

32. Our source for Albrechtsberger’s instruction in this area is the edition of his writings and teaching materials by his pupil, Ignaz von Seyfried. Ignaz von Seyfried, ed., J. G. Albrechtsberger’s sämmtliche Schriften über Generalbaß, Harmonie-Lehre, und Tonsetzkunst; zum Selbstunterrichte, 3 vols, 2nd ed. (Vienna: Tobias Haslinger, 1837). 202 The Art of Gigue of fifths.33 Why this difference? Albrechtsberger does not explain. But it respects an important facet of the chain of fifths’ usage which has rarely been made explicit. Bach’s keyboard gigues suggest that a chain of fifths is about twice as likely in a minor-key movement as in a major-key movement, even when the modality of the sequence itself is reversed by its appearing in the relative. (Fifths chains seldom appear in non-tonic environments besides the relative or dominant.) Another instructive asymmetry in Albrechtsberger’s two drills concerns the harmonic rhythm: the chain of fifths is notated with larger rhythmic values than the ascending sequence, so the root motion proceeds in C s instead of Z s. This shows that, even in the context of a thoroughbass primer, it is possible for an illustration to convey some understanding of not only the rhythm but also the pace of a sequence. However, the actual rate of harmonic progression is largely neglected in theoretical treatments of the chain of fifths. This chapter shows how that neglect of pacing can be reversed, influenced in part by Channan Willner’s fascinating work on Handel.34 Table 4.1 presents data on the pace of fifths chains in Bach’s keyboard gigues. (Two of the keyboard gigues, BWV 808 and BWV 811, contain no fifths chain, so nineteen works are listed here.) The second column from the right records the pace of the underlying cantus descent in each fifths chain, while the rightmost column gives the measure number of the first “fold” of the sequence, i.e. the start of the second segment. Throughout this chapter, I reference chain of fifths passages by this point because it is the most consistently well-defined metric articulation, and the easiest reference point for locating sequence passages quickly in scores. Thus, the shorthand “BWV 815c37” will mean the sequence passage in BWV 815 that occurs circa m. 37; hence the circled measure numbers in the reductions referred to above. To compare with the pace of underlying cantus descent in each fifths chain, Table 4.1 also records the the rhythm value of the main tactus and the duration of the final tonic harmony in each movement. In general, the cantus notes of the sequence schema are longer than the tactus, and equal to or longer than the tonic harmony of an authentic cadence. Grouping by

33. Seyfried, J. G. Albrechtsberger’s sämmtliche Schriften über Generalbaß, Harmonie-Lehre, und Tonsetzkunst; zum Selbstunterrichte, vol. 1, pp. 101–102. Ignaz von Seyfried and Vincent Novello, eds., J. G. Albrechtsberger’s Collected Writings on Thorough-Bass, Harmony, and Composition, for Self Instruction, 3 vols, trans. Sabilla Novello (London and New York: Novello, Ewer & Co. / J. L. Peters, 1855), vol. 1, p. 42.

34. Channan Willner, “Durational Pacing in Handel’s Instrumental Works: The Nature of Temporality in the Music of the High Baroque” (PhD diss., The City University of New York, 2005). Schema 203

Table 4.1: The pace of chain of fifths sequences in Bach’s keyboard gigues. The reductions in this chapter employ the value of a half note for the notes of the cantus’s basic stepwise descent. For movements which feature chain of fifths sequences at more than one speed, this table identifies the primary speed by aligning the relevant value with the BWV number.

Meter BWV Key Tactus Tonic Cantus Location

[ À ] [39] 169

828 D © À

27, 72, 80


q q q q 12 © Œ C 16 816 G
32, 37

, 12 809 F C [sic] C 45 8 827 a ΠC , 111/2, 161/2, 19, 23, 30, 37, 40

807 a Œ C , 23, 42, 63 fast , 832 A Œ C 25 no q q 815 E ’ Œ C , 9, 37 C 8, 291/2 818 a Œ C # , 16, 42 86 831 b Œ C C 10, 26, 38, 43 817 E Œ C C 10 806 A Œ C C 81/2, 13, 28, 37 slow [ Œ ] [231/2] w q q 829 G Œ Œ † # C 16, 211/2

823 f ΠC [ , ] Fonte [13] ΠC C 810 e ? 75 3 8 813 c ΠC , /? C 13

# [ , ] Fonte 61 814 b Œ Œ † C 7, 55

825 B ’ C [sic] ,  7  812 d Z , , 18

C 111/4, 173/4, 183/4, 351/4, 433/4

W 830 e C , , 51/2 (codetta), 221/2  10, 161/2, 30, 34, 421/2, 48

† These short tonic harmonies indicate the slow tempo of their movements. 204 The Art of Gigue

time signature, the most informative part of the table covers the movements 6 in 8 . Within each time signature group, works are ordered by likely tempo from fast to slow, reading from top to bottom. (The gauge here is the length of a measure rather than the tactus, which can sometimes be interpreted more than one way.) This reflects my own musical assessment of appropriate tempos, which is highly personal and provisional, but which at least allows 6 the issue of pace to enter consideration. Of the gigues in 8 , three have

fifths chains whose cantuses proceed only in , s, whereas four have fifths chains whose cantuses proceed only in C s (this includes BWV 829 since BWV 829c231/2 is not a true sequence). Not surprisingly, the former group of movements afford significantly faster tempos than the latter. But caught in the middle is BWV 818: this movement has feet in both camps. For various stylistic reasons, BWV 818 seems the earliest composition of the eight, and this movement almost defies the selection of an effective performance tempo. Whatever might be the precise tempo of BWV 818, it clearly falls awkwardly for the chain of fifths: a cantus in C s seems too quick; a cantus in , s seems too slow. Both speeds have an equal claim to being primary, while in other movements, notably BWV 830, it is easy to characterize any differently paced fifths chains as “ordinary,” “slow,” or “fast.” Thus BWV 818 helps us to define the comfortable tempo range for the fifths chain and understand how that compares to the comfortable tempo range for the tactus of a gigue. The co-operation of these two factors cannot be taken for granted, and the proper calibration of harmonic rhythm is obviously a significant compositional task. Expressed in metronome markings which are probably on the quick end of the spectrum in current performance practice, my personal conclusion regarding the data in Table 4.1 is that the tactus of a gigue has the range of 56–142 beats per minute whereas the cantus of a fifths chain has the range of 18–52 beats per minute. The comparison can be sharpened by reducing the tactus range to 60–120 (i.e. a span of one unit on a logarithmic scale of base 2), and similarly reducing the cantus range to 221/2–45, then scaling it up to reflect the speed of the sequence’s second-species element instead. The two ranges of 60–120 and 45–90 are highly incompatible, which explains the variety of calibrations evident in Table 4.1 between the harmonic rhythm of a sequence and not only the tactus but also the harmonic rhythm of a gigue’s other elements including cadences. In my reading, this goes some way to explain the scarcity of Bach gigues—just BWV 818 and BWV 825—that warrant a tactus inside the range of 80–100 beats per minute.

Uses of the “Sixths and Sevenths Above” Type A pattern of sixths and sevenths above the cantus is—in Bach’s keyboard gigues—much the least prevalent of the three contrapuntal constructions Schema 205 basic to the chain of fifths schema. One would not say so, however, if Bach’s keyboard compositions had stopped with the English Suites. At that stage, the construction of sixths and sevenths above the cantus was evidently quite central to Bach’s conception of the chain of fifths. In the English Suites, five of the nine chain-of-fifths sequences follow this design, and one of the four in BWV 818. But, remarkably, none of the fifths chains in the French Suites and Partitas is constructed this way. Here, the contrapuntal typology is an instrument of stylistic discrimination. An elegant insight to Bach’s process of acquiring and cultivating con- trapuntal schemas during the composing of the English Suites is to be had regarding his use of an altogether different sequence type which shares the upper-voice construction just described. This is the sequence of descending thirds interpolated with back-relating dominants, one of several musical practices from the sixteenth through eighteenth centuries to have earned the name of “Romanesca.” Only two Bach gigues contain Romanesca sequences: those of the English Suites in F major, BWV 809, and G minor, BWV 808. 12 The two movements are both in 8 and inhabit a shared fugal idiom, not yet of the determined three-part writing of the fugal gigues in the E minor and D minor English Suites. According to current historical evidence and on stylistic grounds,35 it is all but certain these movements were written within a couple of years of each other during 1715–1718, with the G minor gigue appearing as the more mature composition. The Romanesca sequences in BWV 809 and BWV 808 are alike both in their realization and their formal position. Reproduced in Example 4.12 and Example 4.13 are the full Romanesca sequences from the first strain of each movement; not shown here is a curtailed reprise that occurs during BWV 809’s second strain. The first similarity between the two full sequences is the harmonic profile, beginning on the tonic of the home key and closing on the dominant of the dominant key. In BWV 809, this motion takes the duration of five bars, whereas in BWV 808, the passage is resolutely quadruple. (The minor tonality is better equipped for quickly settling a repeat of the Romanesca’s initial progression, i–v, in favor of the second chord as the new tonic, on account of the passing motion using ~6.)ˆ The second similarity is that each sequence follows directly a fugal statement; in BWV 809 this is a middle entry which replicates the movement’s opening statement, and in BWV 808 this is the final subject entry of the three-part exposition. In each movement, the length of the fugal subject is two bars, as laid out in previous entries, but the start of the Romanesca overlaps with the moment of resolution to 3ˆ or 1ˆ , reducing the entry to one-and-a- half bars. Another thing the sequences share is that they commandeer a

35. I refer to stylistic factors other than the usage of sequences. 206 The Art of Gigue

BWV 809 ↓ subj. 16½ 
Ë Ë Ë
Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë   Ë Ë æ  ‹  
Ë Ë Ë Ë Ë

 Ë Ë Ë Ë Ë Ë  Ë Ë I

        æ æ  ‹ 

  æ  V of dominant      ‹  
æ Example 4.12: Score of BWV 809, mm. 14–201/2 (Romanesca).

BWV 808 9 Ë

 Ë Ë
Ë
Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë
Ë Ë Ë Ë   Ë Ë
Ë Ë Ë
Ë Ë     Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë þ   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë

↑ subj. i v V of dominant  Ë Ë Ë Ë      Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë   Ë Ë
Ë Ë
Ë Ë Ë Ë
Ë Ë     Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë
Ë Ë Ë  iv i

Example 4.13: Score of BWV 808, mm. 61/2–11 (Romanesca). Schema 207

À V À À À À À 
  i v iv i

Example 4.14: Reduction of BWV 808, mm. 8–11 (Romanesca). All such very simple reductions in this chapter are transposed to the natural diatonic collection and the tonalities of C major and A minor to ease comparison. fragment of the fugal subject—the head in BWV 809, the tail in BWV 808— to propel the bass part’s ascending-fifth motions. There are furthermore obvious parallels between the passages in terms of contrapuntal design, with identical procedures at the level of fourth- and second species counterpoint. Example 4.14 represents the Romanesca in BWV 808 at that level, with the choice of rhythm values accurately reflecting the Romanesca’s fast melodic rhythm compared to the chains of fifths. Lastly, register and tonal proximity are connecting factors in terms of these two passages’ sound and physical feel on the harpsichord. It so happens that in BWV 809, the right-hand motive originates in the exposition codetta at the same G minor pitch of its “sister” movement. One remarkable feature of BWV 808c9 must be mentioned: that the cantus of the sequence—which is quite explicit in the keyboard texture— traces the fugal subject in augmentation.36 Once some jostling between e ’ 4 and e4 is sorted out, the line effectively stands as B ’–A–G–F–E–D– C~, etching the same contour as the earlier alto entry in mm. 3–4 and preparing for the ensuing middle entry one octave lower. This is as clear an indication as any that Bach, at least sometimes, constructed sequence passages around a simple stepwise line that fully merits the name “cantus.” Supporting this particular interpretation is evidence of a general program in BWV 809’s gigue to connect the fugal subject, with its scalar profile, to other scalar elements in the piece. Consider the ascending bassline of mm. 37–40,

36. Here and throughout the chapter, I use the term “subject” inclusively to refer to all statements of a fugal theme, both “subject” and “answer” forms where these can be distinguished. In this case, the form could not be specified anyway, since a clear anacrusis is lacking. Moreover the sequence performs the modulation from G minor— the key of the exposition, where the current augmentation would state the answer form—to D minor—the key of the first middle entry, where the augmentation would state the subject form. 208 The Art of Gigue

subj. (inverted) Ë Ë Ë Ë  Ë Ë Ë Ë Ë ËËË Ë
Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËË  ascending bassline

 
Ë  Ë     Ë  Ë  Ë  Ë  Ë   Ë Ë Ë
Ë Ë Ë
Ë Ë Ë Ë Ë Ë Ë      ËË
Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë  subj.


Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  ↑ altered from here Example 4.15: Left hand of BWV 808, mm. 35–44.

A B
 12 q q q q q  8 q q 
 q q q q q 1   12   q q  8   Example 4.16: Score of BWV 808, m. 1 and m. 21: the opening salvo of the fugal subject in its original and inverted forms. included in Example 4.15. Even as the complete passage has a remarkable sound of its own, it promises a special delight to the performer (or listener) who can connect the bassline gesturally with the fugal subject in its inverted, second-strain guise, heard only moments before in the same register. And augmentation of the thematic gesture is not all. By spanning from e2 to f~ 4, the bass’s slow ascent re-imagines the diminished seventh heavily inscribed in both subject forms and pitched at E ’ and F ~ at the start of each strain (see Example 4.16). The upward scale from ~6ˆ to ~7ˆ is an extraordinary counterbalance to the opposite traversal from 6ˆ down to 7ˆ in the main fugal subject. In light of this passage’s learnèd pastiche, it seems quite plausible that the thematic echo buried in the earlier Romanesca was a deliberate conceit of Bach’s, and represents a clever weaving of the fugal subject into a Schema 209

embedded sequence BWV 809 45 V


q q q 
 q q q q q q q q q q 3 3 q q  q q q
q q q q q  without metrical expansion

   3 3  Ø 

Example 4.17: Reduction of BWV 809, mm. 44–481/2.

V q  q q    q qq 
q q q   q q q 

Example 4.18: Further reduction of BWV 809, mm. 44–481/2 (with metric expansion removed). sequence formula with a particular currency in Bach’s musical thinking as he penned his two earliest properly fugal gigues. a

Like the Romanesca, the chain of fifths constructed with sixths and sevenths above the cantus is found only in the earlier of Bach’s keyboard suites. And the contrapuntal connection between these two kinds of sequence was evidently not lost on Bach. In the second strain of BWV 809, a chain of fifths takes the place of the first strain’s Romanesca, ahead of the main cadence. These parallel sequence passages lead, via half bars of tonic figuration, to matching Schlußsatz sections comprising a two-bar precadence (accentuating 5ˆ in the top voice) and a two-bar authentic cadence in the same key as the closing dominant harmony of the sequence. Reductions of BWV 809’s fifths chain are given in Example 4.17 and Ex- ample 4.18, where one sees the slow melodic rhythm and the homogeneous scaling of sequential repetitions between the hands that set this schema apart from the Romanesca. Another difference is the diatonic stability 210 The Art of Gigue

A B V V q q q q q q q q q q  q q q
q
   q q q q
q q q q q q
q q Example 4.19: Reductions of BWV 818, mm. 40–47.

V q  q q q    q q q q 

q q q  _  q q q Example 4.20: Reduction of BWV 810, mm. 73–80. characteristic of fifths chains: this passages does not modulate like the Romanesca. Nonetheless, the harmonic rhythm is the same, also the ending on dominant harmony, and the overall metric profile is very close, given the indicated expansion in what is essentially a quadratic device. Bach also connects the two passages by incorporating the fugal subject’s head motive to the bass part of the fifths chain, now using the inverted form native to the second strain (compare mm. 151/2 and 441/2 in the score). The essential behavior of BWV 809’s fifths chain is shared by the others of its type: all are metrically quadratic and resolve to dominant harmony in their fourth quarters. Three of the sequences, BWV 809c45 included, have the non-syncopated upper voice—the cantus—begin on so, and trace the root progression so–do–fa–ti in the first half. But it is the fourth-species element which binds these passages most tightly, with one melody working equally well in major or minor. The underlying counterpoints of the two sequences not from BWV 809 are laid out in Example 4.19 and Example 4.20. The minor-mode passage (BWV 818c42) is the most straightforward.37 Per the reading in Example 4.19a, Bach’s only significant embellishment of the basic formula belongs to the alto voice, which tracks the chordal fifths. Perhaps because a rigid extrapolation from the first segment would cause the bass to pre-empt its dominant arrival during the third quarter, the major-mode passages (BWV 809c45 and BWV 810c75) are not as straightforward. Under transposition to the natural diatonic scale, G becomes the note for the bass to

37. This has a contrapuntal ease in stark contrast to BWV 814c55, discussed below, which shares its root progression and, roughly, its cantus. Schema 211

A V B V

 Z Z Z Z Z Z Z Z Z Z Z »

Example 4.21: Reductions of BWV 806, mm. 36–39. Mm. 12–15 are the same. avoid at midway. With BWV 809c45 that means exchanging the bass with the alto, which causes a shift to the “fourths and fifths” kinds of construction; with BWV 810c75 it means diverting the bass to the opposite zig-zag pattern, creating a nine-three chord (see Example 4.24, c.f. Example 4.7). The root progression into that chord may now be read G–C instead of B–E. The fourth sequence of the current type follows throughout the alter- native zig-zag pattern just described, of bass descents within each sequence segment and ascents across segment boundaries; this is BWV 806c37, of which Example 4.21 gives the basic reductions. The diatonic orientation of this passage is different to the others, with a cantus headed do–ti–la. To accommodate resolution to dominant harmony, the fourth-species top voice is now no longer stepwise to the end, but the skip from 4ˆ to 2ˆ is smoothed somewhat by the earlier presence of 3:ˆ at an extreme, 4ˆ can be imagined as an echappée from 3ˆ within a primitive 3–ˆ 2ˆ motion. The fourth-species rendering in Example 4.21b is already something of a stretch, however. From the schematic angle, the top voice is acutely affected by the choice of bass pattern. Closer to the fully realized form, the second-species reduction in Example 4.21a comes much more easily, and once again illustrates the idea of a leaping upper voice which tracks the chordal fifths. In practice, these notes are not all fifths vis-à-vis the most sensible analysis of root motion, but the finer points of root progression are not relevant here. a

The deployment of these sequences within the form of their movements becomes increasingly sophisticated through the probable chronology of composition, even if sophistication is only measured in the amount of mate- rial which follows the sequence and thus directly engages it. Starting with BWV 818 and BWV 806, the sequence idea has only minimal consequences, as Example 4.22 and Example 4.23 illustrate. In an extra segment’s length (or less) relative to the quadruple profile of the sequence schema, an authentic cadence is achieved and the movement or strain is over. In performance, the dominant harmonies must be given a distinct cadential meaning after their 212 The Art of Gigue

BWV 818 42 V AC q q q q q q q q q q



q q q q q ~

q q


~
.  q q

q q q q q q q
Revisions in BWV 818a









 







~

~

Example 4.22: Initial reduction of BWV 818, mm. 40–48. In BWV 818a, Bach’s later version of BWV 818, the chain of fifths is the passage subject to the most revisions. These revisions, though still fairly cosmetic, are enough to inflect the sense of the underlying counterpoint as indicated.

BWV 806 37 (V 6 ) 5 AC

q q
q q q q q
 q q q q 

q q q q
q q q q q q q q q
V   q q q 
q

  Ø q q q Example 4.23: Initial reduction of BWV 806, mm. 36–40. Almost precisely the same at the pitch of a perfect fourth below are mm. 12–16; the only difference is the relative register of the left hand in the final bar. Schema 213

75 BWV 810 ↓ subj. (inverted) in relative V in tonic      æ  Ë  Ë Ë Ë    Ë Ë Ë Ë Ë Ë Ë Ë Ë æ  æ æ  Ë Ë Ë Ë Ë Ë Ë


Ë Ë   Ë Ë Ë Ë  Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë F G running bassline (HC)          Ë Ë  Ë Ë Ë Ë Ë

  Ë    

AC Ë  Ë Ë Ë Ë  Ë Ë Ë Ë    Ë Ë Ë Ë Ë 

  Ë  Ë 
Ë Ë Ë Ë  Ë

Example 4.24: Initial reduction of BWV 810, mm. 73–96. The fully realized texture has three parts during the sequence and only two during the subject entry, but the subject combines two distinct lines and is represented by the complete contents of the treble staff when it occurs. initial arrival as part of the sequence. Next, with BWV 809, the sequence sets up an Schlußsatz of equal scope to itself, as already discussed. Here, and in BWV 818, the sequence directly follows an authentic cadence on re (ii in major, iv in minor) and the motivic pattern of the sequence is initiated during the cadential tonic to make a compelling transition into the new period. Finally, with BWV 810, the movement’s end is longer in coming after the sequence, which is not in the tonic, but the relative. See Example 4.24. BWV 810c75 occupies the fourth of six eight-bar divisions of its strain, so is followed by not one but two units of equivalent scope: the first presents a maneuver to the dominant of the home key and a final entry of the fugal subject (in the inverted form used throughout the strain); the second comprises the authentic cadence and an elaborate treatment of the final tonic. Now that the sequence precedes a fugal entry, it primes important pitch ingredients of that entry, in this case by thematizing the 214 The Art of Gigue

subj. (inverted) rising sequence
q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q descending tenths fifths chain begins q q q q q q q q q q q q q 
q q q q q q q q q 6 q q 6 G: I vi ii ii V 5 I

Example 4.25: Right hand of BWV 810, mm. 61–73.

dyad, F~–G and by giving the rhythm q q q q q q q its sole imitative treatment. (On the first point, see m. 86 of the score and the brackets in Example 4.24; on the second, m. 85 of the score and the eighth-note motion as far as “V” in Example 4.24.) During the sequence, the melodic form of the cited rhythm is not yet close to the fugal subject, but the running bassline beginning at the arrival on V is spun out of the proper head motive in a continuous alternation of inverted and original forms until the full statement arrives in the soprano. The last measure before the soprano entry achieves the intervals of the inverted form exactly, in a clear recollection, down an octave, of the strain’s first measure. Besides thus playing into the subsequent final entry, BWV 810’s chain of fifths also is energized by the preceding ideas. This is partly melodic. Example 4.25 shows the right hand part of mm. 61–73, starting with the culminating statement of the strain’s fugal exposition and ending with the first bar of the sequence. That the sequence begins with a resolution to b4 is significant for completing an octave descent from b5 and homing in on the most prominent pitch of the prior statement; then, the remainder of the fourth-species skeleton, b4–a4–g4–f~ 4, goes over the same ground as the initial head-motive and the rising sequence after the entry. At the same time, the chain of fifths feeds into a rhetorical dimension of the fugal design. Bach’s chosen subject not being translatable to major, the whole non- thematic passage in the relative, G major, stands in contrast to the serious affect of all the entries in E and B minors. The writing of the sequence and the preceding pattern of descending tenths is expressly lyrical, and the transition between these segments introduces another affective contrast of light and sonorous textures. The arrival of the descending tenths pattern is primed as a moment of “breakthrough,” since the norms of tonal polyphony hang by a thread in the rising sequence that leads there. The fifths chain, with its slow melodic rhythm, is really a deepening of the same breakthrough into major-mode lyricism. Schema 215

The E minor Partita as Essay in the Chain of Fifths More than any other of Bach’s gigues, that of the E minor Partita, BWV 830, applies the chain of fifths repeatedly and exposes the schema to intense contrapuntal manipulation. For that reason, this movement merits its own analysis, and has been excluded from the surrounding schematological survey. Moreover, BWV 830’s uses of the fifths chain sit off-center to the general schema and suggest work-specific sub-schemas which would over- complicate the main schematology if fully integrated with it. But to treat BWV 830 separately is not to step aside from the main project, only to respect an important asymmetry that arises in the material being analyzed. BWV 830 includes a total of twelve chain of fifths passages, represent- ing four contrapuntal modules with two or four realizations each. One of these modules produces sequences at the regular pace (in this case, with the basic cantus descending at the rate of , in W , notated as C in my reductions); another of the modules produces fast sequences, at twice the pace; and the remaining two produce slow sequences, at half the regular pace. En masse, these sequences bespeak experimentation.38 In the two modules that have four realizations—one slow, one fast—Bach makes a systematic exploration of contrapuntal inversion. Elsewhere, another source of interest is the application of recurring materials to different tonal situations: one sequence resolves to i6 on its first appearance but later, under transposition, resolves to iv6. And two of the fast sequence passages feature harmonic and metric contortions that shift the point of harmonic arrival to a different key and later temporal position than what is expected. In the form of BWV 830, the distribution of related sequence passages reflects what Joel Lester calls “parallel sections of heightening intensity.”39 The first strain spans 24 bars consisting of three substantial sections and a shorter coda in an apparent play on the idea of 8-bar divisions. After an 8-bar fugal exposition (alto, soprano, codetta, bass), the bulk of the first strain comprises two parallel sections of 61/2 bars each: one slow sequence passage of 2 bars and one fast of 21/2 bars, each followed by a fugal entry in the alto voice.40 Because the two parallel sections are shy of 8 bars, the

38. Famously, Laurence Dreyfus paints a picture of such an experimenting Bach while arguing that a more “paradigmatic” than “syntagmatic” concept of form is appropriate to interpreting his music. Dreyfus, Bach and the Patterns of Invention.

39. Joel Lester, “Heightening Levels of Activity and J. S. Bach’s Parallel-Section Constructions,” Journal of the American Musicological Society 54, no. 1 (Spring 2001): 49–96.

40. Until the coda, the texture adheres to three parts. 216 The Art of Gigue

A B C [i] VI [v] III [ v6 ] III6 C   
   C 
     C  




D [iv] [i] V        

Example 4.26: Reduction of BWV 830, mm. 9–10, 151/2–171/2, 33–34, and 411/2– 431/2. time is bought for a coda that steers from i to Vv.41 In the second strain, the same basic design recurs but with additional entries that expand the strain beyond 24 bars. Weighing the evidence of all Bach’s gigues (their bar counts, proportions, and compositional traits), it seems likely that in BWV 830 Bach planned the length of the first strain, then based the second strain on that without particular regard for proportions, the same being true in BWV 827. Though the second-strain exposition follows the same 8-bar outline as the first (now bass, alto, codetta, soprano, with the bass effectively in tenor register), the remainder of the second strain introduces asymmetries to the parallelism of strains and sections within the strain. The first “parallel section” (mm. 33–411/2) presents two middle entries instead of one, bringing the section to 81/2 bars. The next (mm. 411/2–50) similarly presents two final entries, but loses a bar by abbreviating the fast sequential element and gains two by reprising the exposition codetta between the final entries, for a total of 91/2 bars.42 The slow sequence passages which initiate each of the four “parallel sections” just described are heavily reduced and transposed to A minor in Example 4.26. The first three passages instantiate the chain of fifths

41. I introduce the symbol Vv as a substitute for “V~,” to indicate the major triad on 5ˆ in the minor mode.

42. In the first strain, there is also a reprise of the exposition codetta, but that serves as the coda after the completion of the two parallel sections. Schema 217

arpeggiates underlying harmony BWV 830 10 VI  q q q q q q q q q    q q
  q q
q    q q  q   q
q q q q q q
q q q q q q     Z Z
 Z Z Z Z

  Ø Z Z Z Z

Example 4.27: Initial reduction of BWV 830, mm. 9–10.

BWV 830 16½ III



   6  6 6      6      6   

    6

Ø    6

Example 4.28: Initial reduction of BWV 830, mm. 151/2–171/2. technique, whereas the fourth is a little different. Across the three proper chain of fifths sequences, the schematic cantus is passed from the soprano voice, to the alto, and then the bass. The cantus’s chromatic division in the second half indicates the harmonic gravity of each downbeat at the slow pace, and with it, a sense of linear continuity comes more easily to the elaboration. The chromatic element also means that the formula fits equally well two positions in the key, either beginning on tonic as at (a) or beginning on dominant as at (b) and (c); the harmonic stations (i.e. the roots) on the downbeats can be traced in the second-species element. The realization of these passages is illuminated by Example 4.27, Example 4.28, and Example 4.29, which reflect some of the motivic adjustments Bach 218 The Art of Gigue

BWV 830 34 III q  q q q q q q q q q
q q q   q q q q q q
q
q q q q    q q q q q q q q q q q q q 


q q q  
q q
q 

 
q
q Ø q q  Example 4.29: Initial reduction of BWV 830, mm. 33–34.

BWV 830 42½  V
q q q q q q q q q q q  q
q q
q q q
q
q
q
 q q  q q 
q
q q q q
q
q q 

 q q  q q
  q  q

  q  Ø q q q

Example 4.30: Initial reduction of BWV 830, mm. 411/2–431/2. makes and some of the shifting melodic meanings that occur as the lines are inverted. The brackets highlight an interesting feature of the elaborated cantus: that it arpeggiates the underlying dominant harmonies while the other voices add dissonance. The fourth sequence passage in this group uses the same motives as the parallel passages but is not itself a chain of fifths. Here, instead, the harmonic trajectory is from iv to Vv, which calls for the original fifth motion to be reversed and halved in speed, in order to place the progression iv– i–Vv on the downbeats. As Example 4.30 shows, the elaboration of what was the second-species element is now traded between the upper voices to accommodate fifth progression at the pace of the original cantus. Under this transformation, the sequence shifts to a different kind of texture from Schema 219

A B [v] i6 [i] iv6

Z Z Z Z
Z  Z  Z
Z   Z
Z Z Z    Z
Z Z Z 

Example 4.31: Reduction of BWV 830, mm. 29–30 and 47–48.

BWV 830 30
    Ë Ë Ë Ë Ë Ë
ËË 
Ë Ë 
Ë Ë Ë
Ë Ë Ë Ë ËË Ë Ë ) Ë Ë Ë Ë Ë Ë Ë Ë

↓ subj. (inverted) i6 V i 




  












    




















 
   Example 4.32: Initial reduction of BWV 830, mm. 29–32. before, raising the valuable distinction in seventeenth-century techniques that Daniel Harrison makes between sequences built around fourth-species counterpoint and those based on antiphonal writing.43 Also slow-paced and chromatic at a deep level are the two sequence passages in the second strain which form the exposition codetta and its reprise. Their outlines are given as for A minor in Example 4.31, while more modest reductions from the score appear in Example 4.32 and Example 4.33. Here, not the cantus, but the fourth-species element is chromatically divided and the brackets indicate the notional syncopation. Once again, the same contrapuntal formula is applied to dominant and tonic points of departure. However, in this case, the middle harmonic station of the second passage

43. Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence.” The fourth- species type and antiphonal type are what are referenced by the “Aloysius” and “Rosalia” of Harrison’s title. 220 The Art of Gigue

BWV 830 48
    Ë Ë Ë Ë Ë Ë
ËË 
Ë Ë 
, Ë Ë Ë
Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë

iv6 ↓ subj. AC    
            






      Example 4.33: Initial reduction of BWV 830, mm. 47–50.

A V 6 i B HC  5 Z  Z Z  Z Z Z Z Z Z



 Z
 E  Z Example 4.34: Reduction of BWV 830, mm. 5–6 and 22–24. is not diatonic to the minor key, at least not to the natural or Aeolian scale, since (as shown in Example 4.33) the plain cantus uses f4, a Phrygian 2ˆ in E minor. The given reductions include the fugal entries which the sequences prepare. These are rhetorically the most weighty entries in the entire gigue; the first, the climax of the second-strain exposition with unusually rich sonorities in the accompanying voices, and the second, the last entry of all, which restores the subject to its original, un-inverted form.44 The formal role of the sequence pair just described is fulfilled, in the gigue’s first strain, by the regular-paced chains of fifths whose outlines are given in Example 4.34, with the difference that the second item serves as a coda after the two “parallel sections,” since it follows rather than precedes the final entry. In these new examples, the relation to basic contrapuntal schemas is not easily unpicked. In the exposition codetta

44. The soprano outline of 5–ˆ 4–ˆ 3–ˆ 2–ˆ 1ˆ in the second passage is the clearest of several voice leading connections that span each sequence–statement pair. Schema 221

5½ 6 BWV 830 V 5   Ë Ë Ë  Ë Ë Ë Ë Ë Ë  ËË Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ð 

i 6   vii  i Ë    Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë   Ë Ë Ë
Ë Ë  Ë Ë  Ë

Ë
Ë Ë
Ë Ë
Ë Ë  Ë  
Ë Ë Ë  Ë   ↑ subj.

Example 4.35: Initial reduction of BWV 830, mm. 5–8.

BWV 830 22½ V HC q q q
 q q q q  q q q q q
q q q q q q q q q q q q
q q q
q q q q q q q
ú  q q q  q q q

Example 4.36: Initial reduction of BWV 830, mm. 22–24. 222 The Art of Gigue

(see Example 4.35, comparing Example 4.34a), the texture thickens in the second half as a pattern of sixths and sevenths above the cantus emerges by way of compound melody. The sophistication of the coda, meanwhile, lies in the style brisé texture, and difficulty of resolving the texture into distinct voices, which is compounded by the newly leaping left-hand part (see mm. 5–6 and 22–23 in the score). Example 4.33 suggests one of two or three possible interpretations, in which the alto and bass of a four part texture collaborate in realizing the generic second-species element. These and all of the slower sequences are associated with the archety- pal construction of a fourth-species line in sixths and sevenths below the cantus. However, the pervasive inversion of sixths and sevenths to thirds and seconds, affecting all slow fifths chains after the first, is an unusual procedure. One can hypothesize that the slow speed is instrumental in this transformation. Much more straightforward are the counterpoints of the fast chains of fifths in BWV 830. As always, it appears, the basic procedure for fast-paced sequences is construction by fourths and fifths. For these passages, modest reductions are sufficient to show the simple formulas at work. This series of fifths chains, like the first discussed, explore the possibilities of contrapuntal inversion. The effects of inversion are prominent in the passage shown in Example 4.38, where a thoroughly prototypical fifths chain, BWV 830c173/4, gives way to another in which soprano and bass exchange places while the alto continues its stepwise descent. The stark contrast between the “difficulty” of these sequences becomes clear if one attempts to reduce these fast sequences further to three homorhythmic parts. The first sequence easily reduces to parallel six-three chords over a3–g3–f~ 3, but the second sequence, if it implies parallel six-three chords at all, does so to the exclusion of the alto part, with the original bass part, now in the soprano, connoting two lines. Even less susceptible to homorhythmic reduction is the passage shown in Example 4.37, where the soprano of the sequence, BWV 830c111/4, traces not the roots, per the archetypal bass, but the chordal fifths instead.45 Notice that given the ordering of these passages—the most prototypical sequence does not come first—Lester’s “heightening intensity” is not so appropriate as the basic notion of “parallel sections.”46 The remaining fast chains of fifths that occur in the second strain underscore the idea that returning sequential material might become less, not more complicated over time. BWV 830c44 (see Example 4.40) presents

45. This means that the soprano harmonizes the onset of new notes in the lower parts with thirds and tenths rather than sixths.

46. Lester, “Heightening Levels of Activity and J. S. Bach’s Parallel-Section Constructions.” Schema 223

BWV 830 11¼

 Ë     Ë Ë Ë Ë Ë    Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë     Ë Ë Ë Ë Ë Ë Ø  ‹ Ë


Ø Ø

Ø


    

    Ø Ø Ø   V in tonic Ø            Ø     Ø       Ø  

Ø             Ø

 Ø      

V in ! dominant ↓ soprano omitted
    Ø    Ø  Ø       ↓ subj. Ø  Ø 
Ø  Ø  Ø  Ø  
    Ø         Ø       V Ø    Ø

 Ø  Ø Ø Ø  

Example 4.37: Reduction of BWV 830, mm. 11–151/2. 224 The Art of Gigue

18¾ BWV 830 17¾ i     Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ˆ   Ë Ë



6 iv V 5 i  


















 

 ↑ subj.

 



outer voices omitted

Example 4.38: Reduction of BWV 830, mm. 171/2–21. a reprise of BWV 830c183/4 with the second-species element “restored” to the bass. The connection—between the second parallel sections of each strain—is made quite clear by distinctive motivic content. (See the os- sia in Example 4.40 and mm. 18–19 and 43–44 of the score.) Likewise, BWV 830c351/4 (see Example 4.39) presents a reprise of BWV 830c111/4 with its second-species element “restored” to the bass. This connection— between the first parallel sections of each strain—is especially reinforced by the material which effects the modulation, as indicated in the examples. Concerning these modulations, Bach wrestles a harmonic outcome from the sequence which is not at all typical, adding another string to the bow of BWV 830’s experiment with the fifths chain formula. My reductions interpret the harmonic, melodic, and metric properties of these passages by several stages of reduction (or following Agawu, “generation”).47 Having analyzed BWV 830’s chain of fifths sequences, and included in the reductions any fugal statements that follow the sequences, it is the case that most of the movement is now spoken for, indicating that the study of one schema and its immediate outcomes can amount to a large compositional insight. My reductions can be read through with most of the score as follows: for mm. 5–24, Examples 4.35, 4.27, 4.37, 4.28, 4.38, and 4.36; for mm. 29–50, Examples 4.32, 4.29, 4.39, 4.30, 4.40, and 4.33.

47. Agawu, Music as Discourse: Semiotic Adventures in Romantic Music. Schema 225

BWV 830 35¼


Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë Ë

Ë Ë Ë ¶   Ë Ë Ë
Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë V Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë

  Ë Ë Ë Ë Ë Ë V in tonic Ë Ë   Ë Ë  Ë Ë Ë Ë Ë Ë


 Ë Ë Ë Ë Ë

Ë  Ë Ë Ë   Ë Ë Ë 

  Ë Ë Ë Ë 

↓ V in ! dominant ↓ subj. (inverted) i 6 Ë  iv Ë Ë Ë   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 
fugal entries only  Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë    Ë  Ë Ë


↑ subj. (inverted)

Example 4.39: Reduction of BWV 830, mm. 35–411/2. 226 The Art of Gigue

44 HC BWV 830 soprano omitted    Ë Ë Ë Ë Ë Ø Ë Ø Ë Ë  Ë Ë Ë Ë Ë Ë Ë 

 Ë Ë Ë alternative metric span ↑ subj. (inverted) Ë N  Ø Ë   Ë Ë Ë Ë Ë  Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë
 Ë Ë Ë Ë

  Ë Ë Ë Ë Ë Ë Ë Ë

V i Ø
 Ë  Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ø 

Ë  Example 4.40: Reduction of BWV 830, mm. 43–46. Schema 227

A B C (I9 ) I V vi q q q q q q q q   q q q q q q q q q q q    q q q q q q
q q q q q q q q q q q q q q q q q q  Example 4.41: Reductions of BWV 806, mm. 71/2–111/2, BWV 807, mm. 21–28, and BWV 815, mm. 7–14.

Uses of the “Sixths and Sevenths Below” Type Not much less prevalent than the fourths and fifths type, sequential con- struction around a pattern of sixths and sevenths below the cantus has an important place in Bach’s technique from his earliest keyboard gigues (BWV 818, BWV 806, BWV 807) through one of the last (BWV 828). That said, changes are apparent in Bach’s technique over this time. First, there is a shift of emphasis between the two kinds of second-species counterpoint introduced previously: the bass which harmonizes the upper-voice disso- nances as nine-three chords is used in three works of the Weimar–Cöthen period but in no works of the Leipzig period. Although a small number of examples is considered in this section, the complete picture of Bach’s gigues supports the hypothesis that the bass option just described fell out of favor. A second change is an increase in the complexity of counterpoint, which makes the schema of fourth and second species more remote to the fully realized texture, although Bach’s thinking at the schematic level remains manifestly simple. The examples from BWV 828, the D major Partita, are texturally the most advanced yet indicate a commitment to simple tetrachordal cantuses. The five sequences analyzed in this section which do not belong to BWV 828 are metrically quadruple and have cantuses that begin 5–ˆ 4–ˆ 3,ˆ albeit with various endings capable of steering to either dominant or tonic harmony. Example 4.41 gives the reductions of the three major-mode passages that use nine-three, rather than six-five, chords for the dissonances. The first and last of these are the only sequence passages in all the keyboard gigues to sustain motivic repetition into a fourth segment,48 and the last is fastidious enough that the current reduction registers no deviation what- soever from the sequential pattern. As Example 4.44 shows, the motivic pattern of this last example is only broken at the last moment—the last Œ 6 beat in eight bars of 8 . The mutation prevents e ’ 5 being anticipated before the arrival on vi, and inflects iii instead of I to galvanize the start of the next

48. Except for fast-paced sequences. 228 The Art of Gigue

8½ BWV 806 AC 


q  qq qq q q q q q   q q qq q q q q q q q q q  q q q q q q q 1   q qq q q q q q q q

Example 4.42: Initial reduction of BWV 806, mm. 71/2–121/2.

BWV 807 23 V AC q q q q q q q q q q q q q q q q q q q  q q
q q q q q q
q q q q q q q q q q 1  q q q q q q q q  q q q q q q q q Example 4.43: Initial reduction of BWV 807, mm. 21–34.

9 modulation to dominant BWV 815 (I9 ) vi = ii AC


 ΠΠq
q q  ΠΠq  q q q q q q  q q q q q q   q q q q q    q q q q q 1   q q q q   q q q q

Example 4.44: Initial reduction of BWV 815, mm. 7–22. Schema 229

BWV 807 63 V AC q  q q q q q q q q q q q q q q q q q q q  q q q q q q q q q q q q q q q

q q q q q q q q q q µ  q q q q q q q q
q q q q q  q

 q
q q q q
q q q q q q

 q q q q q q q q  q  Example 4.45: Reductions of BWV 807, mm. 61–74. unit, a modulation and cadence. If mm. 7–14 of BWV 815 are heard without the change, the effect of too strong a tonic prolongation is quite plain. It is worth underscoring that the eighth notes appearing in the soprano line of Example 4.44 are anticipations rather than direct resolutions; it is just one instance of this chapter’s larger analytical program easing effective musical interpretation in an individual case. The other unusually tenacious sequence, as Example 4.42 shows, represents a fundamentally similar approach to the elaboration of the fourth- and second-species lines. A small difference in the bass figuration gives more consonant support to the active cantus and forges a closer motivic connection to the alto. But the profound difference between the sequences in BWV 806 and BWV 815 lies in their formal outcomes: where BWV 806c81/2 has a paltry cadence tacked on, BWV 815c9 is answered by a full cadential phrase that is the metric equal of the sequence.49 Between these extremes, of cursory and substantial approaches to a cadence, sits BWV 807c23, as shown in Example 4.43. In this passage, the bass takes on some of the elaborative work of the alto in the other examples. The second-strain reprise of the passage just mentioned is the one minor-mode application of the current pattern in the Weimar–Cöthen period. As Example 4.45 shows, BWV 807c63 is even closer than its first-strain counterpart to the elaborative strategy of BWV 806c81/2. Here, not the bass but the soprano makes an incursion into what is elsewhere alto business. Meanwhile, BWV 818c8, shown in Example 4.46, is the remaining major-

49. That BWV 806’s cadence is relatively slight is attested by the addition of another sequence-cum-cadence to end the strain, whereas the cited cadence in BWV 815 is followed by explicitly post-cadential material. 230 The Art of Gigue

BWV 818 8 V 7 AC  q q q q q q q q q q q qq q q q q q
 q q q q q q q q q
  q q q
q q q
q q q q q q q
 q q H  q q q
q

q q q q  
q q
q

q q q q  q q  q q q Example 4.46: Reductions of BWV 818, mm. 7–14. mode sequence of the Weimar–Cöthen period; the one to use the bass which creates six-five chords instead of the—later shunned—nine-threes. This sequence, like those of BWV 807, arrives on the dominant and an authentic cadence follows after a certain amount of harmonic stalling. The means of quitting the sequence and moving to a cadence represents Bach’s practice at a more youthful stage that BWV 815 and its more robust, metrical design. a

Written perhaps six years after BWV 815 and a dozen years after the earlier works, the gigue of the D major Partita, BWV 828, is the prime illustration of fifths chains of the “sixths and sevenths below” type. The movement features three unique and highly sophisticated applications of the schema. A more radiant advertisement for the chain of fifths sequence is hard to

imagine, and not only because of the endearing lights of D major tonality and 9 16 meter. Three tetrachordal cantuses are realized in sonorous, ingenious counterpoint, and with a structural bravura that is peculiar to Bach’s mature practice. Across the three fifths chains—one in the first strain, and two in the second—the “cantus” top voice gets incrementally lower, first descending from a5, then g5, then f~ 5. Though the local key varies, the tetrachords are all diatonic to the home key of D major, and in combination, they represent the three kinds of tetrachord inherent in the Guidonian hexachord: sol–fa– mi–re, fa–mi–re–ut, and la–sol–fa–mi. To name the tetrachords that way is to Schema 231

in dominant ↓ subj. [39] I cadenza BWV 828 desc. thirds sequence 27 V ^ ^ ^ ^ 6 5 4 3 Ë Ë
Ë Ë  Ë    Ë Ë Ë Ë Ë Ë Ë Ë Ë     Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 
 Ë
Ë   
Ë       Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë  Ÿ     Ë Ë Ë  Ë Ë Ë Ë
Ë Ë Ë so–fa–mi–re ( ii6 )      Ë  Ë Ë Ë 

Ë Ë  Ë  Ë Ë Ë 

duple sequence

AC  Ë    Ë Ë    Ë
Ë Ë
Ë Ë Ë Ë Ë
  
Ë Ë Ë
Ë  Ë Ë Ë Ë Example 4.47: Reductions of BWV 828, mm. 25–48. Note: the simpler reduction is transposed to the natural diatonic scale. use a language Bach knew well, given the place of hexachordal solmization in German pedagogy till well into the eighteenth century.50 The initial sequence is the main point of departure following the opening fugal exposition.51 This passage and the remainder of the first strain are shown in reduction in Example 4.47. Here we see precisely half of

50. On hexachordal solmization, see Gregory Barnett, “Tonal Organization in Seventeenth- Century Music Theory,” chap. 13 in The Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge University Press, 2002), 407–455. The famous Mattheson–Buttstedt debate is addressed in many places including Joel Lester, Between Modes and Keys: German Theory 1592–1802 (Stuyvesant, NY: Pendragon Press, 1989), chap. 7. On the hexachordal properties of Bach’s fugue subjects, see Schenkman, “The Influence of Hexachordal Thinking in the Organization of Bach’s Fugue Subjects.”

51. The metric and upper-voice melodic work necessary to prepare the start of the sequence is performed by an ascending codetta that bridges from I6, the harmonic terminus of the bass entry at m. 21, to iii, the starting position of the sequence. 232 The Art of Gigue the strain. As indicated, the fifths chain has a metrically duple quality but is coupled to a fast descending thirds sequence which squarely continues the underlying counterpoint52—toward an unusual, and only transitory, harmonic goal of ii6. There follows a move to V, often the internal goal of a fifths chain, from where is launched the sole entry of the fugal subject during the first strain, post-exposition. That subject statement picks up the g5 of the fifths chain,53 and its 6–ˆ 5–ˆ 4–ˆ 3ˆ tetrachord proceeds over the same ground as the descending thirds sequence; and that connection is cemented by the subsequent inflection of c5 in approach to b4. Just as the upper line depicted in Example 4.47 traces an octave descent from a5 to a4, the bassline likewise speaks a strategy of stepwise descent instigated by the sequence. Come the Schlußsatz of the strain (see Example 4.47’s last “bar”), the bass enters the limelight with a descending tetrachord pattern, a scalar precadential device like those described in chapter 2. The bracket in Example 4.47 indicates the metric overlap whereby the emerging Schlußsatz attaches to the concluding tonic of the subject statement. The bass’s scalar descent then continues—with rhetorical flair—to 3,ˆ the threshold of the final cadence.54 While the first strain is precisely bisected by the onset of the fifths chain, the second strain is not. Example 4.48 begins a little before half-way in the second strain. As with BWV 830, it appears that Bach laid out the first strain from a rational vantage point—tidily arranging sixes, threes, and eights to make forty-eight—but composed the second strain as a response to the first, allowing specific musical initiatives to warp the original design. In this movement, there is a commitment, though, to maintain the same overall length, a commitment shared by BWV 829, which was also conceived for publication, unlike BWV 830.55 Here, there are two fifths chains, not one, and these represent the height of the second strain’s independence from the first. Prior to the sequences, the second-strain exposition matches the plan of the first strain, except for omitting the outgoing codetta. Afterward, the parallelism between the strains is restored at the final entry and becomes absolute with the Schlußsatz end-rhyme. Example 4.49 clarifies the content of the two fifths chains: these juxtapose minor and major treatments of

52. In this sequence, dominants preceding their tonics, unlike in the Romanesca type.

53. This note is well-primed since it is struck three times in mm. 27–28.

54. In a marvelous canonic detail, the right hand prefigures the cadential bass in rhythmic ˆ 4 diminution, 3–ˆ 4–5–ˆ 1ˆ and arpeggio, during the prior V2 harmony. 55. On the early appearance of BWV 827 and BWV 830 in the Clavierbüchlein for Anna Magdalena Bach, begun in 1725, see Malcolm Boyd, Bach, 3rd ed., The Master Musicians, ed. Stanley Sadie (New York: Oxford University Press, 2000), p. 193. Schema 233

BWV 828 72

Ë Ë Ë Ë  Ë  Ë  Ë Ë Ë Ë Ë Ë Ë    Ë Ë Ë Ë   
 æ æ 

q   Ë Ë Ë Ë Ë Ë 
Ë Ë Ë  Ë ↑ c-subj. head and first half of tail Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë   Ë Ë Ë Ë   Ë Ë   Ë Ë Ë Ë Ë Ë  Ë Ë in dominant in relative i6 !V 6 / IV  Ë Ë Ë  Ë   Ë Ë Ë Ë Ë Ë    Ë Ë Ë Ë Ë i    Ë Ë Ë Ë  Ë

  Ë Ë Ë Ë 80
 Ë  æ    Ë  æ æ Ë Ë Ë     Ë  Ë Ë Ë

 


    Ë
 Ë Ë Ë in tonic IV I !V 7 / IV  Ë Ë  Ë  Ë  Ë Ë Ë Ë Ë   Ë Ë Ë  Ë Ë Ë Ë Ë ↓ main subj. tail only I
AC Ë Ë Ë     Ë Ë  Ë Ë Ë Ë Ë Ë    ËË Ë Ë Ë Ë  Ë Ë  Ë Ë Ë  ËË Ë Ë   Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë   Ë Ë Ë Ë  Ë  Ë Ë Ë   Ë Ë Ë  Ë Ë Ë    Ë Ë

Example 4.48: Reductions of BWV 828, mm. 70–96. 234 The Art of Gigue

fa–mi–re–do la–so–fa–mi i I q q q 
q q q
q q q   q q q q
q q q q q q q q q q q q q N.B. as for G major

Example 4.49: Further reduction of BWV 828, mm. 70–85. similar tetrachordal cantuses, not starting from 5ˆ as with all other examples here (BWV 828c27 included) but starting from 6.ˆ Stylistically, the 6–ˆ 5–ˆ 4–ˆ 3ˆ cantus is perhaps increasingly prevalent in Bach’s later sequences, as seen in BWV 827 and in BWV 828 specifically, the same tetrachord is thematized in the main fugal subject. Indeed: both statements of that subject in the purview of Example 4.47 and Example 4.48 are necessarily realized as fast fifths chains. The two conjoined sequences in BWV 828 embody a contrast that extends beyond the tonal dichotomy of minor and major, into a contrast of schematic applications: the first sequence passage (and 8-bar hypermeasure) is knotted and ingenious in its counterpoint, whereas the second passage revels in the simplicity of its underlying formula. Yet the two sequences engage the same contrapuntal schema. The clue, in BWV 828c72, is the unembellished middle voice that trails off at mid-way (see mm. 70–73 in the score). Although my simplest reduction shows a switch to the fourths-and-fifths type of construction during the second segment, this arises because the erstwhile bass enters the middle register. If this unique occurrence were unwound, the most appropriate reduction would show a continued sixths-and-sevenths pattern.56 The bassline quits its native register—and thus complicates the counterpoint—in order to accommodate the incoming thematic statement, of the fugal countersubject that is the main theme of the second-strain exposition. (In the second-strain exposition, the original subject appears in counterpoint to the alto entry.) The strategy of incorporating a thematic statement into the second half of a “sequence” schema already had a place in Bach’s practice with the French Suites,57 but the treatment of contrapuntal voices in BWV 828c72 is radically new. By pushing the contrapuntal texture to an extreme of “difficulty” late in

56. In the third segment of the sequence, the bass and the alto both have ~7ˆ for a time. The bass’s having ~7ˆ is, indeed, consistent with a continuation of the pattern from the sequence’s first and second segments.

57. See the analysis elsewhere in this chapter of BWV 812c18 and BWV 815c37. Schema 235 the minor-mode fifths chain, Bach sets up the start of the major-mode equivalent as a moment of “breakthrough,” surpassing the burst of lyrical writing that was already had early in the minor-mode passage. Arguably, it is the movement’s most important articulation, rhetorically and metrically. Elsewhere in this chapter, a similar use of a major-mode fifths chain is observed in the E minor English Suite, BWV 810, probably written eight or nine years before BWV 828. It so happens that BWV 810 and BWV 828 both have 48-bar strains, and, in fact, it is plausible that Bach turned to the earlier work as a guide when tasked with the composition of a new fugal gigue for the Clavier-Übung series. The earlier English Suite intones a high-minded but still playful fugal rhetoric that is largely absent from the French Suites and bypassed by the A minor and E minor Partitas, but is quite relevant to the D major Partita as well as the G major.

Uses of the “Fourths and Fifths” Type In Bach’s keyboard gigues, the general chain of fifths schema supports a number of metric and harmonic behaviors. No single usage is archetypal. Yet some behaviors have a more central place in the schema than others. Regarding the fourths-and-fifths formula in the ordinary pacing, something of a “classic” usage can be identified in the recurrence of metrically quadru- ple passages that settle on dominant harmony in the fourth quarter, and on the back of simple tetrachordal cantuses. The relevant cantuses, transposed to the natural diatonic scale, are G–F–E–D, E–D–C–B, and C–B–A–G~ (so– fa–mi–re, mi–re–do–ti, and do–ti–la–si). Bach’s keyboard gigues contain three clear examples, one for each of the named cantuses, and a further few closely related examples. The French Suites in E ’ major, BWV 815, and E major, BWV 817, demonstrate chains of fifths around mi–re–do–ti and so–fa–mi–re. These cantuses stand as 5–ˆ 4–ˆ 3–ˆ 2ˆ in minor and in major, respectively, with BWV 815’s passage cast in the relative, C minor, and BWV 817’s in the dominant, B major. Comparing BWV 815 and BWV 817, one sees pointed differences in the textures and the formal strategies served by very similar contrapuntal devices. A modest reduction of BWV 815c37 is given in Example 4.50. Here, the annotation “subj. (inverted)” refers to an entry of the gigue’s fugal subject in the middle voice, which fills a gap in the preceding surface texture of two parts. Further reductions of this passage, in Example 4.51, demonstrate the one contrapuntal schema that underlies both episode and entry in the fugal texture. I conceive the entire schema as a “sequence schema,” characterized by the chain of fifths technique. With an authentic cadence appended to the tentative arrival on the dominant, annotated “(V),” the chain of fifths schema becomes the substance for the full second half of the gigue’s second 236 The Art of Gigue

37 BWV 815 (V) AC

Ë Ë
æ æ Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë     Ë Ë Ë Ë Ë Ë ↑ subj. (inverted) ↓ subj. (inv.) Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë #   Ë Ë Ë Ë
  Example 4.50: Reduction of BWV 815, mm. 35–45. The second subject entry marked here represents the start of the gigue’s third of three periods.

V V

 ~


~








Example 4.51: Further reductions of BWV 815, mm. 35–42. period, ten bars to answer the eight-bar exposition that began the current strain. Example 4.52 gives a reduction of the major-mode counterpart, BWV 817c10. Like BWV 815, BWV 817 leads smoothly to an authentic cadence in the same key as the dominant harmony that concludes the sequence schema, but otherwise the two treatments are quite different. The motivic longevity of BWV 817c10, for one thing, is greater. Not until the fourth segment is the pattern abandoned. Here, I show the change to small print at half-way through the dominant harmony since the figurations remain close enough until then, and the marked departure occurs when some shorter repetitions take hold. Another difference of BWV 817 against BWV 815 is the greater time that elapses before the subsequent authentic cadence, and thus the greater space afforded to the dominant arrival. This is not a half cadence (Example 4.52 would show the annotation “HC” if it were) but the dominant harmony is more a point of rest than in BWV 815. Whereas BWV 815c37 had a complicated relationship to the end of the schema, BWV 817c10 is instead unconventional at its start. The transition into the second segment is marked by a non-stepwise correspondence of the upper part at the downbeats and an unusual diatonic shift into B major from C~ minor. The first segment of the sequence retains the diatonic orientation of the preceding Vordersatz in E major, the tonic, but as Example 4.53 shows, the whole passage is easily reconciled to the incoming key. Crucial to the passage’s sense of Schema 237

BWV 817 3 10 V 3 3 3  q q q q q q q q q q q q q q q
q q q qq qq q
q q q qq q q q  3 3 3 3 q q q  3 3  3 q E  q q q q q q q q q q q q q q 3 q q 3 q q 3 q 3 3

q q q
q  q q  q q  q q q

q q
 q q q q

AC q q q q q q q q q q q q q
 q q    q  q q q q
q
q q Example 4.52: Reduction of BWV 817, mm. 9–16.

V V Z Z Z Z Z 
 Z Z Z Z   Z Z Z

Example 4.53: Further reductions of BWV 817, mm. 9–12. 238 The Art of Gigue direction is the chromatic alto line, which plays upon the fourth-species idea as indicated by the brackets. The expansive, lyrical treatment of the chain of fifths in BWV 817’s first period is tied to a formal breadth already established by the preceding Vordersatz. If one interprets the movement by the same framework as Bach’s cello gigues, which I think appropriate in this case, it becomes clear that the Vordersatz material is twice as long as it might have been, at sixteen beats instead of a possible eight: the move to E major’s dominant in mm. 3–4 is destabilized by the seventh (a3) and followed by a matching subphrase that escalates the length of the Vordersatz and commits mm. 1–8 to one large tonic prolongation. This means that the Fortspinnung is initiated at m. 9 under extra pressure to escape the orbit of the tonic, and in the shadow of an enlarged metric expectation. A comparable situation was seen in chapter 2 with BWV 1012, where an enlarged Vordersatz gave rise to a broad, slow-paced sequence. Here, the sequence proceeds at the usual pace but it is coupled to a pseudo-cadential phrase containing shorter sequential repetitions. The resolution to B major, marked “AC” in Example 4.52, is a cadence so far as the underlying schema goes, but all this should be considered Fortspinnung in the larger formal argument. The cadence is, in fact, elided out, and the ideas that supersede it (various patterns of scale and arpeggio) are those that prepare the true cadence; mm. 13–14 by comparison do bear the hallmarks of precadential function as defined in chapter 2. Overall, BWV 817’s first period divides into three segments, each eight bars, which reflect the Vordersatz–Fortspinnung–Schlußsatz paradigm. But under the expansive proportions of the first and third elements, there is some intermixing of functions on the local level, and the Fortspinnung is pressed to be relatively continuous across its two halves.58 The French Suite in D minor, BWV 812, demonstrates a chain of fifths around do–ti–la–si, 3–ˆ 2–ˆ 1ˆ –~7ˆ in minor. This passage, reduced in Exam- ple 4.54, is a close match for the passage in BWV 815 examined above. Possibly, Bach modeled one gigue on the other, although it is unclear which was composed first.59 The formal situation in BWV 812 corresponds to

58. From the cello suites, BWV 1008 would be a good example to contrast with the continuity of BWV 817’s Fortspinnung and the scope of its Vordersatz.

59. Whereas the order of the English Suites was apparently contrived so that the names of the keynotes spell the first phrase of “Jesu, meine Freude,” the order of French Suites 1–5 is presumably the order of composition (with No. 6 certainly being written last). On that basis, BWV 812 precedes BWV 815. However, aspects of BWV 815’s gigue suggest to me an early date for that movement, and one may even speculate some connection to the individually transmitted Suite in E ’ major, BWV 819, which lacks a gigue. It is plausible that the gigue of BWV 815 was originally conceived as part of the suite we now know as BWV 819, and pre-dates the rest of BWV 815, if not also BWV 812. Schema 239

BWV 812 18 not V   HC in ! tonic
Ë Ë Ë Ë  Ë Ë Ë
Ë Ë Ë Ë Ë
      Ë Ë Ë Ë   
  Ë Ë Ë Ë   Ë  ↓ subj. (inverted) ↑ subj.  Ë Ë Ë Ë Ë ò     Ë       Ë  Example 4.54: Reduction of BWV 812, mm. 17–22.

V V Z Z Z Z  Z 

Z Z
Z  »  Z

Example 4.55: Further reductions of BWV 812, mm. 17–20.

BWV 815 in that the sequence passage answers to the fugal exposition that begins the gigue’s second strain, and that the cadence which is appended to the sequence divides the strain, concluding the gigue’s second period. In both cases, the fugal exposition takes sixteen beats and so would the underlying sequence schema, though the cadence in BWV 812 makes for a slightly longer conclusion to the period. Also familiar, here, is the profile of the sequence passage itself: although the operative contrapuntal schema is metrically quadruple, the motivic pattern only extends through the second segment, and a fugal entry occurs in place of the third, smoothed by a continuous three-part texture. However, BWV 812 distinguishes itself from BWV 815 by a more circumspect attitude to its schema as the cadence approaches. Comparing Example 4.54 and the contrapuntal derivations in Example 4.55, one sees that the fugal entry, essentially d3–d4–c4, forces a re-ordering of the contrapuntal voices: the soprano line projected by the sequence (c5–d5–c5–b3) is usurped by the bass then passed to the alto.

David Schulenberg says of BWV 819 that “Perhaps Bach never completed the present suite [BWV 819], or perhaps he originally composed a single series of dances in E ’, then sorted them into two suites [BWV 819 and BWV 815]. In any case, there is no gigue for this suite. It was not unusual for contemporary suites to end simply with a minuet or two, as this one does, but Bach’s only other mature suite to lack a gigue (Partita no. 2) concludes with a large capriccio whose contrapuntal design makes it a substitute for the missing gigue.” David Schulenberg, The Keyboard Music of J. S. Bach, 2nd ed. (New York: Routledge, 2006), 307–308. 240 The Art of Gigue

BWV 831 10 V  AC q
q
q q q q
q q q q q
q q q q
q q 
q  
q 3 
q q
q q 1 
q q q q q
q q q q q q q q q q q 3 3 q  

Example 4.56: Reduction of BWV 831, mm. 9–16.

V q q q q 
 

Example 4.57: Further reduction of BWV 831, mm. 9–12.

Moreover, the expected Vv of A minor is avoided altogether, placing BWV 812 to the far side of BWV 815’s underemphasis of dominant arrival relative to BWV 817. A lurch flatward commits the following cadence to D instead of A minor, but, with a half instead of authentic cadence, the bass still comes to rest on a2, a fifth below the putative e3 (realized as e4) on which the sequence schema ends. The same formula which BWV 812 uses is lucidly illustrated in BWV 831. As Example 4.56 and Example 4.57 show, the passage BWV 831c10 is simple enough hardly to qualify as a chain of fifths, since the bass moves through a tetrachord without the usual interpolations. This gigue from the “French” half of Clavier-Übung II seems deliberately to avoid modern sequential writing as something more characteristic of Italian music.60 Yet, despite its simplicity, BWV 831c10 recalls important attributes of BWV 812 and the other examples addressed above. First, there is the contrapuntal inversion to the second half of the schema. The schematic cantus is traded between the alto and soprano voices, and subject to a change of register; f~ 5–g~ 5–e~ 5 in Example 4.56 corresponds to a4–g5 in Example 4.54. (The passage from BWV 831 is in two parts but well illustrates the realization of three contrapuntal lines.) Second, there is the subsequent authentic cadence. BWV 831’s is laid out the same way as in BWV 817, although

60. Of course, BWV 812 also happens to be styled French, though less as a gigue than an overture, similarly to the fugue in D major from the first book of Das Wohltemperierte Klavier. Schema 241

A B ↓ mi re do V V Ë Ë Ë Ë Ë Ë Ë  Ë Ë
Ë Ë
Ë Ë Ë
Ë Ë ↓ mi re do Ë Ë Ë Ë C  Ë Ë Ë Ë Ë Ë Ë  Ë Example 4.58: Reductions of BWV 814, mm. 53–60.

pre-cadence 55 BWV 814 V AC  q q q
q q q q q q q q q q q q q
q
q q q q q q q q q q q  q q q q q q q q
q q q q q q q q  q q q 
q q q q q q q q q q q q q q q H
q q q q q q q q q Example 4.59: Initial reduction of BWV 814, mm. 53–68. on this occasion, the cadence is not elided and concludes the period, with suitable precadential material in place in mm. 13–14. (BWV 831c10, like BWV 817c10, is part of the first of three periods, whereas BWV 815c37 and BWV 812c18 belong to the second of three.) Lastly, BWV 831 recalls the earlier fugal examples by the textural contrast it applies to the schema’s two halves. The second half is, in this case, marked by the return of continuous sautillant figures in the upper part, and renewed lyricism following the theatrical posture of the sequence’s motivic phase. a

A classic usage for the chain of fifths has been identified in contrapuntal formulas that navigate to dominant harmony using a tetrachordal cantus. One possibility is so–fa–mi–re as 5–ˆ 4–ˆ 3–ˆ 2ˆ in the major mode. It is also possible, however, for cantuses headed by so–fa–mi to serve the minor mode, as will be shown by analysis of passages from the French Suite in B minor, BWV 814, and the Partita in A minor, BWV 827. Reduced to a simple contrapuntal trio in second and fourth species, BWV 814c55 has a cantus of so–fa–mi–ti, as Example 4.58b shows. This metrically quadruple but no longer tetrachordal design appears to bridge the major and minor 5–ˆ 4–ˆ 3–ˆ 2ˆ paradigms. Moreover, as Example 4.58a shows, the soprano line flirts with both so–fa–mi and mi–re–do at the start, even giving more time to the contrapuntally inferior formula. In fact, the contrapuntal implications 242 The Art of Gigue of this passage are fraught with the soprano and bass lines both laying claim to mi–re–do. In Example 4.59, which should perhaps be described as a contrapuntal interpretation rather than a “reduction,” the threat of parallel octaves is evident with A–F~ and E–F~.61 It is worth noting that this interpretation already goes quite far by not reading a d3 in the bass during the sequence’s third quarter (see mm. 57–58 in the score). That d3— the do of mi–re–do—only “resurfaces” in Example 4.58b, once the soprano line is held to the rhythm of a simple cantus. The alto line, meanwhile, is the uncontentious, fourth-species element which anchors the efforts of listeners and analysts to track the schema as a whole. In isolation, the alto line could even be reduced as far as the rhythm of Example 4.2 ( q q q q ), but harmonically it must supply the G~ which the bass cannot. The challenge of navigating the current sequence is rewarded by the gigue’s final cadence (marked “AC” in the reduction). This represents a level of closure beyond the cadence of BWV 831’s first period, and, in turn, the elided cadence in BWV 817 or the internal cadences of BWV 815 or BWV 812. Accordingly, the material immediately following the sequence is the most insistent precadential material yet mentioned; Bach’s simple construction of parallel sixths and tenths against a tonic pedal is plain in Example 4.59, which in fact covers BWV 814’s entire last period (out of an unusual four). The dashed barline now marks a pronounced contrast between the formal attitudes of Fortspinnung and Schlußsatz, greater than with BWV 831c10 and opposite to the continuity of BWV 817c10. As a final comment on BWV 814c55, a hypothesis about the tonal orientation of this “difficult” sequence might be added to the observation about its temporal proximity to the movement’s end. This sequence is the first we have seen in the tonic key and perhaps for that reason it can bear a high level of dissonance. BWV 827c23 is the second example of a minor-mode chain of fifths whose cantus is headed so–fa–mi. As the reduction in Example 4.60a shows, this passage is equal to the harmonic activity of previous examples but has three-quarters their duration given an acceleration in the second half. The cantus closes on mi in this case and, when reduced to four notes as in Example 4.60b, it neatly permutes the Dorian tetrachord. Evident in Example 4.61, with light reductions of the fully realized sequence, is the distribution of the cantus between the alto and soprano lines, and the

61. BWV 814 is written in two parts throughout. During the chain of fifths passage under discussion, mm. 53–60, and the initial four bars of the second strain, mm. 35–38, this two part writing becomes highly sophisticated in the form of a canon at the lower twelfth. The canonic texture is not easily reconciled to simple contrapuntal schemas in any number of parts (the trio interpretation is not the problem here). Schema 243

A V B V  Z Z Z Z Z Z  Z
  Z Z Z Z Example 4.60: Reductions of BWV 827, mm. 22–24.

BWV 827 23 HC q q q q q q q q q q q q q q q q q  q q q q q q q q q q
q
q q q
q q q q q q q q q

q  q q q q q 
q q  q q q q q q
q

 q q q Ø q q q q Example 4.61: Initial reduction of BWV 827, mm. 22–24. 244 The Art of Gigue

↓ subj. BWV 827 19 7 V  Ë Ë Ë Ë  Ë Ë Ë Ë
Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë  Ë
Ë Ë  Ë Ë Ë Ë Ë Ë Ë
 Ë Ë Ë Ë Ë   Ë Ë Ë Ë Ë  Ë  Ë Ë
Ë 
Ë Ë Ë Ë    Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë 

Example 4.62: Reduction of BWV 827, mm. 18–21.

7 V i   

z 



z Example 4.63: Further reduction of BWV 827, mm. 18–19. separation of the tetrachord into two dyads. The “upper” dyad is given to the alto and the “lower” is passed to the soprano in the higher octave, just as in BWV 812c18 and BWV 831c10. The intertwining of voices and registers echoes in fascinating ways through the reductions given here and the fully realized three-part texture visible in the score. By comparison with the cantus, the schema’s fourth-species element is realized fairly simply, like in the previous example. During the first segment of the sequence especially, c5 is a vital foothold, since the schematic cantus’s opening G only shines through at the last moment. If the contrapuntal procedures of BWV 827c23 are familiar from previ- ous examples, what is unfamiliar—and rare in Bach’s keyboard gigues—is the formal placement. Here, the chain of fifths sequence ends the first strain and becomes responsible for a half cadence in the tonic. The cited acceleration of harmonic rhythm helps to secure the appropriate cadential rhetoric. Where previously (in BWV 817, BWV 831, and BWV 814), the sequence was the first of two balanced, eight-beat units, it now takes the second position in a similar construction. But if the sequence is now a kind of Schlußsatz, how is it prepared? Example 4.62 shows the eight-beat unit Schema 245

[i] i [i] i     Z Z  
  Z
 Z  Z      Z    Z  Z Example 4.64: Reductions of BWV 831, mm. 37–40.

BWV 831 38 6 [i] ! iv ~ ~  Z
ZZ     
1
~ ~~ Z  ~ 3

Example 4.65: Initial reduction of BWV 831, mm. 37–41. that goes before, consisting of a brief sequential module and a fugal entry; the custodes indicate the start of Example 4.61. Altogether, this preparatory unit recalls previous chain of fifths passages: BWV 817 et al. in terms of formal usage; BWV 815 and BWV 812 in terms of the episode–entry profile in fugal texture; BWV 812, BWV 831, and BWV 827c23 in terms of the leap- frogging motion of the cantus. Yet the whole is not underpinned by a single contrapuntal schema, and metrically the chain of fifths is duple rather than quadruple, hence the position of the first dashed barline in the reduction. In Example 4.63, where the basic counterpoint is given, the custodes record the melodic and harmonic resolution with which the schema acquits itself, but resolution is extrinsic to the metric duration. The sequence has the character of a linking passage. As for tonal orientation, the cantus is mi–re–(do) as 5–ˆ 4–(ˆ 3)ˆ and the harmonic progression concludes Vv7–(i). This is the only metrically duple fifths chain to appear in minor and at the usual harmonic pace during the current sample. By contrast, I identify a handful of duple fifths chains in major, built around cantuses of not only 5–ˆ 4ˆ but also 2–ˆ 1ˆ , 6–ˆ 5,ˆ and 4–ˆ 3.ˆ a

Once already, we have turned to BWV 831 for lucid illustration of the voice leading behind a chain of fifths formula. Switching from BWV 831’s first strain to an equivalent place in the second strain now, one finds a simple instance of mi–re–(do). The passage reduced to Example 4.64 is 246 The Art of Gigue

BWV 831 43 V 6 5 3 AC  Ë Ë Ë Ë Ë  Ë Ë  Ë
Ë Ë Ë Ë Ë
Ë 
Ë Ë Ë Ë Ë Ë Ë ↑ r.h. à 5  3 Ë Ë Ë Ë Ÿ   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë
Ë Ë Ë Ë Ë Ë Ë Ë Ë

 Ë 
 Ë Ë  Ë Ë Ë Ë
Ë  Ë
Ë 




 Ë Ë     Example 4.66: Reduction of BWV 831, mm. 42–48. The start of this example is indicated in the custodes of Example 4.64. the antepenultimate eight-beat unit of its strain. As Example 4.65 makes plain, root motion by descending fifth is no more than a faint implication (D–G~–C~–F~–B) within the framework of tonic and dominant (B–F~–B).62 In this case, the passage is metrically quadruple and underpinned by one contrapuntal schema, though its sequential character is strictly limited to the first two segments. Harmony is a decisive factor in the meter of this passage, regarding its sense of duple as well as quadruple organization: since the operative schema resolves to tonic instead of dominant, the arrival on mi in the cantus is consistent with the harmonic outcome that shortly follows—or is expected to. As it happens, the underlying formula’s double arrival on tonic harmony supports a surprising turn whereby resolution is delayed until the movement’s final cadence eight bars (and sixteen beats) later. As Example 4.65 records, the formula’s second tonic resolution is substituted by iv6 against the cantus’s ending on la, where begins a brief link to the five-three position of iv for the start of the next large metrical unit. Bracketed in the reduction, that link again uses a nascent chain-of-fifths fragment built around mi–re–(do), here relative to the subdominant triad, E minor. The rhetorical function of this link is to introduce an additional Fortspinnung unit and so escalate the set-up for the final cadence. BWV 831’s final cadence can be seen in Example 4.66 alongside the additional Fortspinnung unit just described. Yet again, this deliberately “French” gigue lays out a descending tetrachord formula bare of the second- species interpolations in the bass that would propagate a chain of fifths. And

62. The triads of the cited fifth motion would use the notes of the Dorian minor scale, with ~6.ˆ Schema 247

6 V 5

  q 
q q q

 




Example 4.67: Further reduction of BWV 831, mm. 42–46.

A B V i Z Z Z Z Z Z   Z Z
Z  Z    Z Z Z Z
Z Z Z Z Example 4.68: (a) Descending tetrachord schema with bass of la–so–fa–mi as 1ˆ –7–ˆ 6–ˆ 5ˆ in minor. (b) Descending tetrachord schema with bass of re–do–ti–la as 4–ˆ 3–ˆ 2–ˆ 1ˆ in minor. in the simplicity of its counterpoint, that descending tetrachord formula offers further valuable insights into Bach’s usage of stepwise sequential devices. Where, till now, the passages analyzed have ended on dominant harmony, we now make a turn toward passages that conclude on the tonic triad. This means looking at contrapuntal schemas whose bass ends on 1ˆ instead of 5.ˆ The current example from BWV 831, in fact, ends on neither 5ˆ nor 1ˆ in the bass, but it straddles in a unique way the two leading practices of dominant-directed and tonic-directed fifths chains. Laid bare in Example 4.67 are the passage’s two unorthodox features: first, the bass’s traversal of a diminished fifth, and second, the deep-seated chromaticism of the upper voice containing syncopation.63 The two features both speak of a sophisticated application of the descending tetrachord schema to a complex tonal situation. We see in this passage an amalgam of two diatonic habitats, subdominant and tonic (D minor and A minor in transposition, or E minor and B minor in the original). The start of the passage is inflected in the subdominant, such that the bass begins on 1ˆ and promises resolution to 5.ˆ If this implication were seen through, the result would be like the earlier passage, BWV 831c10, which the current passage definitely recalls. Per Example 4.68a, echoing Example 4.57, the cantus

63. Not counting ~7ˆ in minor, previous chromaticism, as in BWV 817c10, did not go as deep as the basic texture of fourth and second species counterpoint. 248 The Art of Gigue would be do–ti–la–si. At halfway, however, the passage turns to the home key: what was 1ˆ in the bass now stands as 4ˆ and the bass tetrachord promises to terminate on 1ˆ . The passage now engages the simple diatonic schema shown in Example 4.68b with the tonic triad as harmonic goal. (Worked out as a chain of fifths, that schema would appear as Example 4.2.) Yet the initial promise of harmonic resolution to the dominant is not let go. Tonic resolution would be deflating to the forthcoming cadence. 6 The bass continues past 1ˆ to ~7ˆ and the harmony arrives on Vv 5, first in the guise of vii 7. The rhetoric of the push to an impasse on dominant harmony with 7ˆ or 4ˆ in the bass evokes the theatrical manner of vocal music and the notion of a dramatic break before the cadential phrase. Incidentally, this rhetoric stands firmly in the way of reading the whole of Example 4.66 as an elaboration of a tetrachordal bass, e2–d2–c~ 2–b1. An overall effect of fermata is created by the passage’s metrical expansion into five units, by the deceleration of harmonic rhythm that comes with the voice exchange involving B and G~, and by the accumulation of chord tones that peaks in a 6 64 written texture of six parts at the arrival of Vv 5. The sophisticated engagement of descending tetrachord formulas in this passage also plays into the larger metrical argument of its movement.

In a gigue whose three periods are in the ratio 4 : 3 : 5 (and these numbers 6 count four-bar durations in 8 ), Example 4.65 plus Example 4.66 cover three fifths of the last period, twelve bars in all. Prior to this section, a four-bar hypermeter has been maintained. But the descending tetrachord passage begins out of phase with the established pattern, and although the content of the last twelve bars boils to down a short sequence with deceptive cadence, a substantial Fortspinnung device, and a true cadence, those three elements are not presented in regular units. The idea of quadruple hypermeter is evident at each stage, yet the presentation is irregular. Significant in terms of that larger metrical situation are the textural changes one sees in the realization of Example 4.66. The tetrachord begins out of phase with the previous hypermeter by one bar, and runs long by another bar, which leaves only two bars more for the cadence. However, it would be simplistic to say the cadence is constricted to a two-bar hypermeasure. When, at the passing six-four, the sequence’s motivic pattern is abandoned in favor of new ideas including a sustained e5, the foundation is laid for later feeling the movement’s last four bars as a unit. In line with chapter 3’s argument, the critical factor here is the articulation that occurs with the arrival of i6, where the last two bars of the sequence passage are drawn into a new metric projection (making a duple hypermeasure to straddle the dashed

64. On various “fermata” effects in phrase rhythm, see William Rothstein, Phrase Rhythm in Tonal Music (New York: Schirmer Books, 1989). (Fermata is a term in the index.) Schema 249

resolution 6 6 passing 4 V 5 AC   q q q q q q q q
 q q q q q q q q q q q q q
q q q q q diminution of bass descent over seven bars

Example 4.69: Left hand of BWV 831, mm. 45–48. The slow bass descent from g3 through a~2 can be seen in Example 4.65 and Example 4.66. barline of Example 4.66). The metric overlap gives breadth to the cadence even though its allotted space was encroached on. Another aspect of the sequence’s realization that plays nicely into the cadence is highlighted in Example 4.69. Here, the downward scale incorporated by the bass matches the slow descent from g3, seen above, and triangulates the arrival of a~ 2. The harmonic strength amassed by this move is brilliantly discharged around the cited arrival of i6 when the bass outlines the tonic triad.65 a

From an example that engaged both dominant- and tonic-oriented para- digms of descending tetrachord as special effect, we turn to proper fifths chains that start on subdominant harmony and in some way resolve to tonic. The handful of occurrences in Bach’s keyboard gigues are all in minor, and three of them happen in BWV 827, the A minor Partita. BWV 827 was already discussed for the end of its first strain, and the new examples take us into the second strain, of which more than a third is devoted to chain of fifths sequences. Example 4.70 gives an overview of the whole strain, with the same rhythmic rewriting as before and with circled bar numbers that flag the sequence passages. The metrical meaning of the sequences in this strain is triple rather than quadruple, since the underlying tetrachords finish at the start of the next metrical unit instead of resolving within the current span. Barlines in Example 4.70 mark out hypermeasures of two or 12 three bars of 8 , and most correspond to a statement of the fugal subject or a chain of fifths. The fourth hypermeasure consists of a sequence by stepwise ascent, not a chain of fifths, whereas the last hypermeasure contains the precadence and cadence elements. (The dashed barline marks a similar metric overlap as Example 4.66 so there are really two hypermeasures here.) Above all, the overview demonstrates Bach’s use of the fifths chain as a

65. Anyone who looks closely at the score of BWV 831 will find that the bass is preoccupied with stepwise motion in the range of g3 to a~2 as far back as m. 25. The earlier part of the third period (mm. 29–36) features ascending motion with f~3 as goal. 250 The Art of Gigue

BWV 827 30

 æ ↓ subj. ↑ subj.   æ ) æ 
 E a d

↓ subj. 37                
 a E a

↓ subj. 40     æ ´ æ
  
´ ´ æ   ↑ subj.       
    e b e 7 iv6 V AC æ     æ  æ ↓ subj.   æ
 æ a d Example 4.70: Overview of BWV 827, second strain. Occurences of the fugal

subject are all of the inverted form. Rhythmic conversion: Z of 12 this reduction = C in 8 . Schema 251

A Not this:

 i i q q
q q B  q q q q q q q q q q
q q
q q
q q

B C i6 i  Z Z Z q q
q q q q  q
 q q
q
q q q q q qq
 q q q q q q
q q q

Example 4.71: Further reductions of BWV 827, mm. 29–31, mm. 36–38, and mm. 39–41. Separate transpositions apply. reciprocal of the fugal subject: where the fifths chain leads from iv to i, the fugal subject ends on the dominant of its initial position. All these motions are traced by the annotations under the score, naming the triad at the start of each hypermeasure. Statements of the subject track flatward but sequential episodes track sharpward. The difference here is metrical rather than melodic, since descending stepwise motion is behind both elements.66 The farthest point of remove in BWV 827’s second strain is reached with the tonicization of B minor. The voice leading of the two sequence passages which take us there is unpicked further in Example 4.71 (b and c). The first passage, especially, is harmonically very rich: the written texture of three parts clearly implies four contrapuntal lines. The second passage also suggests an additional line to the usual three, though more mildly. Regarding Bach’s linking together of these sequences and their connection to the earlier one, two themes are worth considering in depth: a shift from complexity to relative simplicity, and an overarching fluency of contrapuntal line and contrapuntal method. It is striking that with repetition, the chain of fifths gets closer to its schematic roots and the formula becomes less obscure. Whereas the bassline of BWV 827c37 jumps ecstatically between the proper bass register and the

66. The fugal entries can be reduced to discrete tetrachord descents in a relatively quick quadruple meter, where the episodes use overlapping tetrachord descents in a slower triple meter. 252 The Art of Gigue territory of the inner voices (see Example 4.71b), regular fourths and fifths are restored in BWV 827c40 (see Example 4.71c). And whereas the extra contrapuntal line of BWV 827c37 is coupled to the existing fourth-species line, adding dissonance, that of BWV 827c40 is coupled to the cantus and sits in the shadow of the bass. The move to relative simplicity begins, moreover, back with BWV 827c30, where an inversion of voices applies that hampers recognition of the common schema and creates a strenuous affect. Also in his trio on “Allein Gott in der Höh” of Clavier-Übung III (one of several organ works to use gigue rhythm), Bach uses a series of recurring, obviously related fifths chains, whose first one shuffles the fourth-species element into the bass. Also adding to the obscurity of the schema in BWV 827’s case is the alteration of the displaced bass line, which now spells not the root progression but the fifth of each chord, as if lagging behind. Altogether, the three fifths chains in BWV 827 express a waning com- plexity as the strain progresses and as the tonality becomes more remote. In a sense, this progressive clarifying is the formula’s undoing. On the other hand, the character of the sequences becomes more assured since the rhythm becomes more percussive; between BWV 827c37 and BWV 827c40, for instance, the cantus goes from being sounded in the buoyant rhythm of q q q to being pulsed in subdivisions of q q (relative to the given reductions). At the moment the push back to tonic begins with the final subject entries in soprano, alto, and bass, the chain of fifths idea stands emboldened yet emptied of the enterprising potential it previously had. The “evolution” (or rather, regression) toward a more generic rendition of the fifths chain takes place against a certain stability of content from one sequence to the next. First, there is the linear continuity between the second and third iterations, especially in the basic upper-voice duet. Beginning with the soprano entry at m. 34 through the end of the last sequence in m. 41, the top line completes an important octave descent from e5 to e4, coupled by the bass in parallel seventeenths. That the sequence picks up the c5 of the subject statement is even clearer in Bach’s score than in the reductions, as is the subject’s own emphatic treatment of the octave descent, e5–e4. Thus, the two sequences are tied together by the most compelling scalar device in a movement already rife with scales. A second agent of continuity is the retention of certain pitch elements across the changes of key. The offbeats d4–c4–b3 of BWV 827c30 recur in BWV 827c37, as the bass wrests control of the second-species element. Meanwhile in BWV 827c37 the offbeats a3–g3–f~ 3, contributed by the added voice, anticipate the bass of BWV 827c40. These are the effects of introducing the chordal fifths to the basic contrapuntal schema. Furthermore, one sequence prepares the next motivically. Example 4.72, reproducing the first bar of each sequence from the score, points out that the variously elegant and audacious figurations of Schema 253

29 36 q q q
q q q
qq q q q q      q q q q q q 
q q q q q q q q q q
q q q  E q q   q q q q  q    39     q q
 q q  qq
q q q  q
q q
q q
q q
q q q q
q q
q q q q q  Example 4.72: BWV 827, m. 29, m. 36, and m. 39.

V 7 Z Z   Z  Z
Z       Z Z

Example 4.73: Reduction of BWV 818, mm. 14–21. the last two sequences are anticipated by the teasing chromatic device of the first. In the A minor Partita, Bach’s fifths chains from iv occupy triple hypermeasures and make their resolutions to tonic extrinsic to the sequence modules themselves. Within the metric unit, which also defines the scope of the sequence in a motivic sense, the harmony thus closes on Vv7. The harmonic meaning of the sequence is complex in this case: the tonic triad is the final outcome but the sequence drives to the dominant seventh first. The dominant seventh becomes even more a goal in its own right if—as in a new example from BWV 818—the cantus of the fa–mi–re–(do) pattern arrests on re as shown in Example 4.73. This is, of course, related to the common harmonic progression shown inExample 4.75. When it is used as a sequence skeleton, though, the slowing in harmonic rhythm creates a sense of fermata, particularly at the already slow tempo of the current example. An initial reduction of BWV 818c16 is given in Example 4.74, where the included cadence ends the first strain. In principle, a similar idea may apply as with the endings of BWV 831 and BWV 827: that this 254 The Art of Gigue

BWV 818 16 V 7 AC

 ~ ~ ~  ~
   ~ Ï
~
~

  ~ ~       ~
~ ~ Example 4.74: Initial reduction of BWV 818, mm. 14–24.

     
3       
Example 4.75: A common harmonic progression. cadence answers metrically to the dominant pedal originally contained by the sequence. But as a whole the passage is much less effective than Bach’s more mature—and published—work in BWV 827 and BWV 831, and at least one reason for that is ventured earlier in this chapter, having to do with the apparent tempo range of Bach’s fifths chains in general. One can certainly point to weaknesses of voice leading by the standards of harmonic richness seen in BWV 827, since the middle part in the three-part keyboard texture is heavy with octave doublings of the outer parts. Nonetheless, Example 4.73 represents an important contrapuntal form for tonic-oriented sequential passages in Bach’s style, since it preserves quadruple hypermeter while saving the tonic resolution for the start of the next module. This is possibly a form better represented in Bach’s concerto-style compositions than in his keyboard suites.

Peripheral Cases Now that most of my analyses are complete, it is worth underscoring the commitment this study makes to full coverage of passages selected by genre and schematic type. All of the fifths chains (and Fontes) in Bach’s gigues for keyboard are analyzed here. This comprehensive attention to detail gives Schema 255

BWV 807 41 in relative in dominant V q  q q q q  q q q q q q q q q q
q q q q q q q q q
 q
q
q q q q q  q q qq q
q q q q Y  q q q q q q q
q
q  q  q q q q Example 4.76: Reduction of BWV 807, mm. 35–47. “Conservative” metric reading.

BWV 807 V embedded sequence in relative in dominant 42



q q 


q  q q






q q q


q q q



  q qq qq
Ï 



q q q




q q q


V






6

6









 Example 4.77: Reduction of BWV 807, mm. 35–47. “Radical” metric reading. rise to a rich and robust understanding of the schema and the techniques of application. With BWV 828, BWV 830, and BWV 827 especially, it has also been shown that analyzing fifths chains and their immediate consequences offers no small insight into Bach’s compositional technique. Any systematic selection of analytical examples has the advantage of not allowing inconvenient or ambiguous cases to be pushed aside. Examples 4.76 through 4.90 present reductions of passages not yet discussed that, for various reasons, do not exemplify one of the three main contrapuntal methods. But in the narrative of the present chapter, these examples are not merely misfits: by defining a periphery for the schema of fifths chain, they illuminate the overall consistency of Bach’s contrapuntal and metric procedures, and they help to reveal what is at stake stylistically and expressively in those procedures. The fifths chain BWV 807c41/42 (see Example 4.76 and Example 4.77) exhibits a metrical uncertainty that otherwise is absent from Bach’s fifths 256 The Art of Gigue

V



  ~

~

 ~

 

~



Example 4.78: Further reduction of BWV 807, mm. 35–47. “Radical” metric reading. chains. The two patterns of sixths and sevenths “above” and “below” both lay claim to this passage, and present competing interpretations of strong and weak beats in the fourth-species line. This ambiguity is not seen anywhere else. BWV 807c41/42 migrates from an “odd–even” parsing of duple hypermeter (in terms of bar numbers) to an “even–odd” parsing. Depending on what melodic features are prioritized, the fifths chain can be heard in the same phase as the preceding music or in a new phase consistent with what follows. After Andrew Imbrie, I label these readings as “conservative” and “radical.”67 Interpretation of the bassline is the decisive factor here. However, neither reading is adequate alone: in practice, the metrical migration happens gradually, with the chromatic descending tetrachord in the alto slowly finding its historically favored form, in which C~ and C relate as a strong–weak pair. In isolation, the “radical” reading makes better sense of the passage with respect to Bach’s core contrapuntal methods across the gigues (see Example 4.78), even if the combination of dissonant ninths with a leaping bassline is novel. Yet the “conservative” reading draws considerable momentum from the clear 4-bar hypermeasure that opens strain 2 and sets up m. 39 as a hypermetric downbeat. The “conservative” reading is also strongly projected by the upper voice through m. 48; in the “radical” reading, the fully realized soprano part is heard to contain pronounced anticipations. BWV 827c161/2/17 also presents metric uncertainty by similar means (see Example 4.79). In this case, the “conservative” reading prevails for longer, and the migration of metric phase is not felt until the arrival of C in the bass, helped by the mild effect of the preceding B6 compared to D~ and C~. The metrical shift here is between , units that are first misaligned, then aligned to the barlines. Not metrical, but tonal ambiguity applies in the fifths chain repre- sented in Example 4.80 ca. m. 16. This is the only fifths chain in Bach’s

67. Andrew Imbrie, “Extra Measures and Metrical Ambiguity in Beethoven,” in Beethoven Studies, ed. Alan Tyson (New York: Norton, 1973), 45–66. Schema 257

BWV 827 16½ ↓ III
Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë t 
Ë Ë
Ë Ë Ë Ë Ë Ë

Example 4.79: Reduction of BWV 827, mm. 151/2–181/2. The arrow marks the start of the next sequence (see Example 4.62).

BWV 829 16 in dominant (IV)   (vi) V Ë Ë

 Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ‹   Ë Ë Ë Ë Ë Ë Ë ↑ subj. as continuous line  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë

Ë Ë  

21½ [23½] ↓ subj. (extended) in tonic 7 3 V / IV I 3 3 V Ë Ë    Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë  Ë Ë Ë Ë Ë Ë  Ë ↑ subj. Ë Ë 3 Ë Ë Ë Ë
Ë
  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 3 3 Ë Ë  vi  I   
Ë Ë Ë    Ë      Ë  Ë  Example 4.80: Reduction of BWV 829, mm. 13–26. 258 The Art of Gigue

A B i Ø

Ø



Ø

Ø
Ø



Ø t Ø Ø 
Ø Ø  Ø
↑ not A C I Ø


 Ø Ø 

Example 4.81: Alternative renderings of BWV 829, mm. 141/2–18.

BWV 827 11½ i  




    Ø Ø

 Ø
Ø Ø
↑ subj.      ÔÔ


2 Ô

Example 4.82: Reductions of BWV 827, mm. 101/2–151/2. keyboard gigues that will not conform, at a basic level, to a single diatonic orientation. For once, the sequence passage can truly be said to modulate from one diatonic collection (two ~) to another (one ~). Example 4.81b and c illuminate this effect by recasting the contrapuntal framework in B minor and G major respectively. Example 4.81a shows that the intermediate harmonic station of A minor has an inferior standing by making explicit the analogy between the sequence passage’s two halves. The next group of examples complicates the schematology of Bach’s fifths chains by mixing the three main types of counterpoint into freer forms. In Example 4.82 (which leads into Example 4.79), the second-species line of the simple reduction steps up instead of down. The intervals struck by g4, a4, Schema 259

BWV 806 28 V   q q q q q q q  q q q q q q q q q q q q q

q q
q q q q q q q q q q q q q q    q q  q q q q q

 q q q Ø  q q q

elided AC q  q q q    q q q q q q q q q q q q q q  q q q q q  q q


q q q q q q q q q  q q q q q q q q q q q q q Example 4.83: Reductions of BWV 806, mm. 27–36. and b4 against the cantus therefore touch on all three constructions, and the bassline accommodates this by switching pattern as well. In Example 4.83, the alto also rises in its first syncopated step motion, and additional freedom in the contrapuntal treatment prevents the basic counterpoint from being obviously sequential at all. The contrapuntal framework is also shorn of sequential patterning in Example 4.84. Significantly, this too comes from an early composition. In the first half of the passage, it is not the intervallic type that changes, but rather the distribution of roles among the voices. To analyze this passage successfully, many interdependencies need to be ironed out. As I read the passage on a basic level, the bassline presents the first segment of the second-species component, B–C, whereas the second segment, A–B, is taken by the soprano; the cantus is traded in the opposite direction. The contrapuntal structure is loose enough that its integrity as one sequence passage could be disregarded, and the second half with its upbeat could be taken for an independent “Prinner reposte” in Gjerdingen’s terms.68 By comparison, Example 4.85 from the B ’ major Partita presents a simple case of construction by sixths and sevenths below, subject to inversion as thirds

68. Gjerdingen, Music in the Galant Style, pp. 45–60. 260 The Art of Gigue

BWV 818 29½ (weak AC)  I q  qqq q q q q
 q q qq q q q q  q q q q q q q q q q q q Z  q q q q q q q q q q q  
q q q q   q q Revisions in BWV 818a q q Z  Z 
 
I Z Z Z  Z

 Z

Example 4.84: Reductions of BWV 818 (and BWV 818a), mm. 281/2–33.

7 (modal mixture) BWV 825 in dominant V AC
q q 6 


q q q q
6

  q  q q q 6  6   6 6 \ 

Example 4.85: Reduction of BWV 825, mm. 1–16.

V q
q q q q q q
q q q


H
q q

Example 4.86: Further reduction of BWV 825, mm. 1–16. Schema 261

25 25 BWV 832 or V V q q q q q
q q q q q q q q
q q q  q q q q q q q q q q q q q q  q q q q q q  q q q q q q 1 q q q
q q q q q q q
q

q q q q q
q q q q q

q q  q q  q q q

Example 4.87: Reductions of BWV 832, mm. 23–28. Note: the simpler reduction is transposed to the natural diatonic scale. and seconds. What is unusual about this passage is the lack of a definite bass. While the second-species line is clearly entrusted to the soprano (as shown in Example 4.86), the hand-crossing leaps to a lower register allude to this contrapuntal element’s conventional role as a bass in the trio texture. The concept of trio texture, even, is cast in doubt in Example 4.87 and Example 4.88, insofar as BWV 832c25 and BWV 816c37 reduce to counterpoints that lack the melodic independence and harmonic richness of Bach’s more contrapuntal methods. A second-species pattern in contrary motion asserts itself in the outer voices of the cited passages; for different reasons, neither passage yields an unembellished cantus line. In BWV 832, especially, the contrapuntal framework is essentially two-part, since the zig-zag pattern of sixths and thirds leaves little room for the middle voice to operate independently. In BWV 816, the element that prevents a simple cantus emerging is the leading tone, D~. The leading tone’s impact is evident by comparison with the prior sequence, BWV 816c32—itself unique for commencing metrically on a diminished harmony. Finally, Example 4.89 and Example 4.90 are peripheral to the schema of fifths chain because they represent the more specialized schema of the Fonte. The Fonte is a two-segment sequence by descending step, with the same root progression as the fifths chain. However, the rhythmic articulation between the segments is more pronounced and the rhetorical function is different. The slow, two-segment sequences in the E minor Partita, BWV 830, are not examples of Fonte. Consistent with Gjerdingen’s definition (mentioned above), the Fonte passages represented here resolve to root- position triads that are minor, then major. As shown in the simple reduction, transposed to the natural diatonic scale, the diatonic orientation of the Fonte 262 The Art of Gigue

↓ subj. (inverted) BWV 816 codetta 32
 Ë Ë Ë Ë Ë Ë Ë Ë Ë 
  k 
Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ø Ë Ë Ë    [ vii 7 ] V Ø     

Ø 

episode 37

Ë
Ë Ë Ë Ë Ë  
Ë Ë
Ë
Ë Ë Ë Ë Ë
Ë Ë Ë Ë Ë 
Ë Ë Ø

  ↑ subj. (inverted) in relative 6 V 5 Ø Ø   

Ø Ø Example 4.88: Reductions of BWV 816, mm. 30–39. Schema 263

BWV 823 13 V

’ ’   q q q q q  ’ ’       q q q



q q q  ’ ’     ’ q q ’ ’  q q   q q q Fonte       

 Ø   
 Example 4.89: Reductions of BWV 823, mm. 9–24.

BWV 813 61 q q  q q q q q q q q q q    q q
q q
q   q q
q 
q 1   q q  q q q q  Fonte Z Z Z Z 

 Z Z Z
Z

no AC     
   
 
 Z   
             
          
        

Example 4.90: Reductions of BWV 813, mm. 57–76. 264 The Art of Gigue changes based on context. BWV 823c13 closes on the dominant in the major mode. BWV 813c61 closes on the mediant in the minor mode. Perhaps not coincidentally, both instances of Fonte from Bach’s keyboard gigues are found in French gigues.

Connections to Other Analytical Studies and Repertories

Before ending this chapter, I will briefly report on two recent studies that consider the chain of fifths in analytical depth, and make connections to the findings of the present study. I regard my own intense, focused study as ripe for opening out into other repertories increasingly distant from Bach’s gigues, illuminating contours of style and genre in European music of the 1710s– 1730s and the neighboring decades. Promising findings are, for example, available by looking to chain of fifths sequences in the complete gigues of other composers—including François Couperin, Louis Marchand, Rameau, Kuhnau, and Handel. Handel’s gigues, for instance, include fifths chains that are definitively un-Bachian in terms of their contrapuntal strategies, their length, and their integration into metric process. Meanwhile, the prevalence of fifths chains is a stylistic indicator: they are frequent in Kuhnau’s sonatinas but rare in his suites, often used by Couperin but seldom by Rameau. The present study is also ripe for opening out into wider approaches to the theory and aesthetics of Baroque form. Although it is beyond this chapter’s scope to do justice to the ideas and the influence of Laurence Dreyfus’s monograph, Bach and the Patterns of Invention, it would be fruitful to consider the ways in which my analysis of Bach’s sequences is sympathetic to Dreyfus’s consideration of Bach’s rhetorical inventiveness, particularly vis-à-vis “the ideal ritornello.”69 In some respects, my analysis poses a challenge to some of Dreyfus’s ideas. That the Fortspinnung is defined by the absence of tonal definition, for instance, runs contrary to my finding that Bach’s sequences are clearly orientated to one key and do not in themselves modulate. Moreover, Dreyfus’s appeal for a “paradigmatic” rather than “syntagmatic” treatment of Bach’s music has limited resonance in those of my analyses that address movements containing multiple sequences. Yet in the main, my detailed treatment of the fifths chain is quite consonant with Dreyfus’s probing interpretation of Bach’s material ingenuity and its stylistic applications.

69. Dreyfus, Bach and the Patterns of Invention. Schema 265

The Chain of Fifths in Bach’s Aria Introductions The doctoral dissertation of Riitta Rautio (University of Jyväskylä, 2004) addresses the chain of fifths sequence within a study of Bach’s Fortspin- nungstypus technique that exposes the instrumental introductions of 125 minor-mode arias from the cantatas to schematic analysis. (Reported as falling outside the study are some 65 aria introductions which are in minor but do not follow the Fortspinnungstypus.)70 Although the methods of this study, and its error-prone text, will require close scrutiny from any- one building on Rautio’s conclusions or hypotheses, it makes a significant contribution to the analytical literature on Bach’s compositional practice in terms of local harmonic and contrapuntal schema, and the nature of the Fortspinnungstypus. The latter phenomenon is approached both as a pitch structure and a rhetorical “plot,” with perhaps the most interesting results on the rhetorical side. This study echoes my finding of five key formal functions in the prototypical first period of a Bach cello gigue, while painting a slightly different picture of the Fortspinnung–Schlußsatz71 area which seems to reflect in equal measure a difference in the genres studied and a difference of theoretical perspective. Compared to me, Rautio gives greater weight to motivic process, and less to hypermeter. The chain of fifths schema mainly belongs to the third of Rautio’s five Fortspinnungstypus functions, the dedicated “sequence” function. This function also supports constructions by descending third, ascending second, and descending fourth—a two-part affair hinging on resolutions to iv then i— in addition to the formula of dominant pedal. There is also the descending tetrachord schema that groups with the fifths chain in the theoretical category of sequence by descending second, and is acknowledged to have a direct schematic affinity. By Rautio’s count, the repertoire of 125 aria introductions includes 77 fifths chains and 6 descending tetrachord passages (here, I substitute my choice of terms) to compare with a total 60 instances of rival schemas. The breakdown of these others is 5 sequences by descending third, 12 by ascending second, and 11 by descending fourth, and 7 dominant pedals that stand instead of a sequence, as well as 8 descending and some 17 ascending sequences that did not easily fit the cited categories. Of the fifths chains, Rautio finds that about three in every four relate to one of three schemas, represented in Example 4.91. Among the “atypical” remainder

70. Riitta Aulikki Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions” (DPhil diss., University of Jyväskylä, 2004). The minor-mode arias addressed and not addressed by the study are listed in Appendices 1 and 2 respectively.

71. Rautio uses the term Epilog. 266 The Art of Gigue

Schema “a1” Schema “a2” Schema “b” ^ ^ ^ ^ ^ ^ 3 2 6 5 6 5  ³ ³ ³ ³ ³
 ³ i iv VII III i iv VII III iv VII III VI ³ S   ³ ³ ³ ³ ³ ^ ^ ^ ^ ^ ^ 1 7 4 3 4 3

Example 4.91: Riitta Rautio’s fifths chain schemas for Bach’s minor-mode aria introductions. These illustrations are adapted from pp. 84, 126, 128, and 130, with corrections.

^ ^ ^ ^ ^ ^ ~ 3 2 ~ 6 5 ~ 6 5 ~  ~

~

  ~ ~

I IV VII III I IV VII III IV VII III VI  ~
~
S ~ ~



^ ^ ^ ^ ^ ^ 1 7 4 3 4 3

Example 4.92: As Example 4.91 but with chromatic major triads on the tonic and subdominant. Schema 267 are “sequences, which instead of starting from the ‘normative’ first-degree chord, start one or more fifths above the tonic, or which have an unclear motivic structure, or a different synchronization between motives and chord progression.”72 Per Example 4.91, Rautio’s primary schemas are defined in fairly bare terms with respect to pitch. To begin with, the polyphonic framework is restricted to two outer voices. Moreover, the behavior of these voices is observed only for the metrically strong half of each sequence segment: though the crosses in Example 4.91 sketch possible pitches, I have added these, surplus to Rautio’s original figures in which crosses are rhythmic placeholders only.73 As to the use of B minor, this is the sample’s best-represented key—out of F through C~ minors, B minor is the key of one in four movements—so it is chosen by Rautio for all generic staff notations.74 Rautio finds that B minor inspires Bach’s most true-to-type fifths chains, whereas G minor, for instance, inspires more eccentric passages. The differences between my and Rautio’s schematic representations of pitch structure are grounded in a divergence of theoretical and method- ological approaches. Each of Rautio’s schemas is—consistent with schema theory in the psychological and cognitive sciences—articulated as a cluster of attributes which coalesce and combine to define prototypical behaviors, yet without any one attribute necessarily being present at all times. Here, the attributes take the following forms: root progressions with specified metric patterns of strong and weak, contexts such as the preceding har- mony or cadence and subsequent events, and—per the staff notations in Example 4.91—stepwise “milestones” in the soprano and bass. Note that although Rautio clearly comes to the observation of stepwise descents by some notation of melodic reduction, the attribute of 3ˆÑ2ˆ in the soprano for schema “a1” and other similar attributes are not claims to good melodic reduction as such. This is vividly apparent, when chromaticism enters in the form of applied dominants, as shown in Example 4.92: ~3ˆÑ2ˆ and ~6ˆÑ5ˆ are not melodically sensible in the traditional sense. The crosses in the illustration are instrumental and a contrapuntal skeleton is not yet established at this level of abstraction. The degree of specification ultimately

72. Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions,” p. 125. “One or more fifths above the tonic” does not include starting from iv if that falls on a strong beat and is preceded by i, since this is the situation in one of the primary schemas.

73. At first glance, parts of Rautio’s figures seem to gesture at possible pitches with the crosses, but this is not so overall.

74. Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions,” p. 73. The use of B minor applies to all music examples in chapters 4 and 5. 268 The Art of Gigue depends upon how many sub-schemas of fifths chain there are, and how the whole sample of musical passages are read for their conceptual proximity to each other. For Rautio, whose approach is guided by mainstream tonal theory, root progression and its metric distribution are the leading factors in sorting the given sample. Thus schema “a1” commences on i with a metrically strong beat, “a2” commences on i with a weak beat instead, and “b” starts from iv on a strong beat; and the possible replacement of these minor, diatonic triads by chromatic, major triads was already alluded to.75 A word, now, about Rautio’s concept of what a sequence passage is, before her study’s methods and findings are explained further. Key to Rautio’s notion of the sequence is the main motivic repetition, which may align with or may straddle the units of metrical organization as I interpret them (the idea of metric hierarchy is not essential to Rautio’s analysis). The boundaries of the sequence passage are, then, established before metrical analysis, and not by it, as in my approach. In Example 4.91, the brackets indicate the fundamental motivic repetition. Rautio conceives of sequences, moreover, as consisting of two segments only, and assigns to a separate “bridge” function, for instance, passages which I conceive as the second half of a metrically quadruple sequence passage. Probably Rautio’s concept is the more conventional, since I frequently interpret the so-called “sequence passage” as continuing after the sequence’s motivic repetitions have expired (where my reductions show a change to small notes ahead of the dashed barline). Rautio’s concept is also, it could be argued, more sensitive to rhetoric and specifically the moment of “process reversal”—the breaking of the sequence pattern— that is rightly identified as crucial to the Fortspinnungstypus “plot”. “In his aria introductions,” Rautio writes, “Bach seldom confirms sequential structure by a second repetition” (here, the word “confirms” is a direct reference to William Renwick’s terms for sequence segments: proposition, digression, and confirmation).76 Where Bach does continue to a second repetition, Rautio reads this as part of the “bridge,” recalling the parsing of a sentence phrase form where continuation begins with a fragmentation motivically similar to what precedes it, but which nonetheless groups

75. On p. 126 Rautio also identifies two more schemas, “c” and “d”, which commence on i but are set apart by having three, not two, roots in one or both sequence segments. Just one instance is cited for each of these supposed schemas, and it appears that one of them must be attributed to schema “b” in Table 20 of Appendix 3 (the likely passage is BWV 101/2, second sequence).

76. Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions,” p. 49; Renwick, Analyzing Fugue: A Schenkerian Approach, p. 140. Schema 269 metrically with what follows. With good reason, Rautio claims that “[t]he bridge function has not been identified by previous studies since Fischer, . . . [and] Schoenberg and Caplin have left unspecified what occurs after the sequence.”77 I fully concur that the harmonic and melodic outcomes of sequential activity are generally under-theorized, even if my study of Bach’s gigues leads me to a rather firm distinction between “bridge” passages that pair with a cadence as part of a Schlußsatz complex and those that are schematically continuous with the counterpoint of the sequence’s motivic phase. Table 4.2 shows a subset of one of Rautio’s tabulations of schema attributes, in this case for fifths chains of schema “a1”.78 I have selected three passages, whose appraisal according to the listed attributes is, following Rautio, indicated by “`,” “(`),” and “´” for positive, partial, and negative findings. At the far right of the table, I also reproduce Rautio’s tallies of the positive results per schema “a”’s total 29 instances (a partial result counts as 0.5), and I have used this measure to put the attributes in order of prevalence. Such tables are Rautio’s tool for discovering what are the “prototypical

Table 4.2: A subset of Riitta Rautio’s tabulation of attributes for fifths chains of schema “a1”. I have added the measure numbers and reworded the descriptions of the attributes listed on the left.

Aria BWV 213/9 BWV 128/4 BWV 22/2

3 6 9 Meter 8 8 8 Key a b c Prev- Location of sequence (mm.) 9–12 7–10 6–7 alence Duration of whole introduction (mm.) 16 14 12 (/29)

Root progression: i(~)–iv, strong–weak ` ` (`) 26.5 Exact transposition ` ` (`) 25 Preceded by “half cadence” on V or v [sic] ` ` ` 24 Bass: 1–ˆ 7ˆ ` ´ ´ 20 Soprano: (~)3–ˆ 2ˆ ` ` ´ 17.5 Chromatic alteration to i~, i.e. V/iv ` ` ` 11.5 Bridge schema: 6–ˆ 5–ˆ 4(–ˆ 3)ˆ ` ´ ´ 6.5

77. Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions,” p. 196.

78. Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions,” p. 225 (Appendix 3, Table 18). 270 The Art of Gigue features” of various schemas, not only of sequences but for all elements of the Fortspinnungstypus. Generally, a tally equivalent to more than half the number of instances in a given category was taken to define a prototypical feature.79 Here, five of the seven attributes are prototypical. But note that, with the fifths chain schemas, the prototypicality of the root progressions is already assumed since these operate as “sufficient condition[s] for category membership.”80 In the present category, Rautio lists two features which are not sufficiently prevalent to be prototypical but which were evidently worth tracking for other reasons. Regarding the contextual feature of leading to a bridge of 6–ˆ 5–ˆ 4–ˆ 3ˆ type, it seems that at least half of such bridges must be preceded by a fifths chain of type “a1”.81 Regarding the feature of chromatic alteration to i~, Rautio observes the emergence of a subcategory within type “a1” whose harmonic and melodic structure is translated in my Example 4.94. Another feature mentioned in Rautio’s text, but not tabulated, 6 is the incidence of half cadences of specific Vv 5–i–Vv type before the fifths chain: some correlation is suggested, though the quantities involved are small and—as Rautio freely acknowledges—properly statistical methods are not deployed in the study, so such correlations have an ambiguous status. The one example from Rautio’s sample that has all the attributes of Table 4.2 is reproduced as Example 4.93. All five prototypical features are present (true of one in every four members of the “a1” category), plus the 6 three features—including the cited Vv 5–i–Vv cadence—which Rautio judges characteristic of the schema in some way though they are absent in the majority of instances. My annotated score reconstructs Rautio’s analysis; I have not shown but will mention that in the analysis of the soprano and bass skeleton, the voice-leading illustrated in Example 4.94 can be found by looking to the interior of each segment. Not coincidentally, the aria illustrated here (best known today as part of the Christmas Oratorio) is from the secular cantata, BWV 213, written in 1733 to celebrate the eleventh birthday of the Saxon crown prince, Friedrich Christian, and its text—spoken by Hercules—is an affirmation of restraint in the face of Lust: the Italian musical idiom, the dramatic sentiment, and the conceit of painting the Saxon prince as a little Hercules all point to a deliberate embrace of formula and a certain ironic charm. The fifths chain aspires

79. Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions,” p. 98.

80. Rautio, “Fortspinnungstypus Revisited: Schemata and Prototypical Features in J. S. Bach’s Minor-key Cantata Aria Introductions,” p. 126.

81. According to Figure 10 on p. 84 and Table 29 on p. 230, there are 13 of these bridge passages, and together they score a tally of 10.5 for the attribute of 6–ˆ 5–ˆ 4–ˆ 3ˆ in the bass. Schema 271

  3  Ë Ë Ë Ë Ë Ë Ë Ë Ë  8 Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ËË Ë unisono e staccato Ë  3     Ë Ë Ë Ë Ë Ë Ë Ë Ë  8 Ë Ë Ë Ë Ë Ë
Ë Ë ^ ^ ^ Ø 3 chain of fifths ( 4 ) 2  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë 6 7 7 V 5 i V (V → iv VII Ë  Ë Ë Ë  Ë Ë  Ë Ë Ë Ë Ë Ë
Ë Ë Ë ^
^ ^ 1 ( 6 ) 7 ^ ^ ( 3 ) 1______ Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë  Ë Ë Ë ËË Ë Ë Ë Ë Ë III Ë   Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë  ^
^ ^ ^ ^ ( 5 ) 6 5 4 3

Example 4.93: Introduction to Bach’s aria, “Ich will dich nicht hören,” BWV 213/9.

^ ^ ^ ^ 7 6 6 5
q q q q 

6 6 V 5 / iv iv V 5 / III III ¯ 


q q q q ^ ^ ^ ^ ~ 3 4 2 3

Example 4.94: A subcategory of “a1” fifths chain as described by Rautio (p. 128). The counterpoint is akin to the three-part schemas I describe with upper voices in sixths and sevenths. 272 The Art of Gigue to be prototypical just as Hercules, by his determination to pursue Virtue, expresses common values and the princely prerogative to make them his own. The fifths chain serves as a musical vehicle for expressing resolve— and affirming what was always the right choice between Lust and Virtue, doing so with purpose and ideally some sense of pleasure. In Hercules’ solo following the introduction, the sequence supports the words, “Ich will nicht,” in a cliché of operatic declamation, distilling the message of the quatrain which fits the melody of the first half of the introduction: “Ich will dich nicht hören, ich mag dich nicht wissen, verworfene Wollust, ich kenne dich nicht.” (“I will not listen, I shall not heed you; degenerate Pleasure, I know you not!”) A telling departure from the plan of the ritornello occurs when a measure is inserted before the fifths chain after the half cadence: this gives Hercules time to enunciate “Ich will nicht” before the sequence starts, and appear as the author of his own moral and musical fate. Another aria introduction featuring a fifths chain of Rautio’s type “a1” is given in Example 4.95. Again, my annotated score reconstructs Rautio’s analysis from the tabulated data. Notice the similarity of the bridge to the previous example: although the table rightly records a negative result for Rautio’s 6–ˆ 5–ˆ 4–(ˆ 3)ˆ schema, the oft-used 4–ˆ 5–ˆ 6–ˆ ~7ˆ formula that is used instead similarly prolongs subdominant harmony (iv colored with ii°7). Some more contentious aspects of Rautio’s analysis should also be noted. The “half cadence” preceding the fifths chain is what would more commonly be called an authentic cadence in the dominant, a stronger cadence whose importance in the vocal reworking will soon become clear. Furthermore, Rautio’s table records the prototypical bass pattern, 1ˆ –7,ˆ as absent, but other analysts might disagree. While it would not be fruitful to comb over questions of voice-leading analysis here, it is important to be aware that simple data regarding the presence or absence of certain features can mask the complexity and uncertainty involved in an underlying analysis. This second aria comes from the sacred cantata Bach composed in 1725 for the Feast of Ascension, BWV 128. The movement is, in fact, a duet, which somewhat explains why the Vordersatz of the introduction runs to six measures rather than eight, since the introduction’s first two measures become four when treated imitatively by the voices. In this piece, the chain of fifths is pointedly absent from the vocal duet and only returns with the outgoing instrumental ritornello. And where, in BWV 213, the presentation of the sequence was nuanced in the vocal section to articulate an attitude of resolve on the part of Hercules, here in BWV 128, the sequence is arguably omitted in an opposite gesture: these poetic subjects point explicitly to their own inaction and dumbfoundedness when faced with the wonder of Christ’s ascension. “Sein Allmacht zu ergründen,” they say, “Wird sich kein Mensche finden, Mein Mund verstummt und schweigt.” (“To fathom Schema 273

 Ë 6  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  8 Ë Ë Ë Ë
ËËË Ë  Ë Ë Ë Ë Ë Ë  6    Ë Ë Ë
 8 Ë Ë Ë Ë Ë

 Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë
Ë Ë vË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë   Ë Ë

^ ^ ^ Ø 3 chain of fifths ( 4 ) 2  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë (V 7 → iv VII7   Ë Ë Ë Ë Ë   Ë Ë  Ë Ë Ë Ë Ë Ë ^ ^ Ë ^ [ 1 ] ( 6 ) [ 7 ] ^ ( 3 )   Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë III Ë  Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë^ ^ ^ ^ ^ ( 5 ) Ë ( 4 ) ( 5 ) ( 6 ) ( 7+ )

 Ë Ë Ë Ë  Ë Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë  Ë Ë Ë Ë Ë Ë  Ë Ë Example 4.95: Introduction to Bach’s aria, “Sein’ Allmacht zu ergründen,” BWV 128/4. 274 The Art of Gigue

His omnipotence no human can discern, my mouth is dumb and silent.”)82 The soaring, lyrical quality of the fifths chain does not, then, belong to the mortal sphere of the poetic voice but to a God whose deeds are beyond lasting comprehension. The harmonic and melodic ideas of the sequence are only later recalled, indirectly, during the B section in the da capo form. Here the text shifts focus to the image of Christ’s ascension: “Ich sehe durch die Sterne, Daß er sich schon von ferne Zur Rechten Gottes zeigt” (“I see through the stars that He already from afar indicates the right hand of God”). Likewise, the rapturous embrace of D major at the end of the B section was indicated from afar by the fifths chain of the A section ritornello.

The Chain of Fifths in Corelli The nearest and most significant precedent for the study just completed is Daniel Harrison’s research into the sequence in the music of Corelli and his Italian forbears.83 While it would be redundant to reproduce Harrison’s own presentation of his findings, I will point out the important connections between Corelli’s use of sequences (as described by Harrison) and Bach’s, with an eye to the opportunities for future discoveries about the chain of fifths and its place in early eighteenth-century musical practice. Harrison’s study has two strands, “genealogical” and typological, of which only the second is emulated in this chapter; the first, historical element addresses the twin origins of the Corellian sequence in suspension chains (including the technique of “cadential prefixion”) and in antiphonal devices. Concern- ing analysis and contrapuntal typology, there is substantial convergence between Harrison’s and my views of the sequence, honed on Corelli and Bach respectively. To some extent, my understanding of Bach’s counterpoint may have been guided by Harrison and other like-minded theorists, but in the main, I attribute the similarity of my and Harrison’s analytical models to a sympathetic engagement with the music at hand. The points of resonance are, first, the primacy of three-part counterpoint; second, the de-emphasis of root motion as an analytically pertinent parameter; third, the attention paid to the durational term of the sequence passage; and fourth, the general picture of diatonic stability within a given sequence. However, I differ from Harrison in the attention I give to basic contrapuntal strategies beyond the cessation of motivic repetition. Very significantly, Harrison’s schematic illustrations attribute a tetrachordal outline to the chain of fifths sequences, yet Harrison is not much concerned with Corelli’s methods for terminating

82. This translation of von Ziegler’s text is by Pamela Dellal (Emmanuel Music, Boston, MA).

83. Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence.” Schema 275

“A1” “A′1” Ë Ë Ë Ë Ë Ë Ë Ë
Ë Ë Ë t  Ë

“B1” “D1” Ë Ë Ë Ë Ë Ë Ë Ë ËË Ë
Ë Ë Ë Ë ËË Ë Ë Ë Ë Ë Ë Ë t  Ë Ë Ë Ë Ë Ë Ë Ë

Example 4.96: Schemas of the Corellian fifths chain according to Daniel Harrison.

the sequence or establishing a point of harmonic repose (if any). While it may be our analytical priorities are simply different, my stronger concept of “the sequence passage” is more plausibly a direct reflection of a stylistic difference between Bach and Corelli. Indeed, Harrison offers insightful comments on how sequence techniques expanded and changed during the early eighteenth-century. Example 4.96 reproduces, with mainly cosmetic alterations, Harrison’s basic contrapuntal schemas for the Corellian fifths chain.84 These represent three of four kinds of descending sequence (there are three ascending also) that Harrison discovers in Corelli. In Harrison’s typological labels, the letters refer to the syncopated element in the soprano, while the numerals refer to the realization of the remaining voices. A series of alternative forms specified by Harrison are illustrated in Example 4.97. (Omitted from this example are sequence types “D2” and “D4,” which Corelli does not use, according to Harrison.)85 Harrison’s “Class A” and “Class B” sequences correspond to two of the principal strategies identified in my analysis of Bach. Not represented here, however, is the method I describe of construction by sixths and sevenths below the cantus; the method that contravenes the tenet of species counterpoint that dissonant sevenths should occupy a strong metrical position. Regarding the various forms Harrison reports for each

84. Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence,” pp. 244, 247, and 249.

85. Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence,” p. 250. 276 The Art of Gigue

“A1a” “A2”








  







Œ

Œ
 “A3” “A4”


Œ
Œ

Œ

Œ

Œ
     
Π
Π   


Œ



Œ
Π

“A5” “B1a”












 

Π
Π Π















“B2” “B3”







 

“B3b” “D3”














Example 4.97: Alternative forms, from Harrison, of the fifths-chain schemas in Example 4.96. Schema 277

“C1” etc.  Z Z  Z  Z Z Z Z
Z Z  »   Z

“C2” etc.  Z Z   Z Z Z Z Z Z Z Z Z Z »  Z Z Z Z

“C2a” etc.  Z Z   Z Z Z Z Z Z Z  » Example 4.98: From Harrison, another schema of descending sequence credited to Corelli. sequence type, the schemas with particular resonance to the present study are “A5,” “B1,” and “B1a.” The last of these was observed in BWV 806 and BWV 815. Also worth citing is Harrison’s fourth kind of descending sequence, the “Class C,” reproduced in Example 4.98. Subject to an inversion of the upper voices, this pattern is reminiscent of Bach’s one modulating sequence, BWV 829c16. According to Harrison, the “Class C” sequence was “apparently an original contribution of Corelli.”86 Thus, on the periphery of Bach’s fifths chain technique, an explicit debt to Corelli is perhaps apparent. But much more deeply, the systematic analyses presented by Harrison and myself place Corelli and Bach in a wider picture of the circulation and cultivation of musical ideas, about which much remains to be learned.

86. Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence,” p. 248. 278 The Art of Gigue

Conclusion

This chapter has offered a comprehensive typology of the fifths chain in Bach’s keyboard gigues, and pointed to some theoretical and historical contexts for the analysis. But other kinds of compositional schema, beside contrapuntal and harmonic devices, have been this chapter’s concern too: customary ways of realizing stock devices, manipulating them, and combin- ing them in sophisticated applications. To learn about these meta-schemas is, of course, one of the main attractions to studying early eighteenth-century contrapuntal schemas from the vantage point of fully fledged composi- tions. In tandem with the study of music pedagogy that has distinguished eighteenth-century music studies in recent years, schematically oriented analysis projects like the one offered here promise to deepen our knowledge of past practice, and attune our senses to the musical values that any analyst must believe are latent in old texts and time-worn sounds. Every tantalizing correspondence, across far-flung musical sources and disparate kinds of musical production, is ultimately testament to the vastness of what might be—and what will never be—known about musical practice across Europe in the early eighteenth century. Even a few dozen gigues by J. S. Bach are touched by a huge range of musical values and technical capabilities. I will conclude by saying that in the face of such historical legacies, schemas like the chain of fifths sequence become as much musicological instruments as musical ones. These are the tools of the music analyst as well. To analyze schemas is to trace patterns through myriad contexts into a deepening expertise that remains vivid—like for the composer—only if the schemas remain volatile, contingent, mobile. To this end, my analysis has tried to preserve a sense of the Bachian fifths chain as a complex and porous object, despite my determined pursuit of typology. If the attraction of both abstract models and specific examples has been felt, a significant aim will have been achieved. For I argue that, dancing between the commonplace and the particular, the chain of fifths sequence and schemas like it must serve their analytical role irreverently. Only through a kind of continuous mocking, on the question of whether we are—and whether we want to be—learning something very general or very specific, do they teach us anything at all about music’s resonant materiality. Appendix A Citations to Scores from the Neue Bach Ausgabe Reproduced in the Supplementary Volume

What Scores Are Included

The supplementary volume contains the scores of Bach’s thirty-four original compositions in the genre of binary gigue, reproduced from the Neue Bach Ausgabe. Two of these movements each survive in two versions whose com- positional differences are significant—BWV 818 was revised as BWV 818a, while BWV 1006 was translated from violin to lute as BWV 1006a—thus the total number of scores in the supplement is thirty-six.

Citations

Listed here are the volume and page numbers in the Neue Bach Ausgabe for all gigues composed by or arranged by Bach. Where the NBA gives multiple texts of a given work, the sign † indicates which text is reproduced in this appendix. The first mention of each volume gives the Bärenreiter catalogue number and the publication date(s). NBA = Johann Sebastian Bach. Neue Ausgabe sämtliche Werke. Edited under the auspices of the Johann-Sebastian-Bach-Institut Göttingen and the Bach-Archiv Leipzig. Kassel and Leipzig: Bärenreiter, 1954–2007.

The Thirty-Four Original Gigues English Suite (No. 1) in A major, BWV 806/8. NBA V/7 [BA 5052-01] (1979; repr. 1998): 18–19. NBA also provides BWV 806a/7 (differences are trivial). NBA V/7: 126–127.

English Suite (No. 2) in A minor, BWV 807/7. NBA V/7: 36–37. 280 The Art of Gigue

English Suite (No. 3) in G minor, BWV 808/7. NBA V/7: 52–53.

English Suite (No. 4) in F major, BWV 809/7. NBA V/7: 68–69.

English Suite (No. 5) in E minor, BWV 810/7. NBA V/7: 86–89.

English Suite (No. 6) in D minor, BWV 811/7. NBA V/7: 110–113.

French Suite (No. 1) in D minor, BWV 812/6. NBA V/4 [BA 5008-01; Klavierbüchlein für Anna Magdalena Bach] (1957; repr. 1963, 1978): 8–9 [1722] and 114–115 [1725]; NBA V/8 [BA 5053-01] (1980; repr. 1996): 8–9 [version A]† and 70–71 [version B].

French Suite (No. 2) in C minor, BWV 813/7. NBA V/4: 14–15 [1722]; NBA V/8: 18–19 [version A]† and 80–81 [version B].

French Suite (No. 3) in B minor, BWV 814/7. NBA V/4: 21–22 [1722]; NBA V/8: 28–29 [version A]† and 90–91 [version B]. NBA also provides BWV 814a/7 (differences are trivial). NBA V/8: 174–175.

French Suite (No. 4) in E ’ major, BWV 815/7. NBA V/4: 28–29 [1722]; NBA V/8: 38–39 [version A]† and 100–101 [version B]. Note: BWV 815a does not include the gigue.

French Suite (No. 5) in G major, BWV 816/7. NBA V/4: 36–39 [1722]; NBA V/8: 48–51 [version A]† and 110–113 [version B]. Note: in most sources for version B, the gigue is the sixth movement since the Loure is absent.

French Suite (No. 6) in E major, BWV 817/7. NBA V/8: 60–61 [version A]† and 124–125 [version B].

Partita in A minor (later version), BWV 818a/6. And the earlier version, BWV 818/4. NBA V/8: 154–155 for BWV 818a; NBA V/8: 134–135 for BWV 818. Note: there are meaningful differences between BWV 818 and BWV 818a.

Suite in F minor (fragment), BWV 823/3. NBA V/10 [BA 5044-01] (1976; repr. 1983, 2007): 52–53.

Partita No. 1 in B ’ major (Clavier-Übung I), BWV 825/7. NBA V/1 [BA 5046-01] (1976, repr. 2013): 12–13. Appendices 281

Partita No. 3 in A minor (Clavier-Übung I), BWV 827/7. NBA V/1: 46–49†; NBA V/4: 57–59 [1725].

Partita No. 4 in D major (Clavier-Übung I), BWV 828/7. NBA V/1: 68–71.

Partita No. 5 in G major (Clavier-Übung I), BWV 829/7. NBA V/1: 86–89.

Partita No. 6 in E minor (Clavier-Übung I), BWV 830/7. NBA V/1: 110–113†; NBA V/4: 78–81 [1725].

Overture in the French Style (Clavier-Übung II), BWV 831/10. NBA V/2 [BA 5048-01] (1977): 36–37. NBA also provides BWV 831a/10 in V/2.

Partita in A major, BWV 832/5. NBA V/10: 59.

Lute Suite in E minor, BWV 996/6. NBA V/10: 100–101.

Lute Suite in C minor, BWV 997/4 and 5 (Double). NBA V/10: 110–113.

Violin Partita in D minor, BWV 1004/4. NBA VI/1 [BA 5012-01] (1958, repr. 2012): 33–34.

Violin Partita in E major, BWV 1006/6. And the transcription for lute, BWV 1006a/7. NBA VI/1: 62 for BWV 1006; NBA V/10: 146–147 for BWV 1006a.

Cello Suite (No. 1) in G major, BWV 1007/7. NBA VI/2 [BA 5068-01] (1988, repr. 2012): 7 [version I] and 59 [version II]†.

Cello Suite (No. 2) in D minor, BWV 1008/7. NBA VI/2: 12–13 [version I] and 64–65 [version II]†.

Cello Suite (No. 3) in C major, BWV 1009/7. NBA VI/2: 20–21 [version I] and 72–73 [version II]†.

Cello Suite (No. 4) in E ’ major, BWV 1010/7. NBA VI/2: 30–31 [version I] and 82–83 [version II]†. 282 The Art of Gigue

Cello Suite (No. 5) in C minor, BWV 1011/7. NBA VI/2: 39 [version I, scordatura notation], 91 and 115 [version II, scordatura notation and sounding notation respectively]†.

Cello Suite (No. 6) in D major, BWV 1012/7. NBA VI/2: 50–51 [version I] and 102–103 [version II]†.

Sonata for Violin and Continuo in E minor, BWV 1023/4. NBA VI/1: 79–80.

Sonata for Flute and Harpischord in B minor, BWV 1030/4 (second section). NBA VI/3 [BA 5022-41] (1963, repr. 2013): 50–53. NBA also includes the text of a surviving harpsichord part in G minor instead of B minor in VI/3: 100–103. Note: this gigue is not titled as such in the sources, but is marked “Presto.”

Orchestral Suite No. 3 in D major, BWV 1068. NBA VII/1 [BA 5030-01] (1967, repr. 1987): 74–78.

Corrupted or Spurious (not reproduced in this appendix) Overture in F major, BWV 820/6. NBA V/10: 49.

Suite in G minor, BWV 822/8. NBA V/10: 78.

Arrangements (not reproduced in this appendix) Sonata in A minor after Reincken (Hortus Musicus, BWV 965/7. NBA V/11 [BA 5088-01] (1997): 184–187.

Concerto after Vivaldi, BWV 975/3. NBA V/11: 36–38. Note: Bach’s arrangement seems to be of a now-lost third movement of Vivaldi’s Op. 4/6 in a pre-publication form.

Concerto, BWV 977/3. NBA V/11: 54–55. Note: the source of this arrangment is unknown. Appendix B Corpus List and Chronology of Bach’s Gigues

Table B.1 begins on next page 284 The Art of Gigue Cello Suites “English” Suites, with prelude Violin Partitas + , / / / / / / / / . / / / / / / / / - , / / / / / / / / . / / / / / / / / - ’ 832 A823 f Harpsichord Harpsichord 810 e 811 d 807 a 809 F 808 g 1011 c 1012 D 1004 d 1006 E 1007 G 1008 d 1009 C 1010 E 806(a) A ✔ ✔ # $ ’ ’ ’ & ’ ’ ’ % $ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ & ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ % # List and working chronology of Bach’s gigues. Table B.1: later in 1708–1714 earlier in 1715–1720 1720 later in 1715–1720 Bach’s Hometown Date of ComposingArnstadt GigueMühlhausen FrenchWeimar BWV Key ca. 1705 Publication Date, Collections, Instrumentation earlier in 1708–1714 996 e [d] 818 Lute (or Lautenwerk) a Harpsichord Cöthen Appendices 285 I, 1731 Clavier-Übung , / / / / / / . / / / / / / - II, 1735 “French” Suites, without prelude 1730 Autumn 1726 1728 1730 Clavier-Übung , / / / / / / / / . / / / / / / / / - ’ ’ 831 b [c] 812 d 813 c 814 b 815 E List and working chronology of Bach’s gigues. ✔ ✔ $ ’ ’ ’ & ’ ’ ’ % Table B.1: (continued) 1725, small revisions 17301726 830 e 825 B 1722 17281730ca. 1730, ca. 173617311733 in c, 1735 1740 1030 b [g] 828 Flute and harpsichord D 829 G ? 1068 D 997 Orchestra c Lute 1724ca. 17251725, small revisions 1727 827 a Michaelmas 1727 1023 817 e E Violin and continuo Bach’s Hometown Date of Composing Gigue French BWV KeyLeipzig Publication Date, Collections, Instrumentation 1723 816 G 286 The Art of Gigue Köthen, 1720 Dance in the Music of J. S. B. a : “Remarks” 1708–17 (or earlier); orig. in d Weimar, by 1717 1720 Köthen, c. 1720 1722 Köthen, c. 1722 c c c Cöthen, 1720; 1006 arr. lute = 1006 Weimar, 1708–14 Weimar, 1708–14 or earlier Weimar, Cöthen, The New Grove Bach Family Cöthen, a Selected authorities for the chronology in Table B.1. † † : “Remarks” Table B.2: † 1720 1705 c New Grove II c 823 1714832 1714 frag.; before 1715 ? before 1708 frag.; Weimar, 1708–14 Weimar, 1708–14 807 1715–1716809 1715–1716 806 ? before 1720 1717–1718 808 1717–1718 810 1719–1720 811 1719–1720 by 1724–5 Weimar–Leipzig, 1715–25 996 1710/1713 ? after 1712; orig. in d 818 1705 1006 1720 1008 1720 1009 1720 1010 1720 1011 1720 1012 1720 1004 1720 1720; 1006 arr. lute = 1006 1007 1720 BWV Per Table B.1 Appendices 287 1736 Leipzig, 1735 (33) Dance in the Music of J. S. B. Köthen/Leipzig, 1722–25 ?Leipzig, c. 1724 Leipzig, 1731 (25 + 27) Leipzig, 1731 (25 + 30) Leipzig, 1731 (26) Leipzig, 1731 (28) Leipzig, 1731 (30) , ii, , i, for erent key Leipzig, 1737–41 ff : “Remarks” Clavierbüchlein , c, Leipzig, by 1733 Clavierbüchlein a , ii (Leipzig, 1735); see 1729–31 Leipzig, 1729–31 c 1724; later modified c also 971; *831 for Anna Magdalena Bach; no.6 cf. 1726–1731) and as op.1 (Leipzig, 1731); nos.3, 6: * 1019, 2nd version Anna Magdalena Bach; no. 6 by Clavier-Übung 1730 c The New Grove Bach Family ?Leipzig, 1738; earlier version,? g, ?rec, in partitas published singly (Leipzig, Leipzig, Leipzig, 1737–41; orig. in di Selected authorities for the chronology in Table B.1. , ii (Leipzig, 1735); see : “Remarks” also 971; early version by 1733 and as op.1 (Leipzig, 1731) Clavier-Übung 1731 1722–1725 nos. 1–5: orig. in 1740 1736; earlier version, g Table B.2: (continued) c in New Grove II c c c 831 1733/1735 997 1740 813 1722 814 1722 815 1722 816 1723 817 1724 812 1722 827 1725/1727 partitas pubd singly (Leipzig, 1726–31) 830 1725/1730 825 1726 828 1728 829 1730 1068 1731 1023 1725 after 1723 Weimar, 1714–17 Weimar, 1714–17 1030 1730/1736 BWV Per Table B.1

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