What is a Cadence? Theoretical and Analytical Perspectives on Cadences in the Classical Repertoire 9789461661739, 9461661738, 9789462700154, 946270015X

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WHAT IS A CADENCE? THEORETICAL AND ANALYTICAL PERSPECTIVES ON CADENCES IN THE CLASSICAL REPERTOIRE

What Is a Cadence? Theoretical and Analytical Perspectives on Cadences in the Classical Repertoire

Markus Neuwirth and Pieter Bergé (eds)

Leuven University Press

© 2015 by Leuven University Press / Presses Universitaires de Louvain / Universitaire Pers Leuven. Minderbroedersstraat 4, B-3000 Leuven (Belgium) All rights reserved. Except in those cases expressly determined by law, no part of this publication may be multiplied, saved in an automated datafile or made public in any way whatsoever without the express prior written consent of the publishers. ISBN 9789462700154 D / 2015 / 1869 / 19 NUR: 664 Cover and layout: Jurgen Leemans Cover illustration: ‘Cadence #1 (a short span of time), Robert Owen, 2003’, CC-BYNC-ND Matthew Perkins 2009.

Contents

5

CONTENTS

Introduction: What is a Cadence?

7

Nine Perspectives Markus Neuwirth and Pieter Bergé

Harmony and Cadence in Gjerdingen’s “Prinner”

17

William E. Caplin

Beyond ‘Harmony’

59

The Cadence in the Partitura Tradition Felix Diergarten

The Half Cadence and Related Analytic Fictions

85

Poundie Burstein

Fuggir la Cadenza, or The Art of Avoiding Cadential Closure

117

Physiognomy and Functions of Deceptive Cadences in the Classical Repertoire Markus Neuwirth

The Mystery of the Cadential Six-Four Danuta Mirka

157

6

Contents

The Mozartean Half Cadence

185

Nathan John Martin and Julie Pedneault-Deslauriers

“Hauptruhepuncte des Geistes”

215

Punctuation Schemas and the Late-Eighteenth-Century Sonata Vasili Byros

The Perception of Cadential Closure

253

David Sears

Towards a Syntax of the Classical Cadence

287

Martin Rohrmeier and Markus Neuwirth

List of Contributors

339

Index

343

Introduction: What is a Cadence?

7

INTRODUCTION: WHAT IS A CADENCE? Nine Perspectives Markus Neuwirth and Pieter Bergé

T

he concept of closure is no doubt crucial to understanding what many consider the essence of eighteenth- and nineteenth-century music: its emphatic goal-directedness.1 The musical “phrase” resulting from the tonal motion towards a goal may consequently be deemed emblematic of tonal music as a whole.2 It is therefore unsurprising that the cadence, the primary means of articulating the tonal goal and thus of achieving closure, has received considerable attention in virtually all scholarly and pedagogical work on tonal music. Especially in more recent writings on the analysis of musical form, the cadence occupies a pivotal position, no matter whether scholars are referring to theme types or to more complex large-scale formal designs such as the sonata form.3 Even if everyone agrees, however, that cadences are of the utmost importance to the analysis of tonal music, a key question remains: what exactly is a cadence? Paraphrasing Augustine, we could answer that if no one asks us, we know; but if we wish to explain it to those who ask, we do not know.4 Part of cadences’ resistance to definition lies in the sheer abundance and almost infinite variety of cadential realizations revealed by even a superficial examination of the actual compositional practice of the eighteenth and (early) nineteenth centuries. This variety not only seems to defy any attempt to provide a clear-cut, unequivocal, and all-encompassing definition, but also stands in sharp contrast to the rather simplistic descriptions of cadential patterns found in numerous modern textbooks on tonal harmony. Part of the problem is due to the fact that cadences have evolved over a long period of time in different stylistic contexts and local traditions, leading both to a multiplicity of cadential patterns and, to complicate things even more, to a Babylonian confusion in the terminology used to describe them.5

1. 2. 3. 4. 5.

E.g., Schenker, Free Composition (1979), 5; Lerdahl and Jackendoff, A Generative Theory (1983), 174; and Caplin, Classical Form (1998), 42. E.g., Rothstein, Phrase Rhythm (1989), 5. See, for instance, Caplin, Classical Form (1998); and Hepokoski and Darcy, Elements (2006). Augustine, The Confessions of Saint Augustine (2006), 214. See Bergé, Martin, Neuwirth, Lodewyckx, and Herregodts, Concise Cadence Compendium (in preparation). Both the sheer infinite variety of cadential realizations and the terminological multiplicity were noted

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Our quest to discover the essential characteristics of the cadence, as implied in the notoriously thorny “What-is?” question, faces the obvious difficulty that we might end up identifying only a “common denominator.”6 It is highly questionable, however, whether such a reductionist approach would be capable of providing the differentia specifica that would allow us to differentiate the cadence from other, non-cadential types of progressions (prolongational or sequential). In other words, any attempt to single out necessary and sufficient criteria underlying the definition of cadence seems doomed to failure, which might suggest that there is no such thing as “the” cadence. If this is the case, one could argue that the various instances (or “tokens”) of the general cadence concept are related to one another not by way of a shared essence, but rather by way of a Wittgensteinian family resemblance, with crisscrossing and overlapping bundles of features as well as more proximate and more distantly related realizations.7 Many researchers specializing in music from the common-practice period might not consider the difficulty involved in creating a water-tight definition to be problematic, as they have acquired an astonishingly robust intuitive understanding of the concept through repeated exposure to numerous instances commonly labeled as “cadences.” They have learned to determine with a comparatively high degree of confidence what constitutes a cadence and which elements must be present (in which temporal order) in order to be able to speak of a cadence. This is not very surprising, given that from the very beginning of their music-theoretical training, students are taught to distinguish between various types of cadences—perfect and imperfect authentic, half, deceptive, and evaded—as well as to perceive the different degrees of closural strength conveyed by each of these types.8 Yet the impression of familiarity with the cadence is deceptive. In fact, despite the importance of cadences in music-theoretical training and their ubiquity in analytical writings, “cadence” remains “one of the most malleable concepts in music theory,”9 with much controversy lingering over what constitutes a cadence. When seeking to substantiate their respective notions of the cadence, modern music theorists will in most cases succeed in identifying a historical precedent, since numerous, partially conflicting definitions and taxonomies of the concept have been put forth over the past four hundred years or so. As Thomas Christensen puts it, “most musicians use the word to designate some sort of closing, although the criteria by which such a closing is defined

6. 7. 8.

9.

as early as 1745 by Meinrad Spieß in his Tractatus Musicus Compositorio-Practicus, 95. In the case of an authentic cadence, a simple dominant-to-tonic motion (see Temperley, The Cognition of Basic Musical Structures [2001], 336). Wittgenstein, Philosophical Investigations (1953), 65–68. Although plagal cadences have been mentioned in numerous textbooks, the notion that there is such a thing as a plagal cadence in the classical style has been challenged quite strongly by William Caplin, most recently in his Analyzing Classical Form (2013), 56, in which he speaks of “the myth of the plagal cadence.” Christensen, Rameau and Musical Thought in the Enlightenment (1993), 113.

Introduction: What is a Cadence?

9

and categorized have varied over the centuries […].”10 The historical diversity of the cadence concept may itself suffice to dash our hopes of finding any simple answer to the question of what a cadence is. An astonishing number of open questions crucial to the definition of cadences still remain, a selection of which appear in the following: Are half cadences, imperfect authentic cadences, and perfect authentic cadences separate cadence types, or should half cadences and imperfect authentic cadences be better understood as transformations of an ideal prototype, the perfect authentic cadence? Similarly, can the deceptive cadence, often described as a separate third (or fourth) cadence type, be better understood as a cadential strategy operating on the norm of the perfect authentic cadence? Is it a necessary requirement for an authentic cadence to feature a penultimate root-position dominant? Is there such a thing as a half cadence ending on a dissonant or inverted dominant(-seventh) harmony? When deciding whether a given harmonic progression represents a cadence proper (as opposed to a prolongational or sequential progression), and, if so, what type of cadence (authentic or half) it might be, are we to rely on harmonic and voice-leading characteristics alone at the expense of allegedly secondary parameters (such as rhythm, meter, dynamics, texture, and instrumentation)?11 Does only the harmonicmelodic content determine the type of cadence (or the musical syntax), as is often assumed, and do secondary parameters affect only the rhetorical strength of the closure conveyed by a given cadence?12 Can different realizations of the same cadential type convey different degrees of closure and thus reflect different degrees of structural significance? For instance, does the presence of dissonance (e.g., a 7–6 ligatura or a cadential 64) have any impact on the structural significance of a given cadence, or should such features just be regarded as expendable embellishments? Is there a natural and unequivocal beginning point for a cadence?13 Is it legitimate and useful to construe an entire movement as a greatly expanded cadential progression, as Riemann, Schenker, and Schoenberg did in their respective theories, to the extent that the cadence becomes a “master formula” or a “signature” for tonality14? Or rather would we be ill-advised to stretch the cadence concept beyond its boundaries so that it becomes nothing but an empty metaphor? Each of these questions calls for a more careful delineation of the cadence concept. Tempting though it may be to adopt a reductionist (or essentialist) approach, it is questionable whether this would truly allow us to penetrate the “deep structure” 10. 11. 12. 13.

Ibid. On the concept of “secondary parameters,” see Meyer, Style and Music (1989), 14ff. On the distinction between syntax and rhetoric, see Caplin, “The Classical Cadence” (2004), 106–112. See, for instance, Richards, “Closure in Classical Themes” (2010), 29, on the difficulty of locating the start of a cadential function. Often the I6 chord (or, alternatively, the ii6 chord) is considered a conventionalized sign announcing an upcoming full cadential progression; see Caplin, Classical Form (1998), 111. 14. See, for instance, Schoenberg, Fundamentals of Musical Composition (1967), 16: “In a general way every piece of music resembles a cadence, of which each phrase will be a more or less elaborate part.”

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of the cadence. However paradoxical this may sound, the quest for the bare essence of “the” cadence could ultimately lead to an overgeneralization in which the distinction between cadential and non-cadential progressions becomes problematically blurred. Through taking seriously the irreducible complexity of the cadence, as well as the resemblance evinced by the innumerable members of the cadence family, this volume does not claim to provide a single, systematic, and exhaustive theory of the cadence. Rather, it seeks to offer readers a multiplicity of different perspectives, from the vantage point of historical treatises, corpus studies, schema theory, experimental psychology, and form-functional theory, among others. Such a multiperspective approach will hopefully enable readers to arrive at a more refined understanding of the multifarious and historically contingent appearances, usages, and functions of the classical cadence, and thus of tonal music in general. • The nine contributions assembled in this volume attempt to address the above open questions in various ways. In the process, some of these questions will be more prominent, while others will remain somewhat in the background. In any case, it will become clear that there is no universal agreement as to how to answer them; a sense of controversy is also reflected in this volume. The book is subdivided into two parts. The chapters making up the first part (Caplin, Diergarten, Burstein, Neuwirth, and Mirka) deal with specific cadence types (the Prinner cadence, half and deceptive cadences) and cadential elements (dissonances such as the cadential 64 and the 4–3 suspension). The second part (Martin & Pedneault-Deslauriers, Byros, Sears, and Rohrmeier & Neuwirth) presents essays that offer methodological innovations and/or are interdisciplinary in nature. In the first chapter, entitled “Harmony and Cadence in Gjerdingen’s ‘Prinner,’” William Caplin focuses on a particular voice-leading model that Robert Gjerdingen, in his recent study of galant schemata, named the Prinner in honor of a seventeenthcentury theorist.15 In accordance with his threefold categorization of harmonic progressions, Caplin examines the cadential, prolongational, and sequential affinities of the Prinner, discussing numerous examples from a variety of mid-century (and later) composers. The reason why the Prinner poses a considerable challenge to any cadence typology lies in the fact that many Prinner realizations lack a crucial cadencedefining feature, namely a root-position dominant at the penultimate stage of a potentially cadential progression. In his seminal 2004 article on the “Conceptions and Misconceptions” of the classical cadence, Caplin persuasively argued that an inverted penultimate dominant-seventh chord would give rise to progressions that

15. Gjerdingen, Music in the Galant Style (2007), 45.

Introduction: What is a Cadence?

11

lack “sufficient harmonic strength to confirm tonality”16 and thus are incapable of fulfilling a proper cadential function. Despite this alleged deficiency, some authors have continued to refer to progressions that lack a final fall (5–1) in the bass, featuring a clausula cantizans (7–1, supporting a V65–I motion) or a clausula tenorizans (2–1, supporting a V43–I or vii°6–I motion) instead, as “contrapuntal cadences.”17 Such cadences may have been used by galant composers, but, as Caplin argues in his chapter, the lack of a root-position dominant has been recognized as a deficiency by later generations. Unlike mid-century composers, classical composers therefore largely avoided placing a Prinner at the end of self-contained primary-thematic units.18 In his chapter “Beyond ‘Harmony’: The Cadence in the Partitura Tradition,” Felix Diergarten introduces the reader to the Southern German and Austrian Partitura tradition. In addition to an historical overview of hitherto largely neglected sources of eighteenth-century music theory, Diergarten also shows that this tradition represents a challenge to current thinking about the classical cadence. First, Diergarten argues that certain progressions, which would not be regarded as genuine cadences from a form-functional perspective (but rather as prolongational progressions), actually convey some sense of closure and hence that they act, albeit on a more local level, as true (“contrapuntal”) cadences. Second, the author seeks to demonstrate that the distinction between a cadentia simplex and a cadentia ligata—the question of whether or not a given cadence features a 7–6 (or 4–3) syncopation dissonance—did not simply concern the presence or absence of an expendable embellishment, as many modern theorists would tend to suspect. Rather, this distinction was of critical importance for both eighteenth-century theorists and composers, as the presence of the syncopation dissonance was taken to signal a higher degree of structural significance. The legitimacy of Diergarten’s historically informed approach is derived from the fact that Southern German and Austrian composers (such as Mozart) grew up and were trained in the Partitura tradition (e.g., in Salzburg). In other words, the author’s approach deliberately avoids the dangers of an anachronistic fallacy by steering clear of projecting our modern standards and systems onto an historical situation, in which entirely different categories and distinctions seem to have been valued. In so doing, Diergarten raises the question of whether or not it is legitimate to remain faithful to our own concepts of the cadence, since we do not know for certain whether our basic 16. Caplin, Classical Form (1998), 27. 17. Aldwell and Schachter, Harmony and Voice Leading (2003), 120; Laitz, The Complete Musician (2003), 188. 18. It is important to note here that Caplin’s approach to the cadence is foundational for his theory of formal functions, as certain functions are defined to a large extent by the presence or absence of a cadential ending. Blurring the crucial distinction between cadential and prolongational progressions would no doubt jeopardize Caplin’s powerful system of classical theme types. This view is extended by Richards, “Closure in Classical Themes” (2010), 31. It would be self-contradictory within Caplin’s theoretical system to claim that a sentence presentation ends with a cadence; similarly, it would be inconsistent to say that the antecedent phrase of a period ends without a (half) cadence.

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premises were shared by eighteenth-century writers and listeners. Keeping this question in mind, the reader may find it stimulating to compare Diergarten’s analyses to those offered in Caplin’s chapter. Poundie Burstein bases his chapter, “The Half Cadence and Related Analytical Fictions,” on a thorough analysis of actual compositional practice as well as on eighteenth-century theoretical writings, and through this challenges the widespread idea that half cadences cannot end on a dominant-seventh chord, as a dissonant sonority is considered incapable of establishing the stable resting point characteristic of any type of cadence.19 In so doing, he not only problematizes the seemingly familiar notion of the half cadence, but also argues that it should ultimately be regarded as an (often useful) analytical fiction. Thus, according to Burstein, reference to a half cadence is not a purely descriptive statement about a musical “fact,” but rather an illuminating metaphor (or characterization) that often quite aptly reflects the way in which we perceive a given musical passage in terms of grouping boundaries. As the locations of such grouping boundaries are crucial for the differentiation between an elided authentic cadence and a half cadence (followed by a tonic chord), and since grouping depends to a large extent on our interpretative engagement with texture, rhythm, and other secondary parameters, Burstein places great emphasis on the rhetorical makeup of cadences.20 Ultimately, one could even go so far as to conclude from Burstein’s argument that the current distinction between the syntactical and rhetorical aspects of cadences can be discarded altogether. Addressing the common notion of the “deceptive cadence,” Markus Neuwirth, in his “Fuggir la Cadenza,” argues that a deceptive cadence is not a particular cadential type, as it is often understood to be, that can be compared to an authentic or half cadence. Rather, he suggests it is a diverse strategy of delaying tonal closure and thus of expanding musical form. Drawing on eighteenth-century theoretical sources, the author shows that this strategy occurs at completely different formal positions and makes use of a greater variety of chords than has hitherto been recognized to replace the tonic at the moment of expected resolution. In addition, it serves a multitude of different large-scale functions, including formal extension, harmonic prolongation, and modulation. Because stock patterns such as cadences are highly conventionalized and thus highly implicative in nature, they invite composers to creatively play on their constitutive elements. In her chapter “The Mystery of the Cadential Six-Four,” Danuta Mirka provides an in-depth analysis of such an element—the so-called “cadential 64”—,

19. See Caplin, “Teaching Classical Form” (2013), 126. Here, Caplin has rejected the idea of a half cadence ending on a dissonant harmony, based on three kinds of arguments: empirical, theoretical, and experiential. 20. See also Richards, “Closure in Classical Themes” (2010).

Introduction: What is a Cadence?

13

focusing in particular on Joseph Haydn’s notoriously subversive engagement with the cadence. As Mirka demonstrates, the harmonic status of the six-four chord was by no means uncontroversial in the eighteenth century. Some theorists interpreted it as a dominant 64, while others viewed it as a tonic 64 (the latter group subscribing to the view of the fourth as a consonance rather than a dissonance). It was precisely the ambiguous nature of this sonority, clearly recognized by Johann Philipp Kirnberger, that inspired composers’ creative efforts. In a cadential context, the composer could choose not to resolve the 64 chord into a dominant sonority as expected, but instead to reinterpret it as a tonic 64 by simply switching to the tonic. This was possible because the two harmonic functions share the same chordal elements of the tonic triad. By acknowledging and exploiting the double identity of the six-four chord, Mirka argues, Haydn seemed to have drawn practical conclusions from a fascinating theoretical controversy of the time and from Kirnberger’s writings in particular. • Over the last two decades, music theory has received and benefited from a number of extra-disciplinary impulses, including input from the fields of cognitive psychology (experimental paradigms and schema theory) and empirical and formal linguistics. In keeping with these recent developments, the second part of this volume assembles contributions that offer new perspectives on cadences by drawing on models and tools that these disciplines have made available to music theorists. In their chapter “The Mozartean Half Cadence,” Nathan Martin and Julie Pedneault-Deslauriers present the results of a comprehensive empirical study of Mozart’s Piano Sonatas, identifying and carefully analyzing all the half-cadential tokens contained in that corpus. Rather than taking as their starting point a clear-cut a priori definition of the half cadence, they depart from a more intuitive understanding of this cadence type. In line with the empirical logic of the authors’ approach, an extensive definition of the (Mozartian) cadence is deferred to the very end of their chapter. In their quest for a descriptive taxonomy of half cadences that is both as powerful and as parsimonious as possible, the authors position statistical prevalence at the heart of their study, specifying which forms of half cadences can best account for the various subtypes found in Mozart’s sonatas. Based on their corpus study, in which special attention is devoted to minute details of the voiceleading treatment, the authors ultimately argue that all forms of half cadences can essentially be derived from—by means of various transformative steps—and understood as extensions of the simple I–V paradigm. This empirical procedure explicitly allows for the possibility of refining and focusing our previous understanding of half cadences, as it is open to potentially new structures and usages within the context of a concrete musical repertoire.

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Through addressing the classical cadence in his chapter “Hauptruhepuncte des Geistes,” Vasili Byros adopts a schema-theoretical perspective that originated in cognitive psychology, clearing up potential misunderstandings about how the schemata concept can be applied to music theory. Technically speaking, the notion of “schema” refers to generalized knowledge structures that embrace all possible levels. It can therefore be applied not only to voice-leading patterns (as previous research has done21) but, following Leonard Meyer’s suggestion, also in principle to all dimensions of musical structure up to the level of large-scale form. From the perspective of schema theory, form can be understood as a multilevel, hierarchically organized, and temporally ordered “script” articulated by moments of interpunction that convey graded degrees of closural strength: in short, cadences. At a lower level, cadences can themselves be understood as forming complex, multidimensional schemata that are embedded within a multistage interpunction script derived from Heinrich Christoph Koch’s theory of musical form. Although a reliance on the Kochian interpunction model is hardly a new idea, reframing this model in terms of schema theory certainly is. In reconstructing the schemata found in the first movement of Beethoven’s Second Symphony and mentally internalized by historical listeners, the author essentially draws on two sources, musical corpora and the (theoretical) writings of the time, and in so doing demonstrates the advantages of a combined approach. The cadence is often identified as one of the most prototypical patterns in tonal music, a pattern that, as it unfolds, creates and ultimately fulfills highly specific expectations of how the music may continue. If it holds true that cadential contexts differ significantly from non-cadential ones with respect to the ways in which they provoke and manipulate listening expectations in real-time, there is a strong motivation to study the cadence from a psychological perspective—a call for research ably answered by David Sears in his chapter “The Perception of Cadential Closure.” Rather than providing a “speculative” theoretical analysis22 of how cadences and the hierarchically graded degrees of closure imparted by various cadence types are presumably perceived, Sears draws on the results of experimental studies of these issues. Sears’ experimental study diverges from previous work in at least two respects. First, the concept of cadence on which it is based is largely informed by William Caplin’s theory and is therefore much more sophisticated than the rather simplistic models previously used. Second, it examines the perception of cadential closure in an “ecological” environment: that is, through the use of “real” art music rather than artificial material generated only for the purposes of the experiment. In this way, Sears’ study demonstrates the possibilities

21. E.g., Gjerdingen, A Classic Turn of Phrase (1988), and Gjerdingen, Music in the Galant Style (2007). 22. By “speculative,” we mean claims based on the perception of one person (the theorist) or a small group of people (the scientific community).

Introduction: What is a Cadence?

15

for a fruitful cooperation between music theory and music psychology, as well as the potential mutual benefits for each of these disciplinary branches. Martin Rohrmeier and Markus Neuwirth’s contribution, “Towards a Syntax of the Classical Cadence,” is a first step towards a “formal,” grammar-based characterization of the structure of different cadence types in the classical repertoire. As the authors argue, the sheer variety of instances commonly labeled as “cadences” can best be accounted for by a formalization that is capable of doing justice to the combinatorial complexity inherent in cadences, using tree and dependency structures borrowed from linguistics. Departing from the claims put forth in music-theoretical studies and textbooks, this approach makes it possible to hone music-theoretical intuitions, as well as to formulate predictions that are both empirically testable and computationally implementable. In particular, the authors offer new explanations of less complete forms of cadences by examining several hypotheses regarding “movement” and “recursion” proposed in the field of linguistics. This contribution thereby illustrates the extent to which music theory (and musicology in general) may benefit from incorporating formalized syntactical descriptions, which have been long established in linguistics and computer science. • The contributions assembled in this volume draw on material first presented at a four-day conference organized by the editors and held in January 2011 at the Academia Belgica in Rome. We would like to thank all of the authors for their willingness to share their viewpoints and to prepare their chapters in such a meticulous manner, as well as the two reviewers, Mark Richards and Joel Galand, for their many valuable suggestions, which have greatly improved the overall quality of the volume, and finally Claire Bacher and Sophia Davis for their thorough copyediting of parts of the manuscript. Furthermore, we owe our special thanks to Leuven University Press, in particular to Marike Schipper and Veerle De Laet, for offering us the opportunity to publish this volume.

Bibliography Aldwell, Edward and Carl Schachter (2003), Harmony and Voice Leading, Australia, United States: Thomson/Schirmer. Augustine (2006), The Confessions of Saint Augustine, book 11, Indianapolis: Hackett Publishing. Bergé, Pieter, Nathan J. Martin, Markus Neuwirth, David Lodewyckx, and Pieter Herregodts, eds. (forthcoming), Concise Cadence Compendium: A Systematic Overview of Cadence Types and Terminology for 18th-Century Music, Leuven: Leuven University Press.

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Caplin, William (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, New York: Oxford University Press. ——— (2013), Analyzing Classical Form: An Approach for the Classroom, New York: Oxford University Press. ——— (2004), “The Classical Cadence: Conceptions and Misconceptions.” Journal of the American Musicological Society 57/1, 51–117. ——— (2013), “Teaching Classical Form: Strict Categories vs. Flexible Analyses,” Dutch Journal of Music Theory 18/3, 119–35. Christensen, Thomas (1993), Rameau and Musical Thought in the Enlightenment, Cambridge: Cambridge University Press. Gjerdingen, Robert O. (1988), A Classic Turn of Phrase: Music and the Psychology of Convention, Philadelphia: University of Pennsylvania Press. ——— (2007), Music in the Galant Style, New York: Oxford University Press. Hepokoski, James and Warren Darcy (2006), Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata, New York: Oxford University Press. Laitz, Steven G. (2003), The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening, Oxford: Oxford University Press. Meyer, Leonard B. (1989), Style and Music: History, Theory, and Ideology, Philadelphia: University of Chicago Press. Richards, Mark (2010), “Closure in Classical Themes: The Role of Melody and Texture in Cadences, Closural Function, and the Separated Cadence,” Intersections: Canadian Journal of Music 31/1, 25–45. Rothstein, William (1989), Phrase Rhythm in Tonal Music, New York: Schirmer. Schenker, Heinrich (1979), Free Composition, trans. and ed. Ernst Oster, New York: Longman. Schoenberg, Arnold (1967), Fundamentals of Musical Composition, ed. Gerald Strang and Leonard Stein, London: Faber and Faber. Spieß, Meinrad (1745), Tractatus Musicus Compositorio-Practicus, Augsburg: Lotters Erben. Temperley, David (2001), The Cognition of Basic Musical Structures, Cambridge, MA: The MIT Press. Wittgenstein, Ludwig (1953), Philosophical Investigations, ed. G. E. M. Anscombe and R. Rhees, trans. G. E. M. Anscombe, Oxford: Blackwell.

Harmony and Cadence in Gjerdingen’s “Prinner”

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HARMONY AND CADENCE IN GJERDINGEN’S “PRINNER”* William E. Caplin

R

obert Gjerdingen’s theory of musical schemata has by now thoroughly proven itself as a major tool for the analysis of eighteenth-century music.1 Among the many schemata defined by Gjerdingen, the melodic-contrapuntal pattern that he has termed the Prinner is perhaps his most important theoretical discovery.2 Once our attention has been drawn to it, we quickly find the Prinner employed in a multitude of compositional contexts throughout the eighteenth century, most especially in its middle third—the galant era.3 In his treatise, Gjerdingen describes many of the ways in which the Prinner is used, with a special emphasis on how it relates to other schemata. Yet despite his many fine observations, considerable work remains to be done on this ubiquitous galant schema. This essay builds upon Gjerdingen’s groundbreaking study by probing deeper into the specific ways in which the Prinner can be realized harmonically, focusing in particular on the possibility of the Prinner acquiring a uniquely cadential role.4 The prototypical Prinner, shown in Example 1, consists of a two-voice framework, in which each voice contains a scalar tetrachord: the soprano voice descends stepwise from scale degree six (6^) to three (3^); the bass voice, from four (‫ )ݛ‬to one (‫)ݘ‬.5 The resulting counterpoint yields descending parallel motion by thirds (or tenths). In addition to labeling the individual scale-degree functions of the pitches, it is often

*

1. 2.

3. 4.

5.

Financial support for this research has been generously provided by the Social Sciences and Humanities Research Council of Canada and the Canada Council for the Arts (Killam Research Fellowship Program). Gjerdingen, Music in the Galant Style (2007). Ibid., chap. 3. Indeed, Ludwig Holtmeier characterizes the Prinner as “the schema in Gjerdingen’s theory” (“Review” [2011], 313). Like many of his schemata, Gjerdingen’s label honors an earlier music theorist, in this case the seventeenth-century pedagogue Johann Jacob Prinner. The Prinner continues to find its occasional use in nineteenth-century repertories, as discussed at the end of this essay. As a general rule, Gjerdingen eschews detailed harmonic descriptions of the various galant schemata, focusing his attention instead on the scale-degree functions expressed by the melodic strands of a given schema. He also does not normally speak of the Prinner as effecting cadential closure, though early in his discussion (46), he associates the Prinner with the “clausula vera,” a type of (weak) closure that he develops in chap. 11. Following the practice initiated by Giorgio Sanguinetti, Partimento (2012), I use an Arabic numeral topped by a caret for scale degrees in the soprano voice and an Arabic numeral enclosed in a circle (after Gjerdingen) for scale degrees in the bass.

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useful to specify four stages of the Prinner schema, corresponding to each pair of pitches in the two voices.6

  3

  Stages: 1













2

3

4

Example 1: Prinner prototype

As for its generalized form-functional expression, Gjerdingen repeatedly refers to the Prinner as a “riposte,” a conventional rejoinder to some immediately prior statement. He thus implies that the schema occupies a “second” position, one that follows directly upon a formal “first,” which fulfills an initiating function of some kind.7 If this second position is the final one of the phrase, then the Prinner will often result in a cadence (as discussed in greater detail below), thus expressing a functional ending. If the schema itself is followed in the phrase by another event, the Prinner then assumes a medial function, and the subsequent event usually brings a cadence. The prototypical Prinner shown in Example 1 does not normally occupy an initiating formal position in a theme, largely because the scale degrees of stage one (6^ and ‫ )ݛ‬cannot project tonic, the harmonic function most suitable for a formal opening. In certain situations, however, a modulating version of the Prinner (see Example 2) can be used to begin a formal unit (such as the transition of a sonata exposition), because the pitches of stage one can express tonic before being reinterpreted as a new set of scale degrees in the key to which the schema modulates—the dominant region.8

6.

7.

8.

Gjerdingen refers to these constituents of the schema as events. He then uses stage to refer to “the longer utterance into which the event is embedded” (21f.). I prefer to speak of stages exclusively, thus allowing me to use the term event as an informal reference to a given musical idea in general, one that does not necessarily constitute the stage of a schema (e.g., “following stage four of the schema, the next event creates a half cadence”). Gjerdingen notes that the Romanesca (3^–2^–1^–7^, supported by ‫ )ݚ–ݝ–ݜ–ݘ‬typically appears as an initiating schema before the Prinner, and we will observe instances of the Romanesca–Prinner combination in the course of this paper (see ahead, Examples 7b, 17, 18, 22b, and 32). If the Romanesca melody is supported in the bass by the variant pattern ‫ݜ–ݝ–ݞ–ݘ‬, then each voice of the Romanesca–Prinner combination projects a complete octave descent in parallel thirds, as discussed ahead in connection with Example 34. See Gjerdingen, Music in the Galant Style (2007), 52f., for more information on the modulating Prinner. This version of the schema appears only sporadically in the examples of this essay (see ahead, Example 29, mm. 5–7, Example 32, mm. 11–14, Example 37, mm. 1–4).

Harmony and Cadence in Gjerdingen’s “Prinner”

19









 









Example 2: Modulating Prinner

Largely missing from Gjerdingen’s presentation of the Prinner is any substantial discussion of the manifold ways in which its constituent scale degrees operate within a broader harmonic context. In order to contextualize my discussion of how an individual Prinner can receive its specific harmonization, I need first to review a fundamental principle, one that I have invoked repeatedly in my writings on classical harmony and form; namely, the categorical distinction among harmonic progressions that are prolongational, sequential, or cadential.9 1. Prolongational progressions sustain in time an individual harmony (the prolonged harmony) through various voice-leading techniques (e.g., voice-exchange) that yield intervening chords (subordinate harmonies), such as neighboring, passing, and substitute harmonies; the harmonic technique of pedal point also serves to prolong a given harmony, one whose root is placed in the bass voice throughout the entire progression (see Example 3).

       a)

      

b)

c)

      

d)

  

   p

  

        

e)

        ped.

Example 3: Prolongational progressions

2. Sequential progressions destabilize the harmonic environment by projecting a consistent pattern of voice-leading and root motion; such progressions can be classified into six types based on the size and direction of the interval between the roots of the individual harmonies of the sequence. Example 4 shows four of these types: (a) descending fifth, (b) ascending fifth, (c) descending third, and (d) ascending second.

9.

See Caplin, Classical Form (1998), chap. 2; see also, Caplin, “Classical Cadence” (2004), 69–72.

20

William E. Caplin a) descending fifth

  

     

 

  

b) ascending fifth

  

  

  

  

  

   

  

 

 



 

seq.

seq.

c) descending third

     

   

  

  

d) ascending second

        

seq.

               seq.

Example 4: Sequential progressions

3. Cadential progressions serve to confirm a tonal region as a genuine “key” by bringing its basic harmonic functions in the following order: an initial tonic (typically I6), a pre-dominant (usually II6, sometimes IV), a dominant (in root position, often embellished by the “cadential six-four”), and a final tonic (also in root position) (see Example 5a–c). This complete set of harmonic functions results in an authentic cadential progression;10 a half-cadential progression arises if the dominant harmony represents the goal of the progression (see Example 5d–e), and a deceptive cadential progression substitutes a different chord (typically VI, but sometimes I6 or VII6/V) for the final tonic (see Example 5f ).11 Most of Gjerdingen’s schemata are associated with one of these types of harmonic progression. The Meyer, the Fenaroli, the Do-Re-Mi, and the Quiescenza, for example, normally effect a prolongation of tonic harmony; the Ponte, a prolongation of dominant harmony. The Fonte and Monte are built as sequential progressions (descending and ascending second, respectively),12 and the Clausulae perfectissimae, the Indugio, and the Deceptive bring cadential progressions. Depending on its specific harmonization, a schema may be categorized by two different progression types. Thus the Romanesca is typically tonic prolongational, but it may acquire a strongly sequential quality if its final stage is harmonized by a five-three chord (thus creating the progression

10. An incomplete authentic cadential progression omits one or both of the first two of these harmonic functions; see Caplin, Classical Form (1998), 27. 11. In order to highlight cadential progressions (as distinct from prolongational or sequential ones), I indicate the harmonies of the progression within a horizontal bracket placed below the Roman numerals. 12. The Fonte also often expresses a local descending-fifth progression, which, at the next higher level reveals a broader stepwise descent.

Harmony and Cadence in Gjerdingen’s “Prinner”

21

I–V–VI–III, a variant of the descending-third sequence), as found at the opening of Pachelbel’s famous “Canon.” The Mi-Re-Do melodic pattern is especially ambiguous, since its standard harmonization, I–V–I, can be either tonic prolongational or authentic cadential. a) authentic

     

b)

  

      

d) half

    

c)

  

e)

  

  

  

 

  

   

  

  

  

   

f) deceptive

  

  

   

  

     

Examples 5: Cadential progressions

What is especially remarkable about the Prinner, and what explains its incredible compositional flexibility, is that, unlike any other schema, it can be harmonized in such a way as to yield any one of the three progression types. We could think of the unharmonized, prototypical Prinner as occupying a central position within a triangular scheme, such as that shown in Example 6. In an actual harmonic realization, the Prinner can be thought to move, to a greater or lesser extent, toward one corner of this triangle, thus projecting a prolongational, sequential, or cadential expression. I will quickly survey the ways in which the Prinner can take on prolongational and sequential aspects respectively, and then turn in greater detail to the cadential potential of the Prinner, identifying two different cadence types associated with the schema.

Example 6: Prinner triangle

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William E. Caplin

Prolongational Prinner The standard harmonization of the prolongational Prinner retaining both the prototypical soprano and bass melodies is shown in Example 7a. Here, the opening IV harmony is an incomplete upper-neighbor chord to the first-inversion tonic, which is further prolonged by a passing dominant (usually VII6, sometimes V43) to achieve a root-position tonic at the end of the schema. Example 7b shows a typical use of a prolongational Prinner, one that first follows upon a Romanesca, and then leads to a half cadence (HC) to close the opening phrase of a movement (or section thereof).13 In such cases, the final harmony of the Prinner serves as the first harmony of the simple half-cadential progression (I–V), as shown by the horizontal bracket below the Roman numerals.

 







 







Example 7a: Prolongational Prinner—standard harmonization PRINNER

ROMANESCA

                      

         



 

                         

 

HC

Example 7b: Galuppi, La diavolessa, mm. 1–4 (G23.1)

Keeping the Prinner melody intact, variations to the schema can be effected by embellishing or altering the bass line, thus conveying an even stronger prolongational impression. (We could think of these variations as pushing the prototype ever closer

13. Many of the examples used in this study are drawn from Gjerdingen’s treatise; in such cases, the original example number is identified in the caption (e.g., G23.1). For most of his examples, I have added harmonic and cadential analyses and have sometimes modified the labels of the schemata, eliminating ones that might obscure the central point being made.

Harmony and Cadence in Gjerdingen’s “Prinner”

23

toward the prolongational corner of the Prinner triangle). Example 8a shows how the bass of stage three can be embellished by a leap to the leading-tone, thus imparting a stronger articulation of the final tonic. Note that in Example 8b, the Prinner schema ends the opening phrase; yet the closure thus achieved must be understood to be non-cadential, since the penultimate dominant harmony is inverted. This distinction between a concluding prolongational Prinner and a cadential Prinner, which (as will be discussed below) brings an actual cadential progression, is crucial for understanding formal articulations in eighteenth-century music.14

 





 



  



Example 8a: ‫ݘ–)ݞ( ݙ–ݚ–ݛ‬ PRINNER

                        :                       

(no cadence)

Example 8b: Graun, Trio Sonata, mm. 1–2 (G9.5)

In the variant shown in Example 9, the bass of stage three sees ‫ ݞ‬fully replace ‫ݙ‬, thus entirely breaking the stepwise motion of the bass. Indeed, the bass line now replicates that of the Fenaroli, itself a highly prolongational schema.15 Note that in the Haydn passage of Example 9b, the melody rises stepwise from 6^ to 8^ before leaping down eventually to 5^, a standard melodic embellishment associated with the Prinner schema.16

14. For more discussion of my view that genuine cadential closure requires dominant harmony to appear in root position exclusively, see Caplin, “Teaching Classical Form” (2013). 15. In fact, Gjerdingen specifically identifies a Fenaroli schema that is practically congruent with the Prinner, as shown in the example. 16. This conventional melodic embellishment often makes up part of what Gjerdingen refers to as the “la-to-sol flourish” (114) typically found with the Prinner.

24

William E. Caplin

     FENAROLI

     Example 9a: ‫ݘ–ݞ–ݚ–ݛ‬ PRINNER FENAROLI

  :            

                    

Example 9b: Haydn, String Quartet op. 20 No. 3/iii, mm. 1–4 (G27.7)

The Prinner can acquire a stronger prolongational expression when stage two brings the tonic in root position, as shown in Example 10a. Note that the specific prolongational Prinner used in the Vanhal quartet (Example 10b) is unsuitable for creating formal closure,17 so the composer then brings an Indugio, which eventually leads to an HC (in m. 20, not shown) to close the ongoing formal process.

 







 







Example 10a: ‫ݘ–ݞ–ݘ–ݛ‬

17. As will be discussed later in the chapter (in connection with Example 31), the uniformity of melodic-motivic material throughout this Prinner inhibits a sense of closure. As well, of course, the prolongational progression underlying this Prinner cannot produce a genuine cadence.

Harmony and Cadence in Gjerdingen’s “Prinner”

25

PRINNER

                                                                         s INDUGIO

                  sf sf           

   



Example 10b: Vanhal, Quartet in A, i, mm. 16–18 (G20.8)

The variant given in Example 11a, which sees all of the harmonies standing in root position, is also normally prolongational, though the final V–I progression also has the potential of articulating a cadence given an appropriate formal context. In the Aubert symphony (Example 11b), the Prinner beginning at m. 5 is entirely prolongational, thus leading directly to an HC.18

 



 



 

 

Example 11a: ‫ݘ–ݜ–ݘ–ݛ‬

18. The imperfect authentic cadence (IAC) that arises with the Prinner in mm. 3–4 will be discussed later.

26

William E. Caplin 3   :   :  4   :   ::   :  :   :    :   :  ::   ::   :   :   :   :     ::   : ::  ::    : : :   :  : : :    :    

IAC (Pr)

3     

5

  :

 :

3      :  :    ::   

3   :   ::           :   :  :  :  :  

  ::           HC

Example 11b: Aubert, Symphony in G, op. 2 No. 2/i, mm. 1–8

The Prinner can be pushed almost all of the way into the prolongational corner when stage one brings the opening subdominant in second inversion, as shown in Example 12a.19 In C. P. E. Bach’s theme (Example 12b), which takes the form of an eight-measure sentence, an initiating presentation phrase, bringing a Meyer schema, is followed by a continuation phrase that begins with a prolongational Prinner and ends with an HC.20

          Example 12a: ‫ݘ–ݞ–ݘ–ݘ‬

19. The most extreme form of a prolongational Prinner would see a pedal ‫ ݘ‬supporting the entire schema. 20. On the sentence theme-type and its constituent presentation and continuation phrases, see Caplin, Classical Form (1998), chap. 3. Note how the Prinner brings a further acceleration in harmonic rhythm in m. 7 (in accord with its continuation function) and that the HC follows directly as a final descent of the melody 3^–2^.

Harmony and Cadence in Gjerdingen’s “Prinner”

27

presentation

continuation b.i.

     : :          :   :           :  :        : 

  :    :   ::    :    :    :    

  ::   

6

 

 ::  :    ::   :   ::       :  :   :       HC

Example 12b: C. P. E. Bach, Piano Sonata in G, W. 65/22, mm. 1–8

Sequential Prinner The Prinner in its prototypical form is fundamentally “sequential” due to the complete parallel motion of its two voices.21 But a straight-forward harmonization of the schema using a single harmony per stage proves problematic in a texture that features more than two voices. If each stage is supported by five-three chords, as shown in Example 13a, then parallel fifths will arise between the bass and some inner voice. If each stage is supported by six-three chords, and if the Prinner melody is to be kept in the soprano voice (where it can thus project the schema most prominently), then parallel fifths will arise between one of the inner voices and the upper voice (Example 13b). Moreover, with a succession of first-inversion triads, the final harmony would emerge as VI6, one that is rarely used to end a descending six-three sequential progression.22

21. Indeed, the more we push the Prinner into becoming prolongational, the more independent the bass becomes in relation to the descending melodic line. 22. If this final VI6 were replaced by I, then the progression would appear more prolongational (of tonic) than genuinely sequential.

28

William E. Caplin

   5 

  

  

  

 

  

  

Example 13a: Descending 5/3 chords

 5   

Example 13b: Descending 6/3 chords

For these reasons, the sequential Prinner normally features the use of passing harmonies between the fundamental degrees of the sequence. One version, which embellishes the basic five-three pattern yields a complete descending-fifth (“circleof-fifths”) sequence (Example 14a). The use of model-sequence technique at m. 14 of the Gaviniés sonata (Example 14b) fully realizes the sequential nature of the Prinner; moreover, the appearance of the prototypical melody and bass pitches at the very start of the model and its sequences further helps to project the underlying schema. A second version of the sequential Prinner (Examples 15a and 15b), one that embellishes the basic six-three pattern, also results in a descending-fifth sequence, but one that begins at a different place within the circle (with a tonicization of II6). Note that the final VI6 has been replaced by I, which (as discussed in n. 22) renders the progression tonic prolongational at its end; nonetheless, the opening two stages project a sufficiently clear sequential pattern, such that we would not want to say that the entire schema is thereby prolongational.23

23. The sequential Prinner warrants considerably greater attention than is possible in this study; see Holtmeier, “Review” (2011), 313–320, for more discussion on the complications associated with sequences and Prinners.

Harmony and Cadence in Gjerdingen’s “Prinner”

 



29





        Example 14a: Descending-fifth sequential Prinner (5/3 embellishment)

    :       :  :            : :  :                   sequence

model

sequence

                               

14

    





         :  :       

17

 





 

      :        : HC

Example 14b: Gaviniés, Sonata in A, op. 3 No. 1/i, mm. 10–16

 







       

Example 15a: Descending-fifth sequential Prinner (6/3 embellishment)



30

William E. Caplin      :   :   : :       :   :   :    :     

     

16

 



 





     



 

  :             

 :   : 







     

Example 15b: Ferrari, Sonata in A, op. 1, No. 3/i, mm. 13–18

Cadential Prinner The Prinner schema can be pushed into the “cadential corner” by adding a bass ‫ݜ‬ following ‫ ݙ‬within stage three. A similar kind of bass embellishment has already been seen in connection with Example 8, but there, the addition of ‫ ݞ‬permitted the progression to remain prolongational. With an additional bass ‫ݜ‬, combined with the harmonization of the preceding ‫ ݙ‬as a pre-dominant II(7), the conditions obtain for us to recognize the presence of a cadential progression.24 In connection with the added ‫ݜ‬, it can be useful to distinguish cases where this bass creates a metrical extension of stage three (see Example 16a) from those in which ‫ ݜ‬appears as a submetrical insertion within that stage (Example 16b). In an appropriate formal context (that is, one where we can expect cadential closure to occur),25 the use of such a cadential progression

24. The opening IV of stage one does not belong, technically, to the cadential progression, but rather prolongs the initial I6 of that progression. For that reason, the cadential bracket in the examples will normally begin with the I6. That the pre-dominant appears as II(7) in root position, rather than as the more typical II6 (or IV), will be discussed in due course. 25. As discussed in Caplin, “Classical Cadence” (2004), not all formal contexts can produce actual cadences by virtue of there being a cadential progression. In other words, a cadential progression is a necessary, but not sufficient, condition for cadence. The use of a cadential progression as the basis of an opening idea of a theme, for example, will not create a sense of thematic closure, since there is nothing yet “to close.”

Harmony and Cadence in Gjerdingen’s “Prinner”

31

can give rise to a particular form of the imperfect authentic cadence (IAC), one that I will term the Prinner cadence (PrC).26

 







 







  PrC

Example 16a: Cadential Prinner, metrical extension

 





 



  



PrC

Example 16b: Submetrical insertion

Prinner cadences tend to be used within main themes of a movement, either as the terminal articulation of a complete theme or as an internal articulation (ending an antecedent phrase) within a periodic thematic structure. A Prinner cadence cannot be used to end a subordinate theme of sonata form (or any allied form of the sonata), since such thematic units require closure by means of a perfect authentic cadence (PAC);27 indeed, the Prinner cadence is rarely, if ever, used as an internal articulation in the context of subordinate themes (though other forms of the IAC may be found there). On occasion, a Prinner cadence is used in connection with the opening of a transition, whereby a modulating Prinner type (see again Example 2) leads to an internal Prinner cadence, after which a subsequent HC closes the transition as a whole.

26. Such a specific Prinner cadence has not yet been identified as such in the theoretical literature. Gjerdingen never defines a Prinner cadence per se, though he discusses how the Prinner is intimately related to the clausula vera (46), a type of clausulae tenorizans (“closes characteristic of a tenor,” 164); see also Holtmeier, “Review” (2011), 320f. Manfred Hermann Schmid’s exhaustive catalogue of “falling third cadences” (“Terzkadenz” [2004]), includes cases that I would identify as Prinner cadences; however, many others are either cadences of a different type (including an IAC variant that I will define later in this essay) or are noncadential, in my terms. 27. See Caplin, Classical Form (1998), 97; James Hepokoski and Warren Darcy advocate a similar requirement, when they define the “essential expositional close” (EEC) as a perfect authentic cadence (Elements [2006], 120).

32

William E. Caplin

A typical case of a Prinner cadence with a metrically extended ‫ ݜ‬is seen in Example 17 (a passage made especially famous by Stravinsky’s adaptation in his Pulcinella ballet). The opening basic idea, built as a Romanesca, is followed by a contrasting idea, a Prinner riposte, that creates a palpable sense of closure, aided by the “cadential” trill on 4^.28 PRINNER ROMANESCA b.i.

c.i.

    :         :                           PrC

Example 17: Gallo, Trio in G, i, mm. 1–2 (G3.9)

A similar Prinner cadence arises in Example 18, though here the situation is somewhat more complex. Note that following a Romanesca basic idea, the contrasting idea beginning with the upbeat to m. 2 sees I6 moving to IV on the downbeat of the measure. Such harmonic motion (I6–IV) suggests that a standard cadential progression were in the making, and we might expect a cadential dominant (in root position) to follow. Instead, the IV initiates the Prinner, which forces the bass downwards, thus “abandoning” the first cadential progression, though leading immediately to a second progression that creates the Prinner cadence.29 While we clearly hear IV as signaling the start of the Prinner proper, this harmony also seems to function as a neighboring chord that embellishes the I6 introduced on beat four of the first measure. We will return to this example shortly and discuss how in some other cases, the initial cadential progression that is here abandoned actually becomes realized.30

28. For definitions of basic idea and contrasting idea, see Caplin, Classical Form (1998), 9, 12. Note that each of these ideas normally lasts two measures. In Example 17b, the notation reflects what eighteenth-century theorists referred to as “compound meter,” whereby each notated compound measure contains two simple measures; for this reason, we can speak in this example of one-measure basic and contrasting ideas. 29. A cadential progression can be deemed “abandoned” if it fails to bring a cadential dominant in root position or if the dominant becomes inverted before resolving to tonic (see ibid., 106f.). 30. Some listeners may hear the I6 on the second eighth-note of m. 2 as merely passing and thus give greater structural importance to the IV chord on the downbeat of that measure. The resulting analysis would thus recognize a conventional cadential progression I6–IV (II)–V7–I supporting the Prinner melodic descent. Likewise, a similarly oriented analysis of Example 17 could see the cadential predominant beginning with the IV6 in the middle of m. 1 and then being prolonged until the final V7–I motion. Though there is nothing “wrong” with either of these two analyses, I find them to be overly reductive in the context of the current discussion, since they effectively obscure the concept of the cadential Prinner developed here, as well as the more specific observation of cadential abandonment for Example 18. I would argue that we must focus our attention on the very foreground harmonic

Harmony and Cadence in Gjerdingen’s “Prinner”

33 PRINNER

ROMANESCA b.i.

c.i.

:       2       :      







 





 :      PrC

Example 18: Marcello, Sonata in F, op. 1 No. 1/i, mm. 1–2 (G3.4)

Example 19 shows a Prinner cadence at m. 7 featuring a submetrical insertion of ‫ݜ‬. This theme (a sentence) actually contains two Prinners, the first of which (mm. 4–5) is highly prolongational due to the emphasized ‫ ݘ‬and the inverted dominant (V43 65) in the first half of m. 5. Thus following a presentation (mm. 1–3), the continuation phrase achieves noncadential closure by means of the first Prinner. When the continuation begins to be repeated at m. 6, a second Prinner, one whose bass line now conforms more to the prototype, brings cadential closure to the theme via a Prinner cadence. Note, by the way, that this cadence type, by definition, achieves only incomplete melodic closure on 3^. It is therefore interesting to observe how following the PrC, Galuppi adds a brief codetta that might be seen to compensate for this lack of full melodic closure by emphasizing the tonic scale degree (1^). An important caveat must be raised at this point: in order to speak of a genuine cadential Prinner, the bass ‫ ݙ‬must first support a pre-dominant harmony (II or II7). If the arrival on ‫ ݙ‬already brings dominant harmony (in the form of V43 or VII6), as seen in Example 20a, then the added ‫ ݜ‬will have lost its cadential potential. We cannot speak of a cadential function when the dominant initially appears inverted, for in such cases, the subsequent “root-position” V gives the impression of being an embellishment of the inverted dominant. The resulting progression is thus rendered prolongational, not cadential. Example 20b provides a concrete illustration of this situation. Here, the appearance of VII6 at the beginning of stage three (second half of m. 31) renders the Prinner prolongational, and thus a genuine HC immediately follows to conclude the phrase.

activity in order to recognize the particular ways in which the galant schemata are harmonized. Indeed, it is perhaps not a coincidence that Gjerdingen, who effectively discovered the Prinner, is a theorist of profoundly “anti-reductionist” proclivities.

34

William E. Caplin presentation

                :                                       b.i.

interpolation

Larghetto

continuation

 3  :           4        







  :   :  : ::      

5

 

:    :

    

               cont. (rep.) 6

                

    :    :                 

codetta

                                                          

7

PrC

Example 19: Galuppi, Sonata No. 40 in B¨, I. 40/i, mm. 1–8

With this caveat in mind, it must be recognized that in the case of a passage with a two-voice texture, such as Examples 17 and 18, it is not always clear just what the implied harmony of stage three really is, especially in the absence of a figured bass that might give some clues as to the complete harmonic texture. But even when the figured bass is present, the situation can remain somewhat ambiguous. Most typically, we find the figures “7–7” associated with the ‫ ݜ–ݙ‬bass, which, when realized, creates a 7–6 motion in an inner, third voice (i.e., alto). In such cases, it would be possible to understand the first 7 (over ‫ )ݙ‬in one of two ways: either as an “essential seventh” (to speak with Kirnberger) within a pre-dominant harmony (II7) that resolves to dominant (over ‫ ;)ݜ‬or, as a “nonessential seventh,” a suspension seventh, within a single dominant harmony that embraces both ‫ ݙ‬and ‫ݜ‬. The former case can

Harmony and Cadence in Gjerdingen’s “Prinner”

35

 





 



  



Example 20a: Prolongational Prinner with added ‫ݜ‬

                                               

 

31

 





                

               

    



     HC

Example 20b: Johann Stamitz, Flute Concerto in D, i, mm. 29–32

be construed as cadential, but the latter cannot, since the dominant would initially appear inverted. It is more likely, however, that we would hear the first interpretation, namely, that of a cadential Prinner, since, as Kirnberger observes, the progression of the bass by a descending fifth (more literally, an ascending fourth) is usually indicative of a resolving essential seventh, not a suspension seventh.31 Nonetheless, a certain harmonic ambiguity remains, which contributes, to some extent, to a general uncertainty about the cadential status of the Prinner configuration. In textures of three or more voices, a clear pre-dominant harmony associated with the beginning of stage three may be discerned more readily, as in the two passages by Mozart shown in Example 21. In both cases, an inner voice completes the sonority, thus providing the chordal “fifth” that unambiguously projects a supertonic harmony with the appearance of ‫ݙ‬. Note, by the way, that like the Galuppi sonata seen

31. “It can be taken as a general rule that every essential seventh is followed by a bass progression by ascending fourth or descending fifth to a triad, unless an inversion of this chord is used” (Kirnberger, Musical Composition [1982], 82).

36

William E. Caplin

in Example 19, the “Prague” symphony theme (Example 21b) follows the cadential arrival on 3^ with a codetta that emphasizes 1^.

                                      PrC

Example 21a: Mozart, Theme for Variations (incomplete), K. anh. 38, mm. 1–6 Allegro vivace

                                                 codetta

 

41

                 

  

43





 

 

 :   :   :   : 

f

PrC

            45              

44

Example 21b: Mozart, Symphony No. 38 in D (“Prague”), K. 504/i, mm. 37–45

The Prinner cadence, as defined and exemplified above, is not the only cadential articulation associated with the Prinner schema. Look again at Example 18 and recall how the move from I6 to IV had the potential of becoming a standard cadential progression (by continuing on to V). There, this progression ended up being abandoned, leading instead to a second progression that brought a Prinner cadence. The possibility of realizing this opening cadential progression is shown in Example 22.

Harmony and Cadence in Gjerdingen’s “Prinner”

37

Here, the use of a standard cadential bass line to support the Prinner melody yields an unequivocal imperfect authentic cadence.32 In order to distinguish this cadence from the Prinner cadence proper, I use the abbreviation IAC (Pr), which stands for imperfect authentic cadence (Prinner type). Another example of this cadence type can be found near the opening of Example 11b, mm. 3–4. In this case, the cadential progression begins directly with the pre-dominant II65 (the preceding root-position tonic obviously belongs to the initiating unit of the phrase), whose immediate move to V and then I creates the IAC (Pr).

 



 



     IAC (Pr)

Example 22a: Imperfect authentic cadence (Prinner type) PRINNER ROMANESCA

 :   :     :      :     :          

    







   





CADENCE



     

IAC (Pr)

Example 22b: Castrucci, Sonata in F, op. 2 No. 4/i, mm. 1–2 (G3.5)

The essential difference between the two cadence types associated with the Prinner involves the motion of the bass: in a PrC, ‫ ݜ‬is immediately preceded by ‫ݙ‬, which itself is either approached from ‫ ݚ‬above, or occasionally, as a variant, from ‫ ݘ‬below; in an IAC (Pr), ‫ ݜ‬ensues directly from ‫ݛ‬. I consider this distinction to be both conceptually and perceptually significant. The imperfect authentic cadence (Prinner type) is a standard variant of the genuine IAC; its bass line is fully differentiated from its melodic line. The Prinner cadence, on the contrary, always brings with it vestiges of a schema prototype that has strong sequential and prolongational implications, since

32. Note that Gjerdingen adds the label “Cadence” to the bass line of Example 22b, thus explicitly recognizing that such a bass differs markedly from the Prinner bass of Examples 17 and 18.

38

William E. Caplin

its bass line derives from a situation of parallel motion and is thus not as differentiated from the melody as a standard cadential bass. The Prinner cadence brings, of course, a cadential dominant exclusively in root position (if it did not, we could not speak of a cadence), yet this ‫ ݜ‬still carries with it the implication of being an embellishment of a more prototypical ‫ݙ‬. This implication is especially strong when the added ‫ݜ‬ takes the form of a submetrical insertion. In other words, the Prinner cadence seems to occupy a middle position between the purely prolongational Prinner, which can, in certain formal contexts, bring about a kind of noncadential ending (as in Example 8b), and the imperfect authentic cadence (Prinner type), which effects an entirely cadential mode of closure.

Degrees of Cadential Strength The preceding discussion suggests that we can identify three types of formal closure associated with the Prinner schema—(1) the noncadential prolongational Prinner, (2) the Prinner cadence, and (3) the imperfect authentic cadence (Prinner type). It also suggests that these three types may exhibit varying degrees of formal closure—from weaker to stronger—a concept that we often associate with the idea of the syntactical strength (or weight) of cadences.33 Assessing a scale of cadential strength is difficult, but two approaches present themselves: one examines actual compositional practice for hints about cadential strength; the other precedes from perceptual experimentation.34 Up to now, the latter has not provided any conclusive results,35 so we can look to certain formal contexts where cadential differentiation would seem to play a crucial role. One such context involves main themes that seem to be organized in a periodic manner, such that we sense that an initial phrase brings a relatively weak degree of closure, one that is matched by a subsequent phrase that brings a stronger sense of ending. The following examples, mostly taken from early Haydn piano sonatas, suggest that the above hypothesized weighting of the three Prinner modes of formal

33. See Caplin, “Classical Cadence” (2004), 106–112, for the distinction between syntactical and rhetorical strength of cadences: the former concept engages the notion of formal closure, the latter evaluates the role that parameters such as dynamics, texture, and metrical placement play in projecting a wide diversity of “strength” and “weakness” that is not directly connected to formal closure. The present discussion concerns syntactical strength exclusively. The standard, textbook theory of cadences suggests that the PAC creates the greatest degree of formal closure and thus is syntactically the “strongest” of the cadence types. The HC is the weakest, and the IAC occupies a middle position between these two extremes. 34. See the chapter by Sears in this volume. 35. The experiment discussed by Sears (ibid.) included only two cases of a PrC (Mozart, K. 282/i, and K. 309/ii), and they were perceived to be equally strong as the regular IACs.

Harmony and Cadence in Gjerdingen’s “Prinner”

39

closure—prolongational Prinner, PrC, and IAC (Pr)—may have some validity, at least provisionally.36 In addition to these three modes of closure, the HC has also been thrown into the mix.

  :     :   : :   :    : :                      Allegro moderato

 

     :  

(no cad.)

  :  :   :    :  

5

:   :  :   :  : 

      

 

 

 

 

 

HC

Example 23: Haydn, Piano Sonata in D, Hob. XVI:14/i, mm. 1–8

The first three examples all feature cases where an opening phrase closes noncadentially with a prolongational Prinner. In Example 23, such an opening phrase is followed by an HC, thus suggesting that the half cadence, a traditionally weak cadential articulation, nonetheless creates a stronger sense of formal closure than a prior phrase that ends without any cadence. Example 24 presents a similar situation, except that this time, a clearly prolongational Prinner closing the opening phrase is matched by a genuine Prinner cadence to close the theme (at m. 8). Finally, Example 25 shows how an opening phrase ending noncadentially leads to thematic closure via an imperfect authentic cadence (Prinner type). These examples support my theoretical contention that any of the cadence types (HC, PrC, and IAC [Pr]) are syntactically stronger than the prolongational Prinner, which I consider to be noncadential. Indeed, the fact that this prolongational mode of closure is never used, to the best of my knowledge, to end a thematic unit is the principle reason why I exclude such prolongational formations from having a genuinely cadential expression. In other words, I recognize that a certain degree of subthematic closure (that is, closure internal to the thematic unit proper) can be achieved by prolongational progressions, yet I want to exclude

36. The following results are based on an informal, limited survey of the repertory; the topic deserves considerably more research (one that exceeds the scope of the present study) into a broader range of compositions from the galant and early classical eras.

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William E. Caplin

such progressions from the concept of cadence, since they are incapable of effecting genuine thematic closure.37 Presto

                                 :    :                   (no cad.)

         :        

6

  

  8   

 



   

  

PrC

Example 24: Haydn, Piano Sonata in A¨, Hob. XVI:46/iii, mm. 1–11

Allegro moderato 

    



: : 

      



 

 :  :     :

       

           :                         

 :   :  :  

      





(no cad.)

6

IAC (Pr)

Example 25: Haydn, Piano Sonata in B¨, Hob. XVI:18/ii, mm. 1–8

37. See Caplin, “Teaching Classical Form” (2013), 120–126. Of course, a genuine cadence type can also function to create subthematic closure, such as when an HC or IAC is used to end the antecedent phrase of periodic themes.

Harmony and Cadence in Gjerdingen’s “Prinner”

41

How, then, do the three actual cadence types relate among themselves as regards syntactical strength? The following two examples suggest a possible ranking. In Example 26 we can witness a thematic unit (which itself serves as first part of a small binary theme-type) whose initial phrase closes with a PrC, but whose final phrase ends with an HC. Insofar as the Prinner cadence would seem to be a special variant of the IAC, we would ordinarily think that an authentic cadence of any type would be stronger than an HC. As a result, the cadential pairing found here might seem anomalous. Yet insofar as the PrC at m. 4 only achieves melodic closure on 3^, the HC cadence leading to 2^ seems to represent a next step—a stronger step—in the melodic descent that will eventually lead to 1^ (as occurs at the end of the second part of the overall binary form, not shown). Indeed, the idea of a broader 3^–2^ melodic progression from m. 4 to m. 8 is replicated on the local level when the second phrase brings another Prinner, this one entirely prolongational, whose final 3^ (end of m. 7) moves directly to 2^ for the HC. Thema

  

   

      





          





4

 



  





PrC

 

5

7

                       

8

  

  

  



::



::

HC

Example 26: Haydn, Piano Sonata in D, Hob. XVII:D1/i, mm. 1–8

If we now compare the PrC to the IAC (Pr), as shown in Example 27, it is not surprising that the former, closing the initial phrase, appears weaker than the latter, closing the final phrase. Note that the PrC here features a submetrical insertion of ‫ݜ‬, thus giving the effect all the more that this bass functions somewhat as an embellishment of the prior ‫ݙ‬. In the final cadence, on the contrary, stage three of the Prinner consists exclusively of the cadential dominant.38

38. A pre-dominant, in fact, is missing from this particular cadential progression.

42

William E. Caplin Allegro

 

                                                                          

5





                                       



 



PrC

 



    IAC (Pr)

Example 27: C. P. E. Bach, Trio Sonata in C, Wq 147/i, mm. 1–9

Given the evidence from these limited number of examples, we can conclude provisionally that, as hypothesized earlier, the three modes of formal closure associated with the Prinner present a graded range of syntactical weights: from weak to strong, they are the noncadential prolongational Prinner, the Prinner cadence, and the imperfect authentic cadence (Prinner type). Just where the half cadence fits within this scheme is more difficult to say: as shown in Example 23, it is stronger than the prolongational Prinner; and in Example 26, it would seem to be stronger than the Prinner cadence. Unfortunately, we cannot speak with any certainty of the relation of the HC to the IAC (Pr), since I have yet to find a case in the repertoire where these two cadence types are matched within a periodic formation, a fact that points to the need for considerably more empirical research on this topic.39

39. To be sure, Example 11b brings this succession of cadences, but the formal context is not periodic; moreover, the first phrase seems to fulfill the formal function of “main theme,” while the second phrase seems to function as a “transition.”

Harmony and Cadence in Gjerdingen’s “Prinner”

43

Undermining the Prinner cadence As just discussed, the Prinner cadence emerges as the syntactically weakest of the genuine cadential types employed by eighteenth-century composers. Indeed, the relative weakness of the Prinner cadence is also manifest in some situations where it seems to be undermined as a genuine cadence by the music that immediately follows the schema.40 Consider Example 28. Here, the main theme of the movement begins with a four-measure initiating phrase supported entirely by a root-position tonic. A second phrase begins with a Prinner that ends with a PrC in the middle of m. 6. But this moment of closure seems to come too early, and we are not surprised when Haydn pushes the music further into another cadential articulation, the HC of m. 8, which leads the melodic line down stepwise from 3^ (at the end of the Prinner) to 7^, recalling a similar continuation of the melodic descent seen earlier in connection with Example 26. The effect is one where the HC seems to undermine the potential of the Prinner cadence to bring genuine cadential closure.     :   :     :                                          

Allegro

5



         6 

  

 



   

  :

(cad?)

 

8

 

   

HC

Example 28: Haydn, Piano Sonata in G, Hob. XVI:8/i, mm. 1–8

Something similar occurs in Example 29, a rounded binary theme whose A and A’ sections contain a number of cadential Prinners. Following the opening basic idea (a Do-Re-Mi schema), a Prinner riposte concludes the 5-m. phrase with a PrC.41 The next 40. Other cadence types can occasionally be undermined, but such situations seem to be more rare than cases of undermining the Prinner cadence. 41. As discussed in connection with Examples 17 and 18, the two-voice texture in mm. 3–5 of Example 29 might raise uncertainties as to whether the Prinner is genuinely cadential; some listeners might want to hear ‫ ݙ‬supporting an inverted dominant, rather than II, especially as the immediately preceding harmony is tonic in root position. My reading, one that responds to the highly conventionalized configuration, identifies a cadential Prinner here (and later again in m. 21), though I acknowledge the harmonic ambiguity that the reduced texture presents.

44

William E. Caplin

phrase begins with a modulating Prinner that directs the music into the dominant region of G major. This is also a cadential Prinner, but there is little sense of a genuine cadence arising after only two bars into the phrase; as well, the continuous eighthnote motion permits this potential PrC (at m. 7) to move directly on to a second, prolongational Prinner, whose completion on the downbeat of m. 9 moves immediately into the PAC that concludes the A section. Note that in a context of continuous sixteenth-note motion, this PAC continues the melodic descent 2^–1^, following the 3^ achieved by the PrC at m. 7 and, more immediately, the 3^ occurring again at m. 9 at the end of the prolongational Prinner. The return of the Do-Re-Mi at m. 17 signals Allegro A moderato Do-Re-Mi

         5                                                   PrC

7

B 8     9             : :  : :                      :: ::    

(cad?)

12



     

   

      





PAC

          

 



  

  

A′

       20              : :      :         :   

Do-Re-Mi

      

17

(cad?)

Example 29: Haydn, Piano Sonata in C, Hob. XVI:7/i

PAC

Harmony and Cadence in Gjerdingen’s “Prinner”

45

the start of the A’ section, after which the opening home-key Prinner cadence comes back at the upbeat to m. 20, bringing once more the cadential trill on scale-degree 4 to help reinforce the idea that this is a genuine cadence. Once again, however, the PrC is undermined when the music continues directly on with a PAC to close the entire form. Except for the very first PrC at m. 4, none of the other cadential Prinners bring about genuine cadential closure. Example 30 shows that a potential Prinner cadence can be undermined by the appearance of new material that deflects the music away from a real sense of closure. The opening 4-m. phrase of this theme concludes in an entirely non-cadential manner (due to the inversions of the harmonies). Like Example 28, the PrC that appears in mm. 5–6 seems “too early” to effect a clear sense of closure. Note, as well, that this Prinner, with its emphasis on root-position tonic in stages one and two, very much suggests that it will be prolongational, not cadential (despite the use of the cadential trill). Thus when Haydn begins to repeat the Prinner at the upbeat to m. 7, we think that perhaps this second time will be more effective in bringing the phrase to an end. Instead, this second Prinner is abandoned, and entirely new music brings about a modulation to the key of the dominant, as confirmed by a PAC at m. 11. Allegro

  :   :               

  

6

        

5   ::              

 7   :    :: :  ::    : :                              (cad?)

    11              

10

PAC

Example 30: Haydn, Piano Sonata in F, Hob. XVI:9/i, mm. 1–11

46

William E. Caplin

The three preceding examples show how easy it is to undermine the Prinner cadence with either an immediately following cadence that seems considerably stronger in effect (the HC in Example 28, the PAC in Example 29), or the appearance of entirely new music (Example 30). The effect of a potential Prinner cadence can be undermined in another way, namely, by retaining the same grouping structure and musical material for each stage of the schema. Example 31 illustrates this situation well. Following an initiating presentation phrase in the subordinate key of G major (mm. 18–21), the Prinner at m. 22 brings fragmentation with a series of one-bar units containing identical rhythmic patterns and pitch contour; each unit is supported by the prototypical bass, except for stage three, which sees a submetrical insertion of ‫ݜ‬. As a result, the potential for speaking of a Prinner cadence arises at the downbeat of m. 25. Yet due to the retention of the same grouping structure and motivic material for each stage of the Prinner, the effect of cadence is particularly weak: as a general rule, a genuine cadence (especially in the galant style) brings a conventionalized melodic formula that differs from what precedes it and helps to articulate the sense of “here is the cadence.” So even though the purely harmonic and formal conditions for a cadence arise at the downbeat of m. 25, the lack of such a conventionalized cadential formula preceding this moment (and continuing as well through most of m. 25), casts some doubt on whether we should hear this moment as bringing thematic closure. Indeed, what follows at the upbeat of m. 26 initiates a more decisive cadential progression (I6–IV–V), one that is ultimately abandoned in m. 27. Eventually, however, real cadential closure appears in mm. 28–29 with entirely new, but fully conventional, melodic and harmonic material in a manner wholly typical of a galant cadence.42 A situation similar to the sonata just discussed occurs in a sonata by Peroti (see Example 32), though the consequences are quite different. The four-measure opening phrase closes with a clear Prinner cadence.43 The cadential idea is then immediately repeated an octave lower. The following passage brings another Prinner in a way that resembles the previous example—the first three stages fragment the grouping into one-bar units, each containing a repetition of the same basic melodic-motivic material (the rising and falling scales). As well, the submetrical insertion of ‫ ݜ‬creates the conditions for another PrC. But unlike the Ferrari sonata, a more obvious

42. In light of the issues being addressed with this example, it is interesting to return to the cadential situation in mm. 8–9 of Example 29 and notice that a motivic idea starting in the first half of m. 8 is immediately repeated in the second half; we thus see a retention of material such that a stereotypical melodic configuration associated with a cadence appears only in connection with the PAC, not the PrC. 43. Note that ‫ ݜ‬appears here as a metrical extension, thus imparting a somewhat stronger rhetorical weight to the cadential dominant compared to the many cases of ambiguous cadences we have just seen, where ‫ ݜ‬usually arises as a submetrical insertion. The triplet descent from 3^ to 1^ is a melodic embellishment of the cadence that Koch identified as an overhang (Überhang); as such, the true melodic goal remains 3^, and the achievement of 1^ is actually post-cadential, somewhat akin to the added codettas we observed in Examples 19 and 21b.

Harmony and Cadence in Gjerdingen’s “Prinner”

47

sense of cadence emerges at m. 10 through the use of such rhetorical features as the cadential trill over 4^ and the complete stopping of melodic activity. What follows at m. 11 is a third Prinner, this one modulating to the new key. Here, the use of VII6 already at ‫( ݙ‬m. 13) completely undermines the potential for a cadential Prinner, even though Peroti cannot resist inserting a submetrical ‫ ݜ‬at the very end of the bar. With this lack of cadential closure, a new phrase starting at m. 14 pushes the music toward the HC that closes the ongoing thematic unit (which here functions as the transition of the exposition). Of the various Prinners found within this passage, the first two (mm. 3–4, 5–6) create a clear sense of cadential close, the third (mm. 7–10) is somewhat suspect, and the fourth (mm. 11–14) emerges as entirely prolongational due to the inverted dominant. presentation b.i.

         :    

             







continuation

   

20

 

  



     



21



 

 frag.

        22



 

 



cad-

   25                                   

23

(cad?)

ential (abandoned)

cad

 29      :    : 28                    ::                

26

(aband.)

Example 31: Ferrari, Sonata in C, op. 1 No. 4/i, mm. 17–31

PAC

48

William E. Caplin

           3      4                        PrC 5

9

                                6

7

10           

  







                        

PrC ? 12

14

11



-

                                                                                                              

 

 HC

Example 32: Peroti, Sonata in B¨, fr. Racolta musicale (1756), iii, mm. 1–16

Many music-lovers, of course, will quickly recognize that this Peroti sonata finds a powerful echo at the opening of Mozart’s late Piano Sonata in C, K. 545 (Example 33). And we must thank Gjerdingen for pointing out the many similarities between these

Harmony and Cadence in Gjerdingen’s “Prinner”

49

passages.44 Yet for all that they resemble each other, it is perhaps their differences that are even more telling. For unlike Peroti, Mozart carefully avoids any suggestion of a cadential Prinner throughout this passage.45 Thus the initial Prinner is strongly prolongational (cf., Example 12a); indeed, the emphasis on ‫ ݘ‬throughout mm. 3–4 allows this idea to participate with the “opening gambit” as a fully initiating phrase (a compound basic idea),46 whose continuation is supported by a second Prinner, one that is also entirely prolongational due to the harmonization of ‫ ݙ‬as VII6. An Indugio schema then leads to the closing HC, followed by a Ponte (what I term, after Ratz, compound basic idea b.i.

c.i.

  4         :   3                      

Allegro

continuation

5

8

                                      cadential                                     :       :   

 

      



          

11

standing on dominant



   

HC

Example 33: Mozart, Sonata in C, K. 545/i, mm. 1–12 (G26.6)

44. Gjerdingen, Music in the Galant Style (2007), 359–368. Kaiser, Die Notenbücher (2007), 183f., also compares these two works. 45. For a different interpretation of this passage, see Diergarten in this volume. 46. A compound basic idea consists of a basic idea followed by a contrasting idea that does not bring cadential closure (see Caplin, Classical Form [1998], 61).

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a standing on the dominant). Throughout the entire movement, in fact, there are no cadential Prinners (neither are there any prolongational ones with an added ‫)ݜ‬, and this in a movement that Gjerdingen proposes to subtitle “The Art of the Prinner.” In other words, by this time in the high classical style, the cadential Prinner has largely died out as a standard device for suggesting, or even fully creating, thematic closure. Prolongational and sequential Prinners, on the contrary, remain fully usable within this period, as exemplified by this very Mozart sonata.

Classical decline – Romantic recollection Just why the cadential Prinner goes into rapid decline after such a powerful flourishing during the galant era is hardly certain, but several interrelated factors could be seen to play a role. In the case of a conventional pairing of a Prinner riposte with a Romanesca opening, for example, the bass line organization features a prominent descending motion; indeed (as earlier mentioned in n. 7), if the Romanesca appears with some inverted harmonies, the pairing of this schema with a subsequent cadential Prinner can bring a complete scalar descent in the bass voice, broken up only by the added ‫( ݜ‬see Example 34a). The opening of an early Mozart piano sonata (shown in Example 34b) illustrates this situation well.47 Such a bass descent (supporting a parallel descent in the melody) flourished in the high baroque era,48 and continued unabated into the galant style. But by the classical period this emphasis on descending bass lines begins to give way to basses that generally ascend melodically toward the dominant scale degree ‫ݜ‬, at which point the dominant leaps back down to the tonic for an authentic cadence.49 Within this pattern (see Example 35), the move from ‫ ݘ‬up to ‫ ݚ‬normally supports prolongational progressions (e.g., I–VII6–I6), while the motion from ‫ ݚ‬to ‫ ݜ‬is cadential (I6–II6–V). Thus in classical themes, the bass largely ascends to support a melody that descends to the cadence. As a result, the classical cadence brings a marked differentiation between the outer voices. The “problem” with the Prinner cadence, of course, is that this functional differentiation of voices is considerably weakened, since the Prinner cadence emerges from a prototypical situation of descending parallel motion. To be sure, the cadential Prinner brings an added

47. Given the slow tempo and the possibility of compound meter, it might be possible to hear an HC on the downbeat of m. 2; if so, then we would find here a situation where an internal HC seems syntactically weaker than a terminal PrC. Note, however, that unlike the other pairing of these cadences discussed earlier (Example 26), where a PrC ending on 3^ is followed by an HC on 2^, the HC in the present example supports a melodic 7^, which then descends further to 3^ in the course of the theme. 48. See Lester, Bach’s Works (1999), 27–33, esp. Exs. 2.3 and 2.5. 49. Caplin, “Schoenberg’s ‘Second Melody’” (2008), 162–165.

Harmony and Cadence in Gjerdingen’s “Prinner”

51

‫ ݜ‬that at least restores harmonic functionality to the bass voice, as it leaps from ‫ ݙ‬to ‫ ݜ‬to ‫ݘ‬, but this motion seems often, especially in cases of a submetrical insertion of ‫ݜ‬, to give the impression of being a mere embellishment of the ‫ݙ‬, whose melodic function is to proceed on to the ‫ݘ‬, in the sense of a prolongational Prinner. Romanesca

 

Prinner



























  



Example 34a: Romanesca-Prinner combination prototype

                   :     :                            Adagio

(HC?) 4

     

              PrC

Example 34b: Mozart, Piano Sonata in E¨, K. 282/i, mm. 1–4

 







 







Example 35: Classical thematic prototype

 

 

 

  

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For all of the foregoing reasons, the true status of the Prinner cadence is thrown into doubt. In some cases, of course, its cadential role is secure, such as when it clearly functions to end a phrase or thematic unit (see again Examples 17, 19, and 34b). But in many other situations, the sense of genuine cadence is obscured or made vague by various compositional contexts in which the sense of genuine closure seems not to emerge (such as with the cases of undermining discussed in connection with Examples 28–32). Finally, we have seen that when ranking the Prinner cadence visà-vis more genuine cadence types (cadences that feature a standard, ascending bass line), it would appear to be the weakest of all, attaining a greater sense of structural strength only in comparison to the fully prolongational Prinner, which carries no cadential implications. It is therefore understandable that the Prinner cadence, with its latent structural ambiguities, looses ground in the high classical style, where the aesthetic of clear cadential goals reigns supreme. Yet like most galant schemata, memory of their earlier ubiquity lingers long, and so we should not be surprised to find the occasional recollection of the Prinner cadence in later musical styles.50 I close this essay with a brief examination of two cadential Prinners from the early Romantic period, showing not only how the schema references past practice but also how it becomes accommodated to a new stylistic environment. The main theme of Mendelssohn’s String Quartet in E-flat, op. 12/i, begins with a four-bar phrase that ends with a Prinner cadence at m. 21 (Example 36). From a galant perspective, we see the parallel motion between the melody and the bass, broken only by ‫ ݜ‬as a metrical extension of ‫ݙ‬. Indeed, parallel motion between the outer voices obtains right from the very beginning in a manner that suggests stages three and four of the Romanesca schema (‫ ݜ–ݝ‬supporting 8^–7^; cf., Example 34a). That the PrC is a truly effective cadence (i.e., not undermined in any way) becomes clear by what follows: a new phrase that leads eventually to an HC at m. 25, in a manner that suggests the formation of a largescale antecedent unit (mm. 18–25). Note that as regards the potential weighting of the cadences, the PrC would appear to be weaker than the subsequent HC, similar to what we saw in connection with Example 26. When the opening phrase returns in mm. 26–29, our suspicion that an overall periodic organization is in the making is eventually confirmed by a PAC at m. 36 (not shown).

50. On the historical trajectories of schemata, see Gjerdingen, A Classic Turn of Phrase (1988), Chapter 6; this study deals with only one schema (the changing note pattern that Gjerdingen later terms a “Meyer”), but its treatment of stylistic development and decline seems applicable to all schemata.

Harmony and Cadence in Gjerdingen’s “Prinner” Antecedent antecedent

contrasting idea

basic idea

Allegro non tardante

18            

f

     

 

53

    :        21

      



 

p

      

 

PrC continuation

       

22

cresc.

      

   

   25 :       :

  

   

f

:

   f



HC Consequent

29                   ::        p               

26

PrC

Example 36: Mendelssohn, String Quartet in E¨, op. 12/i, mm. 18–29

These galant characteristics notwithstanding, Mendelssohn refashions the cadential Prinner to aspects of his style that are more typical of early nineteenth-century practice than of the prior century. Thus unlike galant or classical norms, the theme already starts (with its upbeat) on an inverted tonic; moreover, except for this I6 and the subsequent one in the second half of m. 19, all of the harmonies appear in root position, a standard characteristic of Romantic harmony. This emphasis on root-position chords, along with an even greater use of leaping motion in the bass, occurs in the embellished version of the phrase as it appears in mm. 26–29; indeed, the bass actually acquires a distinctly motivic quality (see brackets). Another somewhat unconventional use of the cadential Prinner concerns its relation to the formal organization of the phrase. As we have seen in many cases, the Prinner cadence typically arises out of a two-bar riposte (a contrasting idea, in my terminology) that follows upon a two-bar

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initiating statement (a basic idea).51 Mendelssohn’s opening 4-m. phrase could also be seen to divide into a two-bar basic idea—framed by the I6 harmony and 5^ in the melody—followed by a two-bar contrasting idea. Yet the Prinner itself already begins midway through the basic idea, thus straddling the grouping structure. A set of cadential Prinners also appears at the opening of Schumann’s Faschingsschwank aus Wien (Example 37). Here, each of the four-bar phrases brings a cadential Prinner. To be sure, the Prinner melody appears only in the alto voice (as shown in the analysis), but otherwise each Prinner largely conforms to one of the two basic Prinner prototypes: a modulating Prinner (cf., Example 2) for the first phrase; a standard Prinner for the second. Interestingly, when put together, these two Prinners result in a descending bass line that spans a full octave, thus recalling the galant Romanesca–Prinner configuration (Example 34). Indeed the opening three harmonies of a modulating Prinner (heard still in the home key) correspond to those of the Romanesca: only the final harmony distinguishes the two schemata (III6 or I6 for the Romanesca, V for the Prinner). From a galant perspective, of course, Schumann’s linking the two Prinners raises a serious problem of voice leading, since he directly follows the root-position F-major harmony of m. 4 with the root-position E-flat harmony of m. 5, thus creating both consecutive octaves and fifths. Sehr lebhaft

      f     

3              

  

  

=

 

 

4

      

 

  

 



(PAC)

  

HC

(reinterpreted) 5

  7                           

  

8

      

 



 

HC

Example 37: Schumann, Faschingsschwank aus Wien, op. 26/i, mm. 1–8

51. See Example 21a, Example 26, mm. 1–4, and Example 29, mm. 1–4. Even Examples 17 and 18 see this balanced relation between the opening idea and the Prinner.

Harmony and Cadence in Gjerdingen’s “Prinner”

55

At least three other anomalies from galant (and classical) practice are worth mentioning. First, the chromatic passing chords that embellish the Prinner’s second stage on the downbeats of mm. 3 and 7, present an obviously Romantic touch. Second, the formal organization of the passage, in which the second phrase is a complete sequential repetition of the first finds little precedent in eighteenth-century practice.52 Finally, the placement of the Prinner melody in the alto voice means the resulting cadence is no longer a variant of an IAC, but rather of a PAC.53 Moreover the relationship of the new melody to the bass creates a contour that differs both from the generally parallel descending motion of the galant Prinner cadence and the specific contrary motion of the classical authentic cadence: in fact, Schumann’s cadences invert the classical relationship, in that the soprano now ascends against a largely descending bass. We see here, as well as in the Mendelssohn, how the Prinner cadence continues to find reverberation in later musical styles, yet the composers find their own manner of adapting this schema to their particular stylistic needs and constraints.54

Future research The foregoing account of the Prinner cadence represents only a small step in the much-needed, broader project of providing form-functional interpretations to the various eighteenth-century schemata identified by Gjerdingen.55 With respect to the Prinner itself, the two other types identified above—the prolongational and sequential Prinner—demand their own detailed investigations of form-functional usage. Rarely, of course, will the standard Prinner project a sense of formal initiation, beginning as it does on subdominant harmony. Indeed as Gjerdingen notes, the Prinner is almost always a riposte to some prior opening statement (oftentimes based on a Romanesca schema). But the notion of riposte can include both medial and ending formal functions. The prolongational Prinner is especially adaptable in its formal usage. As seen in a number of the examples above, the prolongational Prinner can function as a formal middle, one that is followed by a cadence of some kind (as in

52. But see the opening of the Scherzo movements from Beethoven’s Piano Sonata in E-flat, op. 26, and Piano Sonata in C-sharp minor, op. 27 No. 2, as precursors, one or both of which Schumann may have had in mind; indeed, the beginning of the former especially may be the model for Faschingsschwank. 53. The sense of PAC at m. 4 occurs largely in relation to the “modulating” nature of the opening measures. But when the music immediately returns to the home key, ending there with another PAC at m. 8, we can recognized retrospectively that the cadence at m. 4 seems to function in the context of the entire theme as what I call a reinterpreted half cadence (see Classical Form [1998], 57). 54. An extraordinary set of variations on the Prinner schema is found as late as the finale of Brahms’s Symphony No. 1, beginning of the subordinate theme (mm. 118–130). 55. The work of Vasili Byros, including the chapter in this volume, is beginning to address this pressing need.

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Example 7b), or as a non-cadential end (Example 8b). Moreover, the prolongational Prinner may well cross over the boundaries of formal grouping structures, thus presenting a complicated interaction of formal function and schema. Due to its relatively unstable harmonization, the sequential Prinner is most likely to be found in medial formal positions: these can range from simple continuation phrases of sentential theme-types to large-scale model-sequence patterns found in a development section of sonata form. One important question that needs further work is whether all complete circle-of-fifths sequences are best identified as Prinners. Though most such sequences can ultimately be assimilated to the Prinner, it would seem that the particular voice-leading pattern of a given case can sometimes obscure the Prinner-defining lines, especially the bass, and it might be that we sense a broader category of “circle-of-fifths sequence” as the primary schematic identification rather than the Prinner per se. This last point relates to another issue left open in this study: the extent to which a given passage can actually be said to represent a given schema. As we saw in connection with the prolongational Prinner, the closer the passage moves to the corner of the Prinner triangle, the less it resembles the prototypical Prinner. In most cases, the melodic line (6^–5^–4^–3^) is held intact while the bass departs from its normal counterpoint (‫)ݘ–ݙ–ݚ–ݛ‬. Should cases such as those shown in Examples 11b and 12b necessarily be subsumed to the Prinner category? And likewise, how appropriate is it to consider the last two bars of Example 9b as both a Prinner and a Fenaroli? Similarly, it could be asked whether the cadential type that I have identified as IAC (Pr) should be considered an actual Prinner? Throughout this study, I have generally followed Gjerdingen’s mode of schemata identification, which is highly inclusive. Future research will undoubtedly be devoted to clarifying the extent to which schemata labels can meaningfully be applied. As regards the Prinner cadence—the primary topic of this study—the question of how this cadence type and its allied IAC (Pr) fit into a broad model of cadential strength requires extensive empirical research. Many more examples of how these Prinner cadence types are used in relation to other types (PAC, IAC, HC, deceptive, evaded) need to be gathered and analyzed before the hypotheses presented here can be substantiated. Additionally, experimental studies of the kind offered by Sears in his chapter to this volume, ones that include the Prinner cadence along with the IAC (Pr), would help to clarify just how these cadential articulations are to be positioned on a scale from strongest to weakest. The last two decades have seen a remarkable flourishing of new theoretical models and analytical methodologies for music of the eighteenth century: contributions to historische Satzlehre, metrical theory, partimento theory, schema theory, and the revival of the traditional Formenlehre have provided many new tools for analysis and criticism.

Harmony and Cadence in Gjerdingen’s “Prinner”

57

It is thus timely to begin examining ways in which these various approaches can be integrated. A study of the Prinner cadence, bringing together schema theory and a theory of formal functions, represents one step in that direction.

Bibliography Caplin, William E. (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, New York: Oxford University Press. ——— (2004), “The Classical Cadence: Conceptions and Misconceptions,” Journal of the American Musicological Society 57/1, 51–117. ——— (2008), “Schoenberg’s ‘Second Melody,’ Or, ‘Meyer-ed’ in the Bass,” in: Communication in Eighteenth-Century Music, ed. Danuta Mirka and Kofi Agawu, Cambridge: Cambridge University Press. ——— (2013), “Teaching Classical Form: Strict Categories vs. Flexible Analyses,” Dutch Journal of Music Theory 18/3, 119–135. Gjerdingen, Robert O. (1988), A Classic Turn of Phrase, Philadelphia: University of Pennsylvania Press. ——— (2007), Music in the Galant Style, New York: Oxford University Press. Hepokoski, James and Warren Darcy (2006), Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata, New York: Oxford University Press. Holtmeier, Ludwig (2011), “Review of Music in the Galant Style,” Eighteenth-Century Music 8/2, 307–326. Kaiser, Ulrich (2007), Die Notenbücher der Mozarts als Grundlage der Analyse von W. A. Mozarts Kompositionen 1761–1767, Kassel: Bärenreiter. Kirnberger, Johann Philipp (1982), The Art of Strict Musical Composition, trans. David Beach and Jurgen Thym, New Haven: Yale University Press. Lester, Joel (1999), Bach’s Works for Solo Violin: Style, Structure, Performance, New York: Oxford University Press. Sanguinetti, Giorgio (2012), The Art of Partimento, New York: Oxford University Press. Schmid, Manfred Hermann (2004), “Die ‘Terzkadenz’ als Zäsurformel im Werk Mozarts,” Mozart-Studien 13, 87–176.

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Beyond ‘Harmony’

59

BEYOND ‘HARMONY’ The Cadence in the Partitura Tradition Felix Diergarten

Mille viae ducunt hominem per saecula Romam

A

ccording to a Latin proverb, a thousand roads lead men forever to Rome. Of even greater importance for music history might be the fact that for centuries a thousand roads have led musicians back home, and that these musicians imported to their homelands the musical ideas and concepts they had been exposed to in Rome. In the 1680s, for example, Georg Muffat, a young organist in his 30s, travelled back northwards across the Alps towards Salzburg, where he was employed at the time. His Italian journey had given Muffat the opportunity to hear Arcangelo Corelli’s music and to have his own work performed in Corelli’s house, and he had also studied with the famous Bernardo Pasquini. Pasquini and Corelli—two names indicative of one of the most fascinating constellations in music history. In 1706, two decades after Muffat’s stay in Rome, these two composers, together with Alessandro Scarlatti, became the only musicians ever to join the famous Academia dell’Arcadia, a Roman club of intellectuals founded around the eccentric Christina of Sweden. The Italian partimento tradition had important roots in these circles.1 The tradition of a practical musical stenography known since around 1600 as bassus continuus first served as a kind of game and esoteric science for encoding polyphonic compositions into a single bass line, and later—when transferred to Naples and its conservatories—as a pedagogical tool that influenced the training of musicians all over Europe during the eighteenth and nineteenth centuries. The partimento tradition has received intense scrutiny from musicologists, theorists, and musicians over recent years. The time is now ripe to investigate the dissemination and local branches of this tradition and its interactions with other pedagogical and theoretical traditions. The successful and sought-after musicians educated in Naples exported their partimenti to the musical centers of the world, where a thousand roads had led them. At the same time, however, the local musicians were developing or refining their own traditions. Some work has been done in this field with regard to the French

1.

Sanguinetti, The Art of Partimento (2012), 20–23.

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tradition,2 but much research remains to be conducted on the Spanish, English, Eastern European, Southern German, and Austrian teaching methods. It is this final element that represents the primary concern of this text: more precisely, the Salzburgian thoroughbass tradition of the seventeenth, eighteenth, and nineteenth centuries, for which I introduce the term “partitura tradition.” This terminology stresses both the autonomy of the practice and its relationship to the Italian partimento tradition. Instead of “partitura tradition,” one could also speak of a “fundamenta partiturae tradition.” Several Austrian and Southern German treatises employ these two words in their titles, referring both to the partitura tradition and to the tradition of Fundamentbücher, a term linked to manuals circulating in Southern Germany since the fifteenth century intended to teach improvisation on a keyboard instrument.3 In German-language (that is, German-Latin) manuscripts and prints from the period between 1600 and 1800, the term “partitura” is used synonymously with “thoroughbass.” The subtitle of Matthäus Gugls’ 1719 treatise Fundamenta partiturae, for example, promises “a brief but thorough instruction to thoroughbass or partitura.”4 The interchangeable use of the terms “partitura” and “thoroughbass” was already a longstanding practice, as demonstrated by the 1676 Compendium of Alessandro Poglietti, one the most renowned organ teachers of his time. Poglietti writes that “roughly 80 years ago, the partitura, also known as Bassus continuus or General Baß, was invented by Ludovico Vidana [sic].”5 Indeed, Viadana had used the term “partitura” in his famous and influential Cento concerti ecclesiastici, drawing on a terminological tradition of naming tablatures “partiturae,” in reference to their partition by barlines. Interestingly, the Italian term “partimento” was—as far as I can determine—not common to the Austrian tradition. Only in 1833 (that is, post facto) was Michael Haydn’s contribution to the partitura tradition, his Partiturfundament, referred to as “Michael Haydn’s partimenti.”6 A thorough examination of the etymology of the term “partimento” remains a desideratum, as does the history of the terminological dissociation of the Italian partimento from the Austrian partitura tradition. It is obvious, however, that “partire” generated both an Italian (“partimento”) and a Latin term (“partitura”), while at the same time in Italy the term “partitura” took on the meaning it has today (namely, “score”).

2. 3. 4. 5.

6.

Cafiero, “The Early Reception” (2007), and Stella, “Partimenti” (2007). Christensen, “Fundamentum Partiturae” (2008). “Kurzer und gründlicher Unterricht, den Generalbaß oder Partitur nach den Regeln recht und wohl zu schlagen” (Gugl, Fundamenta [1719], my translation). “Ungefehr vor achtzig Jahren ist die Partitur, welche auch genennet wird Bassus continuus oder General Baß mit Notten und Ziffern zu schlagen von Ludovico Vidana [sic] erfunden worden” (Poglietti, Compendium [undated], 54). Somewhat later, Johann Jacob Prinner used the term “partitura” in a similar sense (Prinner, Musicalischer Schlissl [1677], 1). Haydn, Partiturfundament (1833), and Diergarten, “The True Fundamentals” (2011), 60.

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The partitura tradition: A historical-biographical outline As the terminological reflection presented above emphasizes, the Austrian partitura tradition had old Roman roots in the seventh century. But it obviously received another important impulse from Rome around 1700, when Georg Muffat returned to Salzburg. During this time, the terminology used in Austria to classify cadences suddenly transformed into a typology closely related to Italian models, which points to a renewed influence from Rome around that time. A treatise by Wolfgang Ebner (1612–1675) is today considered “the first thoroughbass manual on Austrian soil.”7 The original is lost; only a translation by Johann Andreas Herbst as an appendix to his Arte prattica & poëtica is extant.8 Ebner speaks of “cadentia,” and some of his examples (not referred to as “cadentia”) show the progressions comprised by the later cadence typology; however, the precise classification of cadences as given in later treatises is still lacking here. Likewise, in the Musicalischer Schlissl by Johann Jacob Prinner, cadences are only briefly touched upon.9 Much more abundant in this regard is the aforementioned Compendium by Poglietti from the middle of the seventeenth century, featuring nearly all of the schemata that became so important for eighteenth-century compositional practice. Poglietti’s terminology for describing cadences, however, differs from the terminology used in the partitura and partimento tradition. Against this backdrop, it seems quite probable that Muffat imported not only the spirit of Correlian concerti and Pasquini’s organ music, but also the recent theoretical concepts and pedagogical tools associated with this music. He laid these out in his Regulae concentuum partiturae,10 a thoroughbass manual for the organ11 (most later Neapolitan partimento treatises focus on the harpsichord). This commitment to the organ and to church music was to remain a characteristic feature also of later contributions to the partitura tradition; this is accompanied by a rather traditional musical language in comparison to the more advanced operatic language of many Neapolitan partimento treatises.12 This is obvious, for example, in the persistent adherence to what is called tabula naturalis, a precursor of the “rule of the octave,” regulating progressions of triads in root position over certain movements in the bass. The 7.

“Die älteste Generalbaßlehre auf österreichischem Boden” (Federhofer, “Zur handschriftlichen Überlieferung” [1958], 276, my translation). 8. Herbst, Arte prattica (1653). 9. Prinner, Musicalischer Schliss (1677), Chapter 7. 10. Muffat, Regulae (1699/1991); Muffat, An Essay on Thoroughbass (1961). 11. Muffat, Regulae (1699/1991), xvi. 12. There is no doubt about the fact that composers in Salzburg produced instrumental and operatic music in a more modern style. Consequently, this kind of music must also have played a certain role in their education. The preponderance of church music in the surviving sources might simply be related to certain conditions of the local printing culture as well as to the arbitrariness of manuscript survival.

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reliance of the tabula naturalis on triads in root position lends it a much more conservative sound than the modern rule of the octave;13 this sound was of great importance for the daily lives of musicians and composers working in an ecclesiastic environment. A further difference between the partimento and partitura traditions lies in the fact that most partitura exercises have thoroughbass figures given explicitly, whereas Neapolitan partimento collections typically feature unfigured basses. There could be a variety of reasons for the usage of thoroughbass figures in the partitura tradition. First, partitura treatises are “treatises” in a more narrow sense, offering both textbased and musical examples. The Neapolitan tradition, by contrast, is characterized by the lack of written explanations: Where Italian partimento treatises do include text, the examples tend to have explicative thoroughbass figures as well. Conversely, one could hypothesize that collections of exercises for a partitura student might also have been unfigured, but that these have not been transmitted or have yet to be discovered. But there might also be another reason: Perhaps partitura treatises, focusing on sacred music, adhered to a rather strict concept of counterpoint and voice leading enciphered in precise thoroughbass figures. While there are some obvious differences between the partitura and partimento traditions, there are also remarkable similarities. Both in Salzburg and Naples, for example, musical knowledge was handed down in an almost dynastic line of teachers, students, and successors. Muffat, who is considered to be the founder of the Salzburgian partitura tradition, had a pupil named Johann Baptist Samber (1654– 1717). Samber published a Manuductio ad organum in 1704, followed by a Continuatio three years later. As an organist at the Salzburg cathedral, Samber, like his predecessors and successors, also had to teach at the Kapellhaus, the school attached to the cathedral. In his Manuductio, Samber reports that he taught 300 students there over the years. Samber’s successor as an organist at the cathedral in Salzburg was Matthäus Gugl (c1683–1721), whose 1719 treatise Fundamenta partiturae was obviously influenced by Samber; five additional editions were issued, the last in 1805 (Joseph Haydn had a copy in his library). Gugl’s successor Johann Ernst Eberlin (1702–1762) is well-known from the biography of the Mozart family. Two manuscripts under Eberlin’s name have been preserved, entitled Fundamenta partiturae and Fundamentum praeambulandi. In the latter, a further manuscript by Eberlin, De arte componendi, is mentioned, a work that is considered lost. Eberlin’s student, successor, and son-inlaw was Anton Cajetan Adlgasser (1729–1777), who left a treatise entitled Fundamenta compositionis. Adlgasser’s successor as a cathedral organist was a certain Wolfgang Amadé Mozart, and his successor as an organist at Salzburg’s Dreifaltigkeitskirche was one Michael Haydn. While no doubts have been expressed regarding the authenticity

13. Holtmeier, “Heinichen” (2007).

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of Michael Haydn’s Partiturfundament (the editor Martin Bischofreiter obviously only provided the keyboard realization of Haydn’s basses), the authenticity of the Kurzgefaßte Generalbaß-Schule ascribed to Mozart is rather doubtful and still a matter of debate.14 Some thoroughbass exercises by Leopold Mozart, notated for his children, exhibit a proximity to the exercises used in the Kapellhaus, demonstrating the continuous line of a Salzburgian tradition from Muffat to Mozart.15 Further treatises related to the Salzburgian tradition and indebted to Muffat’s cadence typology include four books published by Lotter in Augsburg: the 1738 manual Die auf dem Clavier lehrende Caecilia (whose second part is entitled “de fundamentis partiturae”),16 Leonhard Reinhard’s Kurzer und deutlicher Unterricht von dem GeneralBass (1744),17 Johann Xaver Nauß’s Gründlicher Unterricht den General-Baß recht zu lernen (1751),18 and Johann Franz Peter Deysinger’s Fundamenta partiturae (1763).19

The “cadences common here” The term “cadentia” has two meanings in the partitura tradition. Following a longstanding terminological tradition, it denotes on the one hand the “ending either of a part of a composition or of a composition as a whole”20 and accordingly a repertory of standardized progressions that form these endings. My text focuses specifically on this aspect of the cadence.21 However, “cadentia” also signified a small musical piece or improvisation ending with (and therefore conceivable as an expanded and embellished version of) a cadence in the first sense. “Just for the fun of it I played the organ here in the chapel last Sunday,” writes W.A. Mozart in a letter from Mannheim. “I entered during the Kyrie and played the end of it. After the priest had intoned the Gloria, I played a cadence. Because it was so different from the cadences common here, everybody turned around, especially [Ignaz] Holzbauer.”22 In this context, “cadence” obviously

14. 15. 16. 17. 18. 19. 20. 21.

Grandjean, Mozart als Theoretiker (2006). Plath, Mozart Werke (1982), vol. 1, xx, and 92; Kaiser, Die Notenbücher (2007), 84. The cadence typology can be found on page 32 of the second part. Cadence typology on page 54. Here a different terminology is used, referring to the “cadenza doppia” as “doppelte Kadenz” (32). Cadence typology on p. 74. Samber, Manuductio (1704), 154. My text only deals with “true” cadences and omits all kinds of “deceptive” cadences. On this topic, see Markus Neuwirth’s contribution to this volume. 22. “vergangenen Sonn=tag spiellte ich aus spass die orgl in der kapelle. ich kamm unter den Kyrie. spiellte das End darvon; und nachdem der Priester das gloria angestimmet, machte ich eine Cadenz. weil sie aber gar so verschieden von den hier so gewöhnlichen war, so gugte alles um, und besonders gleich der holzbauer.” (letter of November 13, 1777, quoted in Bauer/Deutsch, Mozart Briefe [1962], 120, my translation).

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means a short prelude or intonation. This practice of playing small “cadences” on the organ can be studied in Eberlin’s Fundamenta praeambulandi,23 in which Eberlin teaches students to improvise variations and embellishments of small musical units, one of which is termed cadenza (Ex. 1 shows the original cadenza and the first three of Eberlin’s variations).24 In addition to Eberlin’s cadenza, a sketch of an organ improvisation by Mozart (preserved in the context of thoroughbass exercises) might offer a glimpse of the kind of cadence Mozart might have played in Mannheim.25

Example 1: Eberlin, Fundamentum praeambulandi (ms., D-Mbs mus. ms. 261), fol. 19

To return to the cadence in the first sense (a repertory of closing formulas), it is quite easy to determine what the cadences common in Salzburg sounded like, since the partitura tradition is remarkably consistent in this regard (see Table 1 and Ex. 2). Both the partitura and the Italian partimento tradition employ two fundamental criteria to distinguish between cadences: the presence (or absence) of a suspension dissonance in the upper voices and the movement of the bass (by leap or by step). The distinction between consonant cadences and cadences involving a suspension is a tradition that dates back to Renaissance contrapuntal theory. Zarlino, for instance, distinguishes between cadenze semplici and cadenze diminuite: The former move in consonant note-against-note counterpoint (“first species”), while the latter have a suspension dissonance on the

23. Eberlin, Fundamentum praeambulandi (undated), 1. See also Federhofer, “Ein Salzburger Theoretikerkreis” (1964), 65 (n. 58). 24. See also Kaiser, Die Notenbücher (2007), 61–63. 25. Plath, Mozart Werke (1982), vol. 2, xii, and 4; Sulyok, Praeludium (1977).

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antepenultimate note.26 The latter type is preferable for cadences of structural significance, since the dissonant syncopation acts “as the signal that a cadence is coming”27 and combines metrical and contrapuntal features to signal closure. In technical terms, this suspension always works in the following way: The fourth-to-last beat of a section in two-part counterpoint is a consonance; one of the two voices is tied over to the next beat while the other moves to a note that creates a dissonance; then, on the penultimate beat, the voice that has become dissonant resolves downwards by step, and the resulting (imperfect) consonance proceeds to the final octave or unison. The typology based on the presence (or absence) of a dissonance remained valid in contrapuntal theory throughout the seventeenth century. As Giovanni Maria Bononcini writes in 1673, “[a] cadence is the final termination of a part or of a whole composition. It is twofold, simple and compound. The simple proceeds note against note in consonances; the compound uses different notes with a suspension.”28 Zarlino’s term “diminuite” has been replaced by “composta” (“compound”), a term that was to become characteristic of the Italian tradition as a whole in the eighteenth century.29 The term “compound” here refers to the fact that the “compound cadence” is a compound of consonances and dissonances, whereas “simple cadences” only have consonances. In the same manner, “simple counterpoint” is distinguished from “compound counterpoint”: “Compound counterpoint is made up of all kinds of notes, be they consonances or syncopated dissonances, resolved according to the good rules.”30 This terminological differentiation provides an important corrective to how the term “cadenza composta” has been defined in recent (influential) music-theoretical studies. Gjerdingen defines the concept as follows: “If ‫[ ݜ‬in the bass] was repeated an octave lower before continuing to ‫ݘ‬, the clausula was called cadenza composta, a ‘compound ending’ involving the addition of a ‘cadential’ 64 or 54 chord.”31 The octave leap in the bass is, however, by no means a defining feature of the compound cadence, whose conditio sine qua non is the contrapuntal dissonance described above. All of the examples Gasparini provides for the compound cadence lack an octave leap,32 and

26. Zarlino, Istitutioni (1558), Part III, Chapter 53; Schubert, Modal Counterpoint (1999), 131. 27. Schubert, Modal Counterpoint (1999), 131. 28. “La Cadenza è una terminazione finale d’una parte, ò di tutta la Cantilena, & è di due sorti, cioè semplice, e composta; la semplice procede con figure eguali l’una contra l’altra tutte in consonanza, e la composta procede von figure diverse in legatura” (Bononcini, Musico prattico [1673], 80, my translation). 29. Interestingly, Giovanni Maria Artusi uses the terms “semplice” and “composta” in his 1586 treatise L’arte del contrapunto ridotta in tavole (Artusi, L’arte [1586], 30), but adopts Zarlino’s “semplice” and “diminuite” in his later L’arte del contrapunto from 1598 (Artusi, L’arte [1598], 61). 30. “Il Contrapunto composto è quello, che si fabrica d’ogni sorte di figure, e di qualsivoglia consonanza, e dissonanza legata, risoluta con le buone regole” (Bononcini, Musico prattico [1673], 77, my translation). 31. Gjerdingen, Music in the Galant Style (2007), 141. 32. Gasparini, L’armonico pratico (1722), 30. Gasparini’s terminology was applied by Johann Gottfried Walther (Walther, Musikalisches Lexikon [1732], in his articles “Cadenza composta,” “Cadenza composta maggiore,” and “Cadenza composta minore”).

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the example Gjerdingen gives for the simple cadence is in fact a compound cadence according to seventeenth- and eighteenth-century sources, since scale degree ‫ ݛ‬in the bass is figured with a 65 chord, necessitating a suspension in the upper voices.33 Whereas the Italian sources refer to consonant and dissonant cadences as “semplice” and “composta,” Muffat uses the Latin terms “simplex” and “ligata,” the latter referring to the ligature (the tie) used in the suspension.34 Interestingly, none of Muffat’s successors adopts the term “ligata,” even when explaining the same phenomenon. For this reason, I will adhere to the term “compound cadence” (from the Italian “composta”) in the following analysis. It is important to note that such a compound cadence is not necessarily a cadence with an “embellished dominant.” Every cadence that features a suspended discant clausula while moving from the antepenultimate to the ultimate note can be referred to as a compound cadence—for example, a cadence employing a ii65 chord. Table 1: Synopsis of cadence terminology

German / Latin

Italian

Proposed modern terminology

Example

major perfectis

doppia / composta di salto maggiore

doppia

2 m–o

major ligata

composta di salto minore

compound major

2 f–l

major simplex

semplice di salto

simple major

2 a–e

minima ligata (ascendens/ descendens)

composta, di grado

compound minimal 2 q–r (ascending or descending)

minima simplex (ascendens/ descendens)

semplice, di grado

simple minimal 2p (ascending or descending)

minor

minor

2 s–u

33. Ibid., 141, ex. 11.3. 34. Muffat writes that a “cadentia simplex” is a cadence “in which no ligature [tie] is used in the upper voices” (“Cadentia major simplex […], in welcher beÿ den Oberstimmen kein Ligatur gebraucht wird” [Muffat, Regulae [undated], 93, my translation]).

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Example 2: Partitura/Partimento cadences

A subcategory of the compound cadence is the cadence with a consonant fourth, referred to as cadentia major perfectis by Muffat and as cadenza doppia by the Italians (Ex. 2m–o).35 All three thoroughbass exercises Leopold Mozart wrote down for his children end with a cadenza doppia, and it is the final cadence of most partitura exercises. It seems, however, that this cadence was perceived as outmoded or overly formal during the second half of the eighteenth century. Although it still plays an important role in the sacred music of Mozart and his contemporaries (Ex. 3a–e), it is nearly nonexistent in classical instrumental music. The rare exceptions can be found (not surprisingly) in instrumental music that deliberately evokes the “old style” (Ex. 3f–h). Because the Salzburgian partitura tradition was part of an ecclesiastic environment in which sacred music was everyday business for musicians, it comes as no surprise that a more conservative style in general and the cadenza doppia in particular were cultivated in this practice throughout the eighteenth century. 35. Menke, “Cadenza doppia” (2012); Holtmeier, “Heinichen” (2007), 16.

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Example 3: Classical examples of the cadentia perfecta / cadenza doppia. (a) L. Mozart, Missa in A, Kyrie, mm. 15–17; (b) J.E. Eberlin, Missa brevis in a, Kyrie, mm. 12–13; (c) J. Haydn, Missa brevis in F, Hob. XXII:1, Credo, mm. 11–13; (d) W.A. Mozart, Requiem, K. 626, Introitus, mm. 6–7; (e) ibid., Offertorium, mm. 11–13; (f) W.A. Mozart, Präludium (Fantasie) und Fuge K. 394, fugue, mm. 66–67; (g) W.A. Mozart, Zwei kleine Fugen (Versetten) für Orgel, K. 154a, no. 1, mm. 10–12; and (h) ibid., no. 2, mm. 12–13

As mentioned above, apart from the employment of syncopation, the second criterion used to distinguish cadences in the partitura tradition concerns movement in the bass. The Italian tradition (which, however, apparently achieved terminological agreement only with Fenaroli) distinguishes between cadenze di salto (cadences with a leaping bass) and cadenze di grado (cadences with a stepwise bass). The German-Latin tradition uses the terms “maior,” “minor,” and “minima” for this distinction, with “maior” signifying a bass clausula in the bass (falling fifth or ascending fourth), “minima” a discant or tenor clausula in the bass (ascending second or falling second), and “minor” a “plagal” bass clausula (falling fourth or ascending fifth). The final category consists of (and does not distinguish between) “plagal cadences” and “half closes” in the modern sense (Ex. 2s–u).

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Muffat’s terms “maior,” “minor,” and “minima” as descriptors of the bass might possibly have been the result of a (productive) misreading. These terms were current in the Italian tradition but signified something completely different. Gasparini, who spent some time in the Roman circles around Corelli and Pasquini at roughly the same time as Muffat, uses the terms “minore” and “maggiore” to describe two subcategories of the compound cadence: Cadenza minore was the normal compound cadence, while cadenza maggiore referred to the later cadenza doppia described above.36 Perhaps Muffat appropriated these terms but (accidentally?) transferred them to a different part of the typology (the movement of the bass). Further confusion arises from the fact that in traditional contrapuntal theory, the terms “maggiore,” “minore,” and “minima” have yet a different meaning, namely the rhythmic movement of a cadence—a cadenza maggiore being a cadence in breves and semibreves, a cadenza minore in semibreves and minims, and a cadenza minima in minims and semiminims.37 However diverse and confusing the evolution of historical terminology may seem, the criteria invoked by historical theorists to classify cadences are exactly the same in the partimento and partitura tradition; they also have a longstanding tradition in contrapuntal theory. Again, the arrangement of the discant clausula (with or without suspension or “double”) and the movement of the bass (by leap or by step) are decisive.38 The question I will address in the following section is whether this represents just another chapter in the history of theory or whether there are ways in which the cadences of the partitura and partimento tradition can inform our modern understanding of eighteenthcentury cadences. The distinction between consonant and dissonant cadences has been completely neglected in all of our modern cadence typologies that focus primarily on the last two harmonic events (the ultima and penultima) and define a cadence as consisting of a root-position dominant and tonic (Table 2).39 In so doing, they classify cadences on the basis of their harmonic profiles and regard dissonances as a negligible, contrapuntal surface phenomena, thereby missing an important nuance of classical voice leading in general and of the classical cadence in particular. I am convinced (to anticipate my findings) that the cadence typology presented here will help to refine our concept of seventeenth- and eighteenth-century cadences.

36. Gasparini, L’armonico pratico (1722), 29–32. 37. Tigrini, Compendio III (1602), 72. 38. The neglect of rigorous treatment of melodic aspects in eighteenth-century thoroughbass and counterpoint pedagogy is a necessary background for understanding the boom of Melodielehre in the eighteenth century, manuals that filled this gap but sometimes seem to be completely lacking in contrapuntal or harmonic foundation: Thoroughbass was always understood as a fundamental precondition. 39. The partitura and partimento cadences are also neglected in Schmalzriedt, “Kadenz” (1974).

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Table 2: Classification of cadences

Modern classification of cadences by harmonic final

authentic

deceptive

by melodic final

perfect

imperfect

by bass movement

root position

inversion

plagal / half-close

Additional category provided by eighteenth-century classifications by dissonance (implying metre and melody)

simple

compound

The dissonant cadence I: Simple and compound cadences in the sentence The beginning of Mozart’s Piano Sonata K. 279 has been cited by Caplin as an example of the sentence; Hepokoski and Darcy identify it as an example of the “loop,” a subtype of the sentence-presentation introduced in their Elements of Sonata Theory (Ex. 4).40 Mm. 1–4 constitute the presentation (comprising a basic idea and its exact repetition), mm. 5–12 are the continuation, exhibiting the characteristic fragmentation, a first (deceptive) cadence in m. 10, and a final cadence in m. 12. Within Caplin’s theory, this beginning raises certain difficulties, since it seems to contradict his rigid definition of the sentence: “the initial four-measure phrase of the sentence, what I have termed a presentation, never closes with a cadence, even if its final harmonic progression (V–I) suggests one. […] To be sure, there are musical forces that effect closure of some kind for the phrase, or else we would not perceive it to be a unified group; but the nature of that closure—be it harmonic, melodic, rhythmic, or textural—is not cadential.”41 In Mozart’s sonata, however, not only does the presentation end with a PAC, but the basic idea already features a PAC at its end. Within Caplin’s theory, this is a contradictio in adjecto: This cadence cannot be a cadence in a narrow sense, since at this point in the sentence, no cadence is allowed: “For at the level of the theme, a basic idea is exclusively an opening idea; that idea itself cannot bring a formal cadence.”42 Caplin resolves this “dilemma” by introducing the concept of a “limited cadential

40. Caplin, “The Classical Cadence” (2004), 37; Hepokoski and Darcy, Elements (2006), 80. 41. Caplin, “The Classical Cadence” (2004), 59f. Against the backdrop of the wider concept of cadence in eighteenth-century theories, I have difficulty accepting Caplin’s rigid definition of what constitutes a cadence (and this makes it hard for me to agree with several of his conclusions that are built upon this definition; see also the critique in Hepokoski and Darcy, Elements [2006], 66 [n. 5]). I understand, however, the central function that this concept serves within Caplin’s theory. 42. Caplin, “The Classical Cadence” (2004), 86 (emphasis added).

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scope,” a kind of hierarchy (or Schichtenlehre) of cadences that measures the “weight” of cadences not according to their intrinsic features but by their temporal position and context. The appendant observation that a cadence after two measures of a piece is less “convincing” or less “weighty” than a cadence after eight or twelve bars of the same piece is so far beyond dispute that even Hepokoski and Darcy cannot but agree with Caplin on this point (not, however, without adding their own nuance concerning the “loop” structure): “Notwithstanding the two obvious PACs, the positionality of those cadences within the larger sentential-thematic structure, along with their subordination to the circular loops within which they are generated, weakens the usual sense of a PAC as a sign of emphatic structural closure and renders them incapable of functioning as normative structural. These perfect authentic cadences, in short, cannot ‘end’ the theme in question.”43

Example 4: Mozart, Piano Sonata K. 279/i, mm. 1–12

Notwithstanding the necessity and importance of a temporal and context-based approach to cadences, this very example clearly shows that the difference in “weight” of the cadences employed here has been distinctly marked by Mozart by means of the intrinsic features of every cadence. As PACs, all three cadences in this example (mm. 2–3, 4–5, and 12) would fall under the same category according to modern cadence

43. Hepokoski and Darcy, Elements (2006), 85.

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typologies. Considering the employment of dissonances according to the partimento and partitura tradition, however, an important difference is revealed: Only the last cadence is a compound cadence, while the first two are simple cadences. At the same time, this example necessitates the discussion of an important challenge in relation to eighteenth-century keyboard music. Characteristic for broad segments of this repertory are two-voice textures that function as “figurations of a virtual polyphonic texture.”44 Also for Austrian music pedagogy of the eighteenth century, it is a matter of course that a two-voice texture can be regarded as representing a fullvoice texture. Exercises in reducing full-voice textures to two voices and (vice versa) exercises in filling in the “missing” voices of a two-voice setting with the help of thoroughbass figures constituted an important part of compositional training.45 Since the bass lines of piano music do not feature thoroughbass figures, sometimes it is not obvious whether a two-voice cadence was intended as a reduction of a full-voice compound cadence or a full-voice simple cadence. A two-voice cadence’s consonance on paper could be understood as a dissonant cadence whose inner voices are concealed but should be imagined or realized by the player in terms of a dissonance sousentendue.46 To return to the example from the Mozart Piano Sonata, at first sight the cadence in mm. 2–3 simply represents the harmonic progression I6–ii6–V–I (Ex. 5a). If we omit the top voice (doubling the bass in octaves), the consonant contrapuntal outer-voice framework of this passage sounds like what is shown in Ex. 5b. To integrate the b at the end of the bar, one could either accept the purely consonant framework as given in Ex. 5c or assume that the c2 is a sustained dissonance sous-entendue, resulting in the dissonant compound cadence as shown in Ex. 5d.

Example 5: Reduction and analysis of Ex. 4, mm. 2–3

As this analysis suggests, it is by no means obvious that the basic idea and presentation in Mozart’s example end with simple cadences, since a dissonance sous-entendue could make them sound like two-voice reductions of a full-voice compound cadence.

44. Holtmeier, “Review of Music in the Galant Style” (2011), 314. 45. Diergarten and Holtmeier, “Nicht zu disputieren” (2011). 46. Holtmeier, Rameaus langer Schatten (forthcoming), and Holtmeier, “Review of Music in the Galant Style” (2011), 315–320.

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Does this render the cadence typology of the partitura tradition (which is based on full-voice textures) useless for the “free” and thin two-voice textures of galant and classical piano music? Quite the opposite, since the argument presented above reveals further interesting details about the cadences used in this example. The first concerns pianistic instrumentation. Whenever Mozart wanted to employ a “stronger” cadence (mm. 10 and 12), he apparently switched to an explicit full-voice texture, laying open the dissonances of the compound cadences that had remained only implicit (if at all) in the “weaker” cadences at the beginning of the example. So while one might accept the idea of an implicit compound cadence by sous-entendu in mm. 2–3 and 4–5, there are definitely explicit compound cadences in mm. 10 and 12. The second interesting detail is the temporal and metrical duration of the cadences in this example. Even if we accept mm. 2–3 as an implicit compound cadence, the suspension here would be on the metrical level of eighth notes; in contrast, the explicit compound cadences in mm. 10 and 12 are at half speed (quarter notes) and are consequently more conclusive. Another example of the employment of simple and compound cadences in the sentence can be found in a locus classicus of the sentence, the beginning of Beethoven’s Piano Sonata op. 2 No. 3 (Ex. 6). Also here, the presentation ends with a V–I progression in root position leading to a short Einschnitt (caesura). For Caplin, however, it would be an “analytical mistake” to speak of a “cadence” here, but also in this case, his “fundamental reason” seems to run the risk of a circular argument: “Inasmuch as the basic idea itself functions to begin a theme, a repetition of that idea must also express a similar function of beginning.”47 In other words, either the progression in m. 4 is not a cadence because by definition no cadence is allowed there, or mm. 3–4 are not a basic idea and the whole example cannot be a sentence at all. Would it not be more rewarding to leave the firm ground of stipulative definitions, instead asking under what circumstances various kinds of cadences were possible, even at the end of a basic idea and presentation, or exploring (following Wittgenstein’s famous dictum that “the meaning of a word is its use in the language”48) the progressions that would have been described as “cadences” by the theoretical traditions of the eighteenth century? Of course, Caplin is right in claiming that the progression in m. 4 produces a different kind of closure than the later cadences in mm. 8 and 12–13. But also here, it seems more rewarding to me (now following Wittgenstein’s appeal, “do away with all explanation, and description alone must take its place”49) to look for compositional, intrinsic features of the cadence-like progression used by Beethoven than to deductively define which progression “is” a cadence and which “is not.” Caplin himself discusses some of these features. The first feature is “harmonic”: According to Caplin,

47. Caplin, Classical Form (1998), 45. 48. Wittgenstein, Philosophical Investigations (1953), § 43. 49. Ibid., § 109.

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m. 4 is not a cadence in the narrow sense, but rather a “[tonic] prolongation that ends with a root-position dominant resolving to a root-position tonic.” Caplin’s second feature is “melodic”: “Beethoven leaves the melodic line open at the end of the phrase, thus helping to counteract the cadential implications given by the harmony.”50

Example 6: Beethoven, Piano Sonata op. 2 No. 3/i, mm. 1–13

Also here, the categories of the partitura cadence open up new perspectives for an even more nuanced description: The cadence in m. 4 is a “simple cadence,” while the cadences in m. 8 and mm. 12–13 are “compound cadences.” This contrapuntal distinction supports the melodic nuance described by Caplin. With regard to Caplin’s “harmonic” argument, again, instead of delineating “cadences” from “prolongations” by stipulative definition, it seems to me to be more challenging and rewarding to take as a point of departure the broad repertory of progressions that would have been described as “cadences” in the eighteenth century. By means of a thorough examination of contextual and intrinsic features, one could then try to describe what “cadential” or “closing” effects these progressions have (or potentially have) at a certain moment in a given piece of music. On this basis, Caplin’s distinction between a “real” cadential progression on the one hand and a “prolongation with a root-position dominant resolving to a 50. Caplin, Classical Form (1998), 45.

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root-position tonic” on the other might be reformulated as follows: The dissonance of a compound cadence generally has its regular preparation in the preceding beats, and this frequently (though not invariably) leads to one or several “predominant” chords corresponding to Caplin’s examples of a “real” cadential progression. The simple cadence, on the other hand, can occur everywhere without preparation, and for this reason this type of progression can be associated with Caplin’s “prolongational” progressions.

The dissonant cadence II: Simple and compound cadences in the period The concept of period implies that “a musical unit of partial cadential closure is repeated so as to produce a stronger cadential closure.”51 In other words, the cadence at the end of the consequent must express a “stronger” ending than the one found at the end of the antecedent. Most frequently this is realized by the succession HC–PAC, although other examples show the succession IAC–PAC. However, a tonic-key PAC at the end of the antecedent is by definition impossible, “since this strong cadence achieves complete harmonic and melodic closure.”52 But also here, various factors (one of which is the distinction between simple and compound cadences) open up

Example 7: Mozart, Clarinet Quintet K. 581/i, mm. 65–75

51. Ibid., 49. 52. Ibid., 51.

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possibilities to evaluate two otherwise similar PACs in different ways. A passage from Mozart’s Clarinet Quintet K. 581/i serves as an example (Ex. 7). Various factors in this example give the first PAC a more limited cadential scope, turning the entire passage into a period-like theme.53 First, the reentrance of the drum-bass in m. 65 signals that the theme has not yet reached its end. Second, the appoggiatura in the melody at the end of the antecedent weakens the first PAC. Third, the cadential progression at the end of the consequent is expanded by a sequence (m. 72) and by an abandoned cadence (m. 73). This finally leads to a compound cadence, whereas the antecedent had ended with a simple cadence. Periods built in this way are relatively rare, however. More frequent are periods featuring a succession of simple and compound cadences that contrapuntally underpin the melodic succession IAC– PAC. Caplin’s example of a period punctuated by an IAC and a PAC is the beginning of Mozart’s Piano Sonata K. 281, and in fact, the IAC here is a simple cadence, the PAC a compound cadence (Ex. 8).

Example 8: Mozart, Piano Sonata K. 281/i, mm. 1–9

53. Due to the PAC in m. 69, this passage cannot be defined as a period under Caplin’s theory. He describes it as a four-bar codetta-theme “repeated with extension” (ibid., 110).

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The dissonant cadence III: Simple and compound cadences in a classical sonata exposition The distinction between simple and compound cadences is also of great value for larger musical forms. The exposition of Mozart’s Sonata facile (Ex. 9), a work that displays its compositional craft on all levels of the musical fabric including the employment of different types of cadences, may serve as an example. The primary theme (P) is structured as a sentence whose eight-bar continuation ends with a I:HC medial caesura that prepares the secondary theme (S).54 Both the basic idea and its varied repetition end with a simple minimal cadence (the “lightest” category of the partitura cadences)—that is, a cadence without suspension and with a stepwise bass, the first voice ascending, the second descending. The subsequent passage (mm. 5–8) features parallel tenths in the outer voices, referred to by Gjerdingen as a variant of his Prinner schema.55 This passage is punctuated by another descending simple minimal cadence (m. 8) that creates a smooth connection to the end of the basic idea (m. 4). The I:HC medial caesura is marked by another ascending simple minimal cadence (connecting this moment to the end of the repeated basic idea, m. 4). S is also formed as a sentence:

54. Hepokoski and Darcy, Elements (2006), 105–108. 55. Gjerdingen, Music in the Galant Style (2007), 365; but see Holtmeier, “Review of Music in the Galant Style” (2011), 313–322. It should be noted that Gjerdingen takes his musical example from an outdated edition with a flaw in m. 7 (compare Plath and Rehm, Klaviersonaten II [1986], 122).

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Example 9: Mozart, Piano Sonata K. 545/i, exposition

A basic idea, its literal repetition, and a sequential continuation (whose contrapuntal complexity has been demonstrated by Ludwig Holtmeier56) directly lead to the EEC. Until this moment, neither a cadence with V and I in root position (a major cadence) nor a compound cadence has been sounded. Mozart saves both for the EEC in mm. 24–25, a cadence that is furthermore emphasized by its metrical-temporal duration of two measures. Until the end of the exposition, this EEC remains the only compound cadence, since both subsequent PACs are simple cadences: The employment of these two different types of cadences clearly relegates cadences after the EEC to the status of ending formulae belonging to what is commonly considered “post-cadential” space. 56. Holtmeier, “Review of Music in the Galant Style” (2011), 312–322.

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Conclusion Mozart’s Sonata facile and the other examples presented in this text have shown that in order to paint a complete and nuanced picture of classical cadences, modern cadence typologies can and should be complemented by a further criterion that has thus far been overlooked: the employment of suspension dissonances in the cadential process. This criterion also points to a more fundamental problem of music analysis: How much analytical abstraction and reduction of an alleged “surface” is beneficial in the analysis of classical cadences? “Harmonic” analyses based on progressions of a basse fondamentale and voice-leading analyses abstracting from dissonances risk neglecting contrapuntal details that were highly important for eighteenth-century musicians. The partitura cadences suggest that we rethink the generally accepted notion that in the eighteenth century, “cadential classifications became based primarily on harmony rather than on melodic or contrapuntal interval.”57 As numerous musicians and writers from the seventeenth and eighteenth centuries suggest, contrapuntal details played a constitutive role in understanding cadences and their closural implications.

Coda: Two Salzburgians in Rome A thousand roads lead men forever to Rome. Two musicians led to Rome by one of these roads were Leopold and Wolfgang Amadé Mozart. On the Wednesday of Holy Week in 1770, they heard a performance of the legendary Miserere by Gregorio Allegri in the Sistine Chapel.58 Mozart, as is known, transcribed the piece after the performance and returned to the chapel on Holy Friday to hear it again and to check his sketches. The fact that Allegri’s piece is a psalm-composition that uses the same harmonic formula for all verses of the psalm and accordingly involves a great deal of repetition renders Mozart’s achievement much more plausible. Furthermore, to return to the partitura tradition, the music that the Mozarts heard in the Sistine Chapel exhibits exactly those schemata that a young musician in Salzburg would have been familiar with in Mozart’s time. It was not necessary for him to memorize and transcribe a polyphonic texture note by note and voice by voice; he could have memorized (and sketched) a partitura stenography, as suggested by the lowest staff of Ex. 10. The beginning of the 1731 version of the Miserere features a progression according to the tabula naturalis mentioned above (see p. 61), namely triads in root position. The beginning of the second

57. Caplin, “The Classical Cadence” (2004), 54. 58. Amann, Allegris Miserere (1935). See also the essay and edition by Ben Byram-Wigfield at http://www. ancientgroove.co.uk/essays/allegri.html.

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Example 10: Gregorio Allegri, Miserere (vatican version, I-Rvat cap.sis. ms. 205, quoted from http://www.ancientgroove.co.uk/essays/allegri.html), with partitura reduction added for analytical purposes

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line shows the famous sequential progression with ascending fifths in the bass and 4–3 suspensions in the upper voice, as described in most treatises of the partitura tradition.59 The end of the first phrase is punctuated by a cadentia maior perfecta, the cadenza doppia of the Italian tradition, complemented by the characteristic legatura di settima (bound seventh, treble 1, mm. 3–4).60 At the end of the second phrase, there is a combination of a simple major cadence (cadentia maior simplex, the Italian cadenza semplice di salto) and a compound minor cadence (cadentia minor ligata). In the Sistine Chapel, Leopold and Wolfgang Amadé Mozart heard a musical language they had been familiar with ever since childhood. A Roman language, a lingua franca that had its roots in late Renaissance polyphony and was cultivated everywhere along the thousand roads that exported the partitura and bassus continuus from Italy. In Salzburg, this tradition was revitalized around 1700 by Georg Muffat, who had studied under Pasquini in Rome. And finally, if we consider the fact that it was the inspiring atmosphere of Rome that stimulated this book and the present attempt to reanimate the partitura tradition and its dissonant cadences, we can again see another turn of the eternal cycle of musicians going to and leaving Rome.

Bibliography Adlgasser, Anton Cajetan (undated), Fundamenta compositionis, ms., D-Mbs mus.ms. Amann, Julius (1935), Allegris Miserere und die Aufführungspraxis in der Sistina: Nach Reiseberichten und Musikhandschriften, Birkeneck: Druckerei St. Georgsheim. Artusi, Giovanni M. (1586), L’arte del contrapunto ridotta in tavole, Venice: Vincenzi. ——— (1598), L’arte del contrapunto, Venice: Vincenzi. Bauer, Wilhelm A. and Otto Erich Deutsch, eds. (1962), Mozart: Briefe und Aufzeichnungen, vol. 2: 1777–1779, Kassel: Bärenreiter. Bononcini, Giovanni M. (1673), Musico prattico, Bologna: Monti. Cafiero, Rosa (2007), “The Early Reception of Neapolitan Partimento Theory in France: A Survey,” Journal of Music Theory 51/1, 137–159. Caplin, William E. (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, Oxford: Oxford University Press. ——— (2004), “The Classical Cadence: Conceptions and Misconceptions,” Journal of the American Musicological Society 57/1, 51–117. Christensen, Thomas (2008), “Fundamentum Partiturae: Thorough Bass and Foundations of Eighteenth-Century Composition Pedagogy,” in: The Century of Bach and Mozart: Perspectives on Historiography, Composition, Theory and Performance in Honor of Christoph Wolff, ed. Thomas Forest Kelly and Sean Gallagher, Cambridge: Harvard University Press, 17–40. 59. Diergarten, “The True Fundamentals” (2011), 70. 60. Gasparini, L’armonico pratico (1722), 30.

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Deysinger, Johann F.P. (1763), Fundamenta partiturae, Augsburg: Lotter. Diergarten, Felix (2011), “‘The True Fundamentals of Composition’: Haydn’s Partimento Counterpoint,” Eighteenth-Century Music 8/1, 53–75. Diergarten, Felix and Ludwig Holtmeier (2011), “Nicht zu disputieren. Beethoven, der Generalbass und die Sonate op. 109,” Musiktheorie 26/2, 123–146. Eberlin, Johann Ernst (undated), Fundamentum praeambulandi, ms., D-Mbs mus.ms. 261. ——— (undated), Fundamenta partiturae, ms. A-Ssp. Federhofer, Hellmut (1958), “Zur handschriftlichen Überlieferung der Musiktheorie in Österreich in der zweiten Hälfte des 17. Jahrhunderts,” Die Musikforschung XI, 264–279. ——— (1964), “Ein Salzburger Theoretikerkreis,” Acta Musicologica 36/2–3, 50–79. Gasparini, Francesco (1722), L’armonico pratico al cimbalo, 4th edition, Bologna: Silvani. Gjerdingen, Robert (2007), Music in the Galant Style, Oxford: Oxford University Press. Grandjean, Wolfgang (2006), Mozart als Theoretiker der Harmonielehre, Hildesheim: Olms. Gugl, Matthäus (1719), Fundamenta partiturae, Salzburg: author. Haydn, Michael (1833), Michael Haydns Partiturfundament, ed. Martin Bischofsreiter, Salzburg: Oberer. Hepokoki, James and Warren Darcy (2006), Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata, New York: Oxford University Press. Herbst, Johann Andreas (1653), Arte prattica & poëtica, Frankfurt: Hummer. Holtmeier, Ludwig (forthcoming), Rameaus langer Schatten: Studien zur deutschen Musiktheorie des 18. Jahrhunderts, Hildesheim: Olms. ——— (2007), “Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave,” Journal of Music Theory 51/1, 5–49. ——— (2011), “Review of Music in the Galant Style, by Robert Gjerdingen,” Eighteenth-Century Music 8/2, 307–348. Kaiser, Ulrich (2007), Die Notenbücher der Mozarts als Grundlage der Analyse von W.A. Mozarts Kompositionen 1761–1767, Kassel: Bärenreiter. Maichelbe[c]k, Franz Anton (1738), Die auf dem Clavier lehrende Caecilia [...], Augsburg: Lotter. Menke, Johannes (2012), “Die Familie der ‘cadenza doppia’,” Zeitschrift der Gesellschaft für Musiktheorie 9/1. Muffat, Georg (undated), Regulae concentuum partiturae, ms., Vienna, Minoritenkonvent, 1 B 7. ——— (1961), An Essay on Thoroughbass, ed. and transl. Hellmut Federhofer, Rome: American Institute of Musicology. ——— (1991), Regulae concentuum partiturae, ed. Bettina Hoffmann and Stefano Lorenzetti, Bologna and Rome: Associazione Cembalistica Bolognese. Nauß, Johann Xaver (1751), Gründlicher Unterricht den General-Baß recht zu lernen, Augsburg: Lotter. Plath, Wolfgang, ed. (1982), Wolfgang Amadeus Mozart. Neue Ausgabe sämtlicher Werke. Serie IX, Werkgruppe 27 (Klavierstücke), Bärenreiter: Kassel. Plath, Wolfgang and Wolfgang Rehm, eds. (1986), Wolfgang Amadeus Mozart. Neue Ausgabe sämtlicher Werke. Serie IX, Werkgruppe 25 (Klaviersonaten), Bärenreiter: Kassel. Poglietti, Alessandro (1676), Compendium oder Kurtzer Begriff und Einführung zur Musica, Sonderlich einem Organisten dienlich, ms., A-Kr, L. 146. Prinner, Johann J. (1677), Musicalischer Schlissl, ms., US-Wc ML95.P79.

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Reinhard, Leonhard (1744), Kurzer und deutlicher Unterricht von dem General-Bass, Augsburg: Lotter. Samber, Johann B. (1704), Manuductio ad organum, Salzburg: author. ——— (1707), Continuatio ad manuductionem, Salzburg: Mayr. Sanguinetti, Giorgio (2005), “Decline and Fall of the ‘Celeste Impero’: The Theory of Composition in Naples During the Ottocento,” Studi musicali 34, 451–502. ——— (2012), The Art of Partimento: History, Theory, and Practice, Oxford: Oxford University Press. Schmalzriedt, Siegfried (1974), “Kadenz,” in: Handwörterbuch der musikalischen Terminologie, ed. Hans-Heinrich Eggebrecht and Albrecht Riethmüller, Wiesbaden: Steiner. Schmid, Manfred Hermann (2006), Musik in Mozarts Salzburg. Ein Ort für sein Talent, Salzburg: Pustet. Schubert, Peter (1999), Modal Counterpoint: Renaissance Style, Oxford: Oxford University Press. Stella, Gaetano (2007), “Partimenti in the Age of Romanticism: Raimondi, Platania, and Boucheron,” Journal of Music Theory 51/1, 161–186. Sulyok, Imre (1977), W.A. Mozart: Praeludium (ohne Köchel-Nummer): Faksimile-Ausgabe, Budapest: Editio Musica Budapest. Tigrini, Oratio (1602), Il Compendio della musica, Venice: Amadino. Walther, Johann Gottfried (1732), Musikalisches Lexikon, Leipzig: Deer. Wittgenstein, Ludwig (1953), Philosophical Investigations, ed. G. E. M. Anscombe and R. Rhees, trans. G. E. M. Anscombe, Oxford: Blackwell. Zarlino, Gioseffo (1558), Le Istitutioni harmoniche, Venice: Franceschi.

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THE HALF CADENCE AND RELATED ANALYTIC FICTIONS Poundie Burstein

Introduction

I

n summarizing the modern definition of the term “cadence,” William Caplin aptly notes that it “essentially represents the structural end of broader harmonic, melodic, and phrase-structural processes.”1 Such a structural ending is most suitably expressed by an authentic cadence, where the closure is confirmed by a V–I resolution. In contrast, a sense of ending tends to be far less comfortably established by a half cadence, that is, one that concludes on a dominant harmony. After all, owing to its strong tendency to resolve to tonic, the appearance of a dominant chord at the end of a phrase tends to work against resolution and closure. Despite its harmonic volatility, however, most musicians acknowledge that at times a V can effect a sense of a half-cadential ending by being placed in a type of suspended animation, as it were, so as to yield what Leonard Meyer describes as a “parametric noncongruence” in which “a mobile, goal directed, harmonic process is temporarily stabilized by decisive rhythmic closure.”2 Such parametric noncongruence may be witnessed in Ex. 1a. In this passage, the tensions of the dominant harmony of mm. 31ff. are forcefully counterbalanced by various formal, rhythmic, and textural features that stabilize it so as to suggest an ending. For instance, this dominant appears at the termination not only of a sentential phrase, but also of a transition section, a part of the form for which a conclusion on V is conventional and therefore expected. The subsequent passage that starts in m. 39 so plainly establishes what sounds like a beginning—firmly delineated by the entrance of a new melody, hypermeasure, rhythmic pace, texture, and dynamic level—that this in turn suggests that what immediately precedes is to be understood as an ending. The 8-bar standing-on-V in mm. 31–38 and the stark caesura that follows further buttress the impression that the dominant that enters in m. 31 serves as a stable endpoint. 1. 2.

Caplin, Classical Form (1998), 43. Meyer, Explaining Music (1973), 85.

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Example 1a: Beethoven, Sonata for Cello and Piano in F, op. 5 No. 2/i, mm. 64–73

Because it is so clearly heralded as an ending, the motion in mm. 38–39 from V of F directly to an A-flat chord does not come across as an odd tonal regression, as more likely would have been the case had these harmonies appeared mid-phrase. Rather, the V of F wraps up one harmonic process, and the A-flat chord begins another. In other words, there is no harmonic progression between these two sonorities, but merely a harmonic succession, separated by a voice-leading disjuncture between the two phrases. Indeed, unless it appears at the very end of a composition, to label a V as part of a half cadence necessarily implies that its voice leading is to be regarded as essentially disconnected from the harmony that immediately follows it on its own structural level.3 This is so even if the half-cadential dominant is followed immediately by a phrase that begins on the tonic, as is most often the case. To be sure, it is hard not to notice at least some sense of resolution between a half-cadential dominant and the tonic that starts the next phrase. Many times this resolution is even promoted by a brief passage that links these two harmonies, as in mm. 8–9 of Ex. 1b. Yet by definition this interphrase connection must take place on a level closer to the surface: if its voice leading were not in some deeper sense separated from what directly follows it, a dominant could not be regarded as ending a harmonic process, and therefore it could not be understood as establishing a half cadence.4 Consequently, deciding whether to consider a V as half-cadential on the one hand, or as part of a full cadence or mid-phrase V–I motion on the other, often comes down to determining whether the connection

3.

4.

I say “on its own structural level” because something properly understood as a half cadence can also be followed by a prolongation of V (such as in the form of a standing-on-V or a new section in the key of V) or by a post-cadential bridge passage. In such instances the voice leading of the half-cadential dominant might be connected to the ensuing dominant or other harmonies that arise on later structural levels, but still be detached from a new harmony that succeeds it on its own structural level. As Caplin describes it, whereas in an authentic cadence the penultimate dominant “actually progresses to tonic,” with a half cadence “the dominant becomes the goal harmony […] a subsequent resolution to tonic does not belong to the progression proper but occurs at the beginning of the next harmonic progression”; see Caplin, Classical Form (1998), 100.

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between a dominant and the tonic that directly ensues is best characterized as an essential one or a surface one.

Example 1b: Beethoven, Sonata for Piano in C minor, op. 10 No. 1/ii, mm. 1–9

Admittedly, in many situations the difference between an “essential” voice-leading connection versus a “surface” one can be quite nebulous, relying on a distinction that is more conceptual than perceptible. This is especially so when the various melodic, textural, rhythmic, or formal signals that help group the phrases are themselves ambiguous or at odds with one another. In such instances, a dominant may seem to firmly conclude a harmonic progression in certain respects, and yet seem to strongly resolve to the following tonic in other respects, so that classifying the connection between the adjacent V and I harmonies as essential or not may rely on a rough approximation at best. Even when a phrase may be reasonably labeled as concluding with a half cadence, ambiguities or conflicts might nonetheless severely cloud the sense of harmonic closure. Such is the case with Ex. 1c. Caplin categorizes the midpoint of this passage as a half cadence, and no doubt most musicians would agree with this labeling (as would I).5 Yet surely this half cadence asserts a structural ending far more tenuously than does the half cadence of a passage such as is excerpted in Ex. 1a. For instance, the melody in the piano of Ex. 1c arguably is better characterized as abruptly “stopping” in the middle of m. 4 rather than as establishing a true end. What is more, the opening phrases of the violin and of the piano’s left hand seem to halt only at the third quarter of m. 4, upon reaching the tonic, rather than concluding on V (note in particular the dynamics, which change only on the last quarter of this measure, as well as the slur in the violin part). As a result, the dominant harmony that appears at the outset of m. 4 seems to sturdily resolve to the tonic that arrives on the third quarter of this measure.

5.

Ibid., 266 (n. 7).

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Example 1c: Mozart, Sonata for Violin and Piano in A, K. 526/iii, mm. 1–8

Not only is the sense that the V of m. 4 marks the end of melodic and harmonic processes somewhat murky here, but its status as an ending of a formal process is likewise compromised. This dominant unmistakably appears in the middle of a phrase-structural process, that is, in the middle of the period that embraces mm. 1–8. Naturally, it is quite possible for something to lie in the middle of a large formal unit and yet also at the end of a smaller, embedded one. But the same could be said of m. 4 of Ex. 1b, too, which also undoubtedly establishes the end of a melodic, harmonic, and phrasestructural process of sorts. Since it seems to come at the end merely of a “presentation phrase,” however, rather than at the end of a complete sentence, most musicians nowadays would not label m. 4 of Ex. 1b as a half cadence.6 To be sure, it does make sense for a classification scheme to deny cadential status to a dominant that appears at the conclusion of a presentation phrase, for such a V surely establishes a weaker formal ending than one that appears at the end of an antecedent. On the other hand, a V that appears at the end of an antecedent similarly establishes a weaker formal ending than one that appears at the conclusion of a transition, which in turn is weaker than one found at the end of an entire composition. That a V appearing at the end of an antecedent makes the cutoff for what may be labeled as a half cadence, while one appearing at the end of a presentation phrase does not, owes largely to 6.

In using the term “phrase” to describe a sentential presentation, I follow William Caplin; see for instance, Classical Form (1998), 256 (see also Caplin, “The Classical Cadence” [2004], 59). Many others would label a sentential presentation as a subphrase, saving the term “phrase” for something on the level of a complete sentence and the like. Yet however one labels it, most musicians today would unlikely view a presentation as a sufficiently substantial segment so as to allow its ending to be regarded as a bona fide cadence, although (as with many features surrounding cadence terminology), there is hardly universal consensus regarding this matter, as is noted in Caplin, “The Classical Cadence” (2004).

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modern terminological conventions. It is not difficult to imagine other possible cutoff points, however. Indeed, as depicted in Table 1 (and as will be discussed in more detail below) some theorists from earlier generations proposed different—albeit by no means illogical—labelings for these different levels of formal endings. Table 1: Chart comparing labeling of classifications of phrase-structural endings on V

Phrase-structural process … presentation concluding on V appears phrase. at end of ...

… antecedent.

Typical modern classification:

not half cadence

half cadence

H.C. Koch’s 1802 classification:

not half cadence

Typical 18th C. classification:

not half cadence

…transition section.

…movement or large section.

half cadence half cadence

Despite the mitigating factors noted above, surely the V chord of m. 4 in Ex. 1c is highlighted as a type of endpoint, as is underscored by the hypermeter, the sharp break in the piano’s melody, and the thematic layout (which is clearly in dialog with a period construction). As such, the sense of resolution that accompanies the dominant-totonic motion in m. 4 is far weaker than what is found at the point of the authentic cadence in mm. 7–8. Accordingly, it is not unreasonable to regard the V in m. 4 as disconnected from the I that immediately follows it—at least on the deeper levels— and therefore it does seem fair to categorize the midpoint of Ex. 1c as a half cadence. As always, placing different things within the same general classification does not imply that they are structurally equivalent. A risk with almost any music analytic label is that it might be understood in too concrete a fashion—as though pointing to a feature inherent in the music itself—so that borderline members of the category are regarded to share too closely the qualities of the category’s ideal type. Such attitudes can be particularly problematic when dealing with the concept of the half cadence, which even in its ideal manifestations is to some extent an artificial and contingent notion. To label something as a half cadence never suggests that the closure that attends it is absolute, and as comparing the excerpts in Exx. 1a–c bears out, the closure associated with things that are typically designated as half cadences may vary widely. Deciding whether a dominant harmony that appears towards the conclusion of a phrase should be regarded as establishing a structural phrase endpoint depends upon weighing the impact of a various features that might conflict with one another. These include features of texture, hypermeter, surface rhythm, and melody, which in combination might seem either to mark a dominant harmony as something that

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can be understood as a structural conclusion of a phrase, or else undercut such an impression. If the claim that a dominant serves as a phrase endpoint is supported by elements that are more numerous and convincing than those that suggest otherwise, then the V may fairly be classified as half-cadential; if the opposite is the case, then the dominant will be better understood to form part of an authentic cadence or a mid-phrase V–I motion. If the factors that support or contradict the sense of a phrase ending seem more or less equally balanced, on the other hand, the situation might resist ready characterization by a single cadential label—or, for that matter, by a single formal parsing or voice-leading depiction.

The development of the half cadence concept The degree of artificiality that accompanies the notion of a dominant-harmony phrase ending might easily be overlooked nowadays, for the concept of the half cadence has become so engrained in current music analytic approaches and theory pedagogy that to many it might seem to be a natural or obvious notion. Earlier theorists, on the other hand, tended to be more sensitive to the contradictions allied with the concept of a dominant-harmony phrase ending. Accordingly, they often treated this idea somewhat tentatively, at times referring to a large-scale ending on the dominant harmony as a “socalled half cadence” or a “so genannte Halbcadenz.”7 The proposal that a half cadence could arise in the middle of a large section was particularly slow to gain acceptance. Tracing the early development of this concept encourages reconsideration of certain modern commonplaces surrounding this idea that have come to be taken for granted. Assessing earlier attitudes towards the half cadence admittedly can be tricky, however, owing to the wide variety of terms used to describe phrase endings on dominant harmonies. These include words such as imperfect cadence, semicadence, half close, cadence minore, unvollkommener Tonschluss, Halbschluss, Halbkadenz, cadence imparfaite, Aenderungsabsatz, Quintabsatz, dissecta desiderans, among many others.8 Caution must be taken in evaluating these terms—including the early use of the term “half cadence” itself—since they often were defined in ways that depart considerably from the modern concept of the half cadence. For instance, some earlier theorists grouped all melodically unstable cadences within the same general category, so that a single label would be used to describe what modern terminology would differentiate as

7. 8.

See, for instance, Agricola, Art of Singing (1757/1995), 138; Koch, Versuch III (1793), 335 §121 (= Baker, Introductory Essay [1983], 211); and Anonymous, “Recension” (1801–2), 7. See Bergé et al., Compendium (forthcoming).

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either a half cadence or an imperfect authentic cadence.9 Other theorists used a single term for any cadence in which the bass moves up a fifth or down a fourth, thereby not plainly distinguishing a half cadence from what now would be referred to as a plagal cadence.10 Furthermore, several theorists seem to use “half cadence” or a similar term to describe a purely abstract harmonic configuration or progression that ends on a dominant, not necessarily one that appears at the conclusion of a phrase.11 Nevertheless, from the context of their discussions and accompanying examples, it is apparent that many early theorists described situations that modern readers would recognize as involving half cadences. Such is the case within certain discussions from the 1600’s of irregular endings on tones other than the modal finalis.12 For instance, Johann Andreas Herbst (1643) explains that irregular endings occur “when the voices do not close in their natural place (Clave), but rather in another Clausula, namely the Minus principali.”13 To demonstrate this, Herbst provides two examples: although one of these examples would now be understood to involve an authentic cadence in the key of V, the other ends with what would now be categorized as a half cadence.14 Theorists from this century further observed that such irregular endings could produce an effect of incompletion and expectation. Specifically, it was underlined that these endings might conclude not merely on a tone other than the finalis, but indeed could stop on what seems to be a penultimate note or harmony. For instance, in discussing one type of a clausula that he classifies as imperfecta or unvollkommene, Conradus Matthaei (1652) presents an example that would now be labeled as a half cadence, noting that such an “imperfect clausula […] remain[s] on the penult.”15 Likewise, providing two examples that each conclude with a dominant harmony, La Voye-Mignot (1666) remarks that “the ‘suspenseful cadence’ (which involves the upper voices as 9.

10.

11. 12.

13. 14. 15.

See, for instance, Reicha, Treatise (1814), 15 and 124; see also his comments on p. 15 (n. 27) (referring to his example E2) that the melody note of a half cadence could be on the dominant, leading tone, supertonic, or mediant. Elsewhere, Reicha uses the term “demi-cadence” in abstract harmonic terms to describe harmonic motions to the dominant (see his Cours de composition [1816], 13ff.). The practice of discussing half cadences alternately in abstract harmonic terms and in formal/melodic terms—with possible contradictory outcomes—may be found in works of other theorists from around this time as well. See, for instance, Muffat, Essay (1961), 104 and 116–120; Gugl, Fundamenta (1777), 23; and discussions in Burns, “Modal Identity” (1994), 49–52; and Lester, Compositional Theory (1994), 116. Many of those theorists of the eighteenth century who do specify that half cadences must end on the dominant harmony show concern for how the half-cadential V is approached to a far greater extent than theorists tend to do nowadays; see, for instance, Wiedeburg, Der sich selbst informirende Clavier-Spieler (1775), 269–276. See, for instance, Holden, “A Rational System” (1770), 72ff.; discussion in Lester, “Rameau” (2002), 762f.; and n. 9 above. Discussions by earlier theorists of such irregular endings are examined at length in Burns, “Modal Identity” (1994), 44–55; Meier, The Modes of Classical Polyphony (1988), 330ff., and Caleb Mutch, “A History of the Cadence and Its Precedents” (forthcoming). Herbst, Musicae poëtica (1643), 86; translation from Burns, “Modal Identity” (1994), 46. Ibid. Matthaei, Kurtzer Bericht I (1652), 2; translation from Mutch, “A History of the Cadence and Its Precedents” (forthcoming).

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well as the bass) takes place when instead of ascending or descending to the note that marks the perfect cadence [. . .] there is a rest on the penultimate note, & this type of cadence is found at the end of the first line of a couplet, or when the middle of some piece is designed so that all the parts come to a brief moment of silence before beginning anew.”16 As La Voye-Mignot’s description suggests, such a cadence is most appropriately found at the end of a part within a composition that could be answered by a more complete cadence at the conclusion of a subsequent part.17 Prior to the eighteenth century, discussions of irregular endings seemed to focus on those that conclude firmly demarcated sections. It was not until the 1700’s that explicit and extended consideration was given to the more daring idea that a V arising in the middle of a section could establish a formal ending of sorts. This new attitude likely represented a reaction to the increasingly important role of mid-section rhetorical articulations in music of the era. An interest in mid-section endings is particularly evident in the writings of Germanic theorists of the time, a number of whom devoted much attention to describing how resting points of varying degrees of intensity could help shape the flow and create groupings within larger sections.18 These discussions typically focused on punctuations in the main melodic voice, which were often—although not necessarily—supported by simultaneous punctuations in other voices. Firm resting points were regarded as similar to what is expressed by the grammatical punctuation mark of the period; these strong punctuations are

16. “La Cadence attendente (se pratiquent tant aux parties superieures qu’en la Basse) se fait lors qu’au lieu de monter ou de descendre a la notte qui marque la Cadence parfaite [selon les reigles cy dessus] l’on demeure sur la penultiesme, & l’on se sert de cette sorte de Cadence à la fin des premiers couplets, ou lors qu’au milieu de quelque piece l’on a dessein que les parties fassent toutes ensemble un silence pour bien-tost apres recommencer”; from La Voye-Mignot, Traité (1666), 76 (translation mine). See also discussion in Wolfgang Caspar Printz, Phrynis Mitilenæus (1676–1677) of what Printz labels as “dissectae desiderans,” a type of cadence that concludes on what now would be understood as a dominant harmony. As Printz’s label suggests, with the dissectae desiderans the listener “desires” a final chord (i.e., the tonic) has been “dissected” from the cadence; Printz’s discussion of cadences is examined at length in Mutch, “A History of the Cadence and Its Precedents” (forthcoming). 17. See also Herbst, Musica Poëtica (1643), where the author provides an abstract example in which the “Prima pars” concludes on a dominant harmony that is answered at the end of the “Secunda pars” with a cadence on the tonic; this example by Herbst is discussed in Burns, “Modal Identity” (1994), 50f. 18. Most notable among these are Koch, Versuch II and III (1787 and 1793; translated in part in Baker, Introductory Essay [1983]); Riepel, Grundregeln (1755); and Marpurg, Kritische Briefe (1763); see discussion of these and other writers of the time in Vial, The Art of Musical Phrasing (2008). In the following discussion, I cite most frequently the writings of Koch, arguably those most thoroughgoing and articulate of these eighteenth-century theorists. One should not assume uniformity in approach or terminology among these theorists, however: in the 1700’s—much as now—theorists departed from one another regarding many details. Indeed, even around that time it was openly acknowledged that there was no consensus regarding the terminology and concepts surrounding cadences and other phrase demarcations (see, for instance, comments in Wolf, Musikalisches Lexikon [1792], 53, as well as the comment in Urban, “Review” [1813], 461, that “[s]carcely any two writers agree on defining cadences”). The variants regarding conceptual and terminological nuances notwithstanding, there was widespread acknowledgement of the core ideas discussed here regarding the different degrees of intensity that could be accorded to musical resting points.

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typically found at the end of large sections, or Perioden. It was also noted that musical punctuations could be of milder sorts as well, analogous to commas, colons, or semi-colons in language. These slighter melodic punctuations were not considered full-fledged “endpoints” so much as fleeting moments of repose. As a result, there was no contradiction in the observation that such relatively gentle melodic resting points arising within the middle of a section could be—and often are—supported by V chords. A short segment of about two measures, along with the punctuation that delineates its endpoint, was referred to as an Einschnitt or a schwebende[r] Absatz, which may be translated roughly as a “notch” or an “incomplete segment.” An Einschnitt thus is similar to what now would likely be regarded as a subphrase or a subphrase ending. A longer segment, usually of about four bars and containing both a “subject” and a “predicate,” forms what was known as an Absatz, a term that was also used to describe the endpoint of this segment. The term Absatz could be translated as an “indentation” or a “complete segment”; it is more or less similar to what would now be regarded either as a mid-section phrase or as a cadence.19 The melodic point of repose that delineates an Absatz could either be explicit (as in Ex. 2a) or partly implied (as in Ex. 2b).20

Example 2: Examples from Heinrich Christoph Koch, Versuch II (1787): (a) Two phrases, from §97; (b) two phrases connected by linking passage, from §97; (c) single phrase disrupted by a rhetorical pause, from §81

In each case, the melodic segments that result from the Absatz groupings need to form complete musical statements. Thus, for instance, despite the sharp break in the second 19. A phrase or cadence that appears (or is of the type that could appear) at the end of a Periode was known as a Schlußsatz. 20. Koch makes it clear that he regards both these passages to contain a resting point in m. 4. However, concerning the passage cited in Ex. 2b, he points out that the second phrase “is connected more closely with the preceding one” as a result of the “filling in the space”; see Koch, Versuch II (1787), 411f. §97 (= Baker, Introductory Essay [1983], 34).

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measure, there is but a single Absatz in Ex. 2c, since the segments that both precede and succeed the caesura are too short and insubstantial to be regarded as complete.21 When its final melodic note is supported by a dominant harmony, an Absatz was labeled more specifically as either an Aenderungsabsatz or a Quintabsatz. Thus a Quintabsatz approximates to what now would be regarded either as a half cadence, or else as a phrase that ends with a half cadence. There was no expectation for a Quintabsatz—or any Absatz, for that matter—to impart a definitive sense of closure or stability: it merely need establish a relative degree of restfulness (Grad der Ruhe) sufficient to demarcate a subsection. Quintabsätze thus tended to be distinguished from genuine half cadences (Halbkadenzen): for many theorists of this time, only in the unusual situation in which V appears at the end of a movement or of a Periode would it be regarded as marking a half cadence proper (see final row of Table 1 above).22 It was recognized that Quintabsätze could convey varying degrees of repose. This is particularly evident in a discussion in the 1787 volume of Heinrich Christoph Koch’s Versuch, where—in his discussion of the passage cited here in Ex. 3—the author permits an exception to the rule forbidding two Quintabsätze in a row. Koch perhaps allows this exception in tacit reaction to the different senses of restfulness imparted by the two Quintabsätze cited here—the first of which appears at the end of what today would be labeled as a transition section, and the second of which lies in the middle of what today would be regarded as a second theme, at the end of an antecedent. Koch thereby arguably sensed that the Quintabsatz directly preceding a medial caesura falls within a somewhat different category than other mid-section Quintabsätze.23 In his dictionary of 1802, Koch more explicitly distinguishes Quintabsätze associated with medial caesuras by suggesting that they could be labeled as actual Halbcadenzen.24 By thus allowing a mid-section Quintabsatz to be regarded as a bona fide half cadence, Koch was most likely reacting to the powerfully reinforced medial caesuras character-

21. As Koch notes; “resting points are determined not only by being followed by rests,” but also by “the completeness or incompleteness of the sections which thereby arise”; see Koch, Versuch II (1787), 465, (footnote to §81; = Baker, Introductory Essay [1983], 4). 22. See, for instance, Koch, Versuch II (1787), 414 §100; 443 §100, and III (1793), 335 §100 (= Baker, Introductory Essay [1983], 36, 49, and 211). Although theorists at the time did occasionally note the analogies between true cadences and endings of mid-section divisions (see, for instance, Marpurg, Kritische Briefe [1763], 36; and Koch, Musikalisches Lexikon [1802], 1212), they nonetheless often emphasized that the end of a large section was the ideal position for formal cadences, including half cadences. In this regard it should be underlined, however, that the eighteenth-century concept of the formal half cadence should not be confused with the eighteenth-century concept of the half cadence in an abstract harmonic sense, which could appear anywhere in a composition, including mid-phrase (see n. 9 and n. 11 above). 23. Koch, Versuch III (1793), 364f. §141 (= Baker, Introductory Essay [1983], 221f.). Koch mistakenly cites mm. 5–10 of his example (not shown in my Ex. 3) as the first Quintabsatz, but this surely is a careless error, for it produces nonsensical results (as in noted in Baker, Introductory Essay [1983], 221 [n. 42]). He no doubt meant to cite the Quintabsatz in V of mm. 11–22, the end of which is shown in Ex. 3. 24. See Koch, Musikalisches Lexikon (1802), 18f.

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istic of late eighteenth-century music (such as seen above in Ex. 1a). In other words, since the demarcations at points of medial caesuras often do impart a strong sense of closure that is akin to what might be found at the end of a Periode, by 1802 Koch decided it was fair to label them not merely as Quintabätze, but rather as full-fledged half cadences (see middle row of Table 1 above).

Example 3: Example from Koch, Versuch III (1793), §152

This gradual loosening of terminology continued with subsequent generations of theorists, as an increasing number used the term “half cadence” to describe all types of mid-section phrase endings on V—not merely at points of medial caesuras, but anywhere that they might appear. By the mid-nineteenth century almost everything once labeled as a Quintabsatz eventually became regarded as an actual half cadence, and this practice continues today.25 The subtle differences between the various types of endings on V are thereby underplayed by this looser, modern terminology, which tends to obscure the distinctions between the levels of repose underlined by many eighteenth-century writers. Sometimes such mid-section phrase endings are indeed reminiscent of what might found at the end of a large section. Such is the case, for instance, with the close of the first phrase of Beethoven’s Sonata for Piano in A, op. 2 No. 2/i (mm. 17–21). In other instances, however, such an ending seems more like a subtle articulation of the musical surface that only hints at a sense of closure, as in Ex. 1c above. The broader modern concept of a half cadence embraces a wide variety of levels of closure, which in turn can give rise to multiple types of analytic, hermeneutic, and performance implications. As such, care should be taken not to let the large scope of the modern use of the term lure us into overlooking the more nuanced distinctions between the various levels of dominant-harmony phrase endings, such as were well recognized by earlier generations of music theorists.

25. Such loosening was anticipated even by Koch: in describing a rondo-type theme (analogous to what now would be called an antecedent-consequent period) in the 1802 Musikalisches Lexikon, 1271, he waivers regarding how to label the dominant-harmony ending that closes the first half, noting that “das erste seinen Abschnitt auf der Grundlage des Dreyklanges der Dominante, oder einen so genannten Quintabsatz oder eine Halbcadenz macht.”

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The surface appearance of the half-cadential V In order to rein in the unwieldy broadness of the modern notion of the half cadence, it has been tempting to try to isolate elements that must be present in order to establish its appropriate degree of closure. In recent years various theorists have endeavored to do this by focusing on the surface harmonic makeup of the half-cadential V. Specifically, they have demanded that what is labeled as a half cadence must involve a dominant triad in root position, thereby excluding the possibility of half cadences on other types of dominant harmonies. Because of its prevalence in modern music theory discourse, and because of the significance of this attitude for the concept of the half cadence in general, this attempt to formalize the closure associated with the half cadence bears special scrutiny. Admittedly, a phrase ending that is marked by a dominant that is not a root-position triad is less likely to establish a convincing resting point; this is particularly true in eighteenth-century music. The presence of a root-position V triad at a half cadence surely represents only an ideal, however. For instance, most musicians likely would agree with the labelings of the half cadences seen in Ex. 4, where the V triads are obscured on the surface of the music. In each of these passages, a passing tone arises in the bass by the time an appoggiatura in the melody resolves. As a result, a rootposition V triad never literally materializes, so that at no point is there a complete sense of harmonic repose. Nonetheless, owing to the clear melodic, rhythmic, and textural signals, each of these phrase endings suggests a relative degree of stability, one that is akin to what is found in other things that typically are categorized as half cadences.

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Example 4: Half cadences in which a root-position V triad does not literally appear on the surface of the music: (a) Georg Benda, “Selbst die glücklichste der Ehen,” from Walder (cited in Koch, Versuch III [1793], §86); (b) Mozart, Sonata for Violin and Piano in F Major, K. 547/iii, Var. 2, mm. 3–5; (c) J. C. Bach, Sonata in E-flat/iii, mm. 7–9 (cf. Mozart K. 107)

Because in these cases one can easily claim that a root-position V triad is implied, even if not literally present, the cadential labelings in Ex. 4 seem relatively uncontroversial. On the other hand, in recent years some scholars have taken a more extreme view regarding similar situations involving V triads in inversion or V7’s in root-position or inversion. Specifically, it has been argued that by definition the appearance of an inverted V or V7 at the onset of a phrase ending automatically rules out the possibility of a half cadence, regardless of whatever melodic, rhythmic, and formal features might otherwise support such a reading. This stance has been voiced most staunchly by William Caplin, and a number of others have followed him in this regard.26 As Caplin explains, “if the final dominant is inverted or else contains a dominant seventh [. . .] the dominant would then be too unstable to function as a cadential goal.”27 Yet instability is hardly foreign to the half cadence. On the contrary, half cadences are intrinsically unstable. Various features might add to this instability, including the lack of a caesura, a volatile texture, an acceleration, or the presence of an inverted V or V7. In certain situations, these destabilizing features might well argue against the labeling of a half cadence—that is, unless these features are sufficiently counterbalanced by other elements that more solidly assert the dominant harmony’s closing role. The question here is whether just one of these destabilizing elements—specifically,

26. Caplin, Classical Form (1998), 75–77, 79 and “The Classical Cadence” (2004), 70. Among those who have explicitly followed him in this regard are Schmalfeldt, Towards a Reconciliation (1991); Hepokoski and Darcy, Elements (2006), 24; Richards, Viennese Classicism (2010), 205; and Phipps, Schumann’s Piano Quartet (2010). 27. Caplin, Classical Form (1998), 79. Caplin’s attitude in this regard is reflected in many of his analyses; see, for instance, his readings (on pp. 77, 79, and 274 [n. 33]) of the clear phrase endings on V in Beethoven’s op. 49/ii, m. 12, and Mozart’s K. 498/i, m. 24. It should be noted that Caplin regards the defining harmony of the half cadence to be the one that appears at its initiation, and he thus does allow a half cadence to be established by a root-position V triad that is followed by an inverted V or V7 that prolongs it.

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the presence of an inverted V or V7—should by itself prevent the labeling of a phrase ending as a half cadence, regardless of the strength of other contextual features. The a priori determination that phrase endings on inverted V or V7’s cannot be regarded as half cadences departs from a theoretical tradition that stretches back to the eighteenth century. Although almost all writers do emphasize that a half cadence most normally is established by a root-position dominant triad, since the mid-1700s several of them nonetheless have openly accepted the possibility that a half cadence could be established by an inverted V or V7. For instance, F. W. Marpurg (1763) explicitly states that an Absatz can conclude over a dissonant harmony, and he provides an example of one that finishes with an inverted V7.28 Likewise, after noting that a phrase ending on I7 or V7 would most likely lack the stability expected of a cadence, the entry in J. G. Sulzer (1771–1774) nonetheless begrudgingly acknowledges that in special cases involving a fermata a Halbkadenz could be established with a V7.29 Similarly, William Jones (1784) provides many examples of what he labels as half cadences brought about by V7’s; J. P. Kirnberger (1774–1779) notes that the dominant of a half cadence can appear in inversion; J. C. B. Kessel (1791) shows examples of half cadences with inverted V’s; and Koch (1787 and 1802) raises the possibility of a V7 marking the end of a Quintabsatz or even of a movement-ending Halbkadenz.30 To be sure, as noted above, what eighteenthcentury musicians refer to as Quintabsätze, half cadences, and the like does not necessarily match what would be regarded as half cadences today. Nevertheless, the contexts, accompanying examples, or both make it clear that many of these discussions of phrase endings on inverted V or V7’s do indeed conform to the modern concept of the half cadence. And although subsequent generations of commentators continued to encourage the use of a root-position V triad at a half cadence, many of them nevertheless mention the possibility (either explicitly or implicitly through an analytic example) of a half cadence established by an inverted V or V7.31

28. Marpurg, Kritische Briefe (1763), 35. 29. Sulzer, Schöne Künste (1771–1774), 435f. 30. See Jones, A Treatise (1784), 36; Kessel, Unterricht im Generalbasse (1791), 72; and Kirnberger, Die Kunst des reinen Satzes (1771–1779), 177 (see also 118). Koch forthrightly states that a V7 could establish a half cadence in his Musikalisches Lexikon (1802), 716f.; see also his discussions in Koch, Versuch III (1793), 307 §101 (= Baker, Introductory Essay [1983], 199) regarding the end of a symphonic introduction, and his implied reading of a Quintabsatz ending in m. 110 of Joseph Haydn’s Symphony No. 42/ii, on an inverted dominant seventh (Versuch III [1793], 206 §63; = Baker, Introductory Essay [1983], 154). Incidentally, there is also a clear Quintabsatz on V7 in m. 77 of this same Haydn movement, which serves as one of the main examples in Koch’s treatise. 31. See, for instance, Crotch, Elements of Musical Composition (1812), 41; Czerny, Pianoforte-Schule (1839), 5f.; Marx, Musical Form (1997 [1856 and 1886]), 75 (in regards to what Marx describes as “an expedient in certain cases”), see also 123 (regarding a half cadence involving a diminished seventh chord) and 113; Goetschius, Exercises (1900), 56 (tacitly contradicting the more rigid strictures seen in Goetschius and Faisst, Musical Composition [1889], 122; see also Goetschius, Homophonic Forms [1898], 101); Schenker, Harmony (1906/1954), 220 and Tonwille (1922/2004), 55f.; and Berry, Form in Music (1966), 20.

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The notion that an inverted V or V7 could establish a half cadence is amply reflected in the repertoire. Such half cadences are especially ubiquitous in the Romantic era. Although far less common—and thus more notable—in music of the mid-1700s through the first quarter of the nineteenth century, plenty of clear instances nonetheless may found in the music of this time. Such half cadences are found not only in works of various genres by Joseph Haydn, W. A. Mozart, and Beethoven, but by several of their contemporaries, such as Michael Haydn, C. P. E. Bach, W. Pichl, C. G. Neefe, and D. Alberti. A small sampling of such half cadences by composers of this era is presented in Ex. 5 and cited in Table 2.32 That an inverted V or V7 can mark a phrase ending in a manner analogous to a root-position V is suggested with particular clarity by the pairs of passages compared in Ex. 6, in each of which a phrase that ends on a root-position V triad in one appearance is substituted for one that concludes on an inverted V or V7 at an analogous spot of the same composition or of an arrangement of it.33 The phrase endings cited in Exx. 5 and 6 do not seem to be mere rhetorical pauses, but rather each appear to firmly mark a syntactically proper end of a melodic, phrase-structural, and even a harmonic process in the same manner as other things that are typically labeled as half cadences.

32. I cite a surfeit of examples here to counter to persistent “urban myth” that half cadences on inverted V or V7’s are not found in music from the mid-eighteenth through the first quarter of the nineteenth century: as these amply demonstrate, such half cadence were by no means unknown in music of this era. In each case, following Caplin, I take the cadential harmony of the half cadence at the initial arrival of V (according to Caplin’s guidelines explained in n. 27 above). That Joseph Haydn, Wolfgang Amadeus Mozart, and Beethoven are cited most heavily in Ex. 6 and in the somewhat randomly chosen samples found in Table 2 is largely because their works are easier to access, and thus their large representation here should not be taken to suggest that such endings are more common in their music than in the works of their contemporaries. (On the other hand, I cite none of Franz Schubert’s works in this sample simply because such examples in his works are too easy to find, and thus might water down this list.) As with any such massive listings, alternate readings for many of these citations are certainly possible. Nonetheless, I feel that any reasonable reading of the passages cited here would concur that in a majority of them the dominant harmonies assert melodic, harmonic, and phrase structural endings as or more convincingly than in many scenarios involving root-position V triads that are typically and uncontroversially labeled as half cadences. 33. Naturally, it is possible for parallel passages to function differently, especially if a variation is involved. But can one fairly claim that the phrase endings on inverted V or V7’s cited in Ex. 6 sound so much less stable than their counterparts on root-position V’s so as to warrant an entirely different label? See also Koch, Versuch II (1787), 417f. §101 (= Baker, Introductory Essay [1983], 37f.), where immediately after insisting that the final harmony of an Absatz must be in root position, he notes that “now and then” exceptions arise in which the phrase ends over a “six-chord,” thereby suggesting that the rootposition triad—though not literally present—is nonetheless implied in such cases. Compare also Koch’s chorale settings in Koch, Versuch I (1782), 360 and 364 (§§244 and 263) in which a Quintabsatz on a root-position V is exchanged for one on a V in first inversion. One could claim similarly that a root-position V triad is implied at any of the spots labeled as half cadences in Exx. 5 or 6, in the sense that these dominants are located at places where root-position V’s would more typically be found.

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Table 2: Various examples of half cadences demarcated by inverted V or V7’s in works from around 1750–1825 (bar numbers are in parentheses)

J. Haydn: Piano Sonatas 34/i (78); 49/i (24, 194); 50/ii (29); 52/i (77); 52/iii (29). Variations XVII:2 [manuscript] Var. 5 (4); Var. 16 (4); [printed] Var. 8 (4). Violin Duos (attrib.) op. 99/1/i (16, 20, 32, 91, 96, 170, 174; 182, 194 cf. J. Haydn’s op. 33/4/iv); op. 99/3 (Theme, bar 4; Var. 2, bar 4). String Quartets op. 17/1/i (bars 62, 75); op. 17/1/iv (137); op. 17/2/iv (33, 124); op. 17/5/ii (4, 16, 53); op. 20/3/ii (3, 35); op. 20/3/iv (57, 69); op. 20/4/i (214); op. 33/5/iv (270); op. 50/2/iv (17, 153); op. 50/5/iv (110), op. 54/1/iv (4, 17, 22, 62, 69, 92, 97, 122, 155, 160); op. 54/1/ii (13, 51); op. 64/1/i (93); op. 71/2/ii (15) Piano Trios 29/i (154). Symphonies No. 33/iv (75); 35/i (38); 42/ii (77, 110); 42/iv (86); 47/ii (150); 49/i (5); 59/i (87); 93/i (20); 94/i (13); 94/ii (80, 118); 96/iv (199); 104/ii (4, 20, 77, 85). Missa in Tempora Belli Kyrie (63). W. A. Mozart: Violin Sonatas K. 296/ii (4, 38); K. 379/i (61, 73, 129, 145); K. 526/ iii (362); 547/i (4, 35, 60); K. 547/iii, Var. 5 (4); Violin/Piano K. 359/Var. 8 (9); Piano Trios K. 496/i (108); K. 498/i (24, 54, 97); K. 542/i (49); String Quartets K. 80/iv (4, 28, 48); K. 168/iii (20); K. 171/i (14); K. 173/iv (61); K. 387/i (66); K. 458/iv (4, 12, 102, 210); K. 464/Trio (4, 28); K. 499/iv (34); String Quintet K. 406/i (128); Symphonies K. 43/iii (12); K. 128/iii (4, 68, 93); K. 183/i (12, 128); K. 200/iv (181); Piano Concertos K. 595/i, cadenza (9); K. 595/iii (180); Il sogno di Scipione Act I (202); La Clemenza di Tito/overture (28); Don Giovanni, “Dalla sua pace” (35). L. van Beethoven: Piano Sonatas opp. 10/1/iv (54); 10/3/iv (44, 53); 13/iii (58); 28/ iii (47); 49/1/ii (12, 92); 57/i (16); 54/i (102); Sonatina Anh. 5/2/i (4); Bagatelles op. 33/6 (12, 50); 119/5 (4); 119/9 (4, 16); Rondo op. 51/2 (149); Polonaise (137); Menuetto WoO 10/3 (4); WoO 10/6 (4); Violin Sonata op. 12/1/iii (51); Cello Sonata op. 69/i (41, 54, 178, 191); op. 69/ii (8. 17, 22, 30, 115; 123); Piano and Flute or Violin WoO 41 (4, 63, 121); op. 107/1 (22); String Quartet op. 18/1/i (60, 221); op. 18/2/ii (61); op. 18/2 iv (245); Duos WoO 27/2/i (4, 59, 84); WoO 27/2/ii (4); WoO 27/3/ii Var. I (12) Var. IV (12); Piano Trios op. 1/3/iv (7); op. 70/2/i (8); Coriolanus Overture (46); Symphonies op. 36/i (170); op. 36/iv (334); op. 93/iii (60); op. 125/iv (pt. 1: 95, 119; pt. 2: 8, 64; pt. 3: 68); Concerto op. 58/iii (125, 399); op. 73/i (170, 427, 519); An die ferne Geliebte op. 98 (65). D. Alberti: Keyboard Sonata op. 1/4/i (5, 23); op. 3/i (7). F. Asplmayr: String Quartet op. 2/2/i (10). C. P. E. Bach: La Folia Variations Var. 1 (4); Sonata W. 65/3/ii (8). W. F. Bach: Keyboard Sonata F. 8/i (62); F. 7/ ii (28); Viola Duet F. 60/1/ii (31); Flute Duet F. 54/iii (16). J. D. Bontempo: Elementos de Musica p. 47 (4); Piano Sonata (w/ vln opt.) op. 1/2/i (16, 137); op. 18/2/iii (8). J. B. Bréval: Quartet op. 5/1/ii (8, 85, 223). G. Cambini: Duet for Violin and Viola Book 5/3/ii (8); 4/i (4); 4/ii (4, 25, 55, 86); Flute Duet Book 5/3/ii: Theme (4), Var. 1 (4), Var. (4), and Var. 4 (4). M. Clementi: Gradus and Parnassum 11 (4, 10). D. Dragonetti: String Quintet in C/ ii (4). G. Druschetzky: Partita IV, Var. 4 (4). A. Eberl: Piano Sonatine op. 6/iii (17, 81). J. Eybler: String Quartet 10/3/iii (40). F. Giardini: Violin Duo op. 2/1/i (18).

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M. Guiliani: Guitar Rondeaux op. 8/i minore (8); op. 8/ii (16, 164). Guitar and Flute Duet op. 74/5 (23). P. Hänsel: String Quartet op. 5/1/iii (4, 32). M. Haydn: Violin/Viola Duo MH 335/ii (4, 79, 146, 224); String Quartet MH 310/iii (20, 32). A. Kollmann: Hymn w/ Various Harmonies, Ver. 6 (8). L. Kozeluch: Sonata for Keyboard op. 13/2/iii (4, 20, 36); op. 15/3 (4, 22, 40, 98, 128); Rondo in C for Piano or Harp (97); Leichte Stücke für das Klavier 1 (21, 31). F. X. Mozart: Lied “Wie der Tag mir schleichet” (16, 50). Leopold Mozart: Notebook for Wolfgang: Polonaise XV (4). J. Myslivecek: Rondo in B-flat for Keyboard (69). C. G. Neefe: Violin Sonata in C, iii, Var. VI (16). E. Ozi: Bassoon Duet VI (93). F. C. Neubauer: Violin/Viola Duet op. 5/2/ii, Var. 5 (8); V. Pichl: Violin Duet op. 4/1/ii (4, 12, 38, 46). I. Pleyel: String Quartet op. 1/2/i (40, 121). J. Quantz: Flute Duet op. 2/1/i (12, 61); op. 2/1/ii (8). F. X. Richter: String Quartet op. 53/iii (30). A. Rosetti: Symphony A20/I:18 (27, 44). G. Rossini: Duet for Horns 2 (16). F. Sor: Guitar Variations op. 3, Var. 4 (4). A. Stadler: Clarinet Duetto I/iii (8); iv (4). C. Stamitz: String Quartet op. 14/3/ii (129). D. G. Türk: Sonata in D Minor, i (9); Kleine Handstücke 1 (4). J. B. Vanhal: String Quartet Bryn A4/iv (149, 165); Violin Duet op. 17/2/1/i (8, 28). G. J. Vogler: Piece de clavecin faciles 1 (4, 28); Lob der Harmonie (22, 26); 16 Variations in F (bar 4 of Var. 1, 2, 4, 7). P. Wranitzky: Flute Duo 3/iii (8).

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Example 5: Phrase endings on inversions of V or V7 that are best understood as half cadences: (a) Mozart, Quartet for Strings in B-flat, K. 458/iv, mm. 1–8; (b) Joseph Haydn, Symphony No. 104 in D, Hob. I:104/ii, mm. 1–8; (c) Haydn, Quartet for Strings in G, op. 17, No. 5/ii (Hob. III:29/ii), mm. 1–8; (d) G. J. Vogler, Pieces de Clavecin facile, i, mm. 1–8; (e) Haydn, Divertimento in G, Hob. II:3/ii, mm. 1–8; (f) Mozart, Trio in E-flat for Piano, Clarinet, and Viola, K. 498/i, mm. 47–55

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Example 6: Comparison of cadences that appear in analogous parts of the same composition. (a) Mozart, Quartet for Strings in F, K. 168/iii: mm. 1–4, and mm. 17–20; (b) Mozart, Sonata for Violin and Piano in F, K. 547/ii: mm. 3–5 of Theme, and mm. 1–5 of Var. 5; (c) Haydn, Quartet for Strings in B-flat, op. 33, No. 4/iv (Hob. III:29/ iv), mm. 17–20, and contemporary arrangement for two violins, published as “Op. 99”

If labeling it as a non-half cadence is to have any relevance, this would imply that a phrase ending on an inverted V or V7 necessarily has form-functional, voice-leading, affective, and hermeneutic implications that are notably different than those of phrase endings that are labeled as half cadences (including those that are destabilized through other means), and that this difference should somehow affect how these phrases are performed or perceived. But can this fairly be said of the phrase endings cited in Exx. 5 and 6? If anything, owing to their textural and rhythmic contexts, a number of phrase endings on root-position V triads that are uncontroversially labeled as half cadences sound actually less stable than those cited here that involve inverted V or V7’s.

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For instance, compare what is labeled as a half cadence in Ex. 5f with that of Ex. 1c, which—as noted above—most musicians today would acknowledge as a bona fide half cadence. Certainly the sense that formal, rhythmic, and melodic processes come to an end after the V7 of Ex. 5f is far stronger than what is witnessed after the V in m. 4 of Ex. 1c. Owing to its context, the V7 of Ex. 5f even provides a sturdier sense of a harmonic ending than the V of Ex. 1c. Unlike with the half-cadential V of Ex. 1c, the phrase-ending V7 of Ex. 5f is starkly detached from the harmony that immediately follows it: in Schenkerian terms, this V7 would unquestionably be understood as a Teiler whose voice leading is “closed off” from the immediately ensuing harmony. Furthermore, the dominant-seventh chord of Ex. 5f would be defined as a half cadence by the eighteenth-century definition of the term more readily than would the V of Ex. 1c.34 And certainly the phrase ending on V7 in Ex. 5f should be performed in a manner typical of other half cadences. Without any broader analytic or performance implications that would distinguish it from other half cadences that are destabilized in one way or another, to place such a phrase ending into a separate, non-cadential category creates a needless distraction.35 Again, the broader issue here is whether a half-cadential sense can be asserted or negated by any surface factor taken in isolation. To do so would promote the notion that the stability of a half-cadential V is something that is concrete, rather than a

34. For the reasons described above, what is seen in Ex.1c would have be labeled as a Quintabsatz, not as a half cadence, but what it cited in Ex.5f clearly does meet the standards for what eighteenthcentury theorists labeled as a Halbcadenz; see, for instance, Koch, Versuch III (1793), 442f. §11 (= Baker, Introductory Essay [1983], 49). 35. Caplin recommends the label “dominant arrival” to describe a phrase ending that is like a typical half cadence in all respects other than its ending on an inverted dominant or a dominant seventh. Likewise, since he demands that all themes end with cadences, he refers to a theme that ends with an inverted V or a V7 as a “themelike unit,” a period with that has an inverted V or a V7 at the end of the antecedent as a “hybrid 4,” and the like. These vague terms have other uses as well, however, referring to a host of situations that do not involve a firm sense of ending on a dominant harmony (as Caplin himself notes in Classical Form [1998], 75). Yet a sturdy impression of an ending undoubtedly accompanies many phrases that finish on an inverted V or V7, such as are cited in Exx. 5 and 6 and Table 2. Caplin himself acknowledges this last point: for instance, regarding m. 12 of Beethoven’s op. 49 No. 1/ii (which is surely is as clear an ending as is found in m. 4 of this movement—it is not merely a premature or rhetorical “stop”), he states that “Beethoven prompts us to hear this dominant as an ‘ending’ harmony” (ibid., 79); Caplin also notes that at times a dominant seventh “can appear to be an ending harmony” (ibid., 135). One can hardly maintain that employing the term “dominant arrival” allows for finer distinctions of these cases. Quite the contrary: by using this term to label things such as highlighted in Exx. 5 and 6, one essentially lumps them in with all types on phenomena in which no phrase ending is suggested, thereby washing over the important distinction between dominants that mark a form-functional ending and those that do not. If one seeks labels that distinguish cadences and formal units that end on non-triadic or inverted dominants, I propose instead using terms such as “half cadence on a V7,” “sentence that cadences on a first-inversion V7,” or “period in which the antecedent cadences on a V6.” After all, such labels are far more descriptive, allow for far greater subtlety of distinctions, and avoid the looseness and obscurity of the terms such as “dominant arrival,” “themelike unit,” and “hybrid 4,” while nonetheless acknowledging the less-than-typical surface appearance of the cadential dominant.

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rough approximation based on the consideration and balancing of various stabilizing and destabilizing features. The desire to establish exacting criteria for determining half-cadential closure—along with the prioritization of harmony over other parameters—represents modern predilections that are at odds with the attitudes of eighteenth-century theorists. The eighteenth-century attitude was expressed succinctly by Koch, who—in recognizing the haziness of the concept of a mid-section ending—openly belittled attempts to set up such guidelines by noting that “only feeling can determine both the places where resting points occur in the melody, and also the nature of these resting points.”36

Endpoint or midpoint? Essential conclusion or rhetorical pause? Much as a single destabilizing element will not necessarily prevent a V from reasonably being designated as half-cadential, so a single feature that stabilizes a V will not necessarily create a sense of a phrase ending. As suggested earlier, various formal, textural, and rhythmic gestures must be used in combination in order to separate a dominant from what immediately follows and thereby to establish the impression of a half cadential ending. These gestures might include a caesura or strong textural break that follows a V; deceleration of the surface rhythm, harmonic rhythm, or both upon the arrival of a V; or the appearance of a V at the end of a hypermeasure. Naturally, none of these elements is absolutely needed in order to produce the effect of a phrase ending on a dominant harmony. Nevertheless, the more firmly they are present, the more likely it is that a half-cadential reading would be appropriate. Conversely, the weaker the presence of these elements, the more likely the situation would not be classed as half-cadential.37 In addition to such textural and rhythmic demarcations, the sense of a half cadence also depends on the surrounding phrase-structural context. Specifically, in order for a dominant to be properly understood as marking the essential end of a phrase-structural process, the passages that precede and follow it must be able to be regarded as independent, well-formed phrases. Thus, for example, a firmly delineated V cannot be regarded as a half-cadential phrase ending if it appears at the conclusion of a passage that is clearly perceived as a subphrase or as a phrase fragment. Likewise, the more plainly the passage that follows a V sounds like the beginning of 36. Koch, Versuch II (1787), 465, footnote to §81 (= Baker, Introductory Essay [1983], 3f.). 37. Cf. the celebrated discussion of “language games” and the concept of “family resemblance” in Wittgenstein, Philosophical Investigations (1953).

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a complete, independent phrase, the more likely the V would be heard as half cadential. Such a half-cadential reading might be further supported if the resulting formal layout seems to be one that conventionally concludes with a half cadence, such as an antecedent of a period. On the other hand, the more that the passage that follows a dominant seems like what would normally appear in the middle or end of a phrase, the less likely it is that the V would be heard as half-cadential.

Example 7: (a) Mozart, Sonata for Piano in G, K. 283/ii, mm. 1–4; (b) C. P. E. Bach, Rondo in F, Wq. 57/5, mm. 1–8

When textural, rhythmic, and formal features such as noted above are straightforward and appear in tandem, as is the case in Ex. 1a above, they can convincingly counteract the forward-driving tonal tendencies of a dominant harmony so as to suggest a half cadence. But matters are not always so clear. Consider the passages cited in Ex. 7. On the one hand, various details suggest—to varying degrees—that each of these passages might be understood to contain half cadences followed by voice-leading disjunctures. On the other hand, it would not be unreasonable to contend that the V’s here instead arise in the middle of sentential phrases, embedded within unified I–V–I6 motions in which the penultimate V is slightly delineated, and thus do not establish half cadences.38 As suggested by the corresponding pairs of analyses of Ex. 8, these 38. Precisely such an argument has been made regarding Mozart’s 283/ii, mm. 1–4, by Neuwirth, “Fuggir la cadenza” (2011), where it was proposed that this passage is best understood as a single phrase with no cadence in m. 2 (similar to what is depicted in my Ex.8a, ii). Neuwirth’s reading contrasts with the one proposed in Caplin, Classical Form (1998), 266 (n. 7), which does interpret a half cadence at the

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contrasting readings of cadential status yield contrasting formal and voice-leading interpretations as well.

Example 8: Contrasting analyses for passages cited in Exx. 7a and b, respectively: (a) Analyses of Mozart, K. 283, (i) interpretation with half cadence; (ii) interpretation without half cadence; (b) analyses of Bach, Wq. 57/5, (i) interpretation with half cadence; (ii) interpretation without half cadence

For each of the pairs of analyses in Ex. 8, one could put forth a solid argument in favor of one reading or the other. As suggested by the text above and below the staves in Ex. 7, various formal, textural, and rhythmic features of these passages may be cited to provide firm support for whichever reading is chosen.39 Yet it might be wondered whether the differences between these contrasting cadential interpretations point to meaningful distinctions, or whether they simply result from terminological fussiness. Selecting one analysis over the other in each case ultimately depends on a rather fragile decision regarding whether the connection between the highlighted dominant and the ensuing tonic is best characterized as an essential or a surface one, and thus whether the V is best labeled as a weakly demarcated ending or as a strongly demarcated nonending. In any case, the final say on this matter lies in the hands of the performers, who might well sway the interpretations one way or the other. For instance, a keyboard player could promote the sense of a half cadence in m. 4 of Ex. 7b by taking a short end of m. 2. See also reading of C.P.E. Bach Wq. 57/5 in Samarotto, “Temporal Plasticity” (1999), 117, which seems to combine elements of each of the interpretations shown in Ex. 8b. 39. Incidentally, the hypermeter of the passages cited in Ex. 7 argues against the possibility of elided authentic cadences here. Thus if the highlighted V’s are not to be regarded as half-cadential, this would imply that these passages are sentential ones (in which the V appears mid-phrase), not “loops” (see n. 41 below).

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“breath” at the end of this measure, or else could encourage the sense of a subphrase ending here by pushing forward towards the end of the fourth measure.40 Similar possibilities arise on a slightly larger scale in situations where the sense of a phrase ending is clearer, but conflicting features nonetheless make it difficult to decide whether the ending is best considered to be a half cadence or an elided authentic cadence. Such is the case in Ex. 9a, where complications involving the hypermeter affect the perception of the phrase grouping. On the one hand, it may be argued that this theme is a period in which the melody is played by the piano in the antecedent and by the violin in the consequent (as depicted in Ex. 9b). Accordingly, both the antecedent and consequent would each be regarded as lasting for eight bars, with a half cadence in the middle of the period (m. 8) followed by a filled-in caesura. Yet note that each half of this proposed period is not divided into normal 4+4 subgroups, but rather into 1+4+3 groups, with the first measure serving as a type of preface to the sentential structure that follows. The opening measure begins with a curtain-raiser stroke on the downbeat, followed by a gap that precedes the “official” opening of the theme in the pickup to the second measure. When the theme returns in m. 9, the gap—now filled in with a run in the violin—is about as sturdy as the one found in m. 8. As a result, one might wonder whether it is the gap in m. 9—rather than the one in m. 8—that delineates the phrase ending (as is depicted in Ex. 9c). If this is the case, then this theme would not be a period, but rather a “loop,” another conventional layout that frequently frames first themes of sonata-form movements.41 According to this alternate reading, an eight-bar phrase that lasts from mm. 2–9 and that ends with an authentic cadence is followed by a varied repetition (now condensed to seven measures) in mm. 10–16, so that the potential half cadence of m. 8 is retrospectively reinterpreted as part of a full cadence. As may be seen by comparing Exx. 9b and c, these differing interpretations of the cadence in turn encourage differing interpretations of the form, voice leading, and hypermeter grouping, and vice versa.

40. Both such possibilities may be witnessed in recordings of this piece: contrast the renditions of this passage in Gabor Antalff CPO 999 100-2, with that of Sharona Joshua RRLA1104U. 41. A “loop” structure is one in which the first phrase ends with an authentic cadence that elides with the start of the subsequent phrase; see discussion of the “Mozartian loop” in Hepokoski and Darcy, Elements (2006), 80–86. Incidentally, although the simple I–V–I motion of mm. 7–9 is less than typical for an authentic cadence, it is by no means rare (see, for instance, Joseph Haydn’s Divertimento Hob. XVI:9/iii, mm. 1–4).

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Example 9: Mozart, Trio for Piano and Strings in G, K. 564/i. (a) Quotation, mm. 1–16; (b) and (c) possible voice-leading, formal, and hypermetric interpretations of mm. 1–16

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One cannot dispense with these analytic difficulties simply by noting that there is a conflict between structure and rhetoric here. The analyses of Exx. 9b and c both suggest formal and harmonic layouts that are syntactically well constructed. As a result, determining the location of the structural ending of the first phrase depends on gauging the grouping as suggested by the textural and rhythmic signals. The question remains whether the opening phrase comes to a structural end in m. 8, followed by a rhetorical pause on the surface in m. 9; or whether there is a rhetorical pause on the surface in m. 8, followed by a structural end in m. 9. A third possibility is to regard as artificial the notion that one can or even should locate a single structural endpoint in the middle of a passage such as this, to the extent that it makes little sense to characterize an essential ending as occurring in just one of these places or the other. Accordingly, one would claim that the V of m. 8 forms in certain respects an ending whose voice leading is detached from what follows, but in other respects it does not, so that the cadential, formal, voice-leading, and hypermetric layout of this passage resists neat placement into either/or categories such as are depicted in Exx. 9b and c. With the passage seen in Ex. 9, much as with the passages cited in Ex. 7, nuances in performance choices could tip the understanding of the cadential status one way or the other. For instance, the performers might suggest a half cadence by pausing slightly after the V chord of m. 8; or they could promote the sense of an elided authentic cadence with an accelerando and crescendo from the V of m. 8 to the ensuing tonic in m. 9; or they could do a little bit of both, so that the precise endpoint of the phrase remains obscure. This last option has much to recommend it, for much of the fun of this movement arguably results from the way in which the formal and metrical fuzziness of its first theme contrasts with the crisp clarity of the second theme (mm. 23ff.), a variant of the opening theme whose forthright period structure may be said to “resolve” the initial ambiguity. Some of the different ways in which skilled performers can react to such ambiguous cadential situations may be witnessed by comparing the various recorded renditions of the opening theme of Mozart’s Sonata for Piano in A Minor, K. 310/i (Ex. 10a). A survey of these recordings reveals that some pianists slow down at m. 8, take a short “breath” at end of this measure, and then suddenly get louder and faster at the downbeat of m. 9, thereby suggesting that this theme concludes on the dominant harmony of m. 8. In contrast, other pianists gradually increase the volume and tempo to lead from m. 8 to m. 9, with no “breath” in between, thereby suggesting an elided authentic cadence that ends in m. 9. And yet others do a combination of both by first slowing down in m. 8, and then accelerating at the last moment to the downbeat of the next measure, thus leaving the precise location of the phrase ending in doubt.42 42. For performances that seem to play a half cadence in m. 8, hear Malcolm Bilson HUNGAROTON 31009/14; Claudio Arrau PHILIPS 416 648-2; Temenuschka Vesselinova ACC8851-52; for those that seem to play

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Example 10a: Mozart, Sonata for Piano in A minor, K. 310/i, mm. 1–10

It is a conceit among many music theorists that a proper performance interpretation can be uncovered through a proper analysis. Yet in this case and in many others like it, the notes on the page—abstracted from their possible realizations—do not provide sufficient information for one to unequivocally pin down the location of the phrase ending. Solid analytic arguments can be made here in favor of a phrase ending either on V in m. 8 or on I in m. 9.43 In support of the reading a half cadence in m. 8, one may cite the stylistically idiomatic “grand antecedent” structure that would result, as well as the sharp textural and voice-leading disjunction between mm. 8 and 9, without which parallel fifths would arise in the left hand and outer voices (Ex. 10b). In support of the reading of an elided authentic cadence in m. 9, on the other hand, one might note the similarly idiomatic loop structure that would result, the presence of the V7 in m. 8, the weak metric placement of the dominant harmony in this measure, the acceleration from m. 8 into m. 9, and the more normative hypermetric layout in which m. 9 would stand at the end of a four-bar hypermeasure (Ex. 10c).44 These arguments ultimately largely rely on circular reasoning, however, for the understanding of the cadential status depends on the interpretation of the form, voice leading, and hyperan elided authentic cadence in m. 9, hear Ludwig Sémerjian ACD22243; Sviatoslav Richter DECCA 4225832; and Alfred Cortot S3K89698; for a performance that seems to do mixture of each, hear Heidi Lowy, MHS 566052F. 43. Not surprisingly, some leading scholars have disagreed about this very matter. For instance, Schenker, Tonwille (1922/2004), 55f.; Beach, “Mozart’s Piano Sonata in A Minor” (1987); and Rothstein, Phrase Rhythm (1989), 71 read the first phrases as ending on V in m. 8. Conversely, Caplin, Classical Form (1998), 265 (n. 52); and Hepokoski and Darcy, Elements (2006), 101 read the phrase as ending on I in m. 9. Yet another possibility is offered in Dittrich, “Die Klaviermusik” (2005), 514f., with the intriguing suggestion that this phrase ends with a would-be authentic cadence whose final tonic is lopped off after m. 8, disrupted by the sudden entrance of the second phrase. I discuss this theme and the possible interpretations in Burstein, “The Half Cadence” (2014). 44. Incidentally, note that the V7 here is preceded by an appoggiatura (in the form of a cadential six-four), and thus a root-position V triad could conceivably be understood to be implied here in the same sense as what is seen in Ex. 4 above.

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meter, but conversely the understanding of the form, voice leading, and hypermeter depends on the interpretation of the cadential status.

Example 10b and c: Mozart, Sonata for Piano in A minor, K. 310/i, mm. 1–10: (b) Voice-leading and hypermetric interpretation in which phrase ends in m. 8; (c) Voiceleading and hypermetric interpretation in which phrase ends in m. 9

Following one’s own individual taste, a listener may well prefer one performance of this passage over another, and therefore prefer one cadential interpretation over the other. However, it would be fairer to admit that it is the preferred performance that dictates the preferred analysis, rather than the other way around. Acknowledging the ambiguity of the cadential status here—at least as it appears on the printed page— opens the door for an appropriate degree of flexibility in performance. Analysts would unduly limit their interpretive options by regarding cadential status in too tangible a manner, as if the choice between the half- or authentic-cadential readings here—along with the attendant formal, voice-leading, and rhythmic implications—were a blackor-white matter that could be determined solely by data present in the score itself. The kind of excerpts discussed here are hardly the only ones in which one may reasonably question whether a phrase ends with a half or authentic cadence. For instance, with transition or development sections that end (or appear to end?) with a “juggernaut caesura fill,” it frequently is unclear whether to read a half cadence followed by a forceful bridge leading into the next section, or an authentic cadence in which there is

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a rhetorical demarcation of the penultimate dominant.45 The problems with determining cadential status in such situations often relate directly to deeper analytic complications involving locating endings of large formal sections, rhythmic groupings, and voice leading structures. In many such cases, attempts to pigeonhole the cadence and related structures into one category or the other might hamper more the help, especially if performers are encouraged to adhere to such strict binary oppositions. • In all, the notion that a dominant harmony can establish an ending in mid-composition—followed by a break in the form and voice leading—remains a type of story, a fabrication imposed upon the music by analysis. Nonetheless, it has proved to be an immensely satisfying story, one which, as Leonard Meyer notes, “has become archetypal in the stylistic syntax of tonal music.”46 Granted, this tale of a closure marked by a dominant harmony suits some situations better than others. That many a dominant harmony can at times be justly labeled as half cadential should not inure us to the paradoxical implications that accompany this concept, however. Even with relatively clear situations, one can help revivify the sense of paradox and parametric noncongruence associated with the “so-called half cadence” by continuing to question in what ways and to what extent a dominant may seem to establish an ending; to what extent and in what ways it may seem connected or disconnected to what follows; and how this sense of ending and disconnection may relate to the performance and analysis of the passage within which it appears.

Bibliography Agricola, Johann Friedrich (1757/1995), Introduction to the Art of Singing, ed. and trans. Julianne Baird, Cambridge: Cambridge University Press. Anonymous (1801–2),“Recension,” Allgemeine Musikalische Zeitung IV (1 October–22 September), 1–11. Beach, David (1987), “The First Movement of Mozart’s Piano Sonata in A Minor, K. 310: Some Thoughts on Structure and Performance,” Journal of Musicological Research 7/2–3, 157–186. Bergé, Pieter, Nathan J. Martin, Markus Neuwirth, David Lodewyckx, and Pieter Herregodts, eds. (forthcoming), Concise Cadence Compendium: A Systematic Overview of Cadence Types and Terminology for 18th-Century Music, Leuven: Leuven University Press. Berry, Wallace (1966), Form in Music, Englewood Cliffs, NJ: Prentice Hall. 45. Regarding “juggernaut fills,” see Hepokoski and Darcy, Elements (2006), 44f. I discuss one of the many examples of such an situation involving a possible juggernaut fill at the end of a development section (of Beethoven’s Piano Concert No. 4 in G, op. 58/i) in Burstein, “The Off-Tonic Return” (2005), 6f. 46. Meyer, Explaining Music (1973), 85.

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Burns, Lori (1994), “Modal Identity and Irregular Endings in Two Chorale Harmonizations,” Journal of Music Theory 38/1, 43–77. Burstein, L. Poundie (2005), “The Off-Tonic Return in Beethoven’s Piano Concerto No. 4 in G Major, Op. 58, and Other Works,” Music Analysis 24/3, 305–345. ——— (2014), “The Half Cadence and Other Such Slippery Events,” Music Theory Spectrum 36/2, 203–227. Caplin, William (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, New York: Oxford University Press. ——— (2004), “The Classical Cadence: Conceptions and Misconceptions,” Journal of the American Musicological Society 57/1, 51–117. Crotch, William (1812), Elements of Musical Composition, London: Longman, Hurst, Rees, Orme, & Brown. Czerny, Carl (1839), Vollständige theoretisch-praktische Pianoforte-Schule, op. 500, vol. 3, Vienna: Diabelli. Dittrich, Marie-Agnes (2005), “Die Klaviermusik,” in: Mozart Handbuch, ed. Silke Leopold, Kassel: Bärenreiter and Metzler, 482–559. Goetschius, Percy (1898), The Homophonic Forms of Musical Composition, New York: Schirmer. ——— (1900), Exercises in Melody-writing, New York: Schirmer. Goetschius, Percy and Immanuel Faisst (1889), The Material Used in Musical Composition, Leipzig: Breitkopf & Härtel. Gugl, Matthaeo (1777), Fundamenta partiturae in compendio data, Augsburg: Wolf. Hepokoski, James and Warren Darcy (2006), Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata, New York: Oxford University Press. Herbst, Johann Andreas (1643), Musica poëtica sive compendium melopoeticum, Nuremberg: Dimmler. Holden, John (1770), An Essay Towards a Rational System of Music, Glasgow: Urie. Jones, William (1784), A Treatise on the Art of Music, Colcester: Keymer. Kessel, Johann C. B. (1791), Unterricht im Generalbasse zum Gebrauche für Lehrer und Lernende, Leipzig: Hertel. Kirnberger, Johann Philipp (1771–1779), Die Kunst des reinen Satzes in der Musik, Berlin: Decker & Hartung. Koch, Heinrich Christoph (1782–1787–1793), Versuch einer Anleitung zur Composition, 3 vols., Leipzig: Böhme. Reprint, Hildesheim: Olms, 1969. Selections trans. Nancy Kovaleff Baker as Introductory Essay on Musical Composition, New Haven, CT: Yale University Press, 1983. ——— (1802), Musikalisches Lexicon, Frankfurt a. M.: Hermann. La Voye-Mignot (1666), Traité de Musique, 2nd edition, Paris: Ballard; repr. ed. Genève: Minkoff, 1972. Lester, Joel (1994), Compositional Theory in the Eighteenth Century, Cambridge MA: Harvard University Press. ——— (2002), “Rameau and Eighteenth-Century Harmonic Theory,” in: The Cambridge History of Western Music Theory, ed. Thomas Christensen, Cambridge: Cambridge University Press, 753–777. Marx, Adolf Bernhard (1856 and 1886/1997), Musical Form in the Age of Beethoven, ed. and trans. Scott Burnham, Cambridge: Cambridge University Press. Marpurg, Friedrich Wilhelm (1763), Kritische Briefe über die Tonkunst, vol. II, Berlin: Birstiel.

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Matthaei, Conrad (1652), Kurtzer, doch ausführlicher Bericht von den Modis Musicis, Reusner: Königsberg. Meier, Bernhard (1988), The Modes of Classical Vocal Polyphony, New York: Broude Bros. Meyer, Leonard (1973), Explaining Music: Essays and Explorations, Berkeley: University of California Press. Muffat, Georg (1961), An Essay on Thoroughbass, ed. and transl. Hellmut Federhofer, Rome: American Institute of Musicology. Mutch, Caleb (forthcoming), “A History of the Cadence and Its Precedents,” Ph.D. dissertation, Columbia University. Neuwirth, Markus (2011), “Fuggir la cadenza, or The Art of Avoiding Cadential Closure – A Contemporaneous Theoretical Perspective on 18th-century Music,” presentation given at the “What is a Cadence?” Symposium at the Academia Belgica in Rome, 19 January. Phipps, Graham (2010), “Issues of Harmony and Formal Organization in Schumann’s Piano Quartet, Op. 47,” presentation given at the Sixth International Conference on Music Theory in Tallinn, Estonia, 16 October. Printz, Wolfgang Caspar (1676–1677), Phrynis Mitilenæus, Dresden and Leipzig: Mieth & Zimmermann. Reicha, Anton (1814/2002), Treatise on Melody, trans. Peter Landley, Hillsdale N.Y.: Pendragon Press. ——— (1816), Cours de Composition musicale, Paris: Gambaro. Richards, Mark (2011), “Viennese Classicism and the Sentential Idea: Broadening the Sentence Paradigm,” Theory and Practice 36, 179–224. Riepel, Joseph (1755), Grundregeln zur Tonordnung insgemein, Frankfurt and Leipzig: Lotter, Auspurg. Reprinted in Joseph Riepel: Sämtliche Schriften zur Musiktheorie, vol. I, ed. Thomas Emmering, Vienna: Böhlau, 1996. Rothstein, William (1989), Phrase Rhythm in Tonal Music, New York: Schirmer. Samarotto, Frank (1999), “A Theory of Temporal Plasticity in Tonal Music: An Extension of the Schenkerian Approach to Rhythm with Special Reference to Beethoven’s Late Music,” Ph.D. diss., CUNY. Schenker, Heinrich (1935/1979), Free Composition, trans. and ed. Ernst Oster, New York: Longman. ——— (1954), Harmony, trans. Elizabeth Mann Borgese, ed. Oswald Jonas, Chicago: University of Chicago Press. Translation of Harmonielehre, Stuttgart: Cotta, 1906. ——— (1922/2004), “Mozart’s Sonata in A Minor, K. 310,” trans. Timothy Jackson, in: Der Tonwille I, ed. William Drabkin, New York: Oxford University Press, 55–71. Schmalfeldt, Janet (1991), “Towards a Reconciliation of Schenkerian Concepts with Traditional and Recent Theories of Form,” Music Analysis 10/3, 233–287. Sulzer, Johann Georg (1771–1774), Allgemeine Theorie der schönen Künste, 2 vols. Berlin: Winter. Tovey, Donald Francis (1931), Companion to Beethoven’s Pianoforte Sonatas, London: Associated Board of the Royal Schools of Music. Vial, Stephanie (2008), The Art of Musical Phrasing in the Eighteenth Century: Punctuating the Classical “Period”, Rochester: University of Rochester Press. Wiedeburg, Michael Johann Friedrich (1775), Der sich selbst informirende Clavier-Spieler, vol. 3, Halle: Verlag des Waisenhauses.

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Urban, Sylvius (1813), “Review of New Musical Publications,” The Gentlemen’s Magazine 83/1, 459–461. Wittgenstein, Ludwig (1953), Philosophical Investigations, ed. G. E. M. Anscombe and R. Rhees, trans. G. E. M. Anscombe, Oxford: Blackwell. Wolf, Georg Friedrich (1792), Kurzgefaßtes Musikalisches Lexikon, Halle: Hendel.

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FUGGIR LA CADENZA, OR THE ART OF AVOIDING CADENTIAL CLOSURE Physiognomy and Functions of Deceptive Cadences in the Classical Repertoire* Markus Neuwirth

I. On the physiognomy of the deceptive cadence: An eighteenth-century perspective

F

ollowing a topos that is widespread in the analytical literature, music from the second half of the eighteenth century may be described as goal-directed.1 To reflect the teleological qualities inherent in “classical” music, analysts of different persuasions frequently make use of metaphors derived from the source domain of a “journey,” including its cognates “trajectory” and “path” as well as “departure” and “arrival.”2 A musical “phrase” may be considered the smallest building block expressing goal-directedness, as it articulates a tonal motion towards a final sonority (either the tonic or the dominant) that is usually established by means of a cadential progression.3 Expressing the tripartite temporal paradigm of a beginning, a middle, and an end, a phrase may thus rightly be regarded as the prototype of form in classical music in general.4 If we accept such goal-directedness as one of the basic premises for the analysis of classical music, it is uncontroversial to claim, following Leonard B. Meyer, that one of the most important procedures adopted in the classical style was the strategic delay of structural closure. Such a delay had the function of both playing *

1. 2. 3.

4.

Financial support for the research presented in this chapter has been generously provided by The Research Foundation – Flanders. E.g., Schenker, Free Composition (1979), 5; Lerdahl and Jackendoff, A Generative Theory (1983), 174; and Caplin, Classical Form (1998), 42. On the concept of “source domain,” see Lakoff, Women, Fire, and Dangerous Things (2008), 276. Rothstein, Phrase Rhythm (1989), 5: “A phrase should be understood as, among other things, a directed motion in time from one tonal entity to another; these entities may be harmonies, melodic tones (in any voice or voices), or some combination of the two.” See Agawu, Playing with Signs (1991), 51ff.

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with listeners’ expectations and stretching the temporal dimensions of a given composition. Deceptive cadences, one important means of achieving this aim, therefore deserve critical attention.5 In addition to their significant structural impact, deceptive cadences may also have strong psychological implications, as becomes clear from Aldwell and Schachter’s fitting description: Deceptive cadences are inconclusive. They create no sense of repose: on the contrary, they produce suspense that dissipates only when the total stability is regained, usually through an authentic cadence. By delaying resolution to a goal tonic, they intensify the feeling of resolution when that tonic eventually arrives.6

Even a superficial examination of present-day theoretical approaches to the deceptive cadence reveals an astonishing uniformity, as the concept is largely restricted to a rather simple harmonic formula: the motion from dominant to submediant. This is surprising, considering that composers employed a much wider variety of deceptive cadences in actual practice.7 This variety is in part reflected in the confusion over the terminology used to refer to deceptive progressions. The deceptive cadence has been extensively theorized by numerous historical writers, giving rise to a multiplicity of terms in at least five languages (Latin, Italian, French, German, and English): cadentia ficta, cadenza sfuggita, cadenza d’inganno, cadenza finta, cadence evitée, cadence rompue, Trugschluß, Ausfliehen der Cadenz, fliehender Tonschluß, and deceptive cadence, to mention just a few of the terms that were in use in the eighteenth century.8 The simplistic treatment of the deceptive cadence is in part due to the fact that modern textbooks on tonal harmony typically adopt a chord-centered, as opposed to a linear (or contrapuntal), perspective with regard to eighteenth-century music, especially when seeking to explain cadences. However, such a harmonically reductionist approach is by no means self-evident, as Robert Gjerdingen points out in his 2007 study entitled Music in the Galant Style. In fact, it raises two serious problems, one related to anachronism and the other to its limited explanatory scope: Generations of nineteenth- and twentieth-century music students have learned about musical phrase endings—cadences—from textbooks on harmony. This chord-centered view of musical articulation was fully

5. 6. 7.

8.

Meyer, Style and Music (1989), 22, 296. Aldwell and Schachter, Harmony and Voice Leading (2003), 199. A notable exception is Caplin, Classical Form (1998), 29. Caplin offers more variety with respect to the concept of the deceptive cadence than is typically provided in music textbooks and essays. Caplin’s view is anticipated by Schenker’s broader definition of the deceptive cadence: “Finally, also, the deceptive cadence allows for various modifications; for, in a broad sense, any step progression, not merely V–IV or V–VI, may be heard as a deceptive cadence, provided that it prevents the fulfilment of an expected full close” (Schenker, Harmony [1954], 226f.). See, for instance, Schmalzriedt, “Kadenz” (1974).

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appropriate to the aims of general musical education in the Romantic age, but it is too coarse-grained for an esoteric, courtly art like galant music. Or put another way, it highlights only what Locatelli has in common with Rimsky-Korsakov.9

Adopting a common-denominator approach, modern theorists have identified a simple dominant-to-tonic motion as the “essence” of an authentic cadence.10 It might be for this reason that current cadence taxonomies consider only the two final chords of a larger progression as the defining features that characterize the type of a given cadence.11 This approach may be seen as a consequence of Jean-Philippe Rameau’s “long shadow,”12 since Rameau was probably the first theorist to use “cadence” to refer to two-membered fifth-related progressions.13 Owing to this Ramellian heritage, voice leading is understood as a secondary dimension that serves merely to smooth the harmonic progression; in other words, voice leading is taken into account only after categorical distinctions have already been made on the basis of the harmonic analysis. In keeping with this chord-centered perspective, numerous modern textbooks on tonal harmony view the deceptive cadence as arising from a genuinely harmonic procedure: in an otherwise regular cadential progression, the final tonic is unexpectedly replaced by a substitute harmonic function, thus creating the deceptive effect that gives this progression its name. It is usually the triad on scale degree ‫ݝ‬, the submediant, that is interpreted as acting as a tonic substitute, since vi and I have two tones (1^ and 3^) in common and their roots are a minor third apart. This understanding of deceptive cadences in terms of harmonic substitution dates back to Hugo Riemann’s theory of Klangvertretung,14 if not earlier; this Riemannian heritage also surfaces in many modern textbooks, for instance, in Aldwell and Schachter’s Harmony and Voice Leading.15 It must not be overlooked, however, that already in the eighteenth century deceptive cadences were sometimes described in exclusively harmonic terms. Authors as diverse as Johann Adolf Scheibe and Johann Philipp Kirnberger interpreted deceptive cadences as resulting from a chord substitution or from an unexpected harmonic resolution. As Scheibe explains in his Critischer Musicus (1739), a deceptive cadence

9. Gjerdingen, Music in the Galant Style (2007), 140. 10. See Temperley, The Cognition of Basic Musical Structures (2001), 336. V–I is no doubt too unspecific a feature to be used in differentiating the cadence from other (non-cadential) types of progressions; see the Introduction to this volume. 11. E.g., Forte, Tonal Harmony (1974), 50; Caplin, Classical Form (1998), 27–29, 43. 12. Holtmeier’s term; see his “Rameaus langer Schatten” (2010). 13. Rameau, Treatise on Harmony (1722/1971), 63ff. Rameau’s understanding was widely accepted throughout the nineteenth and much of the twentieth century. Furthermore, it should be noted that for Rameau, the “perfect cadence” (cadence parfaite) was considered the prototype of directed harmonic motion in general. 14. See, for instance, Riemann, Handbuch der Harmonielehre (1898). 15. Aldwell and Schachter, Harmony and Voice Leading (2003), 197. See also Gauldin, Harmonic Practice in Tonal Music (1997), 242f., and Caplin, Classical Form (1998), 29, 101.

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arises “when one alters the final note at the end of a phrase and turns to a completely different and unexpected chord”.16 For Kirnberger (1774), the deceptive cadence is the third main type of an ending that arises “if one does not move from the dominant of the key to the tonic.”17 In this chapter, I will adopt a historically informed perspective by placing a linear (or contrapuntal) analysis at the center of my discussion of deceptive cadences. More specifically, I will draw on the centuries-old Klausellehre, according to which closure is brought about by a specific combination of individual voices called clausulae rather than by a specific succession of harmonies. This approach might challenge those theorists who have long been taught that the ways in which cadential closure was achieved in Renaissance and in classical music are categorically distinct. The sources that Gjerdingen and others18 refer to suggest that the Klausellehre was of vital importance to Renaissance music, but also continued to be influential for eighteenth-century music as well. Taking into account the profound insights offered by eighteenthcentury theoretical sources promises to circumvent the pitfalls of anachronism and may additionally increase the descriptive power of a modern theory of the cadence. As the following cursory overview of the historical literature will demonstrate, the Klausellehre proves particularly powerful in addressing the deceptive cadence. Consider one of the earliest and most well-known descriptions of deceptive (or evaded) cadences, that found in Gioseffo Zarlino’s highly influential 1558 treatise Le istitutioni harmoniche—a description that in its focus on the behavior of single voices is markedly different from modern approaches: [T]o make intermediate divisions in the harmony and text, when the words have not reached a final conclusion of their thought, we may write those cadences which terminate on the third, fifth, sixth, or similar consonances. Such ending does not result in a perfect cadence; rather this is now called “evading the cadence” (fuggir la cadenza). It is fortunate that we have such evaded cadences. They are useful when a composer in the midst of a beautiful passage feels the need for a cadence but cannot write one because the period of the text does not coincide, and it would not be honest to insert one. […] From what I have said, it is evident that any cadence not terminating on an octave or unison may be called imperfect because it evades the perfect ending. […] a cadence is evaded […] when the voices give the impression of leading to a perfect cadence, and turn instead in a different direction.19

16. Scheibe, Critischer Musicus (1739), 478 (my translation). 17. Kirnberger, Die Kunst des reinen Satzes (1774), 97f. 18. See, for instance, Holtmeier, “Heinichen, Rameau, and the Italian Thoroughbass Tradition” (2007) and Menke, “Die Familie der cadenza doppia” (2011). 19. Zarlino, Le istitutioni harmoniche (1558), 223 (trans. in The Art of Counterpoint [1968], 151).

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For Zarlino, perfect cadences—whether simple or diminished20—end with an octave or a unison. Any intervallic progression that evolves like a perfect cadence but ultimately refuses to end like one is described as involving an “evaded cadence” (cadenza sfuggita), which the author illustrates by means of various two-voice settings (bicinia). Elsewhere in his treatise, Zarlino dubs this type of incomplete ending an “imperfect cadence” or “improper cadence.”21 In other words, Zarlino uses the concept of the “evaded cadence” as an umbrella term, lumping together all possible kinds of contrapuntal configurations that start as though they were going to bring about a perfect cadence but then frustrate this expectation by ending on third, fifth, or sixth intervals. In general, for Zarlino, the placement of cadences is closely linked to the syntactical subdivisions of the text: While perfect cadences, ranking highest with regard to their syntactical weight, serve to punctuate complete sentences (or thoughts) of the text, the use of evaded cadences is largely motivated by the fact that the text has not yet reached its syntactical conclusion. Zarlino’s contrapuntal (or intervallic) approach resurfaces more than a century later in various French and Italian sources, in which cadences are typically understood as two- or three-part contrapuntal progressions categorized according the final interval established over the bass. As one example of many, La Voye Mignot’s treatment of cadences may be cited here pars pro toto, as it can be considered representative of the theoretical practice of the time. La Voye Mignot distinguishes between three types of cadence—perfect (parfaite), broken (rompue), and waiting (attendante)—, which are said to differ with respect to their degree of finality. The third type, the cadence attendante, ends with ‫ ݜ–ݘ‬in the bass and largely corresponds to our modern half cadence; Charles Masson refers to this as cadence irreguliére.22 Perfect cadences (featuring ‫ݘ–ݜ‬, ‫ݘ–ݙ‬, or ‫ ݚ–ݛ‬in the bass) end on a perfect consonance (the octave or unison).23 By contrast, the broken cadence fails to conclude on the expected perfect consonance because the bass, instead of providing its proper clausula (‫)ݘ–ݜ‬, moves from ‫ݜ‬ either to ‫ ݝ‬or to ‫ݚ‬, thus ending either on a third or a sixth.24 Masson comes perhaps closest to Zarlino’s definition, as he “calls imperfect any cadence in which an interval other than the octave is sounded at the closing.”25 Following this sixteenth- and seventeenth-century tradition, Johann Gottfried Walther in his Musicalisches Lexicon from 1732 describes two possible ways of creating a deceptive ending, depending on the specific treatment of either the bass or one of the

20. 21. 22. 23. 24.

See n. 52. Zarlino, The Art of Counterpoint (1968), 148. Masson, Nouveau traité (1699), 24. See also Nivers, Traité de la composition (1667), 23f.; and Masson, Nouveau traité (1699), 24. La Voye Mignot, Traité de musique (1656), 74ff. Masson refers to the broken cadence as cadence imparfaite, adding to the bass-generated variants those produced by a melodic deviation in the soprano. 25. Christensen, Rameau and Musical Thought in the Enlightenment (1993), 114.

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upper voices (most typically the soprano).26 The first type arises when the bass moves down a third (‫ )ݚ–ݜ‬or ascends by whole- or semi-tone (‫ ݝ–ݜ‬or ‫ )ݝ¨–ݜ‬rather than either leaping down a fifth or up a fourth (‫ )ݘ–ݜ‬as expected. The remaining voices, by contrast, behave as if they were bringing about a full close; it is only the bass that breaks the normative pattern (see Example 1).27 The second type results from the deviant behavior of one of the upper voices: if, unlike the first type, the bass does indeed provide its “normative” bass clausula (the cadenzia basizans), the upper voice may surprisingly resolve the 4–3 suspension to ¨‫ ݚ‬rather than ª‫ ݚ‬as expected.28 This alteration produces what Berardi has called motivo di cadenza (see Example 2);29 in modern parlance, this is seen as giving rise to a Caplinian “abandoned cadence” followed by a descending-fifths sequence that is employed to accomplish a modulation.30

Example 1: Walther, Musicalisches Lexicon (1732), 125: Deceptive cadence produced by bass motion

Example 2: Berardi, Documenti armonici (1687), 151: “Motivo di cadenza”

Walther’s description permits an interesting observation: especially in the first case, the author groups together into a single category what in modern harmonic terms would belong to two (or three) distinct categories because of the different harmonic functions 26. One may assume that Walther’s description, as it appears in a dictionary, reflects an older understanding of cadence. 27. Walther, Musicalisches Lexicon (1732), 125. 28. Ibid. 29. Berardi, Documenti armonici (1687), 152ff. See also Walther, Musicalisches Lexicon (1732), 425. 30. On the modulatory function of the deceptive cadence, see below.

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(I6, vi, or ¨VI) that occur on the ultima. This is because rather than focusing on the harmonic result, Walther instead examines how a deceptive ending is produced, considering the behavior of each individual voice within a genuinely contrapuntal setting. Key to understanding deceptive cadences within the system of Klausellehre is the concept of Klauselverwechslung—that is, the interchangeability or recombination of clausulae. Klauselverwechslung is a common method of varying cadences that has been described in numerous sources, as, for instance, in Andreas Werckmeister’s Harmonologia Musica from 1702.31 Here, let us concentrate on which clausulae can be used to replace the clausula basizans. According to Werckmeister, the clausula cantizans (1–7–1), the clausula tenorizans (3–2–1), and the clausula altizans (5–5–3) can all be transferred to the bass register, thus weakening the sense of closure conveyed by a given contrapuntal configuration.32 The only clausula that is exempt from interchangeability is the bass clausula; its proper place is exclusively in fundamento.33 It should also be noted that a cadence does not necessarily require all four clausula to be present: two or three of them may be sufficient, most importantly the bass clausula and one of the clausulae principales (either the tenor or the discant clausula). Perhaps the most explicit explanation of deceptive cadences in terms of Klauselverwechslung can be found in Meinrad Spieß’s 1745 Tractatus Musicus CompositorioPracticus. In describing deceptive cadences, Spieß quotes almost directly from Walther’s dictionary, but with the addition of an interesting observation. He notes that the deceptive cadence almost coincides with the cadentia altizans (that is, a cadence with the clausula altizans in fundamento).34 Indeed, it is clear from the two examples of cadentia altizans provided by Spieß that he is referring to typical variants of a deceptive cadence (see Example 3). This implies that Spieß regards both ‫ ݚ–ݜ‬and ‫ ݝ–ݜ‬movements in the bass as possible forms of a clausula altizans rather than as manipulations of the bass clausula, the latter being the common view.35 Referring to the ‫ ݚ–ݜ‬variant as a form of the clausula altizans is uncontroversial. This view was put forth by Walther, who, following Printz, called ‫ ݚ–ݜ‬a clausula saltiva imperfectior, emphasizing its similarity to the cadentia altizans.36 In his Praecepta from 1708, Walther used the term clausula minus perfecta to refer to a clausula altizans shifted to the bass, thus suggesting a close relationship between the alto clausula and the deceptive cadence. More debatable, however, is the idea of relating the ‫ ݝ–ݜ‬variant to the 31. See, for instance, Werckmeister, Harmonologia musica (1702), 48. 32. Ibid., 49. 5–5–5, a variant of the clausula altizans, is commonly found in an inner voice. 33. Ibid., 50. See also Printz, Phrynis mitilenæus (1676), 30; and Kellner, Treulicher Unterricht im General-Baß (1737), 22f. For a less restrictive view, see Spieß, Tractatus musicus (1745), 94. 34. Spieß, Tractatus musicus (1745), 95. 35. In the context of a discussion of incises (Einschnitte), Mattheson refers to the 5–6 movement in the bass as clausula imperfecte ascendens; the 5–3 movement is called clausula imperfecte descendens. See Mattheson, Der vollkommene Capellmeister (1739), 186. 36. Printz, Phrynis mitilenæus (1676), 28.

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cadentia altizans. This is because the ‫ ݜ–ݜ–ݜ‬variant lacks the ascending step that for Printz is the defining feature of the clausula ordinata ascendens imperfectior.37 It is arguably the difference between this variant and ‫ ݝ–ݜ‬that prompts Spieß to assert that the latter variant of the deceptive cadence would almost (!) coincide with the cadentia altizans.

Example 3: Spieß, Tractatus Musicus (1745), 96: Deceptive cadence produced by bass motion

As is widely accepted, the clausula altizans is the least important (and most expendable) of the four clausulae, serving merely to fill in missing elements in order to complete the harmony (“Ausfüllung der Harmonie”), hence its designation as clausula explementalis.38 There was no consensus among eighteenth-century theorists regarding the question of whether such an auxiliary clausula might also appear in fundamento. When this form of cadence was allowed at all, theorists such as Walther and Johann Mattheson devalued it, using the term clausula (formalis) minus perfecta.39 They thus suggested that this cadence was considered imperfect in some respects: it could only produce what Mattheson, invoking an analogy to language, calls a comma. Following Lipsius, Mattheson defines a comma as “a little part of the sentence through which the discourse obtains a little caesura.”40 Similarly, Friedrich Wilhelm Marpurg considers the deceptive cadence to be nothing but a “mere Absatz,”41 which, like a comma, is incapable of concluding a larger whole. This type of cadence can therefore only be used in the middle of a composition, never at its end.42

37. 38. 39. 40. 41. 42.

Ibid. Walther, Musicalisches Lexicon (1732), 171. Mattheson, Critica musica (1722), 27. Mattheson, Der vollkommene Capellmeister (1739), 184 (my translation). Marpurg, Kritische Briefe über die Tonkunst (1763), 68. Walther, Praecepta (1708), 162.

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Building on this discussion, we can now consider some of the theoretical implications of conceptualizing the deceptive cadence in terms of a specific combination of clausulae. First and foremost, it is important to recognize that Walther’s rationale helps to explain a particular feature of the V(7)–vi deceptive variant that has long been a topic of discussion among theorists: namely, the doubling of the third of the chord on the sixth scale degree. An explanation based on voice-leading considerations is proposed by Aldwell and Schachter. They argue that the third is usually doubled in a V(7)–vi progression, as this allows the leading tone to be properly resolved upwards to 1^ and simultaneously helps to avoid parallel fifths.43 In addition, it permits the proper resolution of the tritone (4^–7^), since the dominant seventh is able to properly resolve to 3^. From a functional perspective, it has been argued that doubling this chordal element (which is the root of the tonic triad) reflects the close relationship between vi and I, the former referred to as a Riemannian Tonikaparellele.44 This view essentially dates back to Rameau’s pioneering Traite de l’harmonie from 1722. Here, the author argues that “the third implies the true fundamental sound, whose replicate cannot be displeasing.”45 This would make it “preferable to place the octave of the third in the chord [of the sixth degree] rather than the octave of the bass.”46 In order to understand Rameau’s explanation properly, it is important to bear in mind that the ‫ ݝ–ݜ‬movement in the bass poses a serious problem for Rameau’s general theory, as it seems to contradict his essential principle of fifth motion of the fundamental tones. Seeking to resolve this problem, Rameau argues that the submediant chord is really an inverted tonic, with the sixth replacing the chordal fifth and the fundamental bass being the third of the submediant. As Thomas Christensen emphasizes, “[s]ince all other aspects of the voice leading remain unaltered, and the substitution is only of a consonant interval, Rameau can claim that the cadence rompue is still a variety of the cadence parfaite granted by license.”47 From Walther’s perspective, however, these explanations seem insufficient or at the least only partially valid. As we can infer from his description, the doubling of the third is merely an epiphenomenon of the retained basic contrapuntal structure

43. Aldwell and Schachter, Harmony and Voice Leading (2003), 198. 44. Riemann, Handbuch der Harmonielehre (1898), 1ff. 45. Rameau, Treatise on Harmony (1722/1971), 73. See also Agmon, “Functional Harmony Revisited” (1995), 212. 46. Ibid. 47. Christensen, Rameau and Musical Thought in the Enlightenment (1993), 116. See also Caeyers, Het ‘Traité de l’Harmonie’ van Jean-Philippe Rameau (1989), 226–228. Pointing out “obvious inconsistencies with Rameau’s analysis” of the deceptive cadence, Christensen emphasizes that Rameau changes this position in his later writings, in particular the Génération harmonique (Chapter 15) and the Code de musique pratique, renouncing the principle of “fundamental fifth motion in all cadential patterns” (see Christensen, Rameau and Musical Thought in the Enlightenment [1993], 117).

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consisting of two clausulae principales: the clausula cantizans and the clausula tenorizans.48 This two-voice contrapuntal framework can be interpreted as obeying the Aristotelian principle of motion, moving from a state of imperfection to a state of perfection: it articulates the intervallic progression from two imperfect consonances (a sixth interval), the latter of which is typically prepared by a syncopated seventh suspension dissonance, to a perfect consonance (the octave, with 1^ in both voices).49 Suggesting an additive nature of musical settings in the classical style, the clausulae principales constitute a contrapuntal nucleus or skeleton that remains intact, irrespective of how the surrounding voices behave.50 As shown above, the presence of a dissonance was deemed crucial already in Renaissance theories.51 Cadences featuring a suspension dissonance were called formales, diminuite, composte, ligatae, or ornate, whereas cadences lacking this features were referred to as either simplices or purae.52 As René Descartes cogently argues in his Compendium musicae (1618), the syncopated dissonance adds to the sense of closure achieved at the moment of arrival on the final octave because it delays the fulfilment of, and thus increases, expectation.53 Conversely, the absence of a suspension (and hence the dissonance) in a fully consonant homophonic note-against-note counterpoint (in the sense of a Fuxian “first species”) would weaken the sense of closure conveyed by a given cadence. Interestingly, during the 40 or so years following the publication of Walther’s dictionary, composers made use of the 7–6 suspension dissonance (or 4–3 against ‫ݘ–ݜ‬ in the bass) in cadences at structurally significant points. In the context of classical sonata-form movements, this dissonance was not infrequently employed to articulate the moment of structural closure, whether in the exposition (“essential expositional closure” or EEC) or in the recapitulation (“essential structural closure” or ESC).54 This implies that the presence of the dissonance signals a moment of great structural importance, even though definitive closure may be denied at the very last moment due to the deviant behavior of one or more clausulae. To illustrate this situation, let us briefly consider an excerpt from Haydn’s String Quartet op. 17 No. 4 (see Example 4). Towards the end of the first movement’s

48. Walther, Musicalisches Lexicon (1732), 171. According to Walther, these two clausulae are called principales because they can be exchanged. 49. This intervallic pattern (6–7–6–8), the sixth-to-octave progression in contrary motion, is commonly referred to as clausula vera. 50. See Holtmeier’s notion of additiver Tonsatz in his “Rameaus langer Schatten” (2010). 51. See Diergarten in this volume. 52. See Schmalzriedt, “Kadenz” (1974), 5ff. The distinction between cadenze semplici and cadenze diminuite dates back to Zarlino, Le istitutioni harmoniche (1558), 221. The distinction between clausulae simplices and clausulae formales dates back to Calvisius, Melopoiia (1592). 53. Descartes, Compendium musicae (1618), 55. 54. Hepokoski and Darcy, Elements (2006), 20.

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exposition, a “grand cadence”55 is about to materialize, featuring temporally extended functional sonorities (with each stage occupying one full measure), a cadential 64, and a tenor clausula with a trill on 2^ in the soprano (m. 40). Owing to these features, grand cadences are particularly suited to articulating a moment of structural significance in a sonata-form exposition. In addition, a closer look at the first and second violin lines reveals the presence of a characteristic suspension dissonance: 9–10, rather than 7–6, as the tenor clausula lies above the clausula cantizans. Although this two-part counterpoint (9–10–8) could easily give rise to a perfect authentic cadence, the two lowest voices do not make their expected contribution: the cello moves from ‫ ݜ‬to ‫ݝ‬, while the viola proceeds from ‫ ݛ‬to ª‫ݛ‬. Due to the separation of forces combining to establish a full cadence, the deceptive cadence here may come as a surprise not only to listeners but also to (at least two) performers, especially in the case of a prima vista performance.

Example 4: Haydn, String Quartet in C minor, op. 17 No. 4/i, mm. 38–41

The distinction between the variants of a deceptive cadence generated by bass motion and those produced by the upper voices had a notable tradition long before Walther,56 and it remained important throughout the eighteenth century as well. Numerous contemporaneous theorists explained deceptive cadences in terms of the non-normative behavior of one of the voices typically involved in creating a complete cadence. However, not all of them subscribed to Walther’s theory of Klauselverwechslung when describing the various forms of deceptive cadences. For instance, in his Kritische Briefe über die Tonkunst, Marpurg argues that interrupted and evaded cadences arise when either the penultimate or the ultimate stage of the expected succession is altered in either the bass or the soprano. He cites V7–vi, V7–vii°7/vi–vi, and V7–V42–I6, among other harmonic progressions. In the second volume (1787) of his Versuch einer Anleitung zur Composition, Heinrich Christoph Koch likewise categorizes deceptive patterns into soprano- and 55. See Gjerdingen, Music in the Galant Style (2007), 152. 56. See, for instance, Caeyers, Het ‘Traité de l’Harmonie’ van Jean-Philippe Rameau (1989), 217ff.

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bass-generated groups.57 With regard to the bass, Koch cites only the ‫ ݝ–ݜ‬motion and its variant ‫ݝ–ݜ©–ݜ‬, but his soprano-induced deceptive cadences show a greater variety. Three variants end with a V–I progression supporting 2^–3^ in the upper voice, its chromaticized variant 2^–©2^–3^, or (due to octave replacement) 2^–8^ (see Example 5). Similar variants are cited in Daniel Gottlob Türk’s Clavierschule from 1789, but without much additional explanation.58 Interestingly, none of these authors relate the methods of producing deceptive cadences to the procedure of exchanging clausulae.

Example 5: Koch, Versuch II (1787), 445: Four variants of deceptive cadences

Example 6: Riepel, Tonordnung (1755), 61: A melodically deceptive cadence

Anticipating Koch’s discussion of deceptive cadences generated by the upper voice, Riepel provides an interesting case of a “false and deceptive […] cadence”

57. Koch, Versuch II (1787), 444f. 58. Türk, Clavierschule (1789), 352.

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(“falsche und betriegende […] Cadenz”) that illustrates the technique of avoiding cadential closure by melodic means alone: in his example, the melody is expected to go down to scale degree 1^ but instead surprisingly reverts to 3^ (see Example 6).59 The subtlety of Riepel’s interpretation becomes evident when it is compared to a modern analysis: because the harmonic progression that can be inferred from the given melody is V–I, and because the ultimate chord has the third in the soprano, most analysts would be inclined to view this as an instance of an imperfect authentic cadence. However, such a reading would conflate two different types of imperfect cadences: those in which a perfect authentic cadence is expected, and those in which no such expectation has been generated. The latter is the case with the Prinner cadence, in which the third scale degree is actually the expected melodic goal.60 This is not merely a terminological issue; rather, it reflects significant differences in formal expectations, as demonstrated by what usually follows these two types of cadences in a given compositional context: whereas the melodically deceptive PAC cannot stand on its own and is therefore almost invariably followed by phrase repetition that brings about a satisfactory PAC, the Prinner cadence can indeed function as a Kochian Grundabsatz— concluding a self-contained thematic unit that, especially in the galant style, is usually followed by a transitional unit ending with a half cadence in the tonic key. Clearly, the technique described by Riepel has been exploited numerous times in the classical repertoire. Mozart’s Keyboard Trio in B¨ major, K. 502/i (m. 8) provides just one of the many examples of this technique (see Example 7).61 Often, 2^–3^ is decorated by a chromatic passing tone (©2^), as seen in the second movement of the same trio (m. 4). The unsatisfactory nature of such an ending is underscored by the fact that it is followed by an immediate repetition of the previous phrase that ultimately reaches a state of complete closure. Overall, this interpretation suggests that the modern notion that “[t]he deceptive cadence […] [is] a deviation merely in the bass”62 is too limited. The category of the deceptive cadence may be extended to cover the case of a deceptive imperfect authentic cadence as well. The idea that the IAC can also be avoided by a deceptive move in the bass is not explicitly mentioned in the historical literature. Although this strategy seems to have been much less frequently employed than the deceptive PAC, there are some significant examples of this type in the musical literature.63 The comparatively infrequent usage of this strategy may be due to the 59. Riepel, Tonordnung (1755), 61. 60. On the Prinner cadence, see Caplin in this volume. 61. See also Mozart’s Keyboard Sonatas K. 284/ii (m. 25), K. 309/ii (m. 72), K. 310/iii (m. 44), K. 330/iii (m. 55), K. 331/i (m. 16), K. 333/ii (m. 25), and K. 333/iii (m. 32). 62. Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), 138. 63. See Mozart’s Piano Concerto, K. 466/ii (m. 32; compare with the intact IAC in m. 8), the Keyboard Trio, K. 254/ii (mm. 2.3 and 5.3), and the Keyboard Sonatas K. 279/i (mm. 7–10), K. 330/i (mm. 27–31), K. 332/ii (mm. 5– 6), and K. 457/ii (mm. 9–11). Caplin mentions Haydn, Hob. XVI:26/i, m. 18 as a further instance of this type; see Caplin, Classical Form (1998), 271 (n. 25).

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fact that the IAC is already a weaker form of cadence; further weakening it by a deceptive motion in the bass may therefore be deemed ineffective. Finally, there is Sulzer’s argument that the half cadence can also be avoided by means of a vermiedene Kadenz (see below) by adding a seventh to the ultimate V chord.64 Based on the analyses of Riepel and Sulzer, we may conclude that rather than viewing deception as a separate type similar in status to a PAC or an HC, it can best be understood as a technique (or strategy) that could essentially operate on all basic cadential types (PAC, IAC, HC).

Example 7: Mozart, Keyboard Trio in B¨ major, K. 502/i, mm. 1–12 (keyboard only)

II. Formal and tonal functions of the deceptive cadence Having discussed the various forms that deceptive cadences can take, I now focus on the structural roles they can play in different form-functional and tonal contexts. Such contextual usages have most prominently been discussed by Schenkerian theorists. For these scholars, the concrete form of deceptive cadence is less important than the manner in which the deceptive sonority is embedded (and hence functions) in the overall voice-leading structure. Carl Schachter, for instance, examines the

64. See Sulzer, “Cadenz” (1771), 186. See also Burstein in this volume.

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various functions that scale degree ‫ ݝ‬in the bass fulfills in deceptive cadences (usually, but not invariably, supporting vi), demonstrating that ‫ ݝ‬acts as a highly flexible connective element of the bass melody. As Schachter notes, it is precisely this context-dependent flexibility that poses a considerable challenge to any theoretical discussion of the deceptive cadence: “As it happens, […] deceptive cadences are frequently quite difficult to interpret, partly because the ways they relate to harmonic context, to the articulation of formal units, and to the higher levels of tonal structure are so numerous and varied.”65 Crucial to answering the question of the contextual role of the deceptive harmony is therefore what follows that sonority. In this regard, Schenker himself in his Free Composition provides a brief but illuminating discussion of what he refers to as “the so-called deceptive cadence,” devoting particular attention to the events that may follow the deceptive ending (see Example 8): “With the succession V–VI, the bass in a) sets out in the direction of the ascending fourth-progression […] – but it can be led back by means of interpolated fifths into the direction of the descending fifth V–I.”66 As we shall see below (see Example 12), the ascending fourth-progression may form the second half of the rising variant of the “rule of the octave.” The possibilities cited by Schenker are by no means exhaustive, however. In actual compositional practice, ‫ ݝ‬may revert directly to ‫( ݜ‬especially when ‫ ݝ‬supports vii°6/V or V43/V) without interpolating the leap down to ‫ݙ‬. In addition, ‫ ݝ‬may be followed by another ‫ݘ–ݜ–ݛ–ݚ‬ (or ‫ )ݘ–ݜ–ݛ‬bass motion that eventually succeeds in completing the previously interrupted cadential progression.

Example 8: The deceptive cadence in Schenker’s Free Composition, Figure 71

No matter which of these options a composer chooses, the deceptive harmony is usually interpreted by Schenkerians as a prolongation of the dominant; the dominant preceding the deceptive sonority remains active until it is resolved to the tonic that concludes the subsequent phrase.67 The situation is therefore analogous to the type of Schenkerian interruption structure found in a parallel period, in which the V chord ending the first phrase is disconnected from what immediately ensues in the second phrase and resolves only when the final tonic enters.68 (Note that the issue of 65. 66. 67. 68.

Schachter, “Che inganno!” (2006), 281. Schenker, Free Composition (1979), 70. Less frequently, it is interpreted as a prolongation of the tonic. For an account of Schenkerian interruption, see, for instance, Cadwallader and Gagné, Analysis of Tonal Music (2011), 119f.

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whether the harmony following the dominant groups forward or backward is largely irrelevant to decisions regarding harmonic subordination.) One may even take the analogy between these two situations one step further by suggesting that both feature phrase repetition motivated by an incomplete cadence in the structure’s first part—a technique that has later come to be known as the “one-more-time” technique, a term coined by Janet Schmalfeldt.69 In the case of the period, it is either a half cadence or an imperfect authentic cadence that prompts the composer to repeat the previous phrase and to conclude the entire structure with a comparatively stronger type of cadence (a PAC), thus creating the form-defining antecedent-consequent pattern.70 If we accept Schenker’s idea that interruption is crucial to creating form in music, then the deceptive cadence may also be understood as a genuinely form-building device.

(1) Formal extension Although the consideration of the larger-scale functions of cadential devices is more characteristic of twentieth-century theories, it is not the case that eighteenthcentury authors neglected these functions entirely. In fact, Joseph Riepel (in his Grundregeln zur Tonordnung insgemein from 175571) and Johann Friedrich Daube (in his Generalbaß in drey Akkorden from 1756) were among the first theorists to mention the capacity of unfinished cadences to motivate the repetition of a previously incomplete cadential phrase.72 To be sure, for Schmalfeldt, the application of the one-more-time technique is closely linked to what she defines as an “evaded cadence”—that is, a cadential progression whose expected goal harmony (the tonic) is cut off from the preceding group, instead initiating the subsequent group. However, Schmalfeldt’s discussion should not be taken to imply that the one-more-time technique could only be realized by means of an evaded cadence; neither eighteenth-century sources nor the compositional practice of the time support such a view. In fact, any form of inconclusive (or imperfect) cadence, whether deceptive or evaded by modern standards (i.e., irrespective of whether the deceptive harmony groups forward or backwards) can give rise to phrase repetition.73 In addition, the one-more-time technique is not con69. Schmalfeldt, “Cadential Processes” (1992), 1–52. In general, when phrase repetition occurs in these situations, the repeated phrase need not necessarily end on 1^ in the same register promised by the previous phrase (although it often does); it may also close either an octave higher or lower. When it does so, one may speculate as to whether the purpose of the phrase repetition is not only to bring about the full closure previously denied, but also to reach a different (perhaps structurally more conclusive) register. 70. See Aldwell and Schachter, Harmony and Voice Leading (2003), 200: “the deceptive cadence provides the impetus for a varied repetition of the whole four-bar phrase in a kind of antecedent-consequent grouping. This is another frequent possibility.” 71. This is the second volume of Riepel’s Anfangsgründe zur musicalischen Setzkunst. 72. Riepel, Tonordnung (1755), 61f., and Daube, Generalbaß in drey Akkorden (1956), 70. 73. Although Caplin does not state this explicitly, it follows from his discussion that he subscribes to this view; see Caplin, Classical Form (1998), 101.

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fined to the secondary-theme zone; it can be found in a number of formal sections, ranging from the primary and secondary themes (within an exposition) to the end of the development. In the main-theme zone, the one-more-time technique is most commonly used in sentences to effect the repetition of the continuation phrase. In Haydn’s C-major Trio Hob. XV:27/i, for instance, it seems that the sentence continuation (mm. 5ff.) might conclude the main-theme structure with a perfect authentic cadence as early as m. 8 (see Example 9). The fact that the moment of closure is denied by means of a common variant of a deceptive cadence (vii°7/vi–vi) motivates the (almost literal) repetition of this four-measure phrase, this time completing the entire primary theme by means of an elided I:PAC (m. 12).74 Due to the utilization of a deceptive cadence, the sentence continuation is extended from four to eight measures. The same structural effect can be produced by a melodically deceptive PAC (formerly IAC), as seen in the Mozart Trio, K. 502/i (m. 8) cited above (Example 7).

4

8

Example 9: Haydn, Keyboard Trio in C major, Hob. XV:27/i, mm. 1–12 (keyboard only)

One variant of the one-more-time strategy in a sentential main theme involves extended “monofold sentences” with only one basic idea and a repetition of the

74. In Beethoven’s Sonata op. 2 No. 3/i, it is an imperfect authentic cadence that motivates the repetition of the sentence continuation (see mm. 1–13).

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continuation phrase.75 A model example of this type can be found at the opening of Haydn’s String Quartet op. 17 No. 4 (see Example 10). Here, a typical Romanesca bass (‫ݚ–ݝ–ݜ–ݘ‬, in the minor mode) merges into a cadential ‫ ݜ–ݛ–ݚ‬pattern, which proceeds not to ‫ ݘ‬but instead to ‫( ݝ‬m. 6). However, ‫ ݝ‬is not articulated as an ending point, but rather as the initial event of another (this time complete) cadential progression that concludes on ‫ݘ‬. Thus, the continuation phrase (second half of m. 4 to m. 6) and its repetition are linked to each other in a loop-like fashion, and the first failed cadence is best described as an evaded cadence pace Schmalfeldt.76

Example 10: Haydn, String Quartet in C minor, op. 17 No. 4/i, mm. 1–8

The degree of deceptiveness attributed to a particular instance of a deceptive cadence depends not only on the harmony replacing the final tonic (and its relation to both the tonic and the penultimate dominant in terms of common tones), but also to a large extent on the specific formal context in which it is used. For instance, in the context of a sonata-form exposition, deceptive or evaded cadences may be said to occur more frequently in the subordinate-theme area than in the primary theme or transition.77 Likewise, the one-more-time technique has more commonly been associated with

75. Richards, “Viennese Classicism and the Sentential Idea” (2011). In 1960, Wilhelm Fischer gave the resulting formal design the label “A2B”; see Fischer, “Zwei Neapolitanische Melodietypen” (1960), 7–21. 76. See also Mozart’s Keyboard Sonata K. 279/ii, in which the basic idea (mm. 1–2) is followed first by an evaded cadence (mm. 3–4) and then by a complete cadence (mm. 5–6). 77. The transition (almost) never makes use of delaying strategies such as the deceptive cadence.

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the subordinate-theme zone than with the primary-theme zone. Indeed, examples of this technique employed in the S-zone abound in the musical literature. Based on their stylistic knowledge, listeners expect to be fooled at some point prior to the moment of structural closure. However, this is not to say that a deceptive cadence is deprived of its surprising capacity when it is frequently used, and hence in a way expected, in a given formal context. Whether or not it exercises deceptive power ultimately depends on the extent to which conscious stylistic (and thus abstract) knowledge is accessible during our real-time processing of musical information. Here, an interesting cognitive problem arises, as Naomi Cumming has described: the contradiction between the claim that listeners have acquired stylistic competency and the phenomenon of deceived listening expectations. Leonard Meyer’s assertion that listening expectations rely on and are indicative of the internalization of stylistic norms can only be maintained on the basis of a differentiation in the concept of style78: Cumming assumes that only the abstract rules (derived from a given corpus) have been internalized, not the individual solutions and strategies serving the realization of these rules.79 A variant of the problem Cumming describes is the so-called “Wittgenstein paradox”: If a listener is completely familiar with a given piece, this familiarity is viewed as precluding any feeling of surprise; as a result, the piece under consideration would be deprived of its aesthetic qualities. Nevertheless, most of us would agree that a deceptive cadence in a familiar piece still sounds unexpected. This problem can only be resolved by distinguishing between two different types of expectations, one based on “veridical” memory and the other on “schematic” memory.80 Crucially, these two memory systems are assumed to be modularly separated, or, in Jerry Fodor’s terms, “informationally encapsulated.”81 The stylistic knowledge acquired by listeners familiar with the classical style creates the expectation that sometimes subordinate themes will feature not merely a single deceptive (or evaded) cadence but rather a series of several such cadences. Consider the exposition in the first movement of Haydn’s G-major Sonata, Hob. XVI:27 (Example 11). What is remarkable about this movement is that the exposition could have ended 14 measures earlier than it actually does. In other words, it would have been possible for Haydn to establish a moment of structural closure already in m. 43. However, Haydn instead chooses to deny definitive closure no fewer than three times, thus greatly expanding the subordinate-theme zone.82 First,

78. 79. 80. 81. 82.

See, for instance, Meyer, Emotion and Meaning in Music (1956), 72. Cf. Cumming, “Analogy in Leonard B. Meyer’s Theory of Musical Meaning” (1991), 185. On this distinction, see Bharucha, “Music Cognition and Perceptual Facilitation” (1987), 1–30. See Jackendoff, “Musical Parsing and Musical Affect” (1991), 221. In Haydn’s Keyboard Sonata Hob. XVI:26/i, the same type of deceptive cadence (m. 23) is used only once. It is not followed by other instances of deceptive cadences of the same type or other inconclusive

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when the upper voice descends from 6^ to 1^, the bass deviates from the expected cadential pattern by moving from ‫ ݜ‬to ‫( ݝ‬rather than leaping down to ‫)ݘ‬. The fact that this progression is not heard as articulating a true deceptive goal is due to the inner voices (D and G©), which transform what might be fleetingly understood as a stable submediant sonority into a much more active secondary dominant function (vii°6/V; m. 44). A second cadential goal is approached in mm. 47–48. Here again, the soprano carries out its expected typical concluding formula (1^–2^–1^, featuring a trill on the penultimate 2^), but once more the bass denies closure by moving from ‫ݜ–ݛ–ݚ‬ to ‫ݝ‬, with the latter again being harmonized as vii°6/V. The preceding unit is now repeated in its entirety (mm. 48–52 ~ 43–47), but the roles of the soprano and bass are exchanged: Whereas the bass provides its expected clausula ‫ݘ–ݜ‬, the soprano violates expectations by moving from 2^ to 3^ (rather than completing its previous 1^–2^–1^ pattern). This cadence may be heard as an imperfect authentic cadence, but because a perfect authentic cadence is genuinely expected at this point and this expectation is disappointed, we can refer to this pattern as a melodically deceptive cadence (based on Riepel’s suggestion cited above). The unsatisfactory character of the IAC is also revealed by the fact that a two-bar unit is attached to this cadence. This unit not only completes the previously denied 1^–2^–1^ pattern (mm. 54–55) but also restates the same cadential material, thus re-opening the phrase and not allowing S to end until the PAC closing the exposition as a whole is achieved.83 The ensuing three-bar unit functions to confirm the new tonic (mm. 55–57). This example is instructive in a number of respects. For one thing, it illustrates that in the secondary-theme zone, the number of cadence evasions in a row is typically limited to three (or four).84 In addition, the order of the different types of deceptive cadence is also revealing: Haydn first uses very strong deceptive variants in which the chord interrupting the cadential progression is highly unexpected. Only toward the end of the exposition does Haydn use more subtle (milder) variants of inconclusive cadences. Generally speaking, in the case of multiple successive deceptive cadences, the composer seems to prefer deceptiveness to move from strong to weak.85

cadences (e.g., IACs); instead, a second attempt at a complete cadence commences, using different material (mm. 23–27). 83. See also Hepokoski and Darcy’s notion of “EEC-deferral” described in their Elements (2006), 150ff. 84. See also the analogous situations in Mozart’s Piano Sonatas K. 310/i and 332/i. 85. See also Haydn’s Keyboard Sonata Hob. XVI:21/ii (Example 12) and the String Quartet op. 17 No. 4/i (Example 15). This topic merits further examination.

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        p                   43   

                      mf                                                                                            48                      f                                  53                            p                             38

Example 11: Haydn, Keyboard Sonata in G major, Hob. XVI:27/i, mm. 38–57

Another particularly imaginative example of a deceptive cadence motivating further attempts to realize a complete cadence can be found in the second movement of Haydn’s Keyboard Sonata Hob. XVI:21 (see Example 12). The first part of the secondary-theme area (mm. 13–19) is designed as a sentence, featuring a four-measure presentation, a two-measure continuation, and a two-measure (failed) cadence. Following a sequential progression, a tonic chord that is then transformed into a secondary dominant to IV launches a normative cadential progression (mm. 18–19). However, the cadence does not succeed in providing full closure to the S-zone. Rather, Haydn violates listening expectations in a variety of ways, playing not only with the “what” dimension of expectation (the expected tonic vs. a non-tonic harmony) but also with the “when” dimension (the downbeat vs. a subsequent weak beat), thus creating an even stronger effect of surprise: On the downbeat of m. 20, we do not hear a full chord (neither the expected tonic nor a deceptive harmony) but rather the third d2–b2 held over from the preceding measure in the manner of an appoggiatura; the bass drops out at this point (the bass is implied rather than actually present). This delay of resolution heightens or intensifies the state of expectation. At the moment when we

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anticipate that the imagined appoggiatura will resolve on the second, weak beat of m. 20, the soprano moves from 2^ to 1^ (as expected). However, the soprano continues to be shadowed a third below, thus providing a1 as a non-tonic element. Likewise, there is no tonic harmony provided at this point, but rather a fully-diminished sonority (vii°65/V) based on A—a dissonant harmony that propels the music further instead of allowing a resting place. The diminished chord is prolonged into the next bar, where it resolves into a V6 chord; this in turn leads to a root-position tonic preparing a second attempt to achieve a complete cadence. As a result, scale degree ‫ ݝ‬on which the deceptive sonority is based acts as a connective element that forms part of the ascending linear bass motion ‫ݘ–ݞ–ݝ–ݜ‬, as described by Schenker (see above).86 13

16

19

23

Example 12: Haydn, Keyboard Sonata Hob. XVI:21/ii, mm. 13–26

As stated above, the sonorities with which the expected cadential pattern is interrupted at its ultimate stage, thus motivating the use of the one-more-time technique, are limited neither to vi nor to I6. An excerpt from Haydn’s Symphony No. 40/i demonstrates that this technique could begin with almost any harmony initiating the new 86. See also Aldwell and Schachter, Harmony and Voice Leading (2003), 199.

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formal segment (see Example 13).87 Here, following a variant of a Passo Indietro (vii°64– I6), a Cudworth cadence88 typically used to attain a moment of structural closure seems to be about to materialize (m. 43), but the final tonic fails to appear; instead, the music rather abruptly leaps backwards in time in a loop-like manner to IV (m. 44 ~ 41), which initiates another attempt to conclude the previously incomplete cadence. Unlike typical instances of an “evaded cadence,” the tonic is denied entirely: Since “both the third and the root [of the tonic] disappear”89, Riepel argues, the degree of deceptiveness is enhanced in this particular case (see Example 14). 41

Example 13: Haydn, Symphony No. 40/i in F major, mm. 41–46 (piano reduction)

Example 14: Riepel, Tonordnung (1755), 62

Deceptive cadences, especially those featuring chords based on scale degree ‫ݝ‬, frequently serve the purpose of prolonging the penultimate dominant. This dominant prolongation, which can be rather short or highly extended in time, is sometimes not directly followed by a second attempt to complete the cadential progression in the manner of the one-more-time technique. Let us consider two examples of this category, beginning with the first movement of Haydn’s String Quartet op. 17 No. 4 (mm. 38–53; see Example 15). Toward the end of the exposition, it appears that a grand cadence is about to materialize, featuring a complete cadential progression, a comparatively slow harmonic rhythm, a cadential 64, and a trill on 2^. As mentioned above, this type of cadence is commonly used to attain the “Essential Expositional Closure” (EEC) in a sonata-form movement. Despite the unequivocal presence of features belonging to this cadence type, the cadence ultimately fails to establish closure. Although the first violin moves from 2^ to 1^, accompanied by 7^ to 1^ in the second violin, the bass and the viola break the expected pattern by moving from ‫ ݜ‬to ‫ ݝ‬and from 4^ to ª4^, respectively, 87. Cf. also Caplin, Classical Form (1998), 106. 88. Cf. Gjerdingen, Music in the Galant Style (2007), 147. 89. Riepel, Tonordnung (1755), 62 (my translation).

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thus producing the deceptive progression V7–vii°6/V (m. 41). As Schachter notes (see above), scale degree ‫ ݝ‬is a remarkably flexible connective element, irrespective of the harmony (vi or vii°6/V) it supports.90 It can either continue the ascending line by proceeding to ‫( ݞ‬e.g., Haydn’s Hob. XVI:21/ii, see above), or, alternatively, it can return to ‫ݜ‬, as it does here (m. 42). As a result, the deceptive cadence is embedded between two dominant sonorities, with the motion ‫ ݜ–ݝ–ݜ‬in the bass serving to prolong V. This V chord is somewhat disconnected from the subsequent cadential progression both harmonically and texturally, as the progression starts not on the tonic but rather on a ii6 chord. Interestingly, perfect closure is strategically delayed until the very end of the exposition by means of twice avoiding melodic closure in the soprano (mm. 47 and 51), which moves from 2^ back to 3^ rather than to 1^. 38

42

90. Alternatively, a diminished chord (vii°7/V) on ©4 can be used to achieve virtually the same structural effect (as, for instance, in Ignaz Pleyel’s Symphony No. 10 in F major [1786], Them. Index 10, first movement, m. 68).

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45

49

52

Example 15: Haydn, String Quartet in C minor, op. 17 No. 4/i, mm. 38–53

The temporal extension of the dominant prolongation may even go so far as to produce what Bernard Van der Linde has called a Versunkenheitsepisode—that is, a more or less extensive tonal parenthesis.91 Unlike the examples discussed above, in this case, there is no immediate second attempt to complete the previously inconclusive cadence. 91. Van der Linde, “Die Versunkenheitsepisode bei Beethoven” (1977).

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In the first movement of Johann Georg Albrechtsberger’s C-major Symphony (from 1768), the composer opted to follow a widespread mid-century convention of confirming the subordinate key by means of a PAC (m. 21) before the entrance of a more lyrical theme or idea (see Example 16). Usually, after this strong cadence, a contrasting section ensues, one that features a reduced instrumental texture (strings alone), a reduced dynamic level (piano), and (optionally) a sustained ‫ ݜ‬in one of the voices and imitative counterpoint. Although he begins the section with only the first and second violins in piano, Albrechtsberger deviates from this practice by twice inserting a unison cadence (mm. 22–23 and 24–25). The listener naturally expects the second unison cadence (bass progression ‫ )ݜ–ݛ–ݚ‬to conclude on the tonic. However, all voices move on to ¨‫ ݝ‬instead (m. 25), subsequently prolonging the E-flat major sonority for three measures. It is only at the end of m. 27 that Albrechtsberger introduces a 7–6 suspension resolving to the augmented sixth (C©), which in turn resolves to a D-major sonority in the manner of a Phrygian half cadence (m. 28). This cadence is followed by a final tutti section that provides a PAC (m. 34) that is more conclusive than the earlier unison cadence (even if it would not have been interrupted). In retrospect, the extended E-flat sonority acted as an upper neighbor to (and thus as a means of prolonging) V. Introducing ©4^ is a very common way to clarify the function of the chord on the flattened submediant, forcing it to resolve to V.92 21

25

Example 16: Albrechtsberger, Symphony in C major (from 1768), i, mm. 21–28 (piano reduction)

A composer could opt to postpone a structural cadence not only in the exposition but in the development section as well. One rather straightforward example of this strategy can be found in the first movement of Haydn’s F-major Sonata Hob. XVI:23 (Example 17); a more detailed treatment of deceptive cadences in the development can be found in the next section under “modulation.” Following a series of diminished chords, a perfect authentic cadence in the key of the submediant seems ready to 92. See also Haydn, Keyboard Trio in E major, Hob. XV:28/i (mm. 24ff.).

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materialize, one that promises to lend structural closure to the development section as a whole. However, the expected tonic sonority is denied at the ultimate stage of the cadential progression, and a diminished chord on C© (vii°7) is sounded instead (m. 75). As a dissonant sonority, the diminished chord is cut off from the preceding group in the manner of an evaded cadence; at the same time, it gives rise to a second attempt at completing the cadence.93 73

75

Example 17: Haydn, Sonata in F major Hob. XVI:23/i, mm. 73–77

Because the diminished chord is analogous to the chord appearing on the downbeat of m. 73, a loop-like effect is created at this point: It is as if the listener is pushed back to an earlier point in time. This example provides evidence that I6 is only one (although probably the most common) of several options that can be used to interrupt a cadential pattern in order to subsequently launch a second cadential progression. In fact, a variety of other harmonies can fulfill this role; some of these harmonies (especially dissonant ones) seem to automatically give rise to a new beginning (and thus to group forward) rather than providing a genuine goal harmony.

(2) Modulation The second large-scale function of deceptive cadences described in the contemporaneous literature is modulation, a function mentioned by authors as early as Daube, Albrechtsberger, and Reicha. Daube, for instance, presents a list of 17 possible ways of avoiding cadential closure, some of which make use of applied dominants and thus imply a key change (e.g., V7–vii°7/ii, V7–V42/ii, V7–V7/IV, and V7–V42/IV; see Example 18).94 Daube’s list is expanded considerably in Antonin Reicha’s Traité de haute composition musicale from 1824, in which the author cites no fewer than 129 possible forms of decep-

93. After the vi:PAC, we hear a Fonte sequence that realizes the modulation back to the home key (mm. 77ff.). 94. Daube, General-Bass in drey Accorden (1756), 68.

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tive cadences. According to Reicha, a composer may choose to build a substitute chord for the expected tonic on any scale degree of a chromatic scale (including a number of enharmonic variants).95 The examples presented by Daube and Reicha clearly demonstrate that eighteenth- and early-nineteenth-century theorists had a much broader category in mind when they used the term “deceptive cadence” than most theorists do nowadays. In addition, it is evident that theorists of that time shared with modern writers a sensitivity to the structural functions of deceptive cadences.

Example 18: Daube, General-Bass in drey Accorden (1756), 68: Variants of deceptive cadences

The modulatory function of deceptive cadences is explicitly mentioned by Albrechtsberger. Echoing Scheibe’s characterization in terms of a “foreign harmony related to a different key,” Albrechtsberger considers that a deceptive cadence has occurred when a cadential progression ends on a chord that does not belong to the key implied by that progression. In this process, virtually any chord can be chosen to digress from the home key: “To those who are proficient masters in the art of modulation, it will be easy to create these deceptive cadences in an endless variety of shape; for it is possible to modulate from every interval, as through a labyrinth, to every key […].”96 It is precisely the capacity of bringing about a modulation that, in Albrechtsberger’s opinion, sets the Trugschluß apart from what he calls unterbrochene Cadenz (or “interrupted cadence”), both being deceptive cadences. From a lis-

95. Reicha, Traité de haute composition musicale (1824), 686. 96. Albrechtsberger, Gründliche Anweisung zur Composition (1790), 166 (translation by Novello).

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tening perspective (in real-time), however, this distinction becomes evident only in retrospect, as the decisive criterion is whether or not the deceptive harmony (which may even be identical in the two cases) is used to launch and ultimately confirm the modulatory process to a new key. It comes as no surprise that within a sonata-form context, deceptive cadences initiating a modulatory process have exclusively been used in development sections. Consider, for instance, the diatonic modulation employed in the first movement of Haydn’s C-major Symphony No. 38 (see Example 19). In an attempt to conclude the development in the key of the submediant, a cadence is prepared twice but rejected both times by VI (‫ ݝ–ݜ‬in the bass, mm. 107f. and 109f.). The third time, an even clearer cadential progression seems to be about to emerge: a unison ‫ ݜ–ݛ–ݚ‬motion that promises to bring about closure by leading to a ‫ ݘ–ݜ‬bass clausula.97 ‫ ݘ–ݜ‬is denied, however, and instead ‫ ݜ‬proceeds to ‫ݝ‬, with ‫ ݝ‬eventually being contextualized as the root of an F-major sonority. F major is then extended for another twelve measures (mm. 113–124). It is only in m. 125 that F is reinterpreted as IV in the key of C major, turning into a ii6 chord through a 5–6 intervallic progression over a stationary bass note (‫)ݛ‬. The fourth scale degree in the bass is then forced by a V42 chord to drop down to ‫( ݚ‬harmonized as I6), which in turn gives rise to a converging half cadence (m. 128) that concludes the development section (m. 131). 104

113

122

Example 19: Haydn, Symphony No. 38/i in C major, mm. 104–131 (piano reduction)

97. Note that the bass clausula is the only clausula that can realize a cadential effect in the manner of a unison cadence despite the absence of the other clausulae. The bass clausula appearing in all voices is frequently used to articulate the end of a Kochian Schlußsatz (see Koch, Versuch II [1787], 422).

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In retrospect, it becomes clear that the deceptive cadence in m. 112 ultimately served a modulatory purpose. It is important to note here that in a different formal context, such as the exposition, this type of harmonic prolongation is usually deployed to create a tonal parenthesis; by using ¨‫ ݝ‬as the bass note of a German augmented sixth chord, Haydn could easily return to the key of A minor if he had intended to stay in that key.98 Another instructive instance of a deceptive cadence fulfilling a modulatory function in the development section, one that is more difficult to grasp in terms of traditional theory, can be found in the first movement of Haydn’s Symphony No. 8, better known as Le Soir (see Example 20). Here, after a stormy sequential passage in the middle of the development, the main theme is sounded in mm. 143ff. in the subdominant key (subsequent to a IV:HC in m. 141).99 Whereas the antecedent phrase closes with an imperfect authentic cadence, as expected on the basis of the analogous pattern established at the beginning of the movement (m. 146 ~ m. 4), the consequent phrase refuses to conclude with a perfect authentic cadence, which would be required to complete the periodic structure of the theme. Instead, right at the moment when the cadential 64 resolves, the bass begins to move downwards, first to ‫( ݛ‬supporting a V42 chord, m. 149.3), then to ‫( ݚ‬harmonized as I6, m. 150). In other words, whereas the upper voice behaves as expected in a normative cadential context, providing a highly typical descending 5^–4^–3^–2^–1^ line (mm. 149–150), the bass undermines closure by moving down to ‫ݚ‬. 141

Example 20: Haydn, Symphony No. 8/i in G major (Le Soir), mm. 141–152 (piano reduction)

In a different formal context, such as in the subordinate-theme section of an exposition, the harmonic situation described above would be interpreted as involving an evaded cadence—one that raises the expectation of a full cadential progression in the same key to follow, thus realizing the implications that have been created. In the context of the development, however, Haydn chooses to employ a strategy that is both ingenious and remarkably simple. First, no clear grouping boundary is established at the moment of arrival on I6 (m. 150). I6 is not cut off from the preceding progression—for example, by 98. For a non-modulatory usage of the deceptive sonority, see the development section in Leopold Kozeluch’s Piano Sonata op. 15 No. 2/iii: here, the deceptive harmony (VI in the key of the submediant) does not give rise to a modulation but instead fulfills a prolongational function (mm. 100f.). As a result, the development ends on V/vi rather than V/I. 99. Some authors view this thematic return as articulating a false recapitulation, an interpretation that I have challenged elsewhere; see Neuwirth, “Does a ‘Monothematic’ Expositional Design have Tautological Implications for the Recapitulation?” (2010), 383–385.

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a marked textural break, as is usually the case in similar situations that theorists have identified as evaded cadences. Second, the I6 chord is reinterpreted as IV6 of G major (the home key), which can now easily be transformed into a German augmented sixth chord on ¨‫ ݝ‬by chromatic contrary motion of the outer voices (c2–c©2 in the soprano and E–E¨ in the bass, m. 151).100 By resolving the augmented chord, a half cadence in the home key is achieved (m. 152), setting the stage for the subsequent perfect authentic cadence to conclude what previous commentators have described as the development section.101 In other words, the deceptive (or perhaps better, “redirected”) cadence is again used here to return to the home key of a sonata-form movement. However, what is so remarkable about this particular cadence is that there is a seamless transition from the (failed) perfect cadential progression to the goal harmony of the Phrygian cadence (mm. 149–152). This feature makes a classification in terms of either a deceptive or an evaded cadence particularly tricky for the analyst. Daube and Albrechtsberger were not the only eighteenth-century theorists to point out the modulatory usage of deceptive cadences. In his Allgemeine Theorie der schönen Künste, Sulzer (assisted by Kirnberger) describes a situation that he refers to as involving a “vermiedene Kadenz” (“avoided cadence”).102 The defining feature of this technique of cadence deviation is that just at the moment when one expects the final tonic to enter, that tonic is transformed into an applied dominant by adding a lowered seventh (I7 = V7/IV), thus pushing the musical trajectory in a different tonal direction. The entrance of a dissonant sonority at the end of a cadence makes it clear that the deceptive harmony does not articulate a genuine resting point after which the music can simply restart another formal unit to achieve definitive closure in the same key. Rather, in the manner of an evaded cadence, the applied dominant groups forward with the following unit, in which we expect a new key to receive cadential confirmation. Anticipating Schmalfeldt’s (and Caplin’s) grouping-based distinction between deceptive and evaded cadences, Sulzer does not consider this progression to belong to the category of “cadence” at all. Unlike the deceptive cadence, the chord replacing the tonic in a vermiedene Kadenz is a forward-looking dissonant harmony that propels the music onward instead of articulating a point of rest.103 Due to its modulatory capacity, Sulzer’s vermiedene Kadenz was often used in compositional practice to articulate the boundaries between the “development proper” and the retransition. In a number of examples from Haydn’s oeuvre, the deceptive

100. A different possibility is exploited in the recapitulation of Mozart’s Keyboard Sonata K. 283/ii, m. 27, where the I6 in the tonic key is transformed into a V7/IV chord, thus preparing the subsequent entrance of the subdominant key. 101. For a more detailed analysis of the development section, see Neuwirth, “Does a ‘Monothematic’ Expositional Design have Tautological Implications for the Recapitulation?” (2010), 383–385. 102. Sulzer, “Cadenz” (1771), 186. 103. See also Caplin, Classical Form (1998), 29.

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goal serves as a secondary dominant that enables the composer to modulate from the key of vi back to the home key within the retransition: V7/vi–V7/ii–ii64–V7/I–I. Here, the vermiedene Kadenz is typically followed by an elided (or interrupted) Fonte model104 that eventually completes the modulatory process.105 This situation is aptly illustrated by the first movement of Haydn’s Keyboard Sonata in D major, Hob. XVI:37/i (see Example 21), where a cadential 64 (m. 57) resolves into a V7 chord supporting scale degree 2^ (decorated by a trill) in m. 58. However, although the dominant resolves into a chord based on a root a fifth below (B), we do not get the expected B-minor chord, but instead hear yet another V7 based on B (m. 59), which is subsequently prolonged by an (incomplete) neighboring motion. Although the expected cadence is interrupted in m. 59, there is also a sense of elision conveyed at this point, as the harmony replacing the tonic is a closely related substitute for the tonic of B minor and thus articulates both an endpoint and the initial event of the subsequent phrase. This interpretation can account for the fact that no phrase repetition is employed in such situations to close off the harmonic structure, at least on a local level. If we denied any sense of resolution here, the V-implication would remain entirely open. Nevertheless, as a moment of harmonic instability, the deceptive sonority clearly groups forward rather than articulating a resting point (however unexpected) of the previous cadential progression. In addition, it is not only harmonic expectations that are violated here, but melodic implications as well: 2^ does not proceed to 1^ but is instead forced to turn back to ©3^. The first half of m. 59 is then repeated one step lower (m. 60), but the expected neighboring motion is denied; instead, the V7/I sonority is sustained and a forceful scalar lead-in gives way to the emphatic reentrance of the home-key tonic that articulates the start of the recapitulation (m. 61).

104. Fonte is the Italian term for one of three voice-leading patterns (the other two being Monte and Ponte) introduced by Riepel in his Tonordnung (1755), 44–48. Riepel intended the term Fonte (literally, “well, fountain, source”) to indicate “going down a well” (or, in Riepel’s words, “Fonte, Brunn zum hinabsteigen”; see his Tonordnung [1755], 44). This metaphor refers to the characteristic descending motion of the model, as the initial unit (generally in minor mode and with a length that may vary between two and 16 measures) is immediately transposed down a whole step (usually into major mode). Typically, each unit consists of an alternation between a 6/3 and a 5/3 sonority, with 4–3 in the soprano accompanied by 7–1 in the bass. The example given by Riepel shows a descending sequence in a C-major context, in which A–d (V/ii–ii) is followed by G–C (V/I–I), reaching the tonic at the final stage of the model. The Fonte is first and foremost a voice-leading model that can be used to destabilize the main tonality and bring about a modulation. As a result, it appears primarily at two formal positions within the sonataform context: either in the exposition transition or in the developmental retransition. Outside of the sonata-form context, the Fonte has also been used in smaller forms, such as minuets directly after the double repeat sign; this usage can be found in the minuets written by Mozart as a young boy (see Gjerdingen, “Defining a Prototypical Utterance” [1991], 133ff.). 105. Examples from Haydn’s oeuvre include the Keyboard Sonatas Hob. XVI:25/i (mm. 44f.) and Hob. XVI:35/i (mm. 98f.), the Symphony No. 75/i (mm. 111f.), the String Quartet op. 55 No. 3/i (mm. 122f.), and the Keyboard Trio Hob. XV:6/i (m. 97).

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54

56

59

62

Example 21: Haydn, Keyboard Sonata in D major, Hob. XVI:37/i, mm. 54–64

A quite similar situation can be observed in the development section of the first movement of Haydn’s F-major Symphony No. 89 (see Example 22). Here, a cadential process in the submediant key is launched by means of a Neapolitan sixth chord (m. 105), which is subsequently chromatically intensified by moving from ‫ ݛ‬to ©‫ݛ‬ (G–G©). The diminished chord based on ©‫ ݛ‬leads to a cadential 64 that resolves, as expected, to a V chord (m. 107); however, the proper resolution of this chord is denied. Instead of providing the tonic in the next measure, yet another V(7) chord appears (m. 108), one that is expected to resolve to a G-minor sonority (i.e., iv in the context of the submediant key). Although we do not get a G-minor chord in root position, we hear the expected chordal elements over a sustained D in the bass in m. 109 (in the manner of a neighboring motion, as described above in the analysis of Haydn’s D-major Sonata). This neighbor-note motion remains incomplete, as a chromatic passing-note motion (D–D¨–C) in the bass leads to a final V7 chord (m. 110), which prepares us for the home-key entrance of the recapitulation articulated by the main theme’s fanfare-like incipit (mm. 111ff.).

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105

Example 22: Haydn, Symphony No. 89/i in F major, mm. 105–112 (piano reduction)

Other examples from the literature suggest that the deceptive harmony need not necessarily be an applied dominant; a fully diminished sonority can likewise be used to achieve a similar deceptive effect, accompanied by comparable structural consequences. In Haydn’s A-flat major Keyboard Sonata Hob. XVI:43/i (see Example 23), for instance, the development “proper” promises to conclude with a perfect authentic cadence in the submediant key (F minor). However, at the moment of expected tonic resolution, a fully diminished chord on ª‫ ݚ‬enters (m. 88), pushing the music in a different tonal direction and paving the way back to the home key. It first prepares a double dominant (m. 89) before resolving to a dominant (m. 90), which in turn resolves to the tonic (m. 91). The harmonic process in mm. 87–93 can be summarized as follows: V7/vi–vii°7/ii–V7/V–V65–I–ii65–V65/V–V (I:HC). 86

90

Example 23: Haydn, Keyboard Sonata Hob. XVI:43/i in A¨ major, mm. 86–93

A slightly different procedure using a diminished sonority is employed in the development section of Mozart’s Piano Sonata K. 279/ii (see Example 24). Here, the submediant key is unequivocally established in m. 31 by means of a Phrygian progression. The subsequent harmonic progression sets up the expectation of increasing the degree of closure by signaling a perfect authentic cadence. However, the penultimate dominant does not properly resolve into a tonic harmony but is instead sustained by bass motion (‫)ݛ–ݜ‬, thus turning into a third-inversion sonority. Due to the analogy with m. 33 and the resumption of the subsequent cadential progression, a loop-like effect is produced in mm. 35–36. (Note that this mild (or not so mild) shock has

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been carefully prepared by the deceptive cadence we heard in the primary theme of the exposition, m. 4.) Since cadential closure has been denied before, expectations regarding a complete cadence are considerably enhanced at this point in the form. But once again, Mozart refuses to properly resolve the penultimate dominant, instead sustaining ‫ ݜ‬in the bass, chromatically deflecting the upper voice (c©2–c2), and filling in the remaining elements in the inner voices to create a fully diminished chord, vii°43/V (m. 37). This chord considerably increases the sense of denial in comparison to the applied dominant-seventh chord in Haydn’s Hob. XVI:37/i, in which at least some sense of resolution is conveyed, owing to the presence of the chordal root. The diminished chord is used to arrive at a sixth chord (m. 38) that, in turn, carries the potential of acting as the antepenultima ii6 in the home key (F major).106 This makes it clear that any chord that has the potential to push the musical course in 29

33

37

41

Example 24: Mozart, Piano Sonata in F major, K. 279/ii, mm. 29–44

106. That formal context is crucial to the treatment of a given deceptive sonority, becomes evident from the non-modulatory usage of the diminished chord in Mozart’s Piano Sonata K. 281/ii (see mm. 39 and 41, respectively).

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another tonal direction can be used to interrupt the expected cadential progression.107 Continuing the descending-fifths sequence initiated with the dominant of D minor (A–D–g–C–F), Mozart is able to achieve the entrance of the recapitulatory rotation (mm. 43ff.). As this example quite convincingly demonstrates, Mozart indeed reveals himself as one of Albrechtsberger’s “proficient masters in the art of modulation.”

Conclusion By way of conclusion, I would like to summarize the most important findings offered in this chapter. First of all, the various forms that a deceptive cadence can take in the eighteenth-century repertoire exceed by far the simple V(7)–vi (or, in minor, V(7)–¨VI) formula cited in countless modern textbooks on tonal harmony. Second, adopting a linear (as opposed to chord-centered) perspective on deceptive cadences helps to explain in a quite elegant fashion a particular feature that has long been a topic of discussion: namely, the doubling of the third of the submediant. Third, the deceptive cadence is a device that not only plays with listening expectations, but also serves a variety of structural purposes, such as phrase extension (including dominant prolongation and tonal parenthesis) and modulation. To this end, almost any sonority can be chosen to interrupt the expected cadential progression. Some of these sonorities seem to automatically create a mere chord succession (rather than a genuine progression), thus grouping forward, while others represent true goal harmonies. However, no matter whether a cadence is deceptive or evaded by modern standards, the structural consequences (most importantly, phrase extension) may be virtually identical. Therefore, local grouping might seem secondary in a structural sense; what matters is the fact that a given cadential progression does not reach a state of completion and is frequently (but not invariably) followed by a second (successful) attempt to attain closure. Whether a certain deceptive cadence is prolongational or modulatory in nature depends largely on the formal context in which it appears: in an exposition, it typically serves a prolongational purpose, while in the development the same type of deceptive cadence may be used to bring about a modulation. These insights into the structural consequences of deceptive cadences notwithstanding, one of the most important lacunas that must be addressed in future research

107. In Haydn’s Keyboard Trio in F© minor, Hob. XV:26/i, a diminished chord on G© is used as a deceptive harmony at the very end of development section (m. 61f.); this chord is then reinterpreted in such a way as to prepare the subsequent entrance of the recapitulation (m. 63).

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concerns the psychological effects of these devices. Only a more detailed study of the preconditions of these effects—in particular, the intricate and multilayered interaction between intra- and inter-opus knowledge structures—will allow us to arrive at a more complete understanding of the seemingly simple but in fact highly complex art of avoiding cadence closure.

Bibliography Agawu, Kofi (1991), Playing with Signs: A Semiotic Interpretation of Classic Music, Princeton: Princeton University Press. Agmon, Eytan (1995), “Functional Harmony Revisited: A Prototype-Theoretic Approach,” Music Theory Spectrum 17/2, 196–214. Albrechtsberger, Johann Georg (1790), Gründliche Anweisung zur Composition mit deutlichen und ausführlichen Exempeln, zum Selbstunterrichte, erläutert; und mit einem Anhange: Von der Beschaffenheit und Anwendung aller jetzt üblichen musikalischen Instrumente, Breitkopf: Leipzig. Aldwell, Edward and Carl Schachter (2003), Harmony and Voice Leading, Australia, United States: Thomson/Schirmer. Berardi, Angelo (1687), Documenti armonici, Bologna: Monti. Bharucha, Jamshed J. (1987), “Music Cognition and Perceptual Facilitation: A Connectionist Framework,” Music Perception 5/1, 1–30. Cadwallader, Allen and David Gagné (2011), Analysis of Tonal Music: A Schenkerian Approach, New York: Oxford University Press. Caeyers, Jan (1989), Het ‘Traité de l’Harmonie’ van Jean-Philippe Rameau (1722) en de ontwikkeling van het muziektheoretische denken in Frankrijk, Paleis der Academien: Brussels. Calvisius, Sethus (1592), Melopoiia sive melodiae condendae ratio, Erfurt: Baumann. Caplin, William E. (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, New York: Oxford University Press. ——— (2004), “The Classical Cadence: Conceptions and Misconceptions,” Journal of the American Musicological Society 57/1, 51–117. Christensen, Thomas (1993), Rameau and Musical Thought in the Enlightenment, Cambridge: Cambridge University Press. Cumming, Naomi (1991), “Analogy in Leonard B. Meyer’s Theory of Musical Meaning,” in: Metaphor: A Musical Dimension, ed. Jamie C. Kassler, Syndey: Currency Press, 177–192. Daube, Johann Friedrich (1756), General-Bass in drey Accorden, gegründet in den Regeln der alt- und neuen Autoren, Frankfurt a. M.: André. Deppert, Heinrich (1993), Kadenz und Klausel in der Musik von J.S. Bach. Studien zu Harmonie und Tonart, Tutzing: Schneider. Descartes, René (1618/1650), Compendium musicae, Amsterdam: Joannes Janssonius Junior. Fischer, Wilhelm (1960), “Zwei Neapolitanische Melodietypen bei Mozart und Haydn,” Mozart-Jahrbuch 1960-61, 7–21. Forte, Allen (1974), Tonal Harmony in Concept and Practice, 2nd edition, New York: Holt, Rinehart and Winston, Inc.

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Gauldin, Robert (1997), Harmonic Practice in Tonal Music, New York: Norton. Gjerdingen, Robert O. (1988), A Classic Turn of Phrase: Music and the Psychology of Convention, Philadelphia: University of Pennsylvania Press. ——— (1991), “Defining a Prototypical Utterance,” Psychomusicology 10, 127–139. ——— (2007), Music in the Galant Style, New York: Oxford University Press. Hepokoski, James and Warren Darcy (2006), Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata, New York: Oxford University Press. Holtmeier, Ludwig (2007), “Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave,” Journal of Music Theory 51/1, 5–49. ——— (2010), “Rameaus langer Schatten: Studien zur deutschen Musiktheorie des 18. Jahrhunderts,” Ph.D. diss., Technische Universität Berlin. Jackendoff, Ray (1991), “Musical Parsing and Musical Affect,” Music Perception 9/2, 199–229. Kaiser, Ulrich (2006), Die Notenbücher der Mozarts als Grundlage der Analyse von W.A. Mozarts Kompositionen 1761–1767, Kassel: Bärenreiter. Kellner, David (1732), Treulicher Unterricht im General-Baß, Hamburg. Kirnberger, Johann Philipp (1771/2004), Die Kunst des reinen Satzes in der Musik, Kassel: Bärenreiter [English transl. by David Beach and Jurgen Thym (1982), The Art of Strict Musical Composition. Introduction and Explanatory Notes by David Beach, New Haven: Yale University Press]. Koch, Heinrich Christoph (1782–1787–1793), Versuch einer Anleitung zur Composition, 3 vols., Leipzig: Böhme. Reprint, Hildesheim: Olms, 1969. Selections trans. Nancy Kovaleff Baker as Introductory Essay on Musical Composition, New Haven, CT: Yale University Press, 1983. ——— (1802), Musikalisches Lexikon, Frankfurt a. M.: Hermann. ——— (1811), Handbuch bey dem Studium der Harmonie, Leipzig: Hartknoch. Lakoff, George (2008), Women, Fire, and Dangerous Things, Chicago: University of Chicago Press. Lerdahl, Fred and Ray Jackendoff (1983), A Generative Theory of Tonal Music, Cambridge, MA: MIT Press. Marpurg, Friedrich Wilhelm (1760, 1763, 1764), Kritische Briefe über die Tonkunst, Berlin: Birnstiel. Masson, Charles (1699), Nouveau traité des règles de la composition de la musique, Paris: Ballard. Mattheson, Johann (1739), Der vollkommene Capellmeister, Hamburg: Herold. ——— (1722), Critica musica, Hamburg: Herold. Menke, Johannes (2011), “Die Familie der cadenza doppia,” Zeitschrift der Gesellschaft für Musiktheorie 8/3, 398–405. Meyer, Leonard B. (1956), Emotion and Meaning in Music, Chicago: Chicago University Press. ——— (1989), Style and Music: History, Theory, and Ideology, Philadelphia: University of Chicago Press. Mignot, De la Voye (1656), Traité de musique, Paris: Ballard. Mirka, Danuta (2004), “Das Spiel mit der Kadenz,” Die Musikforschung 57/1, 18–35. Neuwirth, Markus (2010), “Does a ‘Monothematic’ Expositional Design have Tautological Implications for the Recapitulation? An Alternative Approach to ‘Altered Recapitulations’ in Haydn,” Studia Musicologica 51/3-4, 369–385. Nivers, Guillaume-Gabriel (1667), Traité de la composition de musique, Paris: Ballard. Printz, Wolfgang Caspar (1676–1677), Phrynis Mitilenæus, oder Satyrischer Componist, Dresden and Leipzig: J.C. Mieth & J.C. Zimmermann.

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Rameau, Jean-Philippe (1722), Traité de l’harmonie réduite à ses principes naturels, Paris: Ballard [English transl. by Philip Gossett (1971), Treatise on Harmony, New York: Dover]. Reicha, Antonin (1824–1826), Traité de haute composition musicale, Paris: Zetter. Richards, Mark (2011), “Viennese Classicism and the Sentential Idea: Broadening the Sentence Paradigm,” Theory and Practice 36, 179–224. Riemann, Hugo (1898), Handbuch der Harmonielehre, 3rd edition, Leipzig: Breitkopf & Härtel. Riepel, Joseph (1996), Anfangsgründe zur musicalischen Setzkunst (= Sämtliche Schriften zur Musiktheorie), ed. Thomas Emmerich, 2 vols., Vienna: Böhlau. Rothstein, William (1989), Phrase Rhythm in Tonal Music, New York: Schirmer. Schachter, Carl (2006), “Che inganno! The Analysis of Deceptive Cadences,” in: Essays from the Third International Schenker Symposium, ed. Allen Cadwallader, Hildesheim: Olms, 279–298. Scheibe, Johann Adolf (1739), Critischer Musicus, Hamburg: Thomas von Wierings Erben. Schenker, Heinrich (1935/1979), Free Composition, trans. and ed. Ernst Oster, New York: Longman. ——— (1954), Harmony, trans. Elizabeth Mann Borgese, ed. Oswald Jonas, Chicago: University of Chicago Press. Translation of Harmonielehre, Stuttgart: Cotta, 1906. Schmalfeldt, Janet (1992), “Cadential Processes: The Evaded Cadence and the ‘One More Time’ Technique,” Journal of Musicological Research 7/1-2, 1–52. Schmalzriedt, Siegfried, Elke Mahlert, and Bernd Sunten (1974), “Kadenz,” in: Handwörterbuch der musikalischen Terminologie, Wiesbaden: Steiner. Schneider, Herbert (1973), “Charles Masson und sein ‘Nouveau traité’,” Archiv für Musikwissenschaft 30/4, 245–274. Spieß, Meinrad (1745), Tractatus musicus compositorio-practicus, Augsburg: Lotters Erben. Sulzer, Johann Georg (1771–1774), Allgemeine Theorie der schönen Künste, 2 vols. Berlin: Winter. Temperley, David (2001), The Cognition of Basic Musical Structures, Cambridge, MA: The MIT Press. Türk, Daniel Gottlob (1789), Klavierschule oder die Anweisung zum Klavierspielen für Lehrer und Lernende, Leipzig and Halle. Van der Linde, Bernard S. (1977), “Die Versunkenheitsepisode bei Beethoven,” BeethovenJahrbuch 1973-77, 319–337. Walther, Johann Gottfried (1708), Praecepta der musicalischen Composition, Weimar. ——— (1732), Musicalisches Lexicon oder Musicalische Bibliothec, ed. Friederike Ramm, Kassel: Bärenreiter, 2001. Werckmeister, Andreas (1702), Harmonologia Musica oder Kurtze Anleitung Zur Musicalischen Composition, Frankfurt and Leipzig: Calvisius. Zarlino, Gioseffo (1558/1968), Le istitutioni harmoniche, part III [English transl. by Guy A. Marco and Claude V. Palisca (1968), The Art of Counterpoint, New Haven: Yale University Press].

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THE MYSTERY OF THE CADENTIAL SIX-FOUR* Danuta Mirka

To begin with the end

O

ne of the favorite tricks played by Haydn on eighteenth-century formal conventions was to begin with a cadence. A celebrated instance occurs in the first movement of his String Quartet in D major, op. 50 No. 6, “The Frog” (Example 1a). This trick has been noticed by several authors1 but none of them has taken note of the complementary trick at the end of the finale. There (Example 1b), the cadence returns in the coda (mm. 229–231), interrupting the course of this section and being interrupted, in turn, by a general pause.2 The following section forms a codetta and draws upon the finale’s croaking theme that gave the quartet its nickname. Consequently, the quartet begins with the end and ends with the beginning—or, it starts with a cadence and closes without it.3 The lack of cadential closure is emphasized in the codetta. Although the function of codettas is to confirm the cadential goal of the preceding section, and many accomplish this through further cadences, this codetta contains no cadence. The final tonic has the third rather than the root in the upper voice, and the bass fills the skip from scale degree 5^ to 1^ with chromatic steps. This affects the status of the dominant *

1.

2.

3.

I thank Markus Neuwirth for his valuable feedback on an earlier version of this article and David Jayasuriya for improving its English prose. See Rosen, The Classical Style (1971), 128; Sutcliffe, String Quartets, Op. 50 (1992), 100; and Grave and Grave, The String Quartets of Joseph Haydn (2006), 237. These authors concentrate on the tonal dimension of this trick. The metrical dimension is discussed in Mirka, Metric Manipulations in Haydn and Mozart (2009), 33f. In mm. 229–231 the melodic motive from mm. 1–2 of the first movement is transposed up a fifth and combined with the cadential harmonic progression from mm. 3–4. At the same time, this motive refers to the subsidiary theme of the finale (Grave and Grave, The String Quartets of Joseph Haydn [2006], 237). For an analysis of the metrical context of its occurrence in the coda, see Mirka, Metric Manipulations in Haydn and Mozart (2009), 179f. The general pause interrupting the cadence after the six-four chord is an ellipsis (Mirka, “Absent Cadences” [2012], 222–226). Sutcliffe (String Quartets, Op. 50 [1992], 103) takes note of the “inter-movement quotation” in the finale but he does not relate the absence of cadential closure at the end of the quartet cycle to its presence at the beginning.

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expected after the cadential six-four (V64) in m. 231. The empty octave A–A following the general pause suggests continuation of the preceding harmony and gives no hint of the dominant. Only with the arrival of the bass on C© does the minor sixth C©–A allow the listener to perceive the first-inversion dominant triad (V6), but this perception is fleeting and delayed because the dominant emerges on the last eighth note of m. 232, stretching back to the octave A–A retained in the listener’s memory. The shadowy status of this dominant, spanned between expectation and memory, means that it is degraded to the role of a passing chord between the cadential six-four and the tonic.4 Consequently, the cadential six-four from m. 231 does not resolve to the dominant in m. 232 but flips to the tonic in m. 233. Given that the chords framing the dominant consist of the same tones, and the tonic triad arises through inversion of the cadential six-four, the six-four chord changes its harmonic function in retrospect from the dominant six-four (V64) to the tonic six-four (I64).

Example 1a: Haydn, String Quartet in D major (“The Frog”), op. 50 No. 6/i, mm. 1–6

4.

This differs from the harmonic context at the beginning of the development. The empty octave D–D (mm. 84–86) following the dominant seventh of the main key (m. 83) cannot be construed as its continuation and it brings a change of harmony to the dominant of the subdominant (G major).

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Example 1b: Haydn, String Quartet in D major (“The Frog”), op. 50 No. 6/iv, mm. 225–243

The fourth and the six-four chord The double identity of the six-four chord was a fresh insight of eighteenth-century music theory, emerging from the controversy around the consonant or dissonant status of the fourth.5 In the old Pythagorean tradition, which classified intervals according to numerical ratios of string divisions, the fourth was a consonance due to its simple ratio 3:4. As such, this interval was part of the senario: the ensemble of intervals arising from string divisions into two, three, four, five, and six equal parts. In the sixteenth century Gioseffo Zarlino posited number six (numero senario) as the upper limit of consonances.6 Intervals between tones arising from string divisions and the fundamental tone of the undivided string formed the class of consonantiae absolutae. The fourth belonged to the consonantiae relativae, i.e., intervals between different string divisions without direct participation of the fundamental tone.7 The consonant status of the fourth between the fifth and the octave of the harmonic triad was also accepted in the tradition of trias harmonica founded by Johannes Lippius. In the early eighteenth century this tradition was continued by Wolfgang Caspar Printz, Andreas Werckmeister, Johann Georg Ahle, and Johann Gottfried Walther, among others. For the representatives of anti-Pythagorean sensualism, gaining the upper hand from the beginning of the eighteenth century, the fourth was a dissonance. This stream of music theory included “Aristoxenos the Younger” alias Johann Mattheson as well

5.

6. 7.

The history of this controversy reaches back to antiquity. My account of the positions taken in the modern era and the state of the debate in the eighteenth century is indebted to Wolfgang Grandjean (Mozart als Theoretiker [2006], 94–99) and Ludwig Holtmeier (“Rameaus langer Schatten” [2010], 221–225). More information about the status of the fourth can be found in Joel Lester, Compositional Theory (1992). Gioseffo Zarlino, Le istitutioni harmoniche (1558), 23–28. In his later treatise, Dimonstrationi harmoniche (1571), Zarlino invokes the invertibility of intervals within an octave and explains that the perfect fourth should be consonant because it is an inversion of the consonant perfect fifth. See Lester, Compositional Theory (1992), 17.

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as the main exponents of the North-German Generalbasslehre, Johann David Heinichen and C. P. E. Bach.8 In spite of its dissonant status, the fourth of the six-four chord was treated by these authors with a certain degree of freedom: it could be introduced without preparation and, if passing, could be doubled and left unresolved.9 The SouthGerman tradition of Generalbasslehre, represented by the Salzburg music theorists Georg Muffat, Johann Baptist Samber, Matthäus Gugl, and Michael Haydn, also subsumed the fourth under the dissonances but at the same time distinguished between quarta dissonans, colliding with the fifth in the five-four chord, and quarta consonans, combining with the sixth in the six-four chord. Irrespective of this distinction, the consonant fourth of some six-four chords was treated as a dissonance: prepared, tied, and resolved.10 Elements of the Zarlino tradition found their way into the new Harmonielehre of Jean-Philippe Rameau presented in his Traité de l’harmonie (1722). For Rameau, the fourth is consonant, even if it is not directly generated by the fundamental tone but arises instead from the inversion of the fifth.11 The principle of invertibility (renversement) allowed Rameau to treat the six-four chord as the second inversion of a triad. The cadential six-four is understood as the second-inversion tonic triad, with the fundamental bass (basse fondamentale) of this chord lying a fifth below the real bass (basse continue).12 In other chords, including the five-four chord, the fourth is in fact the eleventh (onzième), i.e., a dissonance which must be prepared and resolved. Beginning with his Nouveau système (1726) and the Generation harmonique (1737), Rameau justifies the consonant status of the fourth between the fifth and the octave by the fact that it is found in the series of harmonic overtones produced by corps sonore. From the mid-eighteenth century onwards, Rameau’s views on the fourth and the cadential six-four chord were propagated by his chief advocate in Germany, Friedrich Wilhelm Marpurg.13 8.

“Aristoxenos the Younger” was the pseudonym used by Mattheson in some of his publications. The most extensive discussion of the fourth is contained in the second part of Mattheson’s Das Forschende Orchestre (1721), 451–767. 9. See Mattheson (Das Neu-Eröffnete Orchestre [1713], 128; Das Forschende Orchestre [1721], 756–760), Heinichen (Der General-Bass [1728], 173), and Bach (Versuch II [1762], 67). 10. For more information about the Salzburg circle of music theorists, see Federhofer, “Ein Salzburger Theoretikerkreis” (1964), 62–66. The distinction between quarta consonans and quarta dissonans may have influenced Mozart’s distinction between “accordo di quarta consonante” and “accordo di quarta dissonante” introduced in his course of composition for Thomas Attwood (Federhofer, “Mozart als Schüler und Lehrer” [1971/72], 102f.; Grandjean, Mozart als Theoretiker [2006], 95f.). 11. See Rameau, Treatise (1971), 13f. 12. Nathan Martin pointed out (in personal communication) that Rameau’s understanding of the cadential six-four as the second-inversion tonic triad can be inferred from his discussion in the Traité, even if it is not explicitly stated. The inference is confirmed in Nouveau système (1726), 96, where Rameau indicates the tonic as the fundamental bass of a cadential six-four in an excerpt from Corelli’s Sonata in B¨, op. 5 No. 2/iv. Rameau’s view changes in the “Art de la basse fondamentale.” His discussion of a suspended fourth that can be accompanied by a suspended sixth over the dominant note implies that he takes the cadential six-four for a double suspension (Christensen, “Rameau’s ‘L’Art de la Basse fondamentale’” [1987], 30; Martin, “Rameau’s Changing Views” [2012], 144–146). 13. See Marpurg, Handbuch bey dem Generalbasse I (1755), 28. Nevertheless, Marpurg’s discussion of the fourth in the second volume (1757), 78–81, regarding its preparation and resolution, conforms to

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The controversy surrounding the fourth was summarized by Johann Philipp Kirnberger in the article “Quarte”, included in the second volume of Johann Georg Sulzer’s Allgemeine Theorie der schönen Künste (1771–74): Das reine Verhältniß der Quarte gegen den Grundton ist nach den Längen der Sayten wie ¾ zu 1; oder kurz die Quarte wird durch ¾ ausgedrückt. [...] Hieraus läßt sich schon abnehmen, daß die Quarte ein angenehm consonirendes Intervall, und das nächste an Annehmlichkeit nach der Quinte, sey. Dafür ist sie auch von den Alten, ohne Ausnahm immer gehalten worden. Hingegen findet man, daß die besten neuern Harmonisten sie meistentheils, als eine Dissonanz behandeln, und eben den vorsichtigen Regeln der Vorbereitung und Auflösung unterwerfen, als die unzweifelhaftesten Dissonanzen. Da es aber doch auch Fälle giebt, wo Quarten gänzlich wie Consonanzen behandelt werden, so ist daher unter den Tonlehrern, die die wahren Gründe dieses anscheinenden Wiederspruchs nicht einzusehen vermochten, ein gewaltiger Krieg über die Frag entstanden, ob dieses Intervall müsse den Consonanzen oder Dissonanzen zugezählt werden. Und dieser Streit ist bey vielen bis auf diese Stunde nicht entschieden. Und doch scheinet die Auflösung dieses paradoxen Satzes, daß die Quarte bald consonirend, bald dissonirend sey, eben nicht sehr schweer. Alle ältere Tonlehrer sagen, die Quarte consonire, wenn sie aus der harmonischen Theilung der Octav entstehe, und dissonire, wenn sie aus der arithmetischen entstehe. Andre drüken dieses so aus: die Quarte dissonire gegen die Tonica, hingegen consonire die Quarte, deren Fundament die Dominante der Tonica sey. Beyde Arten des Ausdrucks sagen gerade nicht mehr, und nicht weniger, als wenn man sagte, dieser Accord [Example 2a] klinge gut, und dieser [Example 2b] klinge nicht gut. Dieses empfindet jedes Ohr. In beyden Accorden liegt eine Octave, eine Quint und eine Quarte, wie der Augenschein zeiget. Aber im ersten empfindet man die Quinte in der Tiefe, gegen den Grundton und die Quarte in der Höhe, gegen die Dominante des Grundtones; im andern hingegen liegt die Quarte unten, und klinget gegen den Grundton, die Quinte oben, und klinget gegen die Unter-Dominante, oder die Quarte des Grundtones. Hieraus nun läßt sich das Räthsel leicht auflösen.14 The pure ratio of the fourth against the fundamental tone, according to the length of the strings, is ¾ to 1; or briefly, the fourth is expressed by ¾. […] One may infer from this that the fourth is a pleasing consonant interval, the next in this regard after the fifth. This is for what it has always been taken, without any exception, by the older theorists. Instead, one can see that the newer harmonists treat it in most cases as a dissonance and subject it to the Heinichen’s and Bach’s. Marpurg changes his view of the fourth during the dispute with Sorge and then, again, with Kirnberger. Inconsistencies in his position are described by Daniel Gottlob Türk in the second edition of his Anweisung zum Generalbaßspielen (1800), 186f. 14. Kirnberger, “Quarte” (1774), 931f.

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cautious rules of preparation and resolution, like the most clear-cut dissonances. Since there are cases in which fourths are treated like consonances, a violent war has broken out among teachers of composition unable to understand the true reasons for this apparent contradiction, as to whether this interval should be counted among consonances or dissonances. And for many of them the controversy remains unresolved to this day. And yet the resolution of the paradox, that the fourth is sometimes a consonance, sometimes a dissonance, is not very difficult. All older teachers of composition say that the fourth is a consonance when it arises from the harmonic division of the octave, and a dissonance when it arises from the arithmetic division. Others express this as follows: the fourth is dissonant against the tonic but consonant against the dominant. Both formulations say nothing more and nothing less than that this chord [Example 2a] sounds good, and that chord [Example 2b] sounds bad. Every ear perceives this. Both chords comprise an octave, a fifth and a fourth, as one may readily observe. But in the first chord, one perceives the fifth below against the fundamental tone, and the fourth above against the dominant of the fundamental tone; whereas in the second chord, the fourth is below and sounds against the fundamental tone, while the fifth is above and sounds against the subdominant or the fourth of the fundamental tone. The enigma can thus easily be resolved.

Example 2a: Kirnberger, “Quarte” (1774), 932

Example 2b: Kirnberger, “Quarte” (1774), 932

The solution proposed by Kirnberger lies in the relation of the fourth to the series of harmonic overtones. In the first chord the fourth belongs to the overtone series and hence is consonant. In the second chord the dissonant character of the fourth results from its collision with the fifth comprised in the series of overtones: So bald man einen Ton und dessen Octave höret, vornehmlich, wenn man ihn als eine Tonica, als einen Grundton vernihmt, so will das Gehör den genzen Dreyklang vernehmen; besonders höret es die Quinte gleichsam leise mit, wenn sie gleich nicht angeschlagen wird. Nun zwinget man es aber hier die Quarte, statt der Quinte zu hören, die freylich als die

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Unter-Secunde der schon im Gehör liegenden Quinte mit ihr stark dissonirt. Man muß sich also jenen zweyten Accord so vorstellen, als wenn diese Töne zugleich angeschlagen würden [Example 2c], wobey das g nur sehr sachte klänge. Daß dieser Accord dissoniren müsse ist sehr klar. Es ist also klar, daß man die Quarte, so consonirend sie auch an sich ist, gegen den Grundton, wegen der Nachbarschaft der Quinte nicht als eine Consonanz brauchen könne. Daher braucht man sie in dieser Tiefe nicht anders, als einen Vorhalt der Terz, wodurch sie allerdings die völlige Natur der Dissonanzen annihmt, und so wie jeder Vorhalt muß behandelt werden.15 As soon as one hears a tone and its octave, especially when one perceives it as a tonic, or fundamental tone, the ear perceives the whole triad; in particular, one hears the fifth sounding softly, even though it is not struck. But now, instead of the fifth, which it already hears, one forces the ear to hear the fourth, which, as the lower second of the fifth, is strongly dissonant against it. One should thus imagine the second chord as though these tones were struck together [Example 2c], with the G sounding only very weakly. That this chord must be dissonant is very clear. It is also clear that one cannot use the fourth, consonant as it is in itself, as a consonance against the fundamental tone because of the proximity of the fifth. In this location, therefore, one only uses it as a suspension of the third, through which it acquires the status of a dissonance and must be treated like any suspension.

Example 2c: Kirnberger, “Quarte” (1774), 932

As a consequence of the distinction between the consonant and dissonant fourth, Kirnberger distinguished between the consonant and dissonant six-four chord. The consonant six-four results from the second inversion of a triad and the dissonant six-four is understood as a nonessential dissonance (zufällige Dissonanz) made up of suspensions (Vorhalte). This distinction is outlined in the first volume of Die Kunst des reinen Satzes in der Musik (1771): Dieser [consonirende Quart-Sexten-]Accord ist unter den consonirenden Accorden der unvollkommenste, so daß man damit ein Stück weder anfangen noch endigen kann. Sonst hat er alle Eigenschaften eines consonirenden

15. Kirnberger, “Quarte” (1774), 932. A brief summary of this explanation can be found in the articles “Consonanz” and “Dissonanz” from the first volume of Allgemeine Theorie (1771), 224–227, 262–270, and in the first volume of Die Kunst des reinen Satzes in der Musik (1771), 72 (English translation in The Art of Strict Musical Composition [1982], 91).

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Accordes; nemlich sowol die Quarte als Sexte können verdoppelt werden, sie können frey eintreten, und sie bedürfen nicht, wie die Dissonanzen, einer bestimmten Fortschreitung oder Auflösung, wie in folgendem Beyspiel zu sehen ist. Bey D und E kommt dieser Quart-Sexten-Accord vor; an beyden Stellen ist der eigentliche Grundton C. Bey J sind Quart und Sexte dissonirende Vorhalte, und der Grundton ist G. In den beyden ersten Fällen empfindet man den Grundton C, hingegen bey J nur G. Die Quarte dissoniret hier als ein Vorhalt gegen die Terz des Grundtones, welche man empfindet, und die Sexte gegen die Quinte. Dieser consonirende QuartSexten-Accord kann sowol in guten als schlechten Takttheilen vorkommen, der andere aber, wie alle Vorhalte, fällt immer auf den guten Theil des Takts. This [consonant six-four] chord is the least perfect of the consonant chords and thus cannot be used either to begin or to end a composition. Otherwise it has all the properties of a consonant chord; that is, the fourth as well as the sixth can be doubled, both can be introduced without preparation, and neither requires a specific progression or resolution, as do dissonances. This can be seen in [Example 3]. This six-four chord occurs at D and E; in both cases the fundamental tone [Grundton] is C. At J the fourth and the sixth are dissonant suspensions, and the fundamental tone is G. In the first two, C is heard as the fundamental tone, but at J only G is heard as the fundamental tone. Here the fourth and the sixth are perceived as dissonant suspensions that delay the third and fifth of the fundamental tone. The consonant six-four chord can occur on weak as well as strong beats, but the other, like all suspensions, always falls on a strong beat.16

Example 3: Kirnberger, Die Kunst I (1771), 51

In Kirnberger’s example the consonant and dissonant six-four chords consist of the same tones (G–C–E) but, while the fundamental tone of the consonant six-four lies a fifth below the bass (C), the fundamental tone of the dissonant six-four coincides with the bass (G). It follows that the consonant six-four chord represents the tonic

16. Kirnberger, Die Kunst I (1771), 51f. (The Art [1982], 71, translation amended).

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(I64) while the dissonant—cadential—six-four chord is based on suspensions in the dominant triad (V64).17

Kirnberger, Haydn, and the mystery of the cadential six-four Although Die Kunst des reinen Satzes was not published in Vienna,18 and Kirnberger’s writings were not found in Haydn’s library,19 Haydn’s annotations in the copy of Fux’s Gradus ad parnassum include specific references to the second volume of Die Kunst des reinen Satzes,20 and Haydn’s remarks about Kirnberger’s writings are reported by one of his early biographers, Albert Christoph Dies. To be sure, they are not enthusiastic: “He described them as a ‘basically strict piece of work, but too cautious, too confining, too everlastingly many infinitely tiny restrictions for a free spirit.’ I agreed and added, ‘Like tight clothes and shoes, in which a man can neither stir nor move.’ ‘That’s it exactly’, was Haydn’s answer.”21 Equally unenthusiastic are Haydn’s remarks about Mattheson’s Der vollkommene Capellmeister and Fux’s Gradus ad parnassum reported in the further course of Dies’s biography, although independent evidence suggests that Haydn held both these works and their authors in high esteem.22 Dies, who studied landscape painting in Rome and became the gallery director to Prince Esterházy,23 seems to have been strongly influenced by the 17. The distinction between consonant and dissonant six-four is also discussed in Die wahren Grundsätze (1773), 14f., in articles “Quarte” and “Quartsext-Accord” from the second volume of Allgemeine Theorie der schönen Künste (1774), 931–934, 934–936, and in Grundsätze des Generalbasses (1783), 38, 41, 68. The articles were written by Kirnberger with the help of his pupil, Johann Abraham Peter Schulz. The collaboration between Sulzer, Kirnberger, and Schulz in writing articles about music for Allgemeine Theorie der schönen Künste is described by Sulzer in the preface to the second volume of the original edition. In his account, articles from the first volume (letters A–K) were written by himself and Kirnberger. Schulz wrote all articles from the letter S until the end and assisted Kirnberger with earlier articles in the second volume (letters L–R). Schulz himself offers an account of his contribution and claims his authorship of Die wahren Grundsätze in a later article published in Allgemeine musikalische Zeitung (1800), col. 278. 18. The Viennese edition of Die wahren Grundsätze was published in 1793 (Verlag der k. k. pr. chemischen Druckerey am Graben), and that of Grundsätze des Generalbasses by Hoffmeister omits the date of publication. 19. David Beach (“The Harmonic Theories” [1974], 184) states that Haydn owned a copy of Die Kunst des reinen Satzes but he does not disclose the source of this information. 20. Sumner, “Haydn and Kirnberger” (1975). 21. Dies, Biographische Nachrichten (1976), 41. English translation in Gotwals, Haydn (1963), 96. 22. Haydn prepared two summaries of Fux’s Gradus ad Parnassum for his pupils: Gradus-Kommentar and Elementarbuch der verschiedenen Gattungen des Contrapuncts, aus den größern Werken des Kapellmeister Fux, von Joseph Haydn zusammengezogen. In the Elementarbuch he quotes one paragraph from Mattheson’s Der vollkommene Capellmeister (Mann, “Kontrapunktlehre” [1978/79], 195–199). For further influence of Mattheson’s opus magnum on Haydn, see Jones, “Becoming a Complete Kapellmeister” (2010). 23. Gotwals, Haydn (1963), xiv–xv.

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proto-Romantic aesthetics of genius, so the words he ascribes to Haydn may reflect his own disdain for music theory in general and Kirnberger’s theory in particular.24 But, even if Haydn’s remarks about this theory were as critical as Dies wants us to believe, they still betray that Haydn knew it very well.25 One may suppose that this knowledge was not limited to the theory of counterpoint. If Haydn compared Kirnberger’s teaching of counterpoint with Fux’s, he could also have compared Kirnberger’s approach to harmony with theories by other authors. Since he owned the thoroughbass treatises by Mattheson, Heinichen, Gugl, and Kellner on the one hand, and Marpurg on the other,26 he would have been aware of the controversy surrounding the status of the fourth, and might have been intrigued by Kirnberger’s solution presented by its author as an important achievement.27 What might have attracted Haydn’s attention was the fact that the distinction between the consonant and dissonant six-four was not clear-cut. While the metrical position on the weak beat was reserved for the consonant six-four, the strong beat could host both consonant and dissonant six-four chords. Other features of the dissonant sixfour, regarding the preparation and resolution of dissonances and the prohibition of 24. The only author whose work receives praise from Haydn (or Dies) is C. P. E. Bach, himself a prototype of the Romantic genius. According to Dies, the first handbook purchased by Haydn was Bach’s, and Dies’s account of this purchase, leading to the quotation in the main text, plays Bach against Kirnberger: “Haydn had left a lot to chance in the purchase of the work. Fortune was especially kind to him. It played into his hand the winning ticket among so many blanks, but proceeding in this way is not to be recommended and may in most cases cancel out the hoped-for advantage forever. Haydn’s procedure, however, was not so altogether blindly undertaken. He did not buy until he had inspected, and could then trust to his own sound judgment for a correct decision. Still his natural judgment could have led him astray if fortune had dealt him, instead of Bach’s, works like Kirnberger’s, which must also have pleased him and still would have been in a certain way bad for him. But far from finding fault with Kirnberger’s writings in general, I here set down Haydn’s own opinion” (Dies, Biographische Nachrichten [1976], 41; Gotwals, Haydn [1963], 96). Despite the final disclaimer, one cannot avoid the impression that Dies puts the following words in Haydn’s mouth. 25. This is the conclusion drawn from Dies’s report by Pohl (Haydn I [1878], 176) and confirmed by Sumner (“Haydn and Kirnberger” [1775]). Haydn’s familiarity with Kirnberger’s theory could have been fostered by Kirnberger’s pupil, Baron Gottfried van Swieten. Until 1777, van Swieten was the Austrian ambassador in Berlin, where he took lessons in composition from Kirnberger and stayed in close contact with Kirnberger’s patron, Anna Amalia, Princess of Prussia. Mozart too could have learned Kirnberger’s theory in the circle of Baron van Swieten (Mann, “Leopold Mozart” [1989/90], 32). The Attwood exercises show different fundamental basses for consonant and dissonant six-four chords (Gruber, “Mozarts Lehre” [1982], 127–131; Grandjean, Mozart als Theoretiker [2006], 14f.). 26. Pohl, Haydn I (1878), 389–391; Deutsch, “Haydns Musikbücherei” (1969), 220f.; Landon, Chronicle V (1977), 314–316. David Kellner (Treulicher Unterricht [1743], 71f.) briefly reports the controversy around the fourth but follows the representatives of the North-German Generalbasslehre and subsumes the fourth under the dissonances. 27. Not only in the article “Quarte” from Allgemeine Theorie, quoted above, but also in his composition handbook. The distinction between the consonant and dissonant six-four in Die Kunst des reinen Satzes is supplemented by a vast footnote running through four pages and including four musical examples ([1771], 51–54; The Art, [1982], 71f.). When he returns to this distinction in the course of his discussion of suspensions, he concludes in another footnote: “This is the proper way to distinguish between the consonant and the dissonant fourth, about which so much has been disputed” ([1771], 73; The Art [1982], 91). In Die wahren Grundsätze (1773), 15, he flags the importance of his achievement with a similar remark.

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their doubling, are only valid in the strict style. In the free or galant style they lose their binding power. In Kirnberger’s own words, “the freer style permits the introduction of an unprepared dissonance, the omission of resolution, and the resolution of dissonance in another voice.”28 Consequently, a six-four chord can enter as a dissonant six-four but be treated as a consonant six-four. This is what happens in the finale of Haydn’s op. 50 No. 6. It is thus not far-fetched to suggest that the change in harmonic function of the cadential six-four from the dominant to the tonic was Haydn’s practical conclusion drawn from Kirnberger’s theoretical work. Haydn could have found in this work not only the distinction between the dissonant and consonant six-four but also the category of passing chords derived from passing dissonances. Of course, this last category was not new with Kirnberger: passing dissonances were discussed in almost every thoroughbass treatise and the passing seventh (septima in transitu) was usually illustrated with examples of conjunct ascending or descending bass lines against a sustained chord or tone. Similar examples are shown by Kirnberger in Die Kunst des reinen Satzes (Example 4). The ascending chromatic bass line in the finale of op. 50 No. 6 (Example 1b) contains septima in transitu within the dominant triad.29

Example 4: Kirnberger, Die Kunst I (1771), 85; The Art (1982), 104, example 5.9

But the peculiarity of Haydn’s cadential manipulation is that the dominant triad itself forms a passing chord. The category of passing chords had not been exposed before Kirnberger and does not appear in Die Kunst des reinen Satzes but it is introduced by him or Johann Abraham Peter Schulz in Die wahren Grundsätze […] als Zusatz zu der Kunst des reinen Satzes (1773): Es giebt in der Harmonie durchgehende Accorde, die sich auf keine Grundharmonie gründen; sie sind wie die durchgehenden Töne in der Melodie anzusehen, und entstehen aus diesen, wenn verschiedene Stimmen sich durchgehend bewegen. [...] Daher sind durchgehende Accorde Zwischenaccorde, bey denen eine oder mehrere Stimmen durch eine stufenweise mehrenteils consonirende Fortschreitung von dem vorhergehenden 28. Kirnberger, Die Kunst I (1771), 80; The Art (1982), 100. 29. Kirnberger shows a passing seventh between the dominant triad and its first inversion in another example (Die Kunst I [1771], 87; The Art [1982], 106, example 5.15).

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zu dem folgenden Grundaccord übergehen. Sie stehen allezeit zwischen zweyen Grundaccorden, die entweder dieselben sind, oder doch sehr natürlich auf einander folgen.30 In harmony there are passing chords based on no fundamental harmony; they have to be considered like the passing tones in the melody and arise from them when several voices pass through. […] Therefore passing chords can be called chords-in-between. They occur when one or more voices pass from the preceding to the following fundamental chord through a stepwise and largely consonant motion. They always stand between two fundamental chords which are either the same or follow each other in a very natural way.

Because instances of such chords include both dissonances and consonances, the dominant triad from the Haydn example may be subsumed under this category. The emergence of a passing dominant embedded within the tonic can be reconstructed from Example 5a, which shows a series of passing tones in the bass against the tonic triad sustained in the upper voices. The last four notes of the bass line in Example 5a form a diatonic version of the chromatic bass in Example 1b. The metrical reduction of this example (Example 5b) features the eighth-note rhythmical values used by Haydn. If Example 1b featured a sustained triad, equivalent to G–C–E in the righthand part of Example 5b, then the C© of the cello on the last eighth note of m. 232 would be a passing tone, like the B in the left-hand part of Example 5b, and the flip from the cadential six-four in m. 231 to the tonic in m. 233 would be uncovered. The reduction of texture to two voices by dropping the first violin and viola parts conceals the flip in that it allows the listener to relate the C© of the cello to the A of the second violin and to hear it as a harmonic tone of the dominant triad. The perception of this dominant is further enhanced by the descent of the second violin from G to F© in m. 233, which forms a 4–3 appoggiatura within the tonic triad and sets this chord apart from the dominant triad in m. 232. Since passing chords “are based on no fundamental harmony,” the dominant triad has no fundamental tone (Grundton) but it “stands between two fundamental chords” whose fundamental tone is the tonic.31

30. Kirnberger, Die wahren Grundsätze (1773), 34. For the question of authorship, see footnote 17. 31. David Beach points out that the category of the passing chord implies a distinction between chord and harmony, “a distinction which is not fully developed until the twentieth century” and which “would appear to be the origin of Heinrich Schenker’s important definition of chord versus scale step” (“The Harmonic Theories” [1974], 74). He and Jurgen Thym elaborate upon this point in their translation of Die Kunst des reinen Satzes (Kirnberger, The Art [1982], 104).

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Example 5a: Kirnberger, Die wahren Grundsätze (1773), 49

Example 5b: Kirnberger, Die wahren Grundsätze (1773), 50

Traces of Kirnberger’s influence are even more evident in the opening movement of Haydn’s String Quartet in E-flat major, op. 64 No. 6. This movement contains two cadential manipulations based on the equivocation between the dominant and the tonic six-four, in strategies of postponing final cadences within the exposition and the recapitulation. In the exposition (Example 6), the PAC in the dominant key of B-flat major occurs first in m. 36. The following passage of triplet figuration builds to a stronger cadence, which however proves to be deceptive (DC): it runs into the diminished six-five chord on scale degree 6^ (m. 39). This chord turns toward the cadential six-four in m. 41 but the resolution to the dominant-seventh chord is not followed by further resolution to the tonic. Instead, the V64–V7 harmonic progression is repeated piano in m. 42. The following measures bring ever faster repetitions during which the dominant sevenths have ever shorter rhythmical values and fall on ever weaker metrical positions. This technique undermines their harmonic function: rather than resolutions of the dominant six-four (V64), these chords are increasingly heard as neighbor notes of the second-inversion tonic (I64).

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Example 6: Haydn, String Quartet in E-flat major (1790), op. 64 No. 6/i, mm. 35–45

In the eighteenth century such neighbor notes were subsumed under the category of passing notes: notes that pass between metrical beats. While they are only fleetingly mentioned in Die Kunst des reinen Satzes, passing dissonances are posited by Kirnberger as the third category of dissonances (durchgehende Dissonanzen), distinct from essential (wesentliche) and nonessential dissonances (zufällige Dissonanzen), in the article “Dissonanz” from Sulzer’s Allgemeine Theorie der schönen Künste:32 Jedermann fühlt, wie natürlich es ist, wenn der Gesang um eine Terz steigt oder fällt, durch die Secunde in die Terz zu steigen oder zu fallen. Wenn aber die tiefere Stimme inzwischen ihren ordentlichen Gang behält, so werden die Töne, die man im Durchgang berühret, nothwendig gegen sie dissoniren. Fast eben so natürlich ist es auch, daß man anstatt einen Ton zweymal hinter einander, wie die Melodie es erfordert, anzugeben, auf den

32. The three categories of dissonances are reaffirmed in Grundsätze des Generalbasses (1781), 64, where Kirnberger refers his reader to the discussion in Allgemeine Theorie. Before Kirnberger, similar types of dissonances were introduced by Georg Andreas Sorge in Vorgemach der musicalischen Composition (1745– 1747). Sorge adopts the distinction between passing dissonances and syncopations from Johann Crüger (Synopsis musica [1630]) and supplements it with Heinichen’s category of “anschlagenden Dissonanzen” (see Holtmeier, “Rameaus langer Schatten” [2010], 232f.), but this distinction is of no consequences for the six-four chord. For Sorge, who draws upon the tradition of trias harmonica, the fourth is a consonance and the cadential six-four chord is a second-inversion tonic triad.

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zweyten durch einen Vorschlag, von dem halben Ton über oder unter ihm komme, da denn dieser Vorschlag ebenfalls eine Dissonanz ausmacht. Man sehe folgende Beyspiele: [Example 7] Hier ist allemal auf der guten Zeit des Takts die Harmonie völlig consonirend; nur in dem Uebergang von der ersten Zeit des Takts auf den zweyten kommen in den obern Stimmen Töne vor, die gegen die Grundstimme, die inzwischen liegen bleibet, dissoniren. Da diese Durchgänge dem Gesang natürlich sind, so brauchte man sie, ob sie gleich mit dem Baß dissonirend gefunden wurden. Wegen der Geschwindigkeit des Ueberganges wird die consonirende Harmonie nur einen Augenblick unterbrochen, und sogleich auf den folgenden Schlag mit einer doppelten Annehmlichkeit wieder hergestellt.33 Everyone feels how natural it is, when the melody rises or falls by a third, to fill in such a skip with a second. When the lower voice retains its regular progression, the tones touched upon in transition will necessarily be dissonant against it. It is almost as natural, instead of providing one tone twice in a row, as the melody requires, to reach the second tone through a semitone from above or below, which also creates a dissonance. See the following examples: [Example 7]. Here the harmony on the strong beat of the measure is always fully consonant; only in transition from the first to the second beat of the measure do tones in the upper voice occur which are dissonant against the stationary bass. Since these transitions are natural for the melody, they are needed even though dissonant against the bass. Because of the speed of the transition, the consonant harmony is interrupted only briefly, and immediately restored on the following beat to even greater satisfaction.

Example 7: Kirnberger, “Dissonanz” (1771), 264

The musical examples with which Kirnberger illustrates his discussion are strikingly similar to the harmonic progression observed in the Haydn example. If the bass of 33. Kirnberger, “Dissonanz” (1771), 263f.

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Kirnberger’s examples shown in boxes is omitted, what remains in the right-hand part is an alternation between the second-inversion tonic triad and its neighbor-note chord. The rhythmical values of these chords also correspond to those used by Haydn. This issue is addressed by Kirnberger in the further course of his commentary: Damit aber das, was solche Durchgänge würklich im Gesang angenehmes haben, durch das Dissoniren nicht verdorben werde, so müssen die dissonirende Töne schnell durchgehen, und in der nächsten Zeit des Takts muß die consonirende Harmonie wieder hergestellt seyn. Kommen sie im gemeinen oder langsamen Takt vor, so können sie nicht länger als ein Achteltakt, beym Allabreve oder der geschwinden Bewegung aber, nicht länger als Viertel seyn.34 But, in order that the pleasant effect of such transitions in the melody is not ruined by the dissonance, the dissonant tones must pass quickly, and the consonant harmony must be restored on the next beat. If they occur in common time or slow tempo, they cannot be longer than an eighth note, but in alla breve or fast tempo they cannot be longer than quarters.

In the first movement of op. 64 No. 6, notated in C meter, passing dissonances cannot be longer than quarters and these are the rhythmical values chosen by Haydn in m. 43. The diminution of these values in m. 44 can be interpreted as a shift of passing dissonances from beat subdivisions, represented by quarters, to their further subdivisions into eighth notes or as a change from C to c meter.35 By contrast, the seventh chords in mm. 41–42 cannot be interpreted as passing dissonances in the light of Kirnberger’s commentary because the rhythmical values of half notes represent beats (Taktzeiten) of C meter. In the strict style this metrical level is not suitable for passing dissonances but only for suspensions, which fall on strong beats and resolve on weak beats, yet in the free style passing dissonances can be longer than in the strict style and take a full beat or measure.36 This allows Haydn to perform his trick and invite the listener to reinterpret the dominant sevenths in mm. 41–42 as augmented passing notes in the light of the following acceleration. The trick is possible because suspensions (V64––75) and passing dissonances (I64––75) have the same strong–weak metrical profile, with dissonances exchanging their metrical positions: suspensions (V64) fall on strong beats while passing dissonances (I75) occur on weak beat subdivisions. The

34. Ibid., 264. 35. Such changes take place several times throughout the movement and the manipulation of the cadence may refer to them. For detailed discussion of the changes between C and c meter in op. 64 No. 6/i, see Mirka, Metric Manipulations in Haydn and Mozart (2009), 82f., 196f., 202f. 36. Kirnberger makes this observation in connection with Example 4: “In the strict style the notes marked with an asterisk would be passing notes; thus they would have to be of short duration and fall on unaccented beats. But the free style is not bound to this rule, so that these sevenths can last a full measure” (Kirnberger, Die Kunst [1771], 85; The Art [1982], 104).

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final step to the tonic in m. 45 thus forms no resolution of the dominant seventh but a resolution of neighbor notes (I75––64) combined with the flip of the tonic triad from the second inversion to the root position (I64–I). The same trick is repeated in the recapitulation but the strategy of postponing the final cadence is longer than in the exposition and it reveals a further nuance of Haydn’s manipulation (Example 8). After the PAC in m. 118, the triplet figuration of the first violin crashes into the raised-sixth chord on scale degree 6^ (m. 121) but the deceptive cadence takes a different course than in the exposition (m. 39), leading to the six-five chord on scale degree 7^ in m. 122 and the triad on scale degree 1^ in m. 123. This harmonic progression, embedded within a stepwise ascent of the bass 3^–4^–5^–6^–7^–1^, follows the rule of the octave (règle de l’octave): the standard harmonization of an ascending and descending scale.37 Given the familiarity of this schema in the eighteenth century, a step from scale degree 5^ to scale degree 6^ supporting the raised-sixth chord leads the listener to expect a further step up to scale degree 7^ supporting a six or six-five chord.38 This expectation is fulfilled in m. 122, when the bass continues its ascent to the tonic (5^–6^–7^–1^), but it is thwarted in m. 41 (Example 6), when the bass steps down to the dominant. The same surprise takes place at the end

37. The best-known versions of the rule of the octave were published by Gasparini, (L’armonico pratico [1708], 55–58), Heinichen (Gründliche Anweisung [1711], 201–204; Der General-Bass [1728], 745–750), Campion (Traité d’Accompagnement [1716], 21), Rameau (Traité [1722], 384–387; English translation in Treatise [1971], 396–397), Mattheson (Kleine General-Baß-Schule [1735], 250–253), Kellner (Treulicher Unterricht [1743], 29–41), and Bach (Versuch [1762], 328). While Campion, Rameau, Mattheson, and Kellner assign a sixth chord (6) to the sixth degree of the ascending scale in major and reserve the raised-sixth chord (6©) for the descending scale, Gasparini and Bach include the raised-sixth chord in both directions. Heinichen does not show it at all and harmonizes the sixth degree of his schemata with a triad (5) or a sixth chord (6). For further discussion of the rule of the octave, see Christensen, “The Règle de l’Octave” (1992), and Lester, Compositional Theory (1992), 72–74. 38. Deceptive cadences based on the rule of the octave are often used by Haydn and Mozart. So far I have identified such cadences in Haydn’s String Quartets op. 64 No. 4/i (mm. 82–85), op. 64 No. 6/iv (mm. 174–177), op. 76 No. 3/i (mm. 103–104), and op. 77 No. 2/iv (mm. 161–162), in his Piano Trio No. 43 in C major, Hob. XV:27/ii (mm. 61–63) and in Mozart’s String Quintets K. 516/ii (mm. 9–10) and K. 614/iv (m. 302). Some of them feature general pauses between chords on scale degrees 6^ and 7^ and restate the main theme on scale degree 1^. Their interest consists in the tension between the harmonic deception caused by the interruption of the cadential schema before the tonic and the continuation of the rule of the octave up to the tonic in compliance with the natural implication of the ascending scale (see Meyer, Explaining Music [1973]; Narmour, Beyond Schenkerism [1977]). The fact that the rule of the octave complies with the cognitive mechanism of implication–realization accounts for the use of this schema in Mozart’s K. 614/i (mm. 11–14) and Haydn’s op. 54 No. 3/i (mm. 29–32), where it occurs in connection with “overridden caesuras” caused by false half-cadences (see Mirka, “Punctuation and Sense” [2010], 240–242 Ex. 2, 249 Ex. 5).

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of the recapitulation.39 From this point of view the cadential six-four chords in mm. 41 and 140 cause secondary deceptions that prepare the final tricks.40

39. The double format of analytical annotations—combining figured-bass symbols and Roman numerals—in Examples 6, 8, and 9a reflects the tension between the tradition of Generalbasslehre that bore the rule of the octave and the new Harmonielehre advocated by Kirnberger. Even if Kirnberger did not use Roman numerals, his fundamental basses anticipated this system of analysis and stimulated its development by Georg Joseph Vogler around the same time. 40. Since the framework (Gerüst) of the raised-sixth chord on scale degree 6^ can be filled with the perfect fourth or a diminished fifth (see Holtmeier, “Heinichen, Rameau, and the Italian Thoroughbass Tradition” [2007], 38f.; “Rameaus langer Schatten” [2010], 147f.), the diminished six-five chord in m. 138 is equivalent to the raised-sixth chord in m. 121. Given that both chords occur after triplet figuration, the expectation of the former chord to move to the six-five chord on scale degree 7^ is based on both extra-opus and intra-opus styles (Narmour, The Analysis and Cognition of Basic Melodic Structures, [1990]).

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Example 8: Haydn, String Quartet in E-flat major (1790), op. 64 No. 6/i, mm. 117–144

To end with the beginning The last example of cadential manipulation based upon the equivocation between the dissonant and consonant six-four chord to be discussed in this article is chronologically the first. It comes from the opening movement of Haydn’s String Quartet in C major op. 33 No. 3, “The Bird” (Example 9a).41 After the final cadence of the recapitulation (PAC, m. 151), the coda proceeds to build up a more emphatic cadence decorated by soloistic display in the first violin, but instead of resolving to I, the V7 turns toward the raisedsixth chord on scale degree 6^ (DC, m. 161). This turn is surprising not only because it forms a deceptive cadence but also because it comes too early: given the harmonic rhythm of the preceding passage (mm. 156–160), the tonic is expected to occur one measure later. The raised-sixth chord in m. 161 is identical with the one encountered in the first movement of op. 64 No. 6 (Example 8, m. 121) but, rather than ascending to the tonic, the bass steps down to scale degree 5^. The six-four chord in m. 163 thus

41. For my earlier discussion of this manipulation, see Mirka, “Das Spiel mit der Kadenz” (2004), 33–35.

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forms a secondary deception setting the stage for the subsequent trick. Because this chord restores the two-measure harmonic rhythm after the deceptive cadence in m. 161, the dominant is expected to occur in m. 165. Contrary to this expectation, the six-four chord continues, but at the very moment when the listener expects the dominant and is frustrated since it does not occur, she42 recognizes the main theme. Even more: she becomes aware that the theme has started two measures earlier. At first, it was concealed by the continuation of the accompaniment and the motivic material from mm. 161–162. Only in m. 165, when the texture changes and the ostinato accompaniment is abandoned, can one discover the origin of this material in the main theme. This recognition coincides with the moment when, at the beginning of the movement (Example 9b), it becomes clear to the listener that the opening material, in fact, makes up a theme (m. 4). The first three measures give her no hint of this formal function. Likewise, when the main theme returns during the sonata form’s second half (Example 9c), it is only after the first three measures, which now appear under the disguise of a new harmonization, that the listener is capable of recognizing the beginning of the recapitulation (m. 111). Haydn’s manipulation, aiming at the belated recognition of the main theme in the coda, turns out to be part of an over-arching strategy.43

42. My usage of gender-specific pronouns is conditioned by my own gender. 43. Although the first movement of op. 33 No. 3 has been frequently discussed, this strategy has remained unnoticed. Only James Webster (Haydn’s Farewell Symphony [1991], 143) and William Caplin (Classical Form [1998], 275 [n. 15]) observe the delayed entrance of the tonic shortly after the presentation of the main theme’s upper voice at the beginning of the (veiled) recapitulation. However, they do not draw any conclusion from this observation regarding the recognizability of the thematic return nor do they bring it into relation with the statements of the main theme at the beginning and the end of the movement (see Mirka, “Das Spiel mit der Kadenz” [2004], 35 [n. 24]).

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Example 9a: Haydn, String Quartet in C major (“The Bird”), op. 33 No. 3/i, mm. 147–167

This recognition is of consequence for the harmonic function of the six-four chord. Since the equivalent chord in the main theme (Example 9b, mm. 1–3) was the firstinversion tonic and this is what remains of the six-four chord after the dominant root has disappeared from the bass (Example 9a, mm. 163–164), the dominant function of the cadential six-four (V64) coexists with the tonic function (I64). The equivocation between these functions is sustained in mm. 165–166 through adjustments made by Haydn in relation to the equivalent portion of the main theme (mm. 4–6): the bass starts from scale degree 5^ and reaches it again on the second beat of C meter, which enhances the dominant function, while the syncopations fall on scale degree 1^, which emphasizes the tonic function of the six-four chord. The dominant function is further enhanced by the resolution of the six-four chord to the dominant seventh, but this resolution is not followed by further resolution to the tonic. What follows instead is a repetition of the V64––75 harmonic progression in m. 166. Only then does the dominant seventh resolve. Haydn emphasizes this resolution through an octave leap of the cello, dynamic change to forte and multiple stops in the second violin part, but the tonic triad in m. 167 occurs after the tonic harmony has long since been established in the form of the six-four chord, which alternates with the passing chord (I64–I75). The coexistence between the dominant and tonic functions in mm. 163–166 results from an overlap between the cadential six-four and the tonic which is caused by omission

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of the dominant expected to occur on the downbeat of m. 165. This omission is not made up by the dominant seventh on the last quarter of the measure, and the V75–I harmonic progression in mm. 166–167 does not complete the cadence announced by V64 in m. 163. Rather, its formal function is post-cadential: it closes a codetta after an absent cadence. The post-cadential function of mm. 165–167 is evident from the repetition of a segment in mm. 165–166, which is typical of codettas, as is the evaded cadence in m. 166.44 As noted in connection with the finale of op. 50 No. 6 (Example 1b), the function of a codetta is to confirm the cadential goal of the preceding section. If there this function was abrogated in order to emphasize the lack of cadential closure, here the codetta makes up for this lack and creates a false impression of the final cadence. This sheds light on the unusual structure of the main theme: the theme is prepared to function as a codetta. Haydn clearly planned this manipulation from the outset and structured the theme in accordance with it. Just like “The Frog,” “The Bird” begins with the end and ends with the beginning, only this time the end is not brought about by a cadence but by post-cadential material.

Example 9b: Haydn, String Quartet in C major (“The Bird”), op. 33 No. 3/i, mm. 1–6

44. The former feature of codettas, described by Janet Schmalfeldt as “one more time technique,” is closely related to the latter. As Schmalfeldt (“Cadential Processes” [1992], 47f. [n. 12]) points out, this technique was described as “doubling of cadences” (Verdopplung der Cadenzen) by Joseph Riepel (Grundregeln zur Tonordnung insgemein [1755], 61) and as “multiplication of cadences” (Vervielfältigung der Cadenzen) by Heinrich Christoph Koch (Versuch III [1793], 191; English translation in Introductory Essay [1983], 148). The phenomenon of “evaded cadence” is subsumed by Koch under deceptive cadences and explicitly related to codettas: “When several cadences follow one another in a closing phrase (Schlußsatz) by means of either an appendix (Anhang) or the repetition of the cadence, one often places a different tone than the caesura note in one of the last cadences and thus deceives the ear in its expectation of the closing tone. If that occurs it is called a deceptive cadence and can be produced not only by the upper voice but also by the bass” (Versuch II [1787], 444f.; Introductory Essay [1983], 50).

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Example 9c: Haydn, String Quartet in C major (“The Bird”), op. 33 No. 3/i, mm. 108–113

After the end In this article I have concentrated on a specific question of eighteenth-century music theory related to the harmonic function of the cadential six-four chord. I would like in conclusion to raise a general question on the relationship between music theory and composition. Until recently this relationship was usually discussed in terms of the aesthetics of genius inherited by twentieth-century scholars from the nineteenth century.45 In the accounts of the compositional process inspired by this aesthetics, theoretical rules were often presented as restrictions on the free spirits of great composers that fettered their creative fantasy “like tight clothes and shoes, in which a man can neither stir nor move.” In this regard, we were heirs of Albert Christoph Dies.46 But the aesthetics of genius was not Haydn’s aesthetics. This is evident from Haydn’s own description of his compositional method confided to the same biographer: “I wrote what seemed to me good and corrected it afterwards according to the rules of harmony. Other devices I have never made use of. Several times I took the liberty not of offending the ear, of course, but of breaking the usual textbook rules, and wrote beneath these places the words con licenza.”47 The picture of a composer subjecting

45. Even more than for Haydn, this holds true for Mozart. See Grandjean’s brief but instructive reflections about the tension between Mozart’s genius and his theoretical knowledge (Mozart als Theoretiker [2006], 187f.). 46. The same disdain for theoretical rules shows through several anecdotes reported by the other of Haydn’s early biographers, Georg August Griesinger. One of them concerns, in fact, the status of the fourth: “Someone told Haydn that Albrechtsberger wished to see all fourths banished from the purest style. ‘What does that mean?’ replied Haydn. ‘Art is free, and will be limited by no pedestrian rules. The ear, assuming that it is trained, must decide, and I consider myself as competent as any to legislate here’” (Griesinger, Biographische Notizen [1810], 114; Gotwals, Haydn [1963], 61). Griesinger was influenced by Kant and quotes his remarks about genius in reference to Haydn (Biographische Notizen [1810], 113). Dies refers to Schiller (Biographische Nachrichten [1976], 62). See Gotwals, Haydn (1963), 60, 110. 47. Dies, Biographische Nachrichten (1976), 61; Gotwals, Haydn (1963), 109. This and the other quotations from Haydn’s early biographies, contained in footnotes 46 and 49, are cited and related to the aesthetics

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the fruits of his creative fantasy to the rules of harmony is utterly different from the image of a Romantic genius. Haydn’s freedom from textbook rules and references to the ear are not to be taken as signs of his disdain for music theory but originate in music theory. In fact, they stem from the anti-Pythagorean music-theoretical tradition influenced by the sensualist philosophy of John Locke.48 Eighteenth-century treatises by Mattheson and Heinichen include critical reflections about the status of rules and diatribes against “paper rules” that satisfy only the eye. They insist on subjecting theoretical rules to the authority of the ear and acknowledge the right of composers to licences (exceptiones) based on this authority.49 Kirnberger inscribes himself in this tradition in his preface to the first volume of Die Kunst des reinen Satzes: Ich weiß gar wol, daß die größten Meister bisweilen von den strengen Regeln abweichen, und dennoch durchaus wohlklingend sind. Dieses aber konnten sie nur darum thun, weil ihnen die Beobachtung des allerstrengsten geläufig war. Niemand, als sie allein, würde sich aus den Harmonien, die gegen die Regeln gesetzt sind, ohne Nachtheil des Wohlklanges, herausgefunden haben. I know very well that the greatest masters occasionally deviate from the strict rules, and yet their compositions always sound good. However, they could do this only because they were well-versed in the strictest rules. Only they could have found the way out of harmonies that are composed contrary to the rules without detriment to the euphony.50

For him and his predecessors, theoretical rules formed part of the science of composition that had to be studied in order to refine the ear and aid the natural genius.51 The

of genius by Elaine Sisman (“Haydn, Shakespeare, and the Rules of Originality” [1997], 6–8). 48. The first German music theorist to adopt Locke’s sensualist philosophy was Johann Mattheson. In the introduction to his first treatise, Das Neu-Eröffnete Orchestre (1713), 4, he quotes one of Locke’s most famous maxims: “Nihil est in Intellectu, quod non prius fuit in sensu.” For more details about Mattheson’s project of sensualist music theory, see Christensen, “Sensus, Ratio, and Phtongos” (1994), and Hinrichsen, “Mattheson” (2004), 1340. 49. See Mattheson, Das Neu-Eröffnete Orchestre (1713), 2–16; Das Beschützte Orchestre (1717), 103, 143f., 151, 154, 204; Das Forschende Orchestre (1721), 1–450, and Heinichen, Der General-Bass (1728), 2–5, 18–20, 92f., 766f. Another passage of Griesinger’s biography, illustrating Haydn’s attitude toward rules, reflects current debates of eighteenth-century music theory: “Strict theoreticians meanwhile found much to take exception to in Haydn’s compositions […] He was not put out by this, for he had soon convinced himself that a narrow adherence to the rules oftentimes yields works devoid of taste and feeling, that many things had arbitrarily taken on the stamp of rules, and that in music only what offends a discriminating ear is absolutely forbidden” (Griesinger, Biographische Notizen [1810], 16; Gotwals, Haydn [1963], 13). 50. Kirnberger, Die Kunst I (1771), [ii–iii] (The Art [1982], 7f.). 51. Heinichen (Der General-Bass [1728], 20–24) writes about three prerequisites of a good composer: genius (Genie), science (Wissenschaft), and experience (Erfahrung). Together, they make up the most sought-after aesthetic quality—taste (Gout). Haydn’s famous remark to Leopold Mozart about his son’s taste (Geschmack) and the science of composition (Compositionswissenschaft) after the performance of Wolfgang’s String Quartets K. 458, 464, and 465 could have been inspired by Heinichen (Bauer and Deutsch, Mozart: Briefe und Aufzeichnungen III [1963], 373).

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study of this science was not only indispensable to prevent composers from remaining “pure naturalists”52 but could also be a source of their inspiration, if exploration of theoretical rules led them to the discovery of affinities between seemingly unconnected phenomena. The ability to draw connections between such phenomena was the chief characteristic of wit, the central category of late-eighteenth-century aesthetics and, at the same time, a feature that Haydn possessed in abundance. His tricks exploring the affinity between the consonant and dissonant six-four count among the supreme manifestations of wit (Witz) as an intellectual disposition distinct from mere humor (Laune).53 What I have sought to demonstrate here is that these tricks can be described in terms of Kirnberger’s theory; in fact, this is the earliest theory that allows for their description. Of course, Haydn could have intuited the double identity of the six-four chord or derived it from inconsistencies of earlier harmonic theories independently of Kirnberger—but the categorical distinction drawn by Kirnberger between the two functions of the six-four chord might well have inspired Haydn’s attempts to construct a bridge between them. The question as to whether Haydn’s intention was to affirm this distinction by demonstrating the consequences of blurring it, or to ridicule Kirnberger’s theory by showing that the harmonic functions of these two chords can be easily exchanged, must remain open. Whatever the answer, the cadential puns based on the equivocation between the consonant and dissonant six-four reveal Haydn’s knowledge of current harmonic theories and draw witty conclusions from music-theoretical debates of the time.

Bibliography Bach, Carl Philipp Emanuel (1753–1762), Versuch über die wahre Art das Clavier zu spielen, 2 vols., vol. 1, Berlin: Henning; vol. 2, Winter. Reprint, ed. Lothar Hoffman-Erbrecht, Wiesbaden: Breitkopf & Härtel, 1958. Bauer, Wilhelm A. and Otto E. Deutsch, eds. (1963), Mozart: Briefe und Aufzeichnungen, vol. 3, Kassel: Bärenreiter. Beach, David (1974), “The Harmonic Theories of Johann Philipp Kirnberger,” Ph.D. diss., Yale University. Campion, François (1716), Traité d’Accompagnement et de Composition selon la règle des octaves de musique, Paris. Reprint, Geneva: Minkoff, 1976. Caplin, William (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, Oxford and New York: Oxford University Press. 52. Mattheson, Das Neu-Eröffnete Orchestre (1713), 13. 53. For this distinction and a survey of contemporaneous accounts of Haydn’s wit and humour, see Wheelock, Haydn’s Ingenious Jesting (1992), 19–51.

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Christensen, Thomas (1987), “Rameau’s ‘L’Art de la Basse fondamentale,’” Music Theory Spectrum 9, 18–41. ——— (1992), “The Règle de l’Octave in Thorough-Bass Theory and Practice,” Acta Musicologica 64/2, 91–117. ——— (1994), “Sensus, Ratio, and Phtongos: Mattheson’s Theory of Tone Perception,” in: Musical Transformation and Musical Intuition: Eleven Essays in Honour of David Lewin, ed. Raphael Atlas and Michael Cherlin, Deadham, Mass.: Overbird Press, 1–22. Crüger, Johann (1630), Synopsis musica, Berlin: Kally. Deutsch, Otto Erich (1969), “Haydns Musikbücherei,” in: Musik und Verlag: Karl Vötterle zum 65. Geburtstag, ed. Richard Baum and Wolfgang Rehm, Kassel: Bärenreiter, 220–221. Dies, Albert Christoph (1976), Biographische Nachrichten von Joseph Haydn, ed. Horst Seeger, Berlin: Henschelverlag. Federhofer, Hellmut (1964), “Ein Salzburger Theoretikerkreis,” Acta Musicologica 36, 50–79. ——— (1971/72), “Mozart als Schüler und Lehrer in der Musiktheorie,” Mozart-Jahrbuch 1971/72, 89–106. Gasparini, Francesco (1708), L’armonico pratico al cimbalo, Venice. Reprint, New York: Broude, 1967. Gotwals, Vernon (1963), Haydn: Two Contemporary Portraits, Madison: University of Wisconsin Press. Grandjean, Wolfgang (2006), Mozart als Theoretiker der Harmonielehre, Hildesheim: Olms. Grave, Floyd and Margaret Grave (2006), The String Quartets of Joseph Haydn, Oxford and New York: Oxford University Press. Griesinger, Georg August (1810), Biographische Notizen über Joseph Haydn, Leipzig: Breitkopf & Härtel. Gruber, Gernot (1982), “Zu Wolfgang Amadeus Mozarts Lehre im ‘basso fondamentale,’” in: Gedenkschrift Hermann Beck, ed. Hermann Dechant and Wolfgang Sieber, Laaber: Laaber, 127–131. Heinichen, Johann David (1711), Neu erfundene und Gründliche Anweisung zu vollkommener Erlernung des General-Basses, Hamburg: Benjamin Schiller. Reprint, ed. Wolfgang Horn, Kassel: Bärenreiter, 2000. ——— (1728), Der General-Bass in der Composition, Dresden. Reprint, Hildesheim: Olms, 1994. Hinrichsen, Hans-Joachim (2004), “Mattheson, Johann,” in: Die Musik in Geschichte und Gegenwart: Personenteil, 2nd edition, ed. Ludwig Finscher, vol. 11, Kassel: Bärenreiter, cols. 1332–1335. Holtmeier, Ludwig (2007), “Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave,” Journal of Music Theory 51/1, 5–49. ——— (2010), “Rameaus langer Schatten: Studien zur deutschen Musiktheorie des 18. Jahrhunderts,” Ph.D. diss., Technische Universität Berlin. Jones, David Wyn (2010), “Becoming a Complete Kapellmeister: Haydn and Mattheson’s Der vollkommene Capellmeister,” Studia Musicologica 51/1–2, 29–40. Kellner, David (1743), Treulicher Unterricht im General-Baß, 3rd edition, Hamburg: Herold. Kirnberger, Johann Philipp (1771–1774), “Consonanz,” “Dissonanz,” “Quarte,” and “Quartsext-Accord,” in: Allgemeine Theorie der schönen Künste, ed. Johann Georg Sulzer, 2 vols., Leipzig: Weidmann.

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——— (1771), Die Kunst des reinen Satzes in der Musik, vol. 1, Berlin: Decker & Hartung. ——— (1773), Die wahren Grundsätze zum Gebrauche der Harmonie [...] als ein Zusatz zu der Kunst des reinen Satzes in der Musik, Berlin und Königsberg: Decker & Hartung. ——— (1783), Grundsätze des Generalbasses als erste Linien zur Composition, Berlin: Hummel. Reprint, Hildesheim: Olms, 1974. ——— (1782), Gedanken über die verschiedenen Lehrarten in der Komposition, als Vorbereitung zur Fugenkenntniß, Berlin: Decker. Reprint, Hildesheim: Olms, 1974. ——— (1982), The Art of Strict Musical Composition, trans. David Beach and Jurgen Thym, New Haven: Yale University Press. Koch, Heinrich Christoph (1782–1787–1793), Versuch einer Anleitung zur Composition, 3 vols., Leipzig: Böhme. Reprint, Hildesheim: Olms, 1969. Selections trans. by Nancy Kovaleff Baker as Introductory Essay on Musical Composition, New Haven, CT: Yale University Press, 1983. Landon, H. C. Robbins (1977), Haydn: Chronicle and Works, vol. 5: Haydn: The Late Years 1801– 1809, London: Thames & Hudson. Lester, Joel (1992), Compositional Theory in the Eighteenth Century, Cambridge, MA: Harvard University Press. Mann, Alfred (1978/79), “Zur Kontrapunktlehre Haydns und Mozarts,” Mozart-Jahrbuch 1978/79, 195–199. ——— (1989/90), “Leopold Mozart als Lehrer seines Sohnes,” Mozart-Jahrbuch 1989/90, 31–35. Marpurg, Friedrich Wilhelm (1755–1757), Handbuch bey dem Generalbasse und der Composition, vol. 1, Berlin: Johann Jacob Schützens Witwe; vol. 2, Berlin: Lange. Reprint, Hildesheim: Olms, 1974. Martin, Nathan John, “Rameau’s Changing Views on Supposition and Suspension,” Journal of Music Theory 56/2 (2012), 121–167. Mattheson, Johann (1713), Das Neu-Eröffnete Orchestre, Hamburg: Benjamin Schillers Wittwe. Reprint, Hildesheim: Olms, 1993. ——— (1717), Das Beschützte Orchestre, Hamburg: Schiller. Reprint, Kassel: Bärenreiter, 1981. ——— (1721), Das Forschende Orchestre, Hamburg: Schiller. Reprint, Hildesheim: Olms, 1976. ——— (1735), Kleine General-Baß-Schule, Hamburg: Johann Christoph Kißner. Reprint, Laaber: Laaber, 2003. Meyer, Leonard (1973), Explaining Music: Essays and Explorations, Berkeley: University of California Press. Mirka, Danuta (2009), Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791, New York: Oxford University Press. ——— (2004), “Das Spiel mit der Kadenz,” Die Musikforschung 57/1, 18–35. ——— (2010), “Punctuation and Sense in Late-Eighteenth-Century Music,” Journal of Music Theory 54/2, 235–282. ——— (2012), “Absent Cadences,” Eighteenth-Century Music 9/2, 213–235. Narmour, Eugene (1977), Beyond Schenkerism: The Need for Alternatives in Music Analysis, Chicago: University of Chicago Press. ——— (1990), The Analysis and Cognition of Basic Melodic Structures: The Implication–Realization Model, Chicago: University of Chicago Press. Pohl, Carl Ferdinand (1878), Joseph Haydn, vol. 1, Leipzig: Breitkopf & Härtel.

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Rameau, Jean-Philippe (1722), Traité de l’harmonie, Paris: Ballard. ——— (1726), Nouveau système de musique théorique, Paris: Ballard. ——— (1737), Génération harmonique ou traité de musique théorique et pratique, Paris: Prault fils. ——— (1971), Treatise on Harmony, trans. Philip Gossett, New York: Dover. Riepel, Joseph (1755), Anfangsgründe zur musicalischen Setzkunst, vol. 2: Grundregeln zur Tonordnung insgemein, Frankfurt and Leipzig. Rosen, Charles (1971), The Classical Style: Haydn, Mozart, Beethoven, New York: Norton. Schmalfeldt, Janet (1992), “Cadential Processes: The Evaded Cadence and the ‘One More Time’ Technique,” Journal of Musicological Research 12/1–2, 1–52. Schulz, Johann Abraham Peter (1800), “Über die in Sulzers Theorie der schönen Künste unter dem Artikel Verrückung angeführten zwey Beyspiele von Pergolesi und Graun,” Allgemeine musikalische Zeitung 2, cols. 273–280. Sisman, Elaine (1997), “Haydn, Shakespeare, and the Rules of Originality,” in: Haydn and His World, ed. Elaine Sisman, Princeton, NJ: Princeton University Press, 3–56. Sorge, Georg Andreas (1745–1747), Vorgemach der musicalischen Composition, 3 vols., Lobenstein: Author. Sumner, Floyd (1975), “Haydn and Kirnberger: A Documentary Report,” Journal of the American Musicological Society 28/3, 530–539. Sutcliffe, W. Dean (1992), Haydn: String Quartets, Op. 50, Cambridge: Cambridge University Press. Türk, Daniel Gottlob (1800), Anweisung zum Generalbaßspielen, 2nd edition, Halle and Leipzig: Hemmerde & Schwetchke, Schwickert. Reprint, ed. Rainer Bayreuther, Laaber: Laaber, 2005. Webster, James (1991), Haydn’s “Farewell” Symphony and the Idea of Classical Style: ThroughComposition and Cyclic Integration in His Instrumental Music, Cambridge: Cambridge University Press. Wheelock, Gretchen A. (1992), Haydn’s Ingenious Jesting with Art, New York: Schirmer. Zarlino, Gioseffo (1558), Le istitutioni harmoniche, Venice. ——— (1571), Dimonstrationi harmoniche, Venice.

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THE MOZARTEAN HALF CADENCE Nathan John Martin and Julie Pedneault-Deslauriers

A

s is much clearer today than in 1998, when Classical Form first appeared in print, William Caplin’s theory of formal functions rests in considerable part on a careful delimitation of the concept of cadence.1 In 2001, Caplin published a short article in the Tijdschrift voor Muziektheorie that characterized sonata expositions primarily in terms of their cadential goals.2 And in 2004, he presented an extended meditation on cadences in the Journal of the American Musicological Society.3 Yet in all these texts, Caplin attends primarily to the perfect authentic cadence; the half cadence, which plays no less pivotal a role in his theory, receives comparatively little direct scrutiny. Our chapter undertakes to redress this imbalance by providing a detailed study of Mozart’s half cadences. With the aim of sharpening that type’s theoretical definition, we present a corpus study based on Mozart’s piano sonatas.4 Wishing to proceed as empirically as possible, we proposed in our initial survey of this corpus simply to identify any specimen that we thought, taking Caplin’s analytical practice as our guide, might be a half cadence—so as to observe, so to speak, these creatures in their natural environments.5 Our hope was that in assembling this taxonomy we might provide ourselves with a suggestive foundation for subsequent theorizing. We were therefore gratified when in compiling our results we found that the specimens we had collected seemed to fall quite naturally into a comparatively small number of more general classes. In what follows, we first detail those classes, moving from most to least common and providing both abstract templates and illustrative examples, and we comment, to the extent that our data permit, on their statistical prevalence. In our

1. 2. 3. 4.

5.

Caplin, Classical Form (1998). Caplin, “The Classical Sonata Exposition” (2001). Caplin, “The Classical Cadence” (2004). On the use of corpora for music-theoretical ends, see Gjerdingen, A Classic Turn of Phrase (1988); Byros, “Foundations of Tonality as Situated Cognition” (2009), “Towards an ‘Archaeology’ of Hearing” (2010), and “Meyer’s Anvil” (2013). The large-scale digitization project ELVIS (electronic locator of vertical interval successions) is underway at McGill University, MIT, Yale University, and the University of Aberdeen (http://elvisproject.ca). Caplin’s abstract discussion appears at Classical Form (1998), 29. In our initial survey, we oriented ourselves additionally by appealing to the annotated repertory examples provided throughout the treatise. A very different approach to the half cadence, one that instead emphasizes ambiguities between half- and authentic-cadential articulations, appears in L. Poundie Burstein’s essay in this volume; see also n. 7 below.

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chapter’s second part, we exploit the results of this survey in order to work towards a general definition of the Mozartean half cadence.

1. Half cadence types The converging half cadence A particularly common means of half-cadential articulation in the Mozart sonatas is that shown in Example 1a. Here, in what we call (following Robert Gjerdingen) the “converging half cadence,”6 the highest voice passes stepwise down from scale degree 2^ through the tonic 1^ to arrive at the leading tone 7^, while the bass steps chromatically up from 4^ through ©4^ to 5^. Typically, an accompanying alto voice shadows the soprano a sixth below. The rhythmic values assigned to the three-voice template in our abstract example are intended merely as indicative: the actual durations that the predominant harmonies receive vary considerably in practice; however, almost without exception, the initial ii6 and the terminal V fall on beats that are comparatively strong, and without any exception whatsoever, the final dominant groups backwards with its predominant harmonies (there is never, that is to say, a grouping boundary separating a presumptive final dominant from its preceding progression); further, that dominant is in every case the final harmony of its group.7 Of the 185 half-cadential progressions that we identified in Mozart’s sonatas, 35 (or 18.9%) answer to the converging type shown in Ex. 1a.8 Exx. 1b and 1c show the template as it appears in situ. In the latter passage, a Neapolitan sixth chord is substituted for ii6, and the sixths below the soprano line are absent, with the tenor instead shadowing the bass.

6. 7.

8.

Gjerdingen, Music in the Galant Style (2007), 160–162. That is, in Caplin’s terms, it is an ultimate (as opposed to penultimate) dominant (Classical Form [1998], 29). These details of grouping structure can often help to adjudicate in otherwise ambiguous cases. For a famous example, see Schenker’s (mis)identification of a half cadence at m. 8 of K. 310/i in the second volume of the Tonwille essays (Schenker, Tonwille 2 [1922], 7; also discussed in Burstein’s essay in this volume). On grouping structure more generally see Caplin, Classical Form (1998), 9; and Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), 36–67. All 185 half cadences are listed according to type in the appendix to this chapter. Unusual, intriguing, or problematic cases receive a short analytical note.

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(a)

(b)

(c)

Example 1: The Converging Half Cadence: (a) Abstract template; (b) Sonata in F major, K. 280/iii, mm. 140–143; (c) Sonata in D major, K. 284/i, mm. 69–70

A common variant of the converging pattern just described is shown as Example 2a. Here, the original model’s applied chord (between ii6 and V) is omitted and the soprano’s passing tonic scale degree is thus supported only by a 64 embellishment of the dominant; the alto once again shadows below in sixths.9 Cadences of this type account for 19 of the 185 half cadences, or 10.3% of the total. Example 2b provides an instance from our corpus. Naturally, both the sharpened bass scale degree 4^ and the cadential 64 appear in some cases. This happens 6 times (3.2%) in our corpus in all.10 On the issue of the cadential 64 as harmonic support more generally, see Beach “The Cadential SixFour as Support for Scale-Degree Three of the Fundamental Line” (1990) and “More on the Six-Four” (1990), as well as Cadwallader, “More on Scale Degree Three and the Cadential Six-Four” (1992). 10. See, for example, K. 282/ii, mm. 37–40. 9.

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Finally, if one takes all the specimens filed under Examples 1 and 2 as a group, and so counts 61 in all, then 33.0% of the half cadences we identified are accounted for.11 (a)

(b)

Example 2: The Converging Half Cadence, 64 Variant: (a) Abstract template; (b) Sonata in D major, K. 576/i, mm. 9–12

In both of the templates just presented, the soprano and alto lines can also be exchanged, so that the descending third 4^–3^–2^ (the original alto) comes to form a new soprano line covering the original motion from 2^ down to 7^ (see Examples 3a and 4a). A particularly suggestive case here is that shown in Example 4b, which is how the antecedent phrase in 2b is first stated. Beginning in the second half of 4b, the right and left hands are switched (invertible counterpoint at the octave), so that what was the cadential progression’s alto line in 2b—namely the 4^–3^–2^ descent—now migrates to the soprano. The 2^–1^–7^ descent, for its part, appears as a supporting voice below. The abstract template in Example 3a relates to Ex. 1a exactly as Ex. 4a does to Ex. 2a: the original alto line is projected up above the soprano to produce a 4^–3^–2^ descent. On the whole, these new progressions are much rarer than the un-inverted forms (28 of the former as opposed to 61 of the latter). The inverted version with cadential 6 4 (Example 4a) appears 18 times (9.7% of the total), whereas the applied chord version (Example 3a) figures just twice (1.1%). As before, it can also happen that both the applied chord (©4^ in the bass) and the 64 appear, as Example 3b illustrates. This occurs 8 times (4.3%) altogether. If, however, we count all of the templates thus far 11.

One special case presents only natural 4^ in the bass and has no cadential 64: K. 311/iii, m. 8. We include it in our global count, but not in any of our three subcategories.

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introduced as variant manifestations of an underlying converging type—which seems a natural idea to us—we are then able to cover just under half the total number of half cadences in our corpus: 89, or 48.1%. (a)

(b)

Example 3: Converging Half Cadence, Soprano and Alto Inverted: (a) Abstract model; (b) Sonata in A minor, K. 310/ii, mm. 50–51

(a)

(b)

Example 4: Converging Half Cadence, 64 Variant, Inverted: (a) Abstract model; (b) Sonata in D major, K. 576/i, mm. 1–4

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The expanding 6–8 half cadence A second important half-cadential paradigm is the expanding 6–8 pattern shown in Example 5a.12 Here, the bass and soprano move outward from an augmented sixth to an octave. Against this outer-voice scaffolding, the alto shadows the bass in parallel thirds (tenths), creating the harmonic progression It6–V. In fuller textures, the fifth above the bass can be added also, yielding the progression Ger6–V, sometimes with baldly stated parallel fifths.13 (The French sixth appears only once in our corpus.) The parentheses around the model’s first chord (VI) are meant to indicate that it is only one of a number of possible initiating sonorities. Indeed, in contrast to the preceding templates, there is considerable variety in the harmonies from which the cadential dominant may be approached, with VI, IV6, I and I6 being among the most common choices. As in the converging paradigm, the dominant can also be ornamented with a cadential 64 (for the sake of simplicity, we do not separate out these instances). Example 5b, for instance, shows the I variant. In all, the progression shown in 5a, with all its variable initiating sonorities, appears 25 times in our corpus, and so accounts for 13.5% of the total.

(a)

(b)

Example 5: Expanding 6–8 Half Cadence: (a) Abstract template; (b) Sonata in D major, K. 311/ iii, mm. 117–118

12. Unlike the other paradigms we describe, the expanding 6–8 half cadence (with augmented sixth) occurs overwhelmingly in minor-mode contexts; hence we give our abstract templates (Exx. 5a and 6a) in minor. When it appears in major modes, those modes are typically inflected by modal mixture as, for example, in K. 282/i, mm. 19–20. 13. Robert Gjerdingen and Ulrich Kaiser subsume this pattern under the more general category of the clausula tenorizans. See Gjerdingen, Music in the Galant Style (2007), 164–166; Kaiser, “Der Begriff der ‘Überleitung’ und die Musik Mozarts” (2009).

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As in the preceding cases, the soprano and alto parts in Example 5a can be exchanged so as to give the paradigm shown in 6a. Here, the augmented sixth recedes to an inner voice, while the descending parallel tenths between the new soprano and bass come to the fore. Example 6b provides a typical instance. In all, the progression appears 15 (8.1%) times in our corpus. Finally, by taking together the paradigms in Examples 5a and 6a, we can cover some 40 cases, or 21.6% of the whole. (a)

(b)

Example 6: Expanding 6–8 Half Cadence, Soprano and Alto Inverted: (a) Abstract template; (b) Sonata in F major, K. 280/iii, mm. 101–103

A further twist on the progression in 5a replaces that paradigm’s augmented-sixth chord with an applied dominant (or diminished chord), as shown in 7a. This latter template appears just 10 times (5.4%) in our corpus and Example 7b shows a characteristic use. That, in Ex. 7b, the lowered sixth degree (a¨1) appears first in the bass and is only later corrected to aª makes the connection to the augmented-sixth version especially palpable. There are also seven (3.8%) cases in which the soprano and alto lines of Example 7a are switched. In five of these, however, the 1^–7^ motion in the new soprano is covered by 3^–2^ or a reiterated 5^, as in Example 7c.14 When these variants are grouped together with the progression’s original augmented-sixth version, 57 of the total 185 cadences (or 30.8%) are accounted for.

14. This occurs sometimes in the augmented-sixth version in Example 6a as well, as in K. 330/ii, mm. 31–32, and K. 332/iii, mm. 56–57.

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(a)

(b)

(c)

Example 7: Expanding 6–8 Half Cadence, Applied Chord Variant: (a) Abstract template; (b) Sonata in C minor, K. 457/iii, mm. 5–8; (c) Sonata in A major, K. 331/i, mm. 11–12

The simple I–V half cadence Perhaps the most straightforward half-cadential progression of all, however, is one that we have not as yet introduced. Example 8a shows the case where I proceeds directly to V, with 3^ in the soprano stepping down to 2^. Example 8b shows the progression in context, in this case with a cadential 64 ornamenting the final dominant.15 The model, which we dub the “simple I–V half cadence,” occurs 21 times in our corpus, accounting for 11.35% of our 185 cases.

15. It does not seem important to us, in this case, to distinguish between progressions having and not having the cadential 64, since in either case, scale degree 3^ is initially supported by a root-position tonic.

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(a)

(b)

Example 8: The Simple I–V Half Cadence: (a) Abstract template; (b) Sonata in B¨ major, K. 281/iii, mm. 1–4

The doppia half cadence Finally, there are a small number of cadences that are of particular analytic interest—7 in all (3.8%)—and that answer to the model laid out in Example 9a. Here, a V7 chord moves to viiº7/V, which in turn resolves back to V. The progression recalls, in its basic voice-leading, the cadenza doppia shown as 9b.16 To obtain the half-cadential configuration in 9a from 9b, it suffices first to omit the final tonic and then to shuffle the linear motions above the dominant back one beat by allowing the sixth and fourth to resolve simultaneously; finally, let the bass step down by a semitone under this “64” to create an applied diminished seventh (half-diminished in major). Because of this close voiceleading relationship between 9a and 9b, we dub the former the “doppia half cadence.” An obvious question with respect to the doppia half cadence, particularly when the progression is introduced by iv6, is this: where does the final dominant of the half cadence occur? Is it (1) the first dominant chord, in which case the goal dominant bears a dissonant seventh;17 or is it (2) the second dominant, in which case the dis-

16. See Gjerdingen, Music in the Galant Style (2007), 169; Sanguinetti, The Art of Partimento (2012), 105–110; and Menke, “Die Familie der cadenza doppia” (2011). The first sonority of a cadenza doppia can be either a 5/3 or a 7/5/3 chord. The first dominant in our doppia half cadence, however, always bears a seventh. 17. Caplin excludes V7 axiomatically as the goal dominant of a half-cadential progression. In his view, a half cadence must conclude with a dominant triad. As he writes, “[t]o acquire the requisite stability for an ending harmony, the dominant of the half-cadential progression must take the form of a root-position triad. Adding a dissonant seventh—appropriate to the penultimate position in an

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sonant seventh ( f 2 in the example) discharges to the third scale degree (e¨2) contained in the second sonority? For reasons that are best elucidated in relation to particular examples, we prefer the second interpretation as a rule.18 Example 9c gives a particularly interesting passage from the slow movement of K. 280, together with an analytical reduction. The cadential progression in question occupies the example’s final three measures; it is introduced by a IV6 chord (in m. 30), which is chromaticized and ornamented with a 7–6 suspension. This IV6 harmony is reached from the B¨-minor triad in the example’s first measure by means of an implied 5–6 linear progression serving to prepare the suspended seventh. On the larger interpretation shown in our reduction, the bass and alto proceed downward in parallel tenths (b¨–d2 in m. 29; a–c2 in mm. 30–31; g–b1 in m. 32, with the soprano trailing behind thanks to two 7–6 suspensions, the first literal (in m. 30) and the second notional (since the bass moves down to f© under e¨2). The upshot is that the dominant seventh chord on the downbeat of m. 31 is in fact a passing sonority connecting IV6 to viiº7/V, with the latter harmony itself being an embellishment of the former.19 Example 9d shows a similar passage, again with a voice-leading reduction just below. As in 9c, the V7 chord in m. 7 is a passing chord linking IV6 to viiº7/V, and the final dominant of the half-cadential progression is thus reached only at the downbeat to m. 8. (a)

(b)

authentic cadential progression—would overly destabilize the ultimate dominant of a half-cadential progression” (Classical Form [1998], 29). Our survey bears this claim out. 18. In this respect, the doppia half cadence differs markedly from the actual cadenza doppia, in which the cadential dominant arrives at the beginning of the pattern. Our choice of terms is meant merely to underscore the voice-leading relationship between the two templates, not to suggest that they fit into larger harmonic contexts in identical ways. 19. Our analysis of this passage essentially agrees with that given in Beach, Advanced Schenkerian Analysis (2012), 170–174.

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(c)

(d)

Example 9: The Doppia Half Cadence: (a) Abstract template, (b) Cadenza doppia, (c) Sonata in F major, K. 280/ii, mm. 29–32, (d) Sonata in E¨ major, K. 282/i, mm. 6–8

By apportioning our half cadences under the four main categories—converging, expanding 6–8, simple I–V, and doppia—introduced thus far, we are able to account for all but 8 instances. Examining the leftovers suggests that we provisionally formulate one additional category. In Example 10, unisono figuration leads to an arrival on the dominant scale degree in both the lower and the upper line. It could be that this passage and the five other instances like it in our corpus should be understood as elliptical expressions of one or the other of the three-part models developed above.

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Resolving this point satisfactorily would likely require an expanded corpus furnishing further examples.

Example 10: Unisono Half Cadence (Sonata in C major, K. 309/i, mm. 29–32)

With these categories in place, we can account for all but two of the 185 half cadences that we identified: concerning these last two “misfits” we provide analytical commentary in the appendix (for K. 570/iii, m. 52) and in the text below (K. 311/i, m. 20). In the final part of our chapter, however, we wish primarily to reflect on the ways in which the typology we have developed might help to tighten Caplin’s definition of the classical half cadence.

2. The Mozartean half cadence: Towards a definition One result of our survey thus far has been to underscore the sheer variety of halfcadential articulations that are on offer in the Mozart Sonatas. In contrast to the perfect authentic cadence, which is astonishingly uniform in Mozart’s music,20 the half cadence seems to be expressed in sufficiently many ways that one might well wonder whether there is any single underlying pattern that is manifested in all these diverse configurations. Is it in fact possible to offer a single general definition of the half cadence that is flexible enough, on the one hand, to accommodate this panoply of instantiations and yet sufficiently robust, on the other, to avoid being merely vacuous? In brief, we believe the answer is yes. We will begin by considering two motivating examples, both of them converging half cadences of the types described in Examples 2 and 4. These analyses will emphasize the relationship between these particular subtypes and the perfect authentic cadence and will lead us to refine our original, empirically derived paradigms. This revision will in turn suggest how the

20. In “The Classical Cadence: Conceptions and Misconceptions” (2004, 82f.), Caplin retreats somewhat from his earlier characterization of classical cadential melodies as “interchangeable from piece to piece” (Classical Form [1998], 37). In Mozart’s music, however, as opposed to Beethoven’s perhaps, perfect authentic cadential progressions are extremely uniform.

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various other subtypes we have described can be understood as transformations of the converging type. Example 11a shows the antecedent phrase from the main theme of K. 284’s concluding variations. The antecedent’s second half presents a converging half cadence in which the melody descends stepwise from 5^, shadowed by lower thirds in the usual way. The harmony moves directly from ii6 to V, so that the melodic line’s 3^ is supported solely by the cadential 64 (i.e. the progression answers to the paradigm shown above in Ex. 4). When the opening idea returns in mm. 14–17, the original antecedent is recomposed as a consequent phrase ending with a PAC. To do so, Mozart simply shuffles the cadential harmonies backwards in order to leave metrical room for a final tonic. Example 12 shows the corresponding case with the soprano line descending from 3^ (as in Ex. 2). (a)

(b)

Example 11: Sonata in D major, K. 284/iii: (a) Antecedent (mm. 1–4); (b) Consequent (mm. 14–17)

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Example 12: Sonata in G major, K. 283/ii, mm. 1–4

The close relationship between the respective authentic- and half-cadential progressions in Exx. 11–12 helps to explain why converging half cadences seem to appear frequently in the antecedent phrases of eight-measure periods, since the close connection to the PAC that we have just underlined makes their recomposition in the consequent phrase entirely straightforward.21 It also suggests, more generally, that the converging paradigm might be understood as a kind of truncated perfect authentic cadential progression. Indeed, this is how Caplin understands the half cadence in general: In the authentic cadential progression, the final tonic is the harmonic goal of the progression. The dominant occupies the penultimate position and thus creates a powerful dynamic impulse into the final tonic. In the halfcadential progression, the dominant itself becomes the goal harmony and 21. In his article “Schoenberg’s ‘Second Melody’, or, ‘Meyer-ed’ in the Bass,” Caplin describes a second common procedure, in which Mozart attains I6 near the beginning of the antecedent’s contrasting idea only to abandon it, return to the root position tonic, and then write a simple I–V progression. In the consequent phrase, the contrasting idea can then be rewritten so as to take I6 as the initiating tonic for its cadence. See Caplin, “Schoenberg’s ‘Second Melody’” (2008), 165–167. Caplin’s chief example is K. 281/iii, mm. 1–8, the first half of which is analyzed above as Ex. 8b.

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so occupies the ultimate position. […] Except for omitting a final tonic and ensuring that the dominant is a consonant triad, half-cadential progressions can contain the same harmonies as authentic cadential ones do.22

In extrapolating our basic paradigms from the data obtained through our original survey of the sonatas, we tended to begin our half-cadential templates with predominant chords, in accordance with both our own musical intuitions and with Caplin’s usual analytic practice of bracketing a half cadence’s concluding dominant with its preceding harmony only.23 The parallels between the converging half-cadential and authentic-cadential progressions just outlined, however, suggest that we consider emending our original formulations to include initiating tonics in our half-cadential paradigms. Doing so presents considerable theoretical advantages, for it allows us, as we will shortly undertake to show, to relate the other half-cadential paradigms to this underlying model. There are, however, two practical difficulties that deserve comment. First, the initiating tonic of a perfect authentic cadence is most characteristically in first inversion, and the attainment of this inverted tonic (I6) is a crucial signal that an authentic cadence is imminent.24 Our examination of the Mozart Sonatas suggests, however, that in converging half-cadential progressions, a root-position initiating tonic (as in Exx. 11–12) is at least as common as a first inversion one (Ex. 13 below). Which of these two possibilities should be taken as the normative form is a theoretical question that we cannot resolve here. Instead, let us simply note that, in the sonatas at least, Mozart tends to prefer the root-position initiating tonic in converging paradigms beginning from melodic 3^, presumably so as to avoid doubling the tonic chord’s third. Second, it can be difficult to decide, in any particular case, whether to include the tonic in the half-cadential progression or not. In some cases (for instance Ex. 2b above) the tonic harmony seems to belong unproblematically to the cadential progression. In others (see Ex. 3b), it is bound more strongly to the preceding tonic prolongation. Though these two functions (initiating tonic of the cadence, on the one hand, and concluding pole of the opening tonic prolongation, on the other) need not be mutually exclusive, they are nonetheless conceptually distinct. In other words, there are always two discrete analytical possibilities available: either the tonic preceding the predominant chord of the half-cadential progression launches that progression, in which case the progression is complete; or it does not, and the progression is incomplete. Adjudicating between these abstract possibilities in particular cases is a matter

22. Caplin, Classical Form (1998), 29. 23. That practice postdates Classical Form, but see his annotations in “Schoenberg’s ‘Second Melody’” (2008). 24. As well as being a locus for considerable compositional wit, ingenuity, and play. See both Caplin’s schematic discussion of the role of bass scale degree 3 in mediating between prolongational and cadential “streams” in “Schoenberg’s ‘Second Melody’” (2008), 163f., and his discussion of the abandoned cadence in Classical Form (1998), 106f.

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of analytical judgment and depends on such features as grouping structure, textural changes, and rhetorical markers.25 Our use of dotted brackets in the analytical examples above has been meant to leave this decision in abeyance. Including an initiating tonic in the abstract paradigm, however, is advantageous in that it begins to bring out the relation of our half cadence types to one another. Example 13a accordingly presents a complete converging half cadence—that is, one including an initiating tonic. (Example 13b gives a corresponding repertory example, which shows some minor variants: the middle voice holds f 1 rather than moving up to g1 at the predominant, which is therefore IV not ii6 and which is embellished with a voice exchange between the soprano and bass.) (a)

(b)

Example 13: The Converging Half Cadence (revised paradigm): (a) Abstract template; (b) Sonata in C major, K. 309/ii, mm. 5–8

Example 14 shows how this revised converging paradigm relates to the simple I–V half cadence: namely, the simple I–V represents an elliptical expression of the complete converging paradigm in which the predominant harmonies are omitted and the initiating tonic is allowed to progress directly to the goal dominant. Example 14 shows the case in which the converging paradigm’s descending line from 3^ is in the highest voice. To transform the converging template into a simple I–V half cadence, we first delete the predominant and cadential 64, and then, to smooth out the resulting 25. This issue is also discussed, though with different emphasis, in Richards, “Closure in Classical Themes” (2010), 26–31.

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leaps, transpose the tenor d1 above the final dominant up an octave so as to preserve a 3^–2^ motion in the new pattern’s uppermost voice. The simple I–V can of course be constructed equally from the converging paradigm starting from 5^ (i.e. that shown in Ex. 13a) through an analogous series of deletions and adjustments.

Example 14: Simple I–V with Interpolated Converging Half Cadence

If the relationship between the converging (Exx. 1–4) and simple I–V (Ex. 8) paradigms seems relatively straightforward, what of the expanding 6–8 (Exx. 5–7) and doppia (Ex. 9) subtypes? The latter may not in fact be so distinct from the simple I–V as it initially appears. The cadenza doppia model given previously (as Example 9a) is almost identical to the pattern shown here as Example 15, the only difference being that the lower neighbor in the bass has now been eliminated so that the entire progression unfolds over a dominant pedal. (While this progression does not occur in the Mozart sonatas in a context suggesting cadential meaning, it does do so elsewhere in the classical repertory, for instance in the main theme of Pamina’s aria “Ach, ich fühl’s” in Die Zauberflöte.26) If we now agree to allow our routine of swapping voices to apply not only to the soprano and alto lines but to involve the bass as well, then we can turn Example 15 into a simple I–V half cadence by exchanging the alto and bass in measure one (Example 16a). This last, of course, is a particularly common way of approaching a simple I–V half cadence; Example 16b, chosen from our corpus to illustrate, should bring many other comparable instances to mind.27

Example 15: Doppia Half Cadence (Dominant pedal variant)

26. See Martin, “Mozart’s Sonata Form Arias” (forthcoming). 27. It is probably not incidental that the paradigm in Example 16a is the other common way of constructing an antecedent’s half cadence. For it is once again straightforward to recompose the cadential idea into a PAC, the descending line from 5^ needing simply to be reharmonized.

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(a)

(b)

Example 16: Doppia Half Cadence (Bass and Alto Exchanged): (a) Abstract template; (b) Sonata in C major, K. 330/iii, mm. 5–8

The expanding 6–8 model can likewise be derived by rearranging the voices of the converging type, this time in the expanded version given previously as Example 13a. The key is to include that progression’s optional tenor voice—allowing, for theoretical purposes, the parallel fifths that it forms with the soprano to stand—and to take the variant form having IV instead of ii6 as the predominant (Example 17). The expanding 6–8 paradigm (Example 18) can then be derived by moving the tenor voice to the bass and the bass to the soprano so as to obtain the new progression’s outer 6–8 scaffolding. The model’s other characteristic feature—a second upper voice moving in parallel tenths with the bass—arises automatically: the alto of Example 17 is simply left in place and provides the requisite intervals. The fourth, filling voice (shown in in the tenor in Example 18) is the original soprano. As in Examples 1 and 3 above, the parallel fifths that arise when the filling voice is added (here between the bass and tenor) must usually be finessed in practice.

Example 17: Converging Half Cadence (modified template with parallel fifths)

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Example 18: Expanding 6–8 Half Cadence

This final set of transformations might appear far-fetched were it not for one example in which Mozart performs them before our very ears. In the passage shown in Example 19, Mozart feigns an expanded converging half-cadential progression, beginning from the initiating tonic in m. 56. The inner voice g1 in that measure then leaps over the soprano d2 to reach e¨2 in the following bar. In mm. 57–58, a voice exchange between the new soprano and the bass takes c1 to c©2 and e¨2 to e¨1, and the augmented-sixth chord thus obtained then resolves to the dominant in m. 59 to complete an expanding 6–8 half cadence. The notional tenor line 5^/8^–6^–6^–5^ (see again Ex. 17) is thus transferred partway through to the bass; the bass line 3^–4^–©4^–5^ is simultaneously transferred to the soprano; and the notional soprano 5^–4^–3^–2^ (implying the c1 due in m. 57) remains in place (the parallel fifths it forms with the new bass being broken on the surface by the cadential 64). The model’s descending parallel tenths appear as thirds in mm. 58–59, and arise from the retention of g1 as a pedal throughout the preceding measures. As the reader can verify, these are precisely the transformations described in the abstract in connection with Examples 17 and 18: the bass moves to the soprano, the tenor to the bass, and the old soprano, becoming the new alto, stays put.

Example 19: Sonata in B¨ major, K. 281/iii, mm. 55–59

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By means of these various routines, to conclude, we can relate all of our half-cadential paradigms to the converging model in its truncated PAC form. This result allows us to formulate the following general definition: A complete half cadence is a particular harmonic and voice-leading motion that expresses an incomplete ending and consists of a step progression from an initiating tonic to a final dominant through one or more predominant chords, with these harmonies resulting from the following abstract lines:

(1) a soprano clausula moving stepwise from 5^ down to 2^; (2) an alto clausula understood to move 3^–2^–1^–7^ but admitting the substitution of 1^ for the initial 3^, the antepenultimate 2^, or both; (3) a bass line moving 3^–4^–5^ (1^ may be substituted for 3^ and 4^ may be intensified to ©4^); (4) a tenor line moving 5^–6^–5^ or 8^–6^–5^. Crucially, these abstract clausulae are not confined to their notional registers, but may be interchanged under certain constraints; one, two, or even three of the abstract clausulae may be left implied; and the entire progression may be elliptically expressed by sounding only its initial and final sonorities (with appropriate adjustments to the voicings) so as to produce a simple I–V cadence. The harmonies making up a half cadence group together at some relatively surface level, in such a way that the goal dominant is the final harmony of its group and is not separated from its preceding harmony by a grouping boundary; and finally, the goal dominant arrives on a metrically strong beat.

We have shown, by means of the transformations outlined above, how the abstract clausulae just described are disposed and adjusted to form the various half-cadential subtypes (converging, expanding 6–8, simple I–V, doppia) itemized in our chapter’s first part. This procedure has allowed us to propose a single, generic definition of the half cadence that emphasizes its contrapuntal profile in addition to its harmonic content. A significant theoretical result of our discussion is that this contrapuntal profile can be best understood in terms of three-voice templates whose individual clausulae may be freely interchanged. It is the possibility of this generic definition that ultimately justifies the definite article “the” in our title. Given the limited corpus from which our theoretical formation is abstracted, however, we would conclude by emphasizing the provisional status of our definition and by noting certain reservations. First, we have considered only Mozart’s music— and indeed, only his piano sonatas. It is therefore unclear whether we have described the half cadence as it appears in the classical style of Haydn, Mozart, and Beethoven, or whether we are rather describing a Mozartean idiolect. Second, we have confined our attention to a single genre. It may be, for instance, that a study of Mozart’s quartets, operatic arias, or masses would identify further half-cadential patterns or find

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a different distribution of the subtypes than we have reported here. Nonetheless, we believe that conceiving of the classical half cadence as a conglomerate of abstract voice-leading motions that may be transformed and rearranged according to various routines, as we have done, provides a promising means of sharpening our theoretical definition of this particular formal construct. In addition to these reservations, our method also suggests a number of promising expansions. On the one hand, we have attempted, through our discussion of abstract clausulae, to integrate a more horizontal voice-leading perspective into Caplin’s form-functional thinking. That endeavor obviously invites further reflection on the relationship between Caplin’s definitions of intrathematic functions, couched in largely harmonic and rhythmic/metrical terms, and the various voice-leading patterns that might be correlated with these functions, whether those patterns be described in terms taken over from Schenker or from Gjerdingen.28 A particularly promising avenue of investigation would be to extend this kind of treatment not just, as here, to cadential function but to initiating and medial functions as well. On the other hand, we have largely ignored the characteristic interthematic placements of the various half-cadential types we have identified. A second obvious extension of our work would therefore be to consider the probable correlations between half-cadential type and formal location. Still, the work we have accomplished here, allows us both (1) to explicate and to clarify the widely acknowledged link between the half-cadential and perfect authentic cadential progressions, and (2) to provide a general definition of the former while also detailing its diverse manifestations in Mozart’s sonatas.

Bibliography Beach, David (2012), Advanced Schenkerian Analysis: Perspectives on Phrase Rhythm, Motive, and Form, New York, NY: Routledge. ——— (1990), “The Cadential Six-Four as Support for Scale-Degree Three of the Fundamental Line,” Journal of Music Theory 34/1, 81–99. ——— (1990), “More on the Six-Four,” Journal of Music Theory 34/2, 281–290. Byros, Vasili (2009), “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), “Towards an ‘Archaeology’ of Hearing: Schemata and Eighteenth-Century Consciousness,” Musica Humana 1/2, 235–306. ——— (2012), “Meyer’s Anvil: Revisiting the Schema Concept,” Music Analysis 31/3, 273–346.

28. For a classic attempt to combine Caplinian and Schenkerian analysis, see Schmalfeldt, “Towards a Reconciliation of Schenkerian Concepts” (1991).

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Cadwallader, Allen (1992), “More on Scale Degree Three and the Cadential Six-Four,” Journal of Music Theory 36/1, 187–198. Caplin, William E. (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, New York: Oxford University Press. ——— (2004), “The Classical Sonata Exposition: Cadential Goals and Form-Functional Plans,” Tijdschrift voor Muziektheorie 6/3, 195–209. ——— (2004), “The Classical Cadence: Conceptions and Misconceptions,” Journal of the American Musicological Society 57/1, 51–117. ——— (2008), “Schoenberg’s ‘Second Melody,’ Or, ‘Meyer-ed’ in the Bass,” in: Communication in Eighteenth-Century Music, ed. Danuta Mirka and Kofi Agawu, Cambridge: Cambridge University Press. Gjerdingen, Robert O. (1988), A Classic Turn of Phrase, Philadelphia: University of Pennsylvania Press. ——— (2007), Music in the Galant Style, New York: Oxford University Press. Kaiser, Ulrich (2009), “Der Begriff der ‘Überleitung’ und die Musik Mozarts: Ein Beitrag zur Theorie der Sonatenhauptsatzform,” Zeitschrift der Gesellschaft für Musiktheorie 6/2-3, 341–383. Lerdahl, Fred and Ray Jackendoff (1983), A Generative Theory of Tonal Music, Cambridge, MA: MIT Press. Martin, Nathan John (forthcoming), “Mozart’s Sonata Form Arias,” in: Formal Functions in Perspective: Essays on Musical Form from Haydn to Adorno, ed. Steven Vande Moortele, Julie Pedneault-Deslauriers, and Nathan John Martin, Rochester: University of Rochester Press. Menke, Johannes (2011), “Die Familie der cadenza doppia,” Zeitschrift der Gesellschaft für Musiktheorie 8/3, 398–405. Richards, Mark (2010), “Closure in Classical Themes: The Role of Melody and Texture in Cadences, Closural Function, and the Separated Cadences,” Intersections: Canadian Journal of Music 31/1, 25–45. Sanguinetti, Giorgio (2012), The Art of Partimento, New York: Oxford University Press. Schenker, Heinrich (1922), Der Tonwille: Flugblätter zum Zeugnis unwandelbarer Gesetze der Tonkunst einer neuen Jugend dargebracht. Reprint, Hildesheim: Olms, 1990. Schmalfeldt, Janet (1991), “Towards a Reconciliation of Schenkerian Concepts with Traditional and Recent Theories of Form,” Music Analysis 10/3, 233–287.

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Appendix 185 half-cadences Sonatas included: K. 279, 280, 281, 282, 283, 284 (iii=theme only), 309, 310, 311, 330, 331 (i=theme only), 332, 333, 457, 494 (=533/iii), 533, 545, 570, 576 Type CONVERGING HALF CADENCES 2^ 1^ 7^ SOPRANO BASS LINE = 4^ ©4^ 5^ (Example 1a) K. 279/i, 24 K. 279/ii, 10 K. 279/iii, 4 K. 279/iii, 18 K. 279/iii, 30 K. 279/iii, 104 K. 280/iii, 8 K. 280/iii, 32 K. 281/i, 16 K. 281/iii, 10 K. 284/i, 70 K. 309/iii, 137 K. 309/iii, 157 K. 309/iii, 185 K. 310/i, 16 K. 310/i, 97 K. 310/iii, 63 K. 310/iii, 99 K. 311/i, 13 K. 311/i, 75 K. 311/ii, 24 K. 330/i, 79 K. 330/iii, 131 K. 331/iii, 28 K. 332/iii, 6 K. 332/iii, 119

Number 89

% 48.1%

61 35

33% 18.9%

Remarks

Recapitulation version of m. 18 (recomposed) Recapitulation version in F major appears as ex. 1b

NMA gives F© in bass in m. 155; some older editions print Fª

IV and IV6 in voice-exchange (IV6 sounding between 4^ and ©4^ in the bass)

No true harmonic support for 1^; the latter is an accented passing-tone

Implying 2^ in the soprano 2^ appears in an inner voice Some ambiguity in the soprano: 2^–1^–7^ (mm. 118f.) or 4^–3^–2^ (mm. 116–119)? We choose the former on account of the local articulation (note the voice exchange taking d¨2 down into the tenor register).

208

K. 332/iii, 184 K. 333/i, 18 K. 333/iii, 144 K. 545/i, 11 K. 545/iii, 12 K. 576/i, 26 K. 576/iii, 92 K. 576/iii, 114 K. 576/iii, 155 CADENTIAL 64 VARIANT (Example 2a) K. 280/i, 26 K. 281/ii, 26 K. 281/iii, 109 K. 282/iii, 15 K. 283/ii, 2 K. 309/iii, 27 K. 310/ii, 4 K. 310/ii, 14 K. 311/iii, 138 K. 333/ii, 4 K. 494 (3rd mvt of K. 533), 18 K. 533/i, 45 K. 533/i, 53 K. 533/ii, 22 K. 545/iii, 4 K. 570/ii, 8 K. 570/ii, 20 K. 576/i, 12 K. 576/ii, 4 APPLIED CHORD AND CADENTIAL 64 K. 280/ii, 12

K. 280/ii, 46 K. 280/iii, 49

K. 282/ii, 40 K. 494 (K. 533/iii), 6 K. 570/iii, 10

Nathan John Martin and Julie Pedneault-Deslauriers

19

10.3%

ii6-to-ii voice exchange ornaments the converging bass (4^ (2^) 5^)

Implying 2^ in the soprano

6

3.24% Some ambiguity: is this a cadence? (since the phrase is largely supported by a V pedal); but see K. 280/ii, 46 below The corresponding place (to K. 280/ii, 12) in the recapitulation; here the HC is unambiguous Some ambiguity: 2^–1^–7^ or 4^–3^–2^ soprano; we choose the former, again because of local articulation 6^–5^ in soprano (©4^–5^ in inner voice) Because the cadential predominant is V6/V instead of vii°, 1^ comes only over the cadential 64

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EXCEPTION K. 311/iii, 8

1

4^ 3^ 2^ SOPRANO

28 2

15.1% 1.1%

18

9.7%

BASS LINE = 4^ ©4^ 5^ (Example 3a) K. 279/i, 67 K. 283/iii, 39 CADENTIAL 64 VARIANT (Example 4a) K. 279/i, 16 K. 283/ii, 8 K. 284/ii, 8 K. 284/iii, 4 K. 309/ii, 8 K. 309/ii, 44 K. 311/iii, 48 K. 311/iii, 146 K. 330/ii, 12 K. 331/i, 4 K. 332/i, 48 K. 333/iii, 4 K. 457/ii, 3 K. 545/ii, 8 K. 570/ii, 2 K. 570/ii, 37 K. 570/iii, 4 K. 576/i, 4 APPLIED DOMINANT AND CADENTIAL 64 (Example 3b) K. 282/ii, 18

0.54% Converging motion between bass (4^–5^) and soprano (2^–1^–7^); but no ©4^ in the bass and no cadential 64, so 2^ is not properly supported; 7^ in the soprano is covered by 5^

Voice exchange linking IV and IV6 Voice exchange linking IV and IV6 Voice exchange linking IV and IV6 One could argue for 2^–1^–7^ in the soprano. Only a 6–5 suspension over the dominant and not a full cadential 64

Voice exchange linking IV and IV6

8

4.3%

K. 309/iii, 39 K. 310/ii, 51 K. 330/i, 38 K. 333/ii, 13 K. 494 (533/iii), 108 K. 570/ii, 14 K. 576/iii, 54

Some ambiguity: we choose 4^–3^–2^ on account of the upper voice over the cadential 64.

210

6-8 HALF CADENCES EXPANDING AUG6–8 HC SOPRANO = ©4^–5^ (Example 5a) K. 281/iii, 59 K. 281/iii, 63 K. 282/i, 20 K. 282/ii, 55 K. 283/iii, 168

K. 284/ii, 52 K. 310/i, 58 K. 310/i, 74 K. 310/ii, 43 K. 311/i, 86 K. 311/iii, 118 K. 331/ii, 30 K. 332/i, 37 K. 332/i, 123 K. 332/iii, 139 K. 333/iii, 64 K. 333/iii, 72 K. 333/iii, 103 K. 457/ii, 38 K. 457/iii, 58 K. 533/i, 41 K. 545/ii, 44 K. 545/iii, 36 K. 570/i, 95 K. 576/i, 79 SOPRANO AND ALTO INVERTED (Example 6a) K. 279/iii, 70 K. 280/iii, 103 K. 282/iii, 59 K. 283/iii, 123 K. 284/i, 17 K. 284/i, 34 K. 311/ii, 50–52 K. 330/ii, 32 K. 332/iii, 57

K. 333/i, 81

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57 40 25

30.8% 21.6% 13.5% See commentary in text

Preceded by a dominant arrival at m. 154; mm. 160–168 perhaps present features of the doppia half cadence (see ex. 9 below)

French augmented-sixth chord 15

8.1%

Unusual placement immediately following a PAC Soprano 7^ covered by 2^ Slightly unusual: soprano c2 (1^) is transferred to l. h. figuration, so the expected 7^ (above V) is replaced by 2^; compare to K. 330/ii, 32

The Mozartean Half Cadence

K. 494 (K. 533/iii), 58 K. 494 (K. 533/iii), 79 K. 533/i, 116 K. 576/ii, 20 K. 576/ii, 31 M6–8 EXPANDING HC (applied dominant variant) SOPRANO = ©4^–5^ (Example 7a) K. 281/i, 68 K. 457/i, 30 K. 457/iii, 8 K. 533/ii, 10 K. 570/i, 35

211

Repeated at mm. 34f. 17

9,2%

10

5.4%

The surface progression is ii7–V7–I; cf. iii, 34; the 6–8 reading requires holding D notionally over into m. 34

K. 570/i, 125 K. 570/ii, 41 K. 570/iii, 12 K. 570/iii, 34 K. 576/ii, 12 SOPRANO AND ALTO INVERTED K. 279/i, 51 K. 284/iii, 12

Has applied viio65 instead of applied viio6 Reading g1 as the bass note on the second beat of m. 34 7

3.8%

The parallel 10ths in m. 11 strongly suggest this reading, even though the line passes into the l. h. in m. 12 (i.e. we imply c©2 in that measure) Exposition version of K. 311/ii, m. 51; here with applied chord not Ger6; 7^ covered by 5^ 1^–7^ covered by leap up to 3^–2^ over cad. 64 Soprano covered by 3^–2^

K. 311/ii, 15 K. 330/ii, 4 K. 331/i, 12 K. 457/i, 126 K. 457/ii, 30 SPECIAL CASES K. 280/i, 78:

Recapitulation version of K. 457/i, mm. 29f. (recomposed); soprano covered by 5^ 3

1.6% Progression is Ger6–(p64)-viio7/V–V. Here the A6 is converted into a 3rd through a chromatic voice exchange (3–1 resolution instead of A6–8) Gero3–V instead of A6–V; the voice leading is o 3–1 instead of A6–8 Progression is iv6–(p64)–viio7/V–V; similar voice leading to the two cases above

K. 284/ii, 69 K. 332/i, 173 EXCEPTION K. 279/ii, 31f.

1

O.54% Simple Phrygian progression: iv6-V(64–53); similar voice leading to the above 3 special cases, but no A6 or applied chord

212

SIMPLE I–V (Example 8a)

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21

11.35%

K. 281/iii, 4

w/ cad. 64

K. 282/iii, 8

w/ cad. 64

K. 284/ii, 38

w/ cad. 64; initially covered by upper thirds, and includes an intervening I6

K. 309/iii, 8

w/ cad. 64

K. 309/iii, 119

only 6–5 literally present; 4–3 implied

K. 310/iii, 8

only 6–5

K. 310/iii, 28

w/ cad. 64

K. 311/ii, 4

w/ cad. 64

K. 311/iii, 126

no cad. 64

K. 330/i, 18

w/ cad. 64

K. 330/iii, 8

no cad. 64

K. 330/iii, 32

no cad. 64

K. 330/iii, 86

no cad. 64

K. 331/iii, 14

no cad. 64; has intervening I6, and starts from 5^; same progression as K. 284/ii, 38

K. 331/iii, 102

no cad. 64

K. 332/ii, 4

w/ cad. 64

K. 332/iii, 49

no cad. 64

K. 333/i, 30

no cad. 64; intervening vi to break parallels

K. 333/iii, 24

w/ cad. 64

K. 570/i, 22

no cad. 64; 5^ in upper voice.

K. 576/i, 45

w/ cad. 64

DOPPIA HALF-CADENCE (Example 9a)

6

3.24%

K. 280/ii, 32 K. 281/ii, 55 K. 282/i, 8 dim3 replaces A6 here

K. 283/ii, 22 K. 331/ii, 80 K. 332/i, 67 OTHERS UNISONO HALF-CADENCE (Example 10) K. 283/i, 22 K. 309/i, 32

6

3.24% Probably converging implied

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213

K. 309/iii, 51 K. 309/iii, 210 K. 311/iii, 40

Probably implied converging; 2^–1^–7^ soprano, but no ©4 in bass, no cad. 64

K. 576/iii, 23 PROBLEM CASES

Clearly a simple I–V in outline 2

1.1%

K. 311/i, 20

4^–3^–2^ soprano; see commentary in text

K. 570/iii, 52

Progression is V42/IV–viio7/V–V; could be an ornamented version of the simple I–V with chromatic tonic substitute and interpolated applied chord.

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“HAUPTRUHEPUNCTE DES GEISTES” Punctuation Schemas and the Late-Eighteenth-Century Sonata Vasili Byros

H

ad publication practices in the Age of Enlightenment resembled the massmedia distribution and consumption of films in the New Millennium, eighteenth-century music may have come similarly packaged with “alternate versions,” “composer’s cuts,” and “outtakes.” The late-eighteenth-century equivalent of a “Collector’s Edition” Blu-ray disc for Beethoven’s Second Symphony in D major, op. 36 (1801–02), may well have included among its “outtakes” the passage given in Example 1: an alternate version for bars 56–71 of the first movement.1 My ambition with this chapter is to explain the source of this “alternate version” and, in so doing, to provide some theoretical, historical, and analytic foundation to sustain a premise that lies relatively dormant in eighteenth-century Satzlehre. Namely, a cadence is a schema responsible for the cognition of sonata form. Such is my attempt to bring one answer to the query that headlines this symposium. It is a premise most strongly suggested by Heinrich Christoph Koch’s description of “caesuras” (Cäsuren) as “resting points of the mind” (Ruhepuncte des Geistes), and especially his grouping of more strongly weighted cadences into “principal resting points of the mind” (Hauptruhepuncte des Geistes).2 A three-volume tome completed in 1793, the Versuch brings an implicitly cognitive orientation within the epistemology of the cadence that also frames a historically situated discussion of “sonata form” (die Form der Sonate) as a “punctuation form” (interpunctische Form).3 Koch objectifies the sonata concept as a periodized punctuation script,4 one founded on the cognition of structurally weighted 1. 2.

3. 4.

A digital realization of the example may be heard online at http://vasilibyros.com/b2_hyp.aif. Koch, Versuch III (1793), §129, 342–343 (213). All English translations derive from Baker (ed. and trans.), Introductory Essay (1983). Page numbers for the English edition of subsequent citations are given in parentheses alongside the original German references, as in the citation above. In some cases I have modified Baker’s original translation. The most important of these alterations occurs with the translation of “Ruhepuncte des Geistes.” Baker drops the genitive noun, “des Geistes,” owing to its redundancy. I have retained it throughout because of its overt cognitive significance, translated as “resting points of the mind” or “mental resting points.” On the cognitive implications of Koch’s writings, see also Mirka, Metric Manipulations (2009). Koch, Versuch III (1793), § 119, 331 (209); § 113, 322 (205). The term “script,” discussed in detail below, comes from cognitive psychology, where it is used to characterize a serially-organized pattern.

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Vasili Byros

(transition) . . . . . . LONG COMMA

LE–SOL–FI–SOL ( cadenza lunga variant)

...

56

sf

sf

sf

...

... CONTINUATION ⟾ CADENTIAL ( DOMINANT )

PRESENTATION

[Halbcadenz] = 61

(i: hc mc)

...

FENAROLI-PONTE

...

ff sf ...

ff sf

sf

...

... POST-CADENTIAL ( DOMINANT )

[Anhang (transition-suffix)] FENAROLI-PONTE

...

...

= 64

sf ...

sf

...

...

... = 69

sf

sf

...

Example 1: Beethoven, Symphony No. 2 in D major, op. 36/i (1801–02), bb. 56–71: Alternate version

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217

caesuras. The implication is that cadences are a central feature in constructing mental representations of sonata-form syntax, which in turn powerfully influence listening behaviors in the eighteenth century. To explain and build toward these contentions here, and to properly understand the context for this “outtake” from Beethoven’s Second Symphony, I must begin, unceremonious and roundabout as it may be, with a bit of intellectual housekeeping, (meta) theory, and a couple of anecdotes—the latter recounted from memory, so caveat lector. • The publication and influence of Robert Gjerdingen’s Music in the Galant Style in recent years seem to have occasioned a restricted understanding of the term “schema” in North American musicological circles—despite attempts by David Temperley to clarify Gjerdingen’s circumscribed usage of the term to designate certain “scale-degree schemata.”5 Both the nature and potential weight of this limitation only became apparent to me through conversations with North American colleagues in the winter months of 2011 and 2012. The first setting is one of our symposium’s midday interludes, when William Caplin and I discussed the possible intersections between Formenlehre and “schema theory,” while descending the Pincian Hill of the Villa Borghese. The conversation was not without some collegial disagreement, and yet, any differences of opinion, I learned shortly thereafter, were nonetheless of the most unwelcome variety—namely those based in misunderstanding. Though Caplin has been receptive to exploring the form-functional meanings of galant scale-degree patterns, having even investigated Gjerdingen’s PRINNER as a species of cadence,6 all the same he balked at the idea that, from a schema-theoretic window, formal functions, formal types, and especially sonata form are conceptually similar to galant scale-degree patterns at the phrase level. It was Poundie Burstein who, having observed our conversation, clarified the misunderstanding by the time we reached the Pincian’s base: he brought it to my attention that, for Caplin, “schema” meant “galant phrase-level scale-degree pattern.” This misunderstanding likely owes in no small measure to Gjerdingen’s explicit distancing of the schema concept from issues of musical “form,” and especially “sonata form”—viewing the latter as one among several nineteenth-century inventions whose application to music of the eighteenth century is nothing if not anachronistic, and therefore suspect where a historically “authentic” hearing of the music is concerned.7 This constrained meaning of a schema conveyed by Music in the Galant Style would have rendered my suggestion rather flawed indeed, for, among other things, confounding musical parameters as well as hierarchic levels. 5. 6. 7.

Gjerdingen, Music in the Galant Style (2007); Temperley, “Review of Music in the Galant Style” (2008). See Caplin’s contribution to this volume. Gjerdingen, Music in the Galant Style (2007), 22, 370, 415f., 423, 434, passim.

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The issue became thematic when it returned in the following winter during a conversation atop another summit across the pond: East Hill of Ithaca, NY, with James Webster.8 Webster, too, initially expressed reservation at the possibility of a sonata “schema.” Soon enough, however, he inquired, “In Gjerdingen’s sense?”, thus opening the possibility for an alternative understanding. This time, consequently, no real disagreement ensued, as Max Weber and Carl Dahlhaus entered the room: the idea seemed more reasonable when, following a short clarification on my part, Webster himself associated the term “schema” not with a specific musical parameter, but with a musical “ideal type,” which has no parametric or hierarchic limitations in principle, being equally applicable to a cadence, scale-degree progression, contrapuntal idiom, harmonic progression, sentence, period, or larger rounded-binary structure such as sonata form.9 Nor is “schema” limited to any particular domain or hierarchic level in any principled way. The term was a cornerstone of twentieth-century cognitive and social psychology (with long precedents in empirical philosophy),10 used to explain knowledge structures shaped by one’s environment, particularly social and cultural environment—or, in Gibsonian terms, to describe knowledge formed through one’s attunement with the environment.11 The roots of this connotation lie in Aristotle’s treatise on memory, which holds the earliest such use of the term12: “schema” (ɐɖɛρȽ) carried an equivalent meaning as the later Latin “habitus” as well as the English “shape.”13 Thus it came to represent a “shaping” of the mind by the structural conditions of an envi-

8.

The conversation took place after my giving a colloquium at Cornell University, 23 February 2012, “Ethno-Graphing Mozart.” 9. For Weber’s concept of the “ideal type” in general, see Methodology of Social Sciences (1904/2011), 90–93; Dahlhaus, Analysis and Value Judgement (1983), 45–86, passim; idem, Realism in Nineteenth-Century Music (1985), 121, passim. Webster himself discusses the “ideal type” in Bergé (ed.), Musical Form, Forms, and Formenlehre (2010), 126. See also Gossett, “Carl Dahlhaus and the ‘Ideal Type’” (1989). Though Webster’s analogy with the Marxian Idealtypus was a closer approximation of my intended meaning, to bring eighteenth-century style under a schema-theoretic lens is not equivalent to viewing musical categories as Idealtypen, and replacing the term “ideal type” with “schema.” The two are conceptually related as simplified abstractions from complex observable phenomena, but they are not synonyms. Idealtypen are largely unmalleable and idealized models, which often cause severe problems when used to explain the diversity and complexity of musical particulars, as Gossett showed in Dahlhaus’ own analytic application of the Idealtypus. In Weber’s own words, an ideal type “is a conceptual construct which is neither historical reality nor even the ‘true’ reality. It is even less fitted to serve as a schema under which a real situation or action is to be subsumed as one instance. It has the significance of a purely ideal limiting concept with which the real situation or action is compared and surveyed for the explication of certain of its significant components. [… The ideal type is] arrived at by the analytical accentuation of certain elements of reality. […] In its conceptual purity, this mental construct cannot be found empirically anywhere in reality. It is a utopia.” Methodology of Social Sciences (1904/2011), 93, 90. 10. For an intellectual history of the schema concept in philosophy and cognitive and social psychology, see Byros, “Foundations of Tonality as Situated Cognition” (2009), Chapter 5, passim. 11. Gibson, The Ecological Approach to Visual Perception (1986); Gibson, The Senses Considered as Perceptual Systems (1966); Heft, Ecological Psychology in Context (2001). Gibson’s own ecological interpretation of culture is explicitly given in The Senses, 26f. 12. Aristotle, De memoria, in De sensu and De memoria (1906), 114f. 13. Liddell and Scott, An Intermediate Greek-English Lexicon (1989), s.v. “ɐɖɛρȽǤ”

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ronment—a “shaping” by way of habit, or, in Aristotle’s words, “custom.”14 For this reason, the Swiss child development psychologist Jean Piaget characterized a schema as an “exogenous mechanism.”15 Environments, whether natural, social, or cultural, produce structural modifications on the mind by way of a mental “adaptation” to and subsequent “assimilation” of “the particularities of [its] objects.”16 “Schema” has come to represent this relationship between “object” and mind: it refers to the relevant detail in the environment, to its mental representation or “copy,”17 and to the mind’s use of that representation to navigate or comprehend the same environment subsequently, when encountering a similar and familiar situation.18 The objects in question to which the mind is adaptable in this way have no restriction in principle. They may be any ecological feature or collection of features that is amenable to human perception, abstraction, and categorization, regardless of the type of environment—whether cities, languages, novels, musical works, or motion pictures. The schema concept applies to all varieties of knowledge. Indeed “schemata are our knowledge,” as David Rumelhart put it, in “Schemata: The Building Blocks of Cognition,” which stands among the most seminal modern writings on schema theory. They “represent all levels of our experience, at all levels of abstraction. […] All of our generic knowledge is embedded in schemata.”19 Rumelhart is quite clear that “there are schemata for representing our knowledge about all concepts.”20 A “schema theory,” then, as Rumelhart summarizes it, “is basically a theory about knowledge. It is a theory about how knowledge is represented and about how that representation facilitates the use of the knowledge in a particular way.”21 Nothing in the epistemology of the schema concept would belie a schema-theoretic understanding of a harmonic cadence, a sentence, or a concerto form. Nor is this understanding of a schema of course something entirely new to North American music theory and musicology. It was a foundational concept—in spirit, if not always in letter—for the majority of Leonard Meyer’s output, even if he never distributed his ideas consistently under an explicit schema headline (for a time even using the term “ideal type” to get at the concept).22 Most important for our purpose here, in Style and Music of 1989, Meyer characterized various syntactic parameters of eighteenth-century music, what he called “primary parameters,” as “scriptlike

14. 15. 16. 17. 18. 19. 20. 21. 22.

Aristotle, De memoria, in De sensu and De memoria (1906), 111. Piaget, “The Psychogenesis of Knowledge” (1980), 23f. Ibid. Aristotle, De memoria, in De sensu and De memoria (1906), 107. For a recent discussion of the schema concept’s musical application from psychological, compositional, and historical perspectives, see Byros, “Meyer’s Anvil” (2012). Rumelhart, “Schemata” (1980), 41. Ibid., 34. Ibid., 34. See Byros, “Meyer’s Anvil” (2012), 273–275, passim.

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schemata.”23 In this, he was adopting a concept from Yale psychologists Roger Schank and Robert Abelson, who advanced the further specification of a “script” schema: “A script is a structure […] made up of slots and requirements about what can fill those slots. The structure is an interconnected whole, and what is in one slot affects what can be in another. […] Thus, a script is a predetermined, stereotyped sequence of actions that defines a well-known situation.”24 The “scriptlike schemata” Meyer identified with the eighteenth century certainly included “changing-note melodies,” like Gjerdingen’s “Meyer,” “Aprile,” and “Pastorella.”25 These patterns were, after all, first discussed by Meyer himself under more generic titles: 1–7 … 4–3; 1–7 … 2–1, and 3–2 … 4–3, respectively.26 But Meyer never limited the schema concept to the scale-degree level: “Schemata may arise in connection with any parameter”27; and among his “scriptlike schemata” are also “antecedent/consequent phrases, full authentic cadences (subdominant-dominant-tonic), and sonata-form structures.”28 My suggestion to Caplin on the Pincian Hill was, evidently, a mere echo of Meyer’s earlier, historically oriented formulation, which related the schema concept to the syntactic makeup of eighteenth-century musical organization in general. It is not simply that a schema-minded orientation may befit any music-theoretic inquiry because it deals with knowledge in some way—though this is also certainly true with qualification.29 Rather eighteenth-century music is especially apropos to such inquiry, because its environment is multi-parametrically and multi-hierarchically syntactic, or “scripted” in Schank and Abelson’s sense. It consists of numerous levels of “predetermined, stereotyped sequence[s] of action.” It is highly “perceptually redundant” (Meyer’s term) in the domain of syntax on the whole, and therefore schema rich at all levels of abstraction.30 Generalizations about the environment that give rise to schema formation are dependent on statistical regularity. James Gibson defined environments as “probabilistic” and “stochastically regular,” which renders their navigation predictive with experience.31 And Meyer similarly described the musico-stylistic environment in general as a “stochastic process” and “probability system.”32 Because

23. Meyer, Style and Music (1989), 14, 245, passim. 24. Schank and Abelson, Scripts, Plans, Goals and Understanding (1977), 41. Within the schema-theoretic literature, there have been several different approaches to formalizing a “schema,” for example as a prototype, exemplar, script, plan, or frame. See Byros, “Meyer’s Anvil” (2012), 329f. (n. 12). 25. Gjerdingen, Music in the Galant Style (2007), Chapter 9. 26. Meyer, Explaining Music (1973), “Exploiting Limits” (1980), and Style and Music (1989). 27. Meyer, Style and Music (1989), 51 (n. 32). 28. Ibid., 245. 29. Because the schema concept is predicated on cultural or stylistic redundancies and regularity of behavior, it becomes problematic, for example, in some twentieth-century art-music idioms. See Meyer, Music, the Arts, and Ideas (1967/1994). 30. Ibid., 277. 31. Gibson, The Ecological Approach to Visual Perception (1986), 10, 162. 32. Meyer, Music, The Arts, and Ideas (1967/1994), 28, passim.

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eighteenth-century music exhibits high degrees of statistical regularity and probabilistic structure at numerous levels of its syntactic organization, it demands that one adopt a schema-minded approach. (sentence) DO–TI ... RE–DO

p fz

p

p

8va

fz 8va

PRESENTATION

PASSUS DURIUSCULUS-CADENZA LUNGA

sf

5

p

sf

(i: hc)

p p

CONTINUATION ⟾ CADENTIAL

Example 2: Haydn, String Quartet in D major, op. 33 No. 6/ii (1781), bb. 1–8: Structured integration of scriptlike schemata

To do so, moreover, requires a holistic consideration of the various forms and levels of eighteenth-century syntax, as different yet integrated types of schemata, and a scrutinizing of how their interaction affects listening behaviors. Meyer described the changing-note scripts at the foreground level as nested elements within larger syntactic processes: “The form of the [changing-note] schema is strophic (A A´), but on the next hierarchic level, [its] first two elements […] frequently form part of a larger bar form (A A´B).”33 This “larger bar form” is what Caplin calls a SENTENCE. The various “scriptlike schemata” are thus hierarchically differentiated as well as interactive: “In the Classic style, […] changing-note schemata are usually only part of a theme whose full form is A A´ B.”34 This structured integration can be seen in Example 2, which displays the opening theme from the Andante of Haydn’s String Quartet in D major, op. 33 No. 6 (1781). Here, a DO–TI … RE–DO scale-degree and harmonic schema characteristically forms the presentational first half of a SENTENCE, whose continuation 33. Meyer, Style and Music (1989), 226f. 34. Ibid., 231.

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phrase involves another phrase-level pattern, a PASSUS DURIUSCULUS variant of a cadence that eighteenth-century Italians called a cadenza lunga (“long cadence”).35 Together, the DO–TI … RE–DO and cadenza lunga communicate the SENTENCE at the next highest level, and all three scriptlike schemata play integrative roles in communicating the half cadence at bar 8 as the syntactic goal of the entire theme. Most experiences, whether finding one’s feet in a new city or in a new symphony, are simultaneously regulated by numerous types of integrated knowledge. Schemata do not work as hermetically sealed cognitive vacuums but as a structured synergy. Or, as Bradd Shore eloquently phrased it in his Culture in Mind, the mind has a “polyphonic” structure: “A thick and complex texture of conscious experience is made possible by the simultaneous interactions of several ‘layers’ of different sorts of knowledge. […] [E]xperience[s] are layered.”36 To be sure, “[a]ccording to schema theories [generally], all knowledge is [viewed as] packaged into units. [And t]hese units are the schemata. Embedded in these packets of knowledge is, in addition to the knowledge itself, information about how this knowledge is to be used.”37 But these units are not isolated representations in the mind. They result from consortiums of even smaller units of knowledge, and participate in the framing of largerscale experiences. The mental organization of experience is a structured aggregate involving sequential, associative, as well as hierarchical relations among knowledge units. Schemata are, in essence, cognitive hierarchies built up of numerous, embedded subschemata, that define a broader concept through their interaction: “A schema is a network […] of subschemata, each of which carries out its assigned task of evaluating its goodness of fit whenever activated. These subschemata represent the conceptual constituents of the concept being represented. […] [A] schema uses results produced by its subschemata to carry out its tasks.”38 As the ecological psychologist Ulric Neisser describes the concept, a schema is something like a “cognitive map [...] Units at different ‘levels’ are not just related sequentially; […] they are embedded. […] Actions are hierarchically embedded in more extensive actions and are motivated by anticipated consequences at various levels of schematic organization.”39 The SENTENCE in Example 2, for instance, plays such a charting role as a listener navigates the opening theme. Each harmonic and scale-degree subschema at the phrase level is hierarchically embedded in a more extensive action: namely, the cadence at bar 8, as an anticipated consequence at the highest level of schematic organization

35. The cadenza lunga takes many different forms, see Sanguinetti, The Art of Partimento (2012), 107–110, passim, and 145–146 on descending chromatic basses. Cadenze lunghe are conceptually synonymous with Caplin’s concept of “expanded cadential progression” (see n. 93 below). 36. Shore, Culture in Mind (1996), 93. 37. Rumelhart, “Schemata” (1980), 34. 38. Ibid., 39; see also 40f. 39. Neisser, Cognition and Reality (1976), 123f., 113.

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for the opening theme. But at the same time, the SENTENCE and its broader cadential goal are (reciprocally) enabled by these lower-level, subschematic processes. The DO–TI … RE–DO is a phrase-level form of syntax that exemplifies PRESENTATION function, as one among several tonic-dominant statement-response paradigms. The inconclusiveness of its PRESENTATION function motivates the larger-scale structure: as Meyer put it, “closure is not very decisive in most instantiations of this schema. This is because in most cases the changing-note pattern is part of a higher-level melodic process […] and larger bar form (A A´B).”40 Not only does the PASSUS DURIUSCULUS variant of the cadenza lunga bring the necessary cadential closure to round off the SENTENCE, but the DO–TI … RE–DO retrospectively emerges as an inner-voice pattern within a “higher-level melodic process”: a hexachordal descent that begins with the sustained A of the first violin and closes with the resolution of the cadenza lunga and C© in the melody. To paraphrase Rumelhart, the SENTENCE schema uses results produced by these subschemata to carry out its tasks. It “emerge[s] from the interaction of […] [these] simpler elements all working in concert with one another.”41 The same principle applies to the largest level of schematic organization, so that syntactic forms that occupy the SENTENCE level of structure (like the PERIOD and HYBRID forms), in turn, become subschemata within a more global script: “formal schemata such as theme and variations, rondo, da capo arias, and sonata form.”42 And so, the various forms of “replicated patterning” in eighteenth-century music share deep conceptual resonances insofar as they all are statistical regularities in the environment, are cognitive hierarchies composed of lower-level subschemata, are all syntactic (or “scripted”) in their makeup, and they all contribute to the formation of a summit of syntactic organization in a higher-level formal genre, like SONATA FORM. As a global script schema, SONATA FORM emerges from but also inversely subsumes all other varieties of syntax as its embedded subschemata. Meyer defined “[e]ighteenthcentury sonata form [a]s a script-based schema whose parts are […] articulated into an arched hierarchy according to the degrees of closure created by several [primary] parameters involved. […] [T]he possibility of [such] hierarchic organization depends on the existence of different kinds and strengths of closure created by syntax. [. . .] [T]he formation of a hierarchy depends on the existence of closure.”43 This last formulation is most suggestive in the context of eighteenth-century music theory, and contemporaries’ punctuative descriptions of musical form in general—as displayed in several writings by Johann Mattheson, Johann Adolph Scheibe,

40. 41. 42. 43.

Meyer, Style and Music (1989), 229, 227. Rumelhart, Smolensky, et al., “Schemata and Sequential Thought Processes” (1986), 20. Meyer, Style and Music (1989), 51. Ibid., 303f., 15, 330 (my emphasis).

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Joseph Riepel, Friedrich Wilhelm Marpurg, Johann Philipp Kirnberger, and Koch.44 Today the sonata form concept is often viewed as a largely mid-nineteenth-century invention,45 and the term itself a neologism attributed to Adolph Bernhard Marx.46 Yet 1803 issues of the Leipzig Allgemeine musikalische Zeitung reference “sonata form” as a compositional norm. For example, when the publisher Nägeli announced the printing of Beethoven’s op. 31 set of piano sonatas, he described them as having “many departures from the customary sonata form” (Abweichungen von der gewöhnlichen Sonaten-Form).47 This sonata form “custom” or “habit”—the adjective gewöhnlich conceptually implies a noun-form, Gewohnheit—is likely a reference to the concept objectified some years earlier in Johann Georg Sulzer’s 1774 article on the “Sonata” (Sonate), from the Allgemeine Theorie der schönen Künste, and especially in volume 3 of Koch’s Versuch from 1793.48 Both speak of “the form of the sonata” (die Form der Sonate). If not a nineteenth-century invention, something about the late-eighteenth-century view of the concept was certainly lost by the Romantic generation, as Karol Berger has argued for years—specifically, the importance of cadential punctuation, a view that has been gradually revitalized in recent decades, in more or less explicit terms, by Berger as well as by Carl Dahlhaus, Leonard Ratner, James Hepokoski and Warren Darcy, William Caplin, and Michael Spitzer, among others.49 Discussions of a SONATA schema in the eighteenth century are most implicit in Koch’s definition and elaboration of “die Form der Sonate” as a “punctuation form” (interpunctische Form).50 In the Versuch, “form” is described as a cognitive hierarchy of different states of musical closure, punctuation, and rest, what Koch called Ruhepuncte des Geistes.51 These “resting points of the mind” produce a hierarchy of closure, and 44. Mattheson, Der vollkommene Capellmeister (1739); Scheibe, Der critische Musikus (1738–1745); Joseph Riepel, Anfangsgründe (1752–1768); Marpurg, Kritische Briefe (1759–1763); Kirnberger, Die Kunst des reinen Satzes (1771–1779); and Koch, Versuch (1782–1793). For a survey of the concept of musical punctuation in the eighteenth century, see Stephanie Vial, The Art of Musical Phrasing (2008). 45. Gjerdingen, Music in the Galant Style (2007), 22, 370, 415f., 423, 434, passim. 46. Hepokoski and Darcy, Elements (2006), 14f. 47. Nägeli, “Ankündigung: Repertoire des Clavecinistes” (1803). The term “allzugewöhnlichen SonatenForm” also appears in the “Recensionen” section of the 11 May 1803 issue (No. 33) of the Leipzig AmZ, 559–560, which announces the publication of several keyboard works by Anton Eberl. 48. Sulzer, Allgemeine Theorie (1774–1794), s.v. “Sonate”; Koch, Versuch III (1793), §119, 331 (209); §113, 322 (205). 49. Dahlhaus, “Der rhetorische Formbegriff H. Chr. Kochs” (1977); Ratner, Classic Music (1980); Budday, Grundlagen musikalischer Formen (1983); Forschner, Instrumentalmusik Joseph Haydns (1984); Berger, “Toward a History of Hearing” (1992), “The Second-Movement Punctuation Form” (1992), “The First-Movement Punctuation Form” (1996); Hepokoski and Darcy, “The Medial Caesura” (1997); Berger, “Mozart’s Concerto Andante Punctuation Form” (1998); Caplin, Classical Form (1998), “The Classical Sonata Exposition” (2001), “The Classical Cadence” (2004); Spitzer, Metaphor and Musical Thought (2004); Hepokoski and Darcy, Elements (2006); Berger, Bach’s Cycle, Mozart’s Arrow (2007); Burstein, “Mid-Section Cadences” (2010); and Diergarten, “Jedem Ohre klingend” (2012). 50. Koch, Versuch III (1793), §20, 52 (83); §31, 82 (95); §38, 124 (116); §150, 395 (234); passim. Koch also uses the plural, “interpunctische Formen,” as he describes several types of punctuation form in vol. III, whose differences are affected by, among other things, genre. 51. Koch, Versuch (1782–93), passim; see especially vol. II, §§77–79, 342–348 (1–3).

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thus of different formal sections, because they are varied in their markedness—or, in Meyer’s terms, they afford “different kinds and strengths of closure created by [different kinds of] syntax.”52 And this gradation enables “the possibility of hierarchic organization.” The “most marked [merklichsten] resting points” articulate “periods” (Perioden), the “less marked” (weniger merklichen) “single phrases” (einzelne Sätze) and “incises” (Einschnitte).53 Thus a hierarchy arises from the “more or less marked resting points of the mind” that produce these formal divisions. The largest divisions of a sonata or symphony that Koch advances are the equivalents of the present-day exposition, development, and recapitulation, which he called the first, second, and third “main periods” (Hauptperioden).54 Each “period” (Periode) is subdivided into different kinds of “phrases” (Sätze): one or more “internal phrases” (Absätze)—which are further qualified as “a basic phrase” (enger Satz), “an extended phrase” (erweiterter Satz), or a “compound phrase” (zusammen geschobener Satz)—and a “closing phrase” (Schlußsatz), which ends a Hauptperiode.55 (Because translations of Satz as “sentence” or “phrase” invite confusion with the more familiar North American meanings of such terms, the German is retained hereafter.) The argument for an arched hierarchy within this punctuation form emerges most conspicuously in the Sätze that Koch associated with cadences of greatest structural and perceptual weight, which function as “landmarks” within the “cognitive map” of a sonata or symphony. These hierarchically superordinate caesuras Koch designated Hauptruhepuncte des Geistes (“principal resting points of the mind”), which sit atop the arch of the hierarchy, as they represent the highest degrees of closure.56 They also define large-scale syntactic relationships within the punctuation form. Koch maintained that only some cadences (Cäsuren) within a period share in the “collation of phrases by means of punctuation” (interpunctische Vergleichung der Sätze),57 so that structural cadences themselves form a higher-level syntactic script: a predetermined, stereotyped sequence of actions on a large-scale level. This script consists of a series of weighted caesuras and their attendant Sätze, and admits of several variants. At the uppermost level of the Hauptruhepuncte sequence is the “closing Satz” (Schlußsatz) of the exposition and recapitulation (erste or dritte Hauptperiode), produced by a perfect authentic cadence in the key of the dominant and tonic, respectively. This PAC is a particular kind of “caesura” (Cäsur) for which Koch specially reserved the term Cadenz.58 It sits atop the hierarchy because only this Cadenz may close a period, which 52. 53. 54. 55. 56. 57. 58.

Meyer, Style and Music (1989), 15. Koch, Versuch II (1787), §§77–79, 342–348 (1–3). Ibid., vol. III (1793), §110, 318–319 (204). Ibid., vol. II (1787), §§79–80, 346–349 (2–3); passim. Ibid., vol. III (1793), §129–132, 342–347 (213–215); §149, 394f. (233). Ibid., vol. II, §112, 440 (48); vol. III, §58, 197 (150). Ibid., vol. III, §129, 342f. (213); vol. II §102, 419f. (38f.); passim. Koch also uses the term förmliche Cadenz; ibid., vol. III, §86, 260 (177), passim.

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is the largest formal division and strongest Ruhepunct. Each period-ending Schlußsatz is preceded by various arrangements of tonic- and dominant-oriented “internal Sätze” (Absätze) in the key of the tonic and dominant. Tonic-oriented Sätze go by the term Grundabsatz (“I-phrase”), and close with tonic harmony (with a perfect or imperfect authentic cadence),59 and dominant-oriented Sätze go by Quintabsatz (“V-phrase”), directed at dominant harmony or a half cadence.60 Depending on a composition’s scope, size, and grandiosity, the outer Hauptperioden of a sonata or symphony will have three or four such Sätze and Hauptruhepuncte in total.61 Koch’s main script types for the major mode are outlined in Table 1. As seen, a sonata-form exposition consists of a stereotyped sequence of cadences: an opening Hauptruhepunct, produced by the Thema or Hauptsatz (“theme” or “principal Satz”),62 one or more medial Hauptruhepuncte, and a closing Hauptruhepunct produced by the Cadenz of the Schlußsatz. A further hierarchic division is supplied by Koch’s distribution of these three or four Hauptruhepuncte into two halves. “This first period is […] divided into two parts.”63 Its “second half ” consists of “those melodic ideas […] which follow the Quintabsatz in the fifth.”64 This two-part conception of the exposition suggests that the Cadenz which closes the Hauptperiode, and the Quintabsatz that divides it into two halves, are the structurally most weighted cadences. Later in his Musikalisches Lexicon of 1802, Koch would more explicitly identify the structural weight of the medial Quintabsatz to that of the Cadenz, by designating the former Absatz a Halbcadenz.65 These two Hauptruhepuncte, the Cadenz and Halbcadenz, are equivalent to the “generically obligatory cadences” that underlie Hepokoski and Darcy’s sonata theory: the Cadenz marks the “essential expositional closure” (EEC) and “essential structural closure” (ESC) of an exposition and recapitulation respectively, while the Halbcadenz is synonymous with the half cadence of the “medial caesura”—specifically, the “strong half cadence that [is] rhythmically, harmonically, or texturally reinforced,” which the “medial caesura is built around.”66 The 59. Tonic-oriented contrapuntal cadences and tonic-prolongational phrases more generally would also fall under the Grundabsatz category. 60. Koch, Versuch (1787 and 1793), vols. II, III, passim. 61. Although Koch introduces the term Hauptruhepuncte des Geistes when discussing larger compositions which contain four Hauptruhepuncte, the term should not be misunderstood as applying only to compositions containing four such types of punctuation. That is, compositions which contain three Sätze per period vary only quantitatively, not qualitatively. This becomes clear from Koch’s overall discussion of the “The Arrangement of Larger Compositions” (§72–159). 62. Ibid., vol. II, §79, 347 (3); passim. 63. Ibid., vol. III, §129, 342f. (213). 64. Ibid., vol. III, §103, 311 (201); also §129, 342f. (213). 65. Koch, Musikalisches Lexicon (1802), s.v. “Quintabsatz.” See also Poundie Burstein’s contribution to this volume on this usage of Halbcadenz in Koch, and its relation to what Hepokoski and Darcy call the “medial caesura” (see their Elements [2006], Chapter 3, passim). 66. Hepokoski and Darcy, Elements (2006), 24. The medial caesura is discussed in Chapters 3, 7–8, 11, and passim. In all uses of the term “medial caesura” in this chapter, I mean the entire multi-staged “process” that Hepokoski and Darcy outline in the Elements (30–36). To be sure, they most commonly use the term to reference the actual moment of gap between the transition and second theme, whether

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overall picture of SONATA FORM in Koch’s Versuch is a “periodic structure [Periodenbau] [that] depends on th[e] alternation [of] […] Grundabsätze, Quintabsätze, and Cadenzen.”67 The Hauptruhepuncte des Geistes and their attendant Sätze are explained as large-scale syntactic regularities in the eighteenth-century musical environment, which define the SONATA concept’s representative constituents as a periodized punctuation script. Table 1: Punctuation scripts for a sonata-form exposition in Koch 1782–1793, 1802 first half Hauptsatz Type 1 (Vol. III, §45, §128) Type 2 (Vol. III, §45, §128) Type 3 (Vol. III, §45, §128) Type 4 (Vol. III, §129)

I: GA I: QA I: GA I: GA

second half

medial Halbcadenzen* V: QA V: QA I: QA I: QA

V: QA

Schlußsatz V: Cadenz V: Cadenz V: Cadenz V: Cadenz

[Anhang] [Anhang] [Anhang] [Anhang]

*Musikalisches Lexicon (1802), 1212.

The broader significance of this script-based conception is that higher-level subschemata, like the Hauptruhepuncte, have a top-down influence on lower-level, embedded forms of syntax—or, from the other way round, lower-level forms of syntax have a bottom-up obligation to communicate the Hauptruhepuncte script. In their function as the primary subschemata of the SONATA schema, the Hauptruhepuncte are not isolated events within the cognitive hierarchy. The “periodic structure” (Periodenbau) abstracted in Table 1 is communicated by further layering of syntax in the cognitive hierarchy. As Meyer relates it, SONATA FORM is not only scripted as “a tonally defined hierarchic schema of slots,” but is also “script-dominated”—that is, dependent on lower-level subschemata: “patterns [. . .] are hierarchically connected [. . .] by virtue of their participation in the higher-level syntactic process of [a] whole movement.”68 Like Meyer, Koch specifies that hierarchically varied forms of closure (Ruhepuncte)—be they local-level

filled in or not; but they also use the term to reference a broader syntactic plan: “in order to function as a normative medial caesura, the forte half-cadence arrival within TR must be additionally reinforced. The whole process often proceeds as follows” (30). They then go on to describe the various stages of that process, which begins with a cadential progression (often including ©4), and ends with a normative beginning of the second theme. To my way of thinking, the thrust of the medial caesura concept lies in its dynamic qualities: it too is a multi-staged scriptlike schema, not any isolated moment in time (whether that of the actual half cadence, or of the gap which follows)—for neither the medial caesura cadence nor the medial caesura gap may carry structural significance in the absence of the other. Both are components of a larger medial caesura schema. This perhaps becomes most explicit in the rationale Hepokoski and Darcy advance for their “shorthand symbols I:HC MC” and “V:HC MC”: “we […] use [these] symbols […] to suggest this whole complex of musical activity, one in which the literal MC moment [that is, the gap] is to be interpreted referentially to any preceding moment of half-cadential arrival” (24). In what follows, any references to particular stages in the medial caesura schema will be done so by name: “medial caesura cadence,” “medial caesura gap,” etc. 67. Koch, Versuch III (1793), §39, 128 (118). 68. Meyer, Style and Music (1989), 246, 330, 40.

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Einschnitte or large-scale Hauptruhepuncte—are communicated by hierarchically specific syntactic processes, which he variously termed “punctuation formulas,” “punctuation figures,” and “punctuation signs” (interpunctische Formeln; interpunctische Figuren; interpunctische Zeichen).69 The Cadenz, for example, is the punctuation formula specifically designated for the Schlußsatz. It is but one of several harmonic and contrapuntal patterns Koch discusses in Volume 1 of the Versuch.70 These formulaic, phrase-level signs are one of “two main characteristics [. . .] through which [. . .] the various sections in musical works [that] compose their periods [. . .] distinguish themselves as divisions of the whole. [. . .] The endings of these sections are certain formulas, which let us clearly recognize the more or less marked resting points. [. . .] [W]hat is important for all of these divisions is the formula through which they become marked as resting points, or, to use our chosen term, their punctuation sign [Zeichen].”71 This last phrase is perhaps most indicative of the cognitive implications of punctuation form: it suggests a listener is in a constant state of attunement with some form of closure, or rest, depending on the “punctuation formula” or “scriptlike schema” currently in force. Indeed Koch’s specific turn of phrase, “mental resting point,” suggests that a listener is actively doing something in between moments of punctuation— conceivably tracking various forms of closure. And, if the different types of closure are themselves regulated by commensurately varied forms of syntax or punctuation formulas, and therefore integrated within the cognitive hierarchy, then lower-level forms of closure would be directed to a higher-level state of attunement with the Hauptruhepuncte at the top of the hierarchy. In Neisser’s words, “[a]ctions are hierarchically embedded in more extensive actions and are motivated by anticipated consequences at various levels of schematic organization.”72 Lower-level forms of syntax are designed to make the uppermost level of syntax, here the Hauptruhepuncte, most clear to a listener: “what is important for all of these divisions is the formula through which they become marked as resting points.”73 Berger, in his own reflections on Koch, characterizes this cognitive implication of punctuation form in semiotic terms. A cadence, as the ultimate goal of a phrase, is not only a terminal point, but a representation of the collective syntactic processes leading to it: “It symbolizes closure—not as an arbitrary signal but as the experience of reaching a goal.”74 Michael Spitzer voices a similar sentiment: “Riepel and Koch shared the same insight that phrase endings are understood

69. Koch, Versuch II (1787), §79, 347f. (2–3); §94, 390 (22); ibid., vol. III (1793), §5, 7 (64); §150, 395 (234); passim. 70. As Koch notes, “[t]he nature of the cadence [Cadenz], as the ending formula of the closing phrase, has already been treated in section 179 of the first volume” (38). 71. Ibid., vol. II (1787), §79, 347f. (2f.). 72. Neisser, Cognition and Reality (1976), 123f., 113. 73. Koch, Versuch II (1787), §79, 347f. (2f.). 74. Berger, Bach’s Cycle, Mozart’s Arrow (2007), 180.

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by the listener as comprehending the entire phrase, as a kind of musical ‘sign’.”75 So closure is not an isolated moment in time, but a complex layered experience involving a consortium of subschemata, all of which are part of this experience of not only reaching but also setting up a goal. Musical punctuation is graded and processive. To view the SONATA punctuation script as an arched hierarchy of closure is to view multiple, integrated levels of syntax as variously “anchored” to structurally weighted cadences (Hauptruhepuncte) at the top of the hierarchy. Table 2 displays this integration in the exposition of Beethoven’s Second Symphony. The tabular analysis serves to align and thus illustrate the interactions among different levels of syntactic subschemata: specifically, how phrase-level patterning (DO–TI … RE–DO types of syntax, registered in Column PHL) and middleground phrase-structure (SENTENCE and PERIOD types of syntax, registered in Column FT) produce “different degrees and strengths of closure,” or variously “marked resting points.” These foreground and middleground grammars are shown to be synergetically oriented toward the larger stereotyped sequence of actions represented by the Hauptruhepuncte script, through the chunking design of the table: boxes refer to cognitive chunks at the various syntactic levels, beginning with individual bars in the leftmost column. The Hauptruhepuncte and their attendant Sätze are the largest chunks given in the Column designated HRP: bars 34–47, Grundabsatz or I:PAC; bars 47–69, Halbcadenz or v:HC; bars 73–112, Cadenz or V:PAC. The latter two cadences correspond to Hepokoski and Darcy’s medial caesura half cadence (HC MC) and cadence of essential expositional closure (EEC), respectively.76 The experience of large-scale musical organization in the Symphony is represented as various states of cadential attunement with the structurally weighted cadences at the top of the hierarchy. These states are registered in four successive columns to the left of the table as cadential implication (I), cadential realization (R), cadential denial (D), and cadential extension (E). For example, bars 44–46, which consist of a PRINNER and CADENZA SEMPLICE sequence at the phrase level (Column PHL), project a cadential implication (I), a state which shifts to cadential realization (R) with the I:PAC at bar 47.77

75. Spitzer, Metaphor and Musical Thought (2004), 216. 76. Hepokoski and Darcy, Elements (2006), Chapters 3, 7f., 11, passim. Hepokoski and Darcy place the medial caesura for the Sympony’s exposition at bar 71, with a half cadence at bar 69, and caesura fill in bars 71f. See Elements, 25f., 45. The problem of the medial caesura half cadence in the exposition is taken up in detail below. 77. The cadential attunement categories have been registered as a simple “on” or “off” state for the sake of economy. Ideally, and in reality, the monochrome grey in Columns I–E of Table 2 should be a spectrum, to register degrees of “on-ness,” where lighter and darker shades represent more pronounced or marked instances of the perceptual category.

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Table 2: Beethoven, Symphony No. 2 in D major, op. 36/i (1801–02), bb. 34–133: Cadential anchoring and structured integration of syntactic subschema in the sonata form schema legend (B.: bar) (I: implication) (R: realization) (D: denial) (E: extension) (CAD: cadence) (K: key) (PHL: phrase level) (FF: formal function) (FT: formal type) (FS: formal section) (HRP: Hauptruhepunct) B. 34 35

I

R D E

CAD.

36 37 38 39 40 41 42 43 44 45 46 47 48

I: PAC

49 50 51 52 53 54 55 56 57 58 59 60 61 62

i: HC EV.

63 64 65 66 67 68 69

v: HC*

70 71 72 73 74 75 76 77 78 79 80 81

V/V: PAC

82 83 84 85 86 87 88 89 90 91 92 93

V/V: PAC

K

D D D D D D D D D D D D D D D D D D D D D d d d d d d a a a a a a a a a a A A A A A A f f –E E E A A A A f f –E E E–A A A A A A

PHL Tonic Arpeggiation

Indugio/Converging . . .

FF b.i. (or c.b.i.)

consequent ~ ~ b.i.´

FT Hybrid 4 ~

~ Sentence

a

FS PT

G R U N D A B S A T Z

a´

b

[ . . . Monte . . . ]

cont.

Prinner . . .

cont.

Cadenza Semplice Tonic Arpeggiation . . .

cadential post-cad. (intro.)

Quiescenza

post-cad. (b.i.)

a

post-cad. (b.i.´)

a´

Le–Sol–Fi–Sol Cad. Lunga . . .

cont.⟾ cad.

b

Fenaroli-Ponte

post- cad.

Stand. on Dom.

Passus duriusculus Ponte

cadential post-cad.

Stand. on Dom.

Sentence

HRP

TR (Diss. Cod.)

I: GA

[Long Comma] Quiescenza

H A L B C A D E N Z

[Long Comma]

Caesura Fill (5–4–3–2–1)

lead-in

Tonic Arpeggiation

c.b.i.

Tonic Arpeggiation . . . Cadenza Lunga

consequent (cadential)

Tonic Arpeggiation

c.b.i.

Tonic Arpeggiation . . . Cadenza Lunga

consequent (cadential)

Sol–Fa–Mi (x4, stretto) . . .

continuation

Sentence [ Hybrid 4 ]

[ Hybrid 4 ´ ]

v: QA/HC MC *

a

a´

b

ST

C A D E N Z

“Hauptruhepuncte des Geistes” 94 95 96 97 98 99 100

V: DC

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

V: PAC

A A A A A A A A A A A A A A A A A A A A–d d d d d d d d d d d d d–A A A A A A A D D

Falling 3rds/Romanesca . . .

231 continuation

[Indugio] Comma . . . Cadenza Semplice Long Comma (incomplete) . . .

cadential cadential

Grand Pause Indugio/Converging . . .

cadential

Cadenza Composta

cadential

Tonic Arpeggiation ~ ~ Ponte ~

post-cad.

C A D E N Z

b´

Codetta

CT

V: Cadenz/EEC

A N H A N G Tonic Arpeggiation

Ponte

retran.

RT

The idea represented in these columns is that the process and perception of closure, and thus of large-scale sonata-form organization, amounts to a continuous and graded process of cadential anchoring, analogous to what Jamshed Bharucha called “melodic anchoring” in a tonal melodic context, where some tones are perceived as stable points.78 In a SONATA-FORM context, “stable points” or, in Koch’s terms, “more marked resting points,” are the collective and synergetic result of the hierarchically varied and integrated syntactic processes outlined in Columns PHL, FF, and FT. The states of attunement, or “degrees and strengths of closure,” in Columns I–E were determined in accordance with the normative formal functions of the phrase-level syntactic patterning of Column PHL, as well as the hierarchical position of these subschemata within higher-level, form-functional syntactic types like SENTENCES, PERIODS, and so forth. The formal functions of the phrase-level patterning are given in Column FF, their larger formal type context in Column FT. The PRINNER and CADENZA SEMPLICE

78. Bharucha, “Anchoring Effects in Music” (1984).

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sequence (Column PHL) in bars 44–46, for example, communicates continuation– cadential syntax at the form-functional level (Column FF) within the larger syntactic context of a SENTENCE (Column FT). Together, these various levels of syntax serve as orienting subschemata that are anchored to the Hauptruhepuncte in Column HRP—or, in Hepokoski and Darcy’s language, they constitute the “trajectories toward generically obligatory cadences.”79 In this case, the generically obligatory or scripted cadences conform to Koch’s Type-1 exposition script of Hauptruhepuncte (Table 1). The layered integration of these micro- and macro-structured scriptlike schemata in the Symphony brings a positive form of evidence that contemporaries’ descriptions of the “gewöhnliche Sonaten-Form” and “die Form der Sonate” implied a conception of SONATA FORM as a punctuation script schema. But there is a complementary, and perhaps even stronger, piece of analytic evidence in the Symphony that would support this hypothesis: namely, an “Abweichung von der gewöhnlichen Sonaten-Form”—a marked deviation from this custom, which brings a kind of negative evidence for a SONATA punctuation schema. Exceptio probat regulam (“the exception confirms the rule”). Beethoven interjects a powerful syntactic deviation that disrupts the multiple levels of syntax in one sweeping gesture—a gesture that unsettles the otherwise structured integration of subschemata and, by extension, the entire SONATA FORM schema they represent as its conceptual constituents. At the middleground level (Column FT), all three Hauptruhepuncte are communicated by SENTENCE forms. The principal theme (Grundabsatz, bb. 34–47, I:PAC) and second theme (Cadenz, bb. 73–112, V:PAC) are syntactically normative in this regard; they feature no disruption in the overall SENTENCE script: PRESENTATION–CONTINUATION–CADENCE. The principal theme is a 14-bar compound sentence with a compressed continuation, and the second theme a 40-bar, doubly-compound sentence (based on a 32-bar sentence norm) with an extended continuation via a deceptive cadence (bar 100). The transition, however, bears a pronounced syntactic violation in the SENTENCE script. Bars 47–56 present the first half of a compound (16-bar) sentence: an extended presentation phrase (2 + 4 + 4). This Absatz, which begins in bar 47, is a transition of the “dissolving codetta” type in Hepokoski and Darcy’s language, and of the “false closing section” type in Caplin’s.80 The 10-bar first half (8-bar presentation in bb. 49–56, plus a 2-bar “introduction,” bb. 47–48) implies an approximate 8-bar continuation phrase to follow. The continuation does begin at bar 57, but is interrupted at bar 61 by what Caplin has described as a “premature dominant arrival.”81 The entrance of this dominant is less an arrival than a sublime intrusion. In Caplin’s own words, the dominant of A minor in bars 61ff. “arrives [. . .] in a noncadential manner,” and the “complete change of musical material following the dominant

79. Hepokoski and Darcy, Elements (2006), 13 (emphasis in original). 80. Ibid., 102–105; Caplin, Classical Form (1998), 129. 81. Caplin, Classical Form (1998), 135.

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arrival gives the impression of being a typical standing on the dominant, despite the lack of cadential articulation.”82 The implication is that a cadence was expected and denied, and yet a standing-on-the-dominant process, which normally proceeds from an achieved half cadence, follows in bars 61ff. nonetheless. The cadential anchoring for this passage in Table 2 (Columns I–E) captures this impression by showing a transformation from a state of cadential denial (bb. 61–62) to cadential extension (bb. 63–67). This succession of cadential anchoring states of course makes no logical sense, as a cadence must first be produced in order for it to be extended or prolonged by ancillary material. The analysis is deliberately meant to capture a sense of disorientation on the part of a listener as regards their cadential anchoring (“what’s coming next?”) and therefore formal orientation (“where are we?”). This premature dominant arrival at bar 61 represents a disruption on three hierarchically varied syntactic levels: phrase level (PHL), formal function (FF), and Hauptruhepuncte des Geistes (HRP). Bars 57–61 present the first two-thirds of a phrase-level harmonic pattern that I have styled the LE–SOL–FI–SOL. This schema (and its many variants throughout the long eighteenth century) was the centerpiece of a previous study dedicated to the historical perception of tonality, which focused on Beethoven’s Eroica Symphony (1804).83 The schema is essentially a chromaticized species of one type of cadenza lunga.84 The pattern expands and chromatically intensifies predominant harmony (something of a composing-out of an augmented-sixth chord) through a chromatic turn of phrase in the bass that is oriented around the dominant: ¨6–5–©4–5. Figure 1 shows an abstract representation

le—sol—fi—sol cadenza lunga 1

1

1

1

-3

-3

-3

-3

7 2

* 15e

i

*

5e -6

VI

6r 5

(i6/4)

7tK∂ 6tK∂ +4

+ivo7

∂ ®6r

7tK

5

(i6/4) V

*

Figure 1: le–sol–fi–sol schema, cadenza lunga variant: Abstract representation, from Byros 2009; 2012 82. Ibid. 83. Byros, “Meyer’s Anvil” (2012); idem, “Foundations of Tonality” (2009). 84. See n. 35 above.

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of its full form, which admits of three variables highlighted by asterisks: 1) an abbreviated version that omits the passing 64 chord between ¨6 and ©4; 2) the possibility of a 65 chord on scale degree ©4 as an alternative to the diminished seventh; and 3) the optional placement of tonic harmony (on scale degree 1) at the beginning, giving rise to a longer descending thirds pattern in the bass characteristic of cadenze lunghe in general, though here chromatically altered: 1–¨6–(5)–©4–5. The cadential 64 prior to the final dominant is also optional, according to customary usage of this chord. An instance from Haydn’s Symphony in C major, No. 60 (1774) is shown in Example 3.

(transition) LE–SOL–FI–SOL (cadenza lunga) 49

-

-

(v: hc mc)

-

CADENTIAL ( DOMINANT )

[Halbcadenz] Example 3: Haydn, Symphony No. 60/i in C major (1774), bb. 49–52: le–sol–fi–sol schema, Halbcadenz usage

Figure 2 displays the cadential usage of 747 instances of this schema in a corpus of roughly 3000 musical works from 1720–1840.85 As seen in these statistics, the LE–SOL– FI–SOL is a punctuation formula strongly associated with the production of Quintabsätze in general: 63% of the time the (sub)schema articulates a half cadence, compared to 20% and 3% for a PAC (Cadenz) and IAC (Grundabsatz), respectively. More importantly, the LE–SOL–FI–SOL holds a strong affinity to a particular kind of Quintabsatz: it carried a specific syntactic function within the larger SONATA punctuation script.

85. The statistics are taken from the corpus data presented in Byros, “Foundations of Tonality,” Appendix B.

“Hauptruhepuncte des Geistes”

500

235

((63%) 3 )

450 400 350 300 250 200 150

((20%) (13%)

100 50

(3%)) (1%) (1%) (3

0

hc pac iac ec dc de hc = half cadence pac = perfect authentic cadence iac = imperfect authentic cadence ec = evaded cadence dc = deceptive cadence de = dominant expansion Figure 2: le–sol–fi–sol schema: Cadential usage from 1720–1840 (corpus sample size ~3000 compositions), from Byros 2009, Appendix B

Table 3 registers the schema’s SONATA-FORM usage in a smaller representative sample from the larger corpus, chosen here for the sake of economy: the opening movements of Haydn’s Symphonies in a fast tempo, where the LE–SOL–FI–SOL appears 31 times. In this circumscribed sample, once again about 65% of the time (20/31) it closes a Quintabsatz, compared to 16% for a PAC. Of these 20 Quintabsatz examples, 14 (70%) are used to punctuate the cadential goal of the transition—the Halbcadenz, or the medial Hauptruhepunct in Koch’s exposition scripts (Table 1). Table 3: le–sol–fi–sol schema: Sonata-form usage in the opening movements of Haydn’s Symphonies in a fast tempo 1757/61c. 1757/61c. 1761? 1762? 1760c. 1760c. 1757/63 c. 1757/63 c. 1766–68c. 1766–68c. 1774

Symphony No. 2 in C major, i, bb. 53–57 {g minor–major} Symphony No. 2 in C major, i, bb. 167–168 {c-minor–major} Symphony No. 8 in G major, “Le Soir,” i, bb. 109–113 {e minor} Symphony No. 9 in C major, i, bb. 55–58 {a minor} Symphony No. 18 in G major, i, bb. 20–24 {d minor–major} Symphony No. 18 in G major, i, bb. 57–61 {g minor–major} Symphony No. 20 in C major, i, bb. 50–54 {g minor–major} Symphony No. 20 in C major, i, bb. 162–166 {c minor–major} Symphony No. 59 in A major, “Feuersymphonie,” i, bb. 25–27 {e minor} i, bb.100–102 100–102{a{aminor} minor} Symphony No. 59 in A major,, bb. Symphony No. 60 in C major, i, bb. 50–52 {g minor}

HC HC HC HC HC HC HC HC HC HC HC

236 1774 1771/73c. 1771/73c. 1778 c. 1786 1787 1788 1793–94 1793 1765 1772 1785 1791 1791 1765 1771/73 1791 1792 1792 1774

Vasili Byros i, bb. Symphony No. 60 in C major, bb. 174–177 174–177 {c {c minor} minor} Symphony No. 65 in A major, i, bb. 33–34 {e minor} Symphony No. 65 in A major, i, bb. 111–112 {a minor} Symphony No. 67 in F major, i, bb. 104–114 [B-flat–d minor] Symphony No. 86 in D major, i, bb. 118–124 [G major–b minor] Symphony No. 89 in F major, i, bb. 122–127 {f minor} Symphony No. 91 in E-flat major, i, bb. 124–127 {c minor} Symphony No. 100 in G major, “Military,” bb. 144–146 {d minor} bb.242–254 242–254{d{dminor} minor} Symphony No. 101 in D, ‘The Clock,’ i ,bb. Symphony No. 29 in E major, i, bb. 83–86 {c-sharp minor} Symphony No. 46 in B major, i, bb. 96–99 {g-sharp minor} Symphony No. 83 in G minor, “La Poule,” i, bb. 115–120 {d minor–major} Symphony No. 94 in G major, ‘Surprise’, i, bb. 64–67 {d minor–major} Symphony No. 95 in C minor, i, bb. 128–129 {c minor–major} Symphony No. 28 in A major, i, bb. 40–44 {e minor} Symphony No. 51 in B-flat major, i, bb. 104–107 [g minor–c minor] Symphony No. 96 in D Major, “Miracle,” i, bb. 63–64 [C major–e minor] Symphony No. 97 in C Major, i, bb. 66–68 [A-flat major–g minor/major] Symphony No. 97 in C Major, i., bb. 206–08 [D-flat major–c minor/major] Symphony No. 57 in D major, i, bb. 25–31 {d minor}

HC HC HC HC HC HC HC HC HC PAC PAC PAC PAC PAC EC EC EC EC EC DE

This is the larger formal context for the occurrence in Haydn’s Symphony in Example 3. Another instance, given in Example 4, shows the same medial caesura context, now in the recapitulation, from Haydn’s Clock Symphony in D major (1793–94). And the medial caesura is precisely the context suggested by bars 57–60 of Beethoven’s Second Symphony. The G© that sounds in the bass at bar 61 is the expected, or wouldbe, ©4 of the LE–SOL–FI–SOL cadenza lunga variant, the third stage of the punctuation formula’s chromatic falling thirds pattern (passage shown below in Example 7). Bar 57 thus begins a stereotypical push to a medial caesura half cadence in D minor, which would conform to Type 3 of Koch’s Hauptruhepuncte scripts (Table 1): a i:QA, or a i:HC MC in Hepokoski and Darcy’s terms.86 In light of this (sub)schematic context, bars 57–60 project a strong implication for a half cadence and Quintabsatz in D minor, owing to the orienting or anchoring function of the LE–SOL–FI–SOL, as a punctuation formula that communicates this specific Hauptruhepunct within the larger stereotyped sequence of actions, script, or cognitive map for a SONATA FORM. To paraphrase Neisser once more, the LE–SOL–FI–SOL is an “action hierarchically embedded in the more extensive action of the Hauptruhepuncte script, and is motivated by these anticipated consequences at the highest level of schematic organization.” But the expectation for a D minor Quintabsatz is aggressively interrupted by the intrusion of a new phrase, which immediately recontextualizes the G© of bar 61 into a new tonal context: it becomes the leading tone of the dominant, A minor. This new phrase introduces a syntactically competing punctuation formula at the phrase level, and in a new key at that. Bars 61–68 are a particular variant of a phrase-level pattern that Joseph Riepel called a PONTE, a variant which shares features with the schema Gjerdingen has

86. As occurs in Beethoven’s First Symphony, though without the chiaroscuro change of mode to minor.

“Hauptruhepuncte des Geistes”

(transition)

LE–SOL–FI–SOL

237

(i: hc mc)

240

CADENTIAL ( DOMINANT )

[Halbcadenz]

Example 4: Haydn, Symphony No. 101/i in D major (1793–1794), bb. 240–246: le–sol–fi–sol schema, Halbcadenz usage

termed a FENAROLI.87 In its typical form (Figure 3a), the FENAROLI consists of alternating dominant and tonic harmony, guided by a paradigmatic 7–1–2–3 scale-degree progression, typically in the bass, and a quasi-canonic 4–3–7–1 countermelody, which sometimes is realized as a pure canon, 2–3–7–1. The schema also characteristically features a dominant pedal in the soprano or in a “filler” voice. The end result is a fourstage structure, with the four stages normally repeated. The pattern is therefore quite cyclical, both in its dominant-tonic oscillation and in its repetition.

Figure 3a: Fenaroli schema: Abstract representation, from Gjerdingen 2007

87. Riepel, Anfangsgründe (1752–1768); Gjerdingen, Music in the Galant Style (2007), Chapter 14, passim.

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Vasili Byros

The phrase in bars 61–68 is a hybrid version of this schema, a “Fenaroli-style Ponte” that Gjerdingen briefly mentions in passing, while working through Riepel’s discussion of the PONTE,88 and that I treat more extensively elsewhere (hereafter FENAROLIPONTE).89 This hybrid (Figure 3b) is an explicit dominantizing of the standard FENAROLI, which carries a latent potential to become a dominant pedal: normally contained in a “filler” or upper voice of the standard version, in the FENAROLI-PONTE the dominant is positioned in the bass, while the paradigmatic 7–1–2–3 line and its countermelody are relocated to upper voices, typically the soprano and tenor, resulting in a sopranotenor exchange, as seen in Figure 3b.

fenaroli-ponte 1

7 4

( ]

2

7

5

2

3

3

)

1 7

6r

5

7

5

6r

}

5

V(7) I6/4 V(7) I6/4 Figure 3b: Fenaroli-Ponte schema: Abstract representation, after Byros 2013

The end result is a phrase-type that Caplin would call a “standing on the dominant” and Hepokoski and Darcy a “dominant lock.”90 The normative usage of the FENAROLI-PONTE is to expand a structural half cadence—hence Caplin’s description of bar 61 in the Second Symphony as a “complete change of musical material following the dominant arrival[, which] gives the impression of being a typical standing

88. Gjerdingen, Music in the Galant Style (2007), 202, 207. 89. Byros, “Trazom’s Wit” (2013). 90. Hepokoski and Darcy, Elements (2006), 24, 30–34, passim; Caplin, Classical Form (1998), 16, 77, passim. The two terms are actually not precise synonyms insofar as the structural weight of the dominant pedal is concerned. Superficially, the terms are identical, in that both designate a dominant-pedal phrase, but they differ in the implied form-functional meaning of the dominant prolongation. For Caplin, a “standing on the dominant” represents incidental material that is supplied after the cadence proper. For Hepokoski and Darcy (2006), a “dominant lock” actually prolongs the space of the half cadence until the end of the dominant expansion—in their words, the half cadence is “kept alive” (24, 31) until the close of the dominant pedal-point. In this view, the dominant pedal is form-functionally essential, not incidental, an interpretation that is consistent with Koch’s description of the phenomenon as an Anhang (“appendix”), discussed below. See especially n. 95.

“Hauptruhepuncte des Geistes”

239

on the dominant, despite the lack of cadential articulation.”91 Example 5 illustrates this cadence-extensional usage in the first movement of Beethoven’s C minor Piano Concerto, op. 37 (c1800).92 And so, there is a local, phrase-level syntactic deviation at bar 61 of Beethoven’s Symphony, where a FENAROLI-PONTE interrupts a LE–SOL–FI–SOL cadenza lunga variant.

(transition) (iii: hc) FENAROLI-PONTE 34 ˙. n œ. œ. ˙ b œ œ. b ˙ œ œ œ. ˙ œ œ œ. ˙ b &b b sf

sf

sf

sf

sf

. . . ? b Œ b œ œ œ œ œ˙ n œ œ œœ œ˙ œ b œ œœ œ˙ œ œ bb . . . sf

. . . . . . œbœ œ œ œ œ œ œ œ œ

sf

. œ bœ œ œ œ œ œœ sf

sf

. œœ œ˙ . œ œ sf

POST-CADENTIAL ( DOMINANT )

[Anhang (transition-suffix)]

40

. ... . ˙ n˙ b œ b œ œ œ œ œ œ. œ. œ œ œ. œ. œ. œ. œ. œ. œ œ œ. œ. œ. œ. œ. b œ œ œ œ œ œ œ œ œ b ˙ &b b æ æ æ sf sf sf . . . nœ œ ? b b œœ œ˙ œ b œ œœ œ˙ œ œ œœ b œœ œœ œœ œ ˙ œ. b œ. œ. b . . sf

sf

sf

sf

POST-CADENTIAL ( DOMINANT )

[Anhang (transition-suffix)] Example 5: Beethoven, Piano Concerto in C minor, op. 37/i (c1800), bb. 34–44: FenaroliPonte, standing-on-the-dominant function

This disruption at the phrase level also introduces a form-functional non sequitur at the next highest syntactic levels: the SENTENCE and its formal functions (Columns FT and FF). The LE–SOL–FI–SOL, as a cadential pattern, begins to unfold the second half of 91. On the context-independence of a pattern’s inherent formal function, see Agawu, Playing with Signs (1991), 103; Caplin, Classical Form (1998), 111; and Vallières et al., “Perception of Intrinsic Formal Functionality” (2009), 17–43. There are some cases where the FENAROLI-PONTE exhibits continuation function, specifically in what Caplin calls a Hybrid 3 context (compound basic idea + continuation). This is the case, for example, with the opening theme of K. 452/ii (bb. 5–8) and of K. 246/i (bb. 5–8). 92. I have deliberately avoided Caplin’s qualification of the standing on the dominant as “post-cadential” for the reasons outlined in n. 90. and n. 95.

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Vasili Byros

the compound SENTENCE initiated at bar 47, specifically a fused formal function that Caplin calls a “continuation Ÿ cadence,” where a continuation consists entirely of a cadential progression—in this case the LE–SOL–FI–SOL variant of a “long cadence,” which is conceptually similar to Caplin’s “expanded cadential progression.”93 The FENAROLI-PONTE interrupts this process, creating a form-functional non sequitur that is accompanied by an abrupt change of key: a cadence-extensional FENAROLI-PONTE in A minor intrudes on a cadential LE–SOL–FI–SOL in D minor mid-process. Both the phrase-level (PHL) and middleground (FT) deviations are further coordinated to create a larger-scale disruption at the highest level of the arched hierarchy: the Hauptruhepuncte script. A corpus analysis of the FENAROLI-PONTE’s sonata-form usage also reveals an affinity to a medial caesura Quintabsatz, as is the case with the LE–SOL–FI–SOL, but from the opposite end of the Hauptruhepunct, as a clarifying punctuation formula.94 Whereas the LE–SOL–FI–SOL is typically used to produce the moment of cadence itself (the arrival of the dominant), the FENAROLI-PONTE was a standard formula for extending the cadence with ancillary material. Koch also discussed certain after-the-fact punctuation signs which function as an “appendix” (Anhang): an “explanation […] which further clarifies the phrase,” and a “means through which a phrase[’s] […] substance [is] more closely defined.”95 The Anhang affords a kind of retrospective anchoring of closure in marking the Hauptruhepuncte des Geistes—it communicates a state of attunement described as cadential extension (E) in Table 2. In the 88 extant movements of Cimarosa’s Keyboard Sonatas, the FENAROLI-PONTE appears a total of 21 times, 14 of which (66.7%) are Anhänge to a Quintabsatz that produces the medial caesura half cadence (Table 4).96

93. Indeed Caplin’s category of ECP which normally holds this formal function is one species of cadenza lunga described in the eighteenth century. See Sanguinetti, The Art of Partimento (2012), 107–100, passim. On the concept of a “continuationŸcadence,” see Caplin, Classical Form (1998), 45–47, 61, 70, passim. 94. The corpus analysis is featured and outlined in Byros, “Trazom’s Wit” (2013). 95. Koch, Versuch II (1787), §110, 435 (45). Crucially, for Koch (and for Hepokoski and Darcy), a dominant Anhang or pedal-point prolongs the half cadence until the end of the Anhang. In Koch’s discussion of Anhänge, he makes clear that the terminal point of the Anhang and the cadence that precedes it constitute a single structural event insofar as the punctuation form is concerned: “In the comparison of the punctuation of phrases, only that phrase-ending with which the phrase attains its maximum completeness is taken into consideration. The preceding phrase-endings on exactly the same triad are not taken into account, but are considered as mere incises. Thus this multiplication of phraseendings by means of an appendix takes place without transgressing the rule given in section 34” (vol. III [1793], §58, 197 [150f.]). This rule concerns the “sequence of phrase-endings,” specifically the syntax of Grundabsätze and Quintabsätze: “neither two I-phrases nor two V-phrases in one and the same key may be composed immediately after one another with melodic sections which differ from each other” (vol. III [1793], §34, 111f. [110], original emphasis). 96. Byros, “Trazom’s Wit” (2013).

“Hauptruhepuncte des Geistes”

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Table 4: Fenaroli-Ponte sonata-form usage in the Cimarosa Keyboard Sonatas (corpus sample size 88 movements), after Byros 2013 c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s c1770s

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Keyboard Sonata in D major, c8, bars 16–17 Keyboard Sonata in D minor, c17, bars 24–27 ___________, bars 28–30 Keyboard Sonata in F major, c24, bars 8–10 ___________, bars 23–25 Keyboard Sonata in C minor, c28, bars 7–9 Keyboard Sonata in A major, c29, bars 11–13 Keyboard Sonata in E-flat major, c44, bars 9–10 Keyboard Sonata in C minor, c49, bars 5–8 Keyboard Sonata in F major, c71, bars 17–20 ___________, bars 78–81 Keyboard Sonata in E-flat major, c74, bars 19–23 ___________, bars 51–54 Keyboard Sonata in E-flat major, c77, bars 68–72 Keyboard Sonata in B-flat major, c78, bars 29–33 ___________, bars 77–80 ___________, bars 81–84 ___________, bars 93–97 Keyboard Sonata in B-flat major, c80, bars 9–15 ___________, bars 25–29 ___________, bars 41–47

HC HC PAC HC HC HC HC HC HC HC HC HC HC DA HC HC HC HC DA DA DA

retrans.-suffix retrans.-suffix (repeat of no. 2) transition-suffix transition-suffix transition-suffix transition-suffix transition-suffix transition-suffix transition-suffix transition-suffix transition-suffix transition-suffix retrans.-suffix transition-suffix retrans.-suffix retrans.-suffix transition-suffix transition-suffix retrans.-suffix transition-suffix

This punctuation formula exhibits an almost identical syntactic affinity to the medial Hauptruhepunct as the LE–SOL–FI–SOL in the Haydn Symphonies (70% compared to 66.7%), but from the opposite end of the cadence, as a transition-suffix, of sorts. And roughly the same percentage (60%) obtains in randomly encountered occurrences of the FENAROLI-PONTE in the music of Mozart, C. P. E. Bach, Haydn, Beethoven, and their contemporaries: Johann Christian Bach (1735–1782), Josef Antonín Sˇteˇpán (1726– 1797), Johann Schobert (c1720, 1730, or 1745–1767), Josef Myslivecˇek (1737–1781), Leopold Mozart (1719–1787), Baldassare Galuppi (1706–1785), and Johann Gottfried Eckard (1735–1809).97 This Halbcadenz-extending function is the formal context for the passage from Beethoven’s C minor Piano Concerto, shown in Example 5. In the recapitulation of Beethoven Two, shown in Example 6, the transition (now also fused with the principal theme)98 is recomposed, and the FENAROLI-PONTE’s normative sonata-form usage restored: it appears in bar 236 as an Anhang to a medial caesura half cadence (Halbcadenz), now in the tonic (Example 6). Beethoven’s recomposition of the passage renders the recapitulated FENAROLI-PONTE an explicit commentary on and corrective to its “premature” entry in the exposition. The latter causes one of the most powerful syntactic elisions in the repertoire, by producing a non sequitur that affects a listener’s orientation on numerous levels: tonal orientation (change of key),

97. Ibid. 98. See Caplin, Classical Form (1998), 165–167.

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phrase-level orientation (breaking of local syntax), middleground form-functional orientation (disruption of the compound sentence), and ultimately one’s location within the Hauptruhepuncte sequence that frames the entire cognitive map of a SONATA. The end product is an abrupt clashing of keys and formal functions and an “absent cadence”99 at the global level. (pt ⟾ transition) . . . CONVERGING

(i: hc)

sf

235

FENAROLI-PONTE

f ... CADENTIAL ( DOMINANT )

[Halbcadenz]

240

sf

POST-CADENTIAL ( DOMINANT )

[Anhang (transition-suffix)]

FENAROLI-PONTE

(i: hc)

sf

sf

sf POST-CADENTIAL ( DOMINANT )

[Anhang (transition-suffix)]

Example 6: Beethoven, Symphony No. 2 in D major, op. 36/i (1801–02), bb. 235–44: Normative Fenaroli-Ponte usage restored in recapitulation

This calculated deviation in the exposition, surely among the types of devices that Sulzer, Koch, and others associated with “sublime” (erhab[e]ne) effects most suitable and even expected for a symphony,100 could not produce such a wondrous effect had the large-scale goal of a medial Hauptruhepunct not been anticipated in the mind of a listener—that is, if one did not expect to be anchored to the “predetermined, stereotyped sequence of actions” one expects at the large-scale level of the SONATA punctuation script, as they are shaped and communicated by the lower-level, embedded 99. Mirka, “Absent Cadences” (2012). See also Mirka, this volume. 100. See e.g., Webster, Haydn’s “Farewell” Symphony (1991), 162f., 230f., 247f., 365, 369; Sisman, Mozart: The “Jupiter” Symphony (1993), 79; Baker and Christensen (eds.), Aesthetics and the Art of Musical Composition (1995), 106, 147, 152; Brown, “The Sublime, the Beautiful, and the Ornamental” (1996); and Bonds, “The Symphony as Pindaric Ode” (1997).

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subschemata. The force of the subschematic violations at the foreground (PHL) and middleground (FT) levels is compounded by this larger-scale “navigation” through the “cognitive map” for a SONATA FORM. The deviation is strategically targeted at, and therefore framed within, the larger-scale expectations formed by the Hauptruhepuncte des Geistes as the principal subschemata of the SONATA concept. It consequently imposes a reorientation in the mental representation or cognitive map of this expected “periodic structure” (Periodenbau), as communicated by the structured integration of subschemata, in the mind of a listener. And this change in orientation—effectively, a schema violation—at the SONATA-FORM level is responsible for the passage’s affective significance and sublime qualities.101 Beethoven Two presents a situation where no medial Hauptruhepunct ever properly materializes in the exposition. The deviation at bar 61 causes a shift from a Koch-Type 3 exposition script, anchored by the LE–SOL–FI– SOL punctuation schema, to a Koch-Type 1, retrospectively anchored by the FENAROLIPONTE. But a cadence is never articulated in either scenario. The LE–SOL–FI–SOL projects a i:QA that never materializes, the FENAROLI-PONTE retroactively expands a v:QA that never arrives by way of a cadence (a “lack of cadential articulation,” as Caplin put it). A half cadence does finally appear at bar 69, the only suitable candidate for an HC MC,102 but is articulated only at the most local level. It sounds within a larger standing on the dominant context (see Table 2), and is therefore not “cadential” in the sense of the end of a syntactic process, or goal.103 In Koch’s terms, it represents not a structural Halbcadenz, but a more local Ruhepunct (more along the lines of an Einschnitt) within a larger Anhang—an Anhang to a Hauptruhepunct that never materialized. The medial Hauptruhepunct is only represented by each punctuation (sub)schema from either end of the cadence, as shown in Example 7. Because neither cadence is fully articulated, the exposition is a member of neither Hauptruhepunct script category fully. In Hepokoski and Darcy’s language, a unique and powerful case of “medial caesura declined” results, whereby the Symphony suddenly leaps ahead in the “deployment sequence” of medial caesura options,104 from a projected i:HC MC to an after-the-fact v:HC MC (Example 7). The exposition of Beethoven Two is therefore part Koch-Type 3, part Koch-Type 1. By representing both i:QA and v:QA medial Hauptruhepuncte via their respective punctuation schemas (LE–SOL–FI–SOL and FENAROLI-PONTE), it also touches on Koch’s Type 4 exposition script. 101. On the affective and emotional consequence of schema violations, see Meyer, Emotion and Meaning in Music (1956), and Huron, Sweet Anticipation (2006). 102. Hepokoski and Darcy place the medial caesura at bar 71, with a half cadence at bar 69, and caesura fill in bars 71f. (see Elements [2006], 25f., 45). 103. For a more thorough consideration of this point, see Poundie Burstein’s contribution to this volume. See also Caplin, Classical Form (1998), 43: a cadence “essentially represents the structural end of broader harmonic, melodic, and phrase-structural processes.” See also Caplin, “The Classical Cadence” (2004). 104. Hepokoski and Darcy, Elements (2006), 36–40.

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(transition) LE–SOL–FI–SOL ( cadenza lunga variant)

...

FENAROLI-PONTE

...

57

ff ...

sf

sf

ff ...

...

CONTINUATION ⟾ CADENTIAL ( DOMINANT )

(elision)

[Halbcadenz]

POST-CADENTIAL ( DOMINANT )

[Anhang]

(i: hc mc)

(v: hc mc)

Example 7: Beethoven, Symphony No. 2 in D major, op. 36/i (1801–02), bb. 57–63: Elision and symbolic references of the Halbcadenz

These discrepancies and ambiguities may invite the question as to what the “true” form of the exposition to this symphonic movement may be. But from a schematheoretic perspective, these formal types are not candidates for a final interpretation. To search for “the” form of the Symphony is to labor under a misapprehension. The exposition has no “final” form that can be represented by any one of Koch’s categories for a sonata-form exposition. Hepokoski and Darcy go some way to bring this point in relief when characterizing musical form in general as essentially “dialogic.”105 Beethoven’s exposition is, once again to use their language, “in dialogue with” all three Hauptruhepuncte scripts. From a schema-theoretic window, the dialogue or plurality of knowledge extends further to other lower-level features of syntax. Every utterance in a composition is somehow framed within a generic, culturally regulated context (even if by deviation or omission),106 and these various frames themselves are interconnected in a complex web of intra-opus, inter-opus, associative, sequential, and hierarchical relations. Koch’s several exposition scripts of Hauptruhepuncte (here most relevantly Types 1, 3, and 4), the LE–SOL–FI–SOL and FENAROLI-PONTE as lower-level punctuation (sub)schemas, the middleground syntactic category of SENTENCE, these are all des Geistes—mental representations of past experiences through and against which Beethoven Two is heard, understood, and communicated. They are, to invite the communication theorist Paul Cobley to the seminar table, integrated “cues” that collectively prompt generic expectations in the minds of listeners:

105. Ibid., 10f. See also Hepokoski, “Approaching the First Movement of Beethoven’s Tempest” (2009). 106. Cf. Hepokoski and Darcy, Elements (2006), 7: “[…] deviations helped to reinforce the socially shared norm that was temporarily overridden.”

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[I]t would be a mistake to imagine, as has traditionally been the case, that genres can be identified simply by examining some formal qualities of texts. Rather, genre should be understood as a set of expectations on the part of audiences; these expectations are sufficiently prominent in audiences’ minds, and prompted by numerous cues, that they impute a great deal of flexibility in the process by which a text might be said to be part of a genre.107

These “numerous cues” are structured and involve musical knowledge at all levels of abstraction. Past experiences, when operating together as an organized whole, produce an emergent concept, a structured configuration of different types of knowledge, a particular activation of the mind as a “polyphonic structure”—in short, a “schema.” Koch’s several exposition scripts of Hauptruhepuncte, the LE–SOL–FI–SOL and FENAROLIPONTE as lower-level punctuation formulas, the middleground phrase-structural category of SENTENCE, these are different varieties of eighteenth-century syntax that, through their structured integration, build to such a schema—to a SONATA-FORM schema. This “schema” conceivably figured into contemporaries’ reasoning, when they speak, as does Nägeli in 1803, of both customary (“gewöhnliche”) and deviant (“abweichende”) aspects of “Sonaten-Form.” And it is reasonable to conclude that Beethoven’s gesture in the Second Symphony was calculated to deliberately exploit the generic expectations his listeners had formed on account of this SONATA-FORM schema. Bob Snyder, in his Music and Memory, suggests that “large-scale representations of musical form […] result in […] listeners having a sense of familiarity and increasingly specific expectations around the chunk boundaries,” and especially at the “higher-level chunk boundaries.”108 From an eighteenth-century perspective, these larger boundaries would correspond to Koch’s Hauptruhepuncte. Not only does Koch’s end-oriented approach to phrase-structure and phrase-definition in general support such an interpretation, but he also explicitly identifies the higher-level chunks—the “principal punctuation sections” (interpunctische Hauptteile)—with the means of their production: the boundary markers produced by the “principal resting points of the mind.”109 Beethoven’s deviation is targeted precisely at the boundary of one of these higher-level chunks, the medial caesura half cadence. In light of the normative punctuation scripts reconstructed via corpus analysis, it stands to reason that a SONATA-FORM punctuation script was among the culturally shared cognitive contexts by which composers and listeners communicated in the eighteenth century. This “schema,” finally, is the context for the “outtake” given in Example 1. The alternate version for bars 56–71 might well have come from a Beethoven sketchbook.

107. Cobley, “Communication and Verisimilitude” (2008), 24. 108. Snyder, Music and Memory (2000), 222, 219; also 54f. 109. Koch, Versuch III (1793), §129, 342 (213).

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Indeed several folios in Landsberg 7,110 which contains sketches for the first movement, and six drafts of the exposition, show Beethoven working through several different versions of its transition and medial caesura. These include a diatonic form of the cadenza lunga, as seen in the excerpt from a first draft reproduced in Example 8, which develops the primary motive from an early version of the Symphony.111 The “outtake” in Example 1, however, is a hypothetical recomposition that realizes the implications of the SONATA-FORM schema presupposed by the events of bars 47–61.

[ ] 2 Va [ ] Example 8: Beethoven, Symphony No. 2 in D major, early draft of the transition in the Landsberg 7 sketchbook: p. 39 (Karl Lothar Mikulicz, ed. [1927], Ein Notierungsbuch von Beethoven, Leipzig: Breitkopf und Härtel. Repr., Hildesheim: G. Olms, 1972)

The hypothetical recomposition features two basic “corrections” that restore the deviation to the anticipated course in the SONATA script. First, four additional measures have been added at bar 61 in order to complete the LE–SOL–FI–SOL cadenza lunga variant initiated at bar 57, as well as the hypermetric and middleground form-functional implications of the compound SENTENCE initiated at bar 47.112 Second, the actual music from bars 61–71 of Beethoven’s Symphony has been recast in D minor, so that the FENAROLI-PONTE now functions as a proper cadential extension of a normalized Halbcadenz in D minor, which is fully realized by the completion of the LE–SOL–FI–SOL. To facilitate comparison, Example 9 aligns the bass line for the reconstruction with the bass line from Beethoven’s original in the smaller ossia staff. In sum, the hypothetical recomposition reconstructs a plausible (sentence-)continuation as expected by a listener fluent with the interactions among different kinds of eighteenth-century syntax—fluent, that is, with the SONATA-FORM schema.

110. Mikulicz (ed.), Ein Notierungsbuch von Beethoven (1927/1972), 38–53. 111. The six drafts of the exposition in Landsberg 7 show an overall transition from a I:HC and V:HC (a Koch Type 4 script) to a V:HC MC. 112. The recomposition uses a protracted form of the LE–SOL– FI–SOL that appears in cadenza lunga contexts. See for example, Mozart’s Symphony No. 27, K. 199/ii, in G major, Andantino grazioso, bb. 22–32, and 79–89.

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56

= 61

sf

sf

ff

sf

sf

sf

sf

61

sf

ff

65

sf

sf

sf

sf

sf

sf

Example 9: Beethoven, Symphony No. 2 in D major, op. 36/i (1801–02), bb. 56–71: Bass-line comparison of original (ossia staff) and hypothetical versions

• In navigating this SONATA schema landscape, I have undoubtedly left many stones unturned. But my ambition, in tying schema theory and the historical context of “interpunctische Form” to this passage in Beethoven’s Symphony (and its alternate version outtake), was not to bring a definitive answer or conceptualization to the table: where the cognition and listening practices of late-eighteenth-century SONATA FORM are concerned, thereby hangs a long tale. My intention was simply to offer but a prologue for such a tale, to maintain that it is a tale worth telling, that the CADENCE is among its main protagonists, and that such a conception has strong roots in the late eighteenth century. This brief case study suggests there are indeed stones to be turned in the first place, and the CADENCE plays a fundamental role in determining which stones need turning.

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Cobley, Paul (2008), “Communication and Verisimilitude in the Eighteenth Century,” in: Communication in Eighteenth-Century Music, ed. Danuta Mirka and Kofi Agawu, Cambridge: Cambridge University Press, 13–33. Dahlhaus, Carl (1983), Analysis and Value Judgement, trans. Siegmund Levarie, New York: Pendragon Press. ——— (1985), Realism in Ninteenth-Century Music, trans. Mary Whittall, Cambridge: Cambridge University Press. ——— (1978), “Der rhetorische Formbegriff H.Chr. Kochs und die Theorie der Sonatenform,” Archiv für Musikwissenschaft 35/3, 155–177. Diergarten, Felix (2012), “Jedem Ohre klingend.” Haydns sinfonische Formprinzipien, Laaber: Laaber. Forschner, Hermann (1984), Instrumentalmusik Joseph Haydns aus der Sicht Heinrich Christoph Kochs, München-Salzburg: Katzbichler. Gibson, James J. (1966), The Senses Considered as Perceptual Systems, Boston, MA: Houghton Mifflin. ——— (1986), The Ecological Approach to Visual Perception, New York: Psychology Press. Gjerdingen, Robert O. (2007), Music in the Galant Style, New York: Oxford University Press. Gossett, Philip (1989), “Carl Dahlhaus and the ‘Ideal Type’,” 19th-Century Music 13/1, 49–56. Heft, Harry (2001), Ecological Psychology in Context: James Gibson, Roger Barker, and the Legacy of William James’s Radical Empiricism, Mahwah, NJ and London: Lawrence Erlbaum. Hepokoski, James (2009), “Approaching the First Movement of Beethoven’s Tempest Sonata through Sonata Theory,” in: Beethoven’s Tempest Sonata: Perspectives of Analysis and Performance, ed. Pieter Bergé, William E. Caplin, and Jeroen D’hoe. Leuven: Peeters, 181–212. Hepokoski, James and Warren Darcy (2006), Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata, New York: Oxford University Press. ——— (1997), “The Medial Caesura and Its Role in the Eighteenth-Century Sonata Exposition,” Music Theory Spectrum 19/2, 115–54. Huron, David (2006), Sweet Anticipation: Music and the Psychology of Expectation, Cambridge, MA: MIT Press. Kirnberger, Johann Philipp (1771–1779), Die Kunst des reinen Satzes in der Musik. 2 vols. (volume 1, Berlin, 1771; volume 2, sections 1–3, Berlin and Königsberg, 1776, 1777 and 1779). Selections trans. David Beach and Jurgen Thym as The Art of Strict Musical Composition, New Haven: Yale University Press, 1982. Koch, Heinrich Christoph (1782–1787–1793), Versuch einer Anleitung zur Composition, 3 vols., Leipzig: Böhme. Reprint, Hildesheim: Olms, 1969. Selections trans. Nancy Kovaleff Baker as Introductory Essay on Musical Composition, New Haven, CT: Yale University Press, 1983. ——— (1802), Musikalisches Lexicon, Frankfurt a. M.: Hermann. Liddell, H. G. and Robert Scott (1989), An Intermediate Greek-English Lexicon, Oxford and New York: Oxford University Press. Marpurg, Friedrich Wilhelm (1753–1754), Abhandlung von der Fuge, 2 vols. Berlin: Haude & Spencer. ——— (1759–1763), Kritische Briefe über die Tonkunst, 2 vols. Berlin: Birstiel. Mattheson, Johann (1739), Der vollkommene Capellmeister, Hamburg: Herold. Meyer, Leonard B. (1956), Emotion and Meaning in Music, Chicago: University of Chicago Press. ——— (1967/1994), Music, the Arts, and Ideas: Patterns and Predictions in Twentieth-Century Culture, Chicago: University of Chicago Press. ——— (1973), Explaining Music: Essays and Explorations, Berkeley: University of California Press.

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Vallières, Michel, Daphne Tan, William E. Caplin, and Stephen McAdams (2009), “Perception of Intrinsic Formal Functionality: An Empirical Investigation of Mozart’s Materials,” Journal of Interdisciplinary Music Studies 3/1–2, 17–43. Vial, Stephanie (2008), The Art of Musical Phrasing in the Eighteenth Century, Rochester: University of Rochester Press. Weber, Max (2011), Methodology of Social Sciences, trans. and ed. Edward A. Shils and Henry A. Finch, New Brunswick, NJ: Transaction Publishers. Webster, James (1991), Haydn’s “Farewell” Symphony and the Idea of Classical Style: ThroughComposition and Cyclic Integration in his Instrumental Music, Cambridge and New York: Cambridge University Press.

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The Perception of Cadential Closure

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THE PERCEPTION OF CADENTIAL CLOSURE* David Sears

H

ow does music end? This question has occupied a central position in music scholarship for centuries. The eighteenth-century cadence perhaps best exemplifies this point, as it is a foundational concept in the Formenlehre tradition that continues to receive attention and undergo refinement by the scholarly community. Indeed, the revival of interest in theories of musical form over the last few decades has prompted a number of studies that reconsider previously accepted explanations of how composers articulate cadences in the classical period,1 that classify instances in which cadential arrival fails to materialize,2 and that situate the concept of cadence within a broader understanding of both tonal and formal closure.3 Yet despite such intense theoretical scrutiny, it remains unclear how cadential patterns are represented in the mind, how they are perceived and remembered, and finally, how the various features of cadences contribute to the experience of closure. In the pages that follow I will first review the treatment of closure in music psychology and then summarize a study I conducted with William E. Caplin and Stephen McAdams that investigates the perception of cadential closure using examples drawn from Mozart’s keyboard works.4 I will conclude by discussing the impact of musical expertise on the many issues surrounding hierarchical models of cadential strength. While the systematic study of listening behavior normally rests outside the sandbox of music theory, scholars nonetheless remain highly sensitive to the potential effects of ending formulæ on listeners. Descriptions of cadential arrival as a moment of rest, finality, or repose—terms that abound in the history of theory—imply that closure is inherently felt during the act of listening. Heinrich Christoph Koch, a theorist and contemporary of Haydn and Mozart known today for his contributions to the theory of musical form, notably referred to such moments as “resting points of the *

1. 2. 3. 4.

This research was funded first by a Richard H. Tomlinson fellowship (2008–2011) and then by a doctoral fellowship from the Fonds de recherche du Québec — Nature et technologies. The experiment summarized in this chapter was conducted at the Centre for Interdisciplinary Research in Music, Media, and Technology (CIRMMT). Caplin, “The Classical Cadence” (2004), 51–117. Schmalfeldt, “Cadential Processes” (1992), 1–52; Hatten, “Interpreting Deception in Music” (1992), 31–50; Caplin, Classical Form (1998), 101–111; Hepokoski and Darcy, Elements (2006), 150–179. Anson-Cartwright, “Concepts of Closure in Tonal Music” (2007), 1–17. Sears, Caplin, and McAdams, “Perceiving the Classical Cadence” (2014), 397–417.

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spirit,” noting that “only feeling can determine both the places where resting points occur in the melody and also the nature of these resting points.”5 By referring to “the spirit,” Koch thus implies that closure is not an external property of the sounding stimulus, but instead is determined internally by the listener. Some two centuries later, many theorists have accounted for the perception of closure by appealing to theories of expectation. Leonard Meyer, attempting to relate emotional experience with listener expectations, considered the classical cadence the quintessential compositional device for eliciting specific expectations. Following the first musical example of his book Emotion and Meaning in Music (see Example 1), he writes, In Western music of the eighteenth century, for example, we expect a specific chord, namely, the tonic (C major), to follow this sequence of harmonies […]. Furthermore, the consequent chord is expected to arrive at a particular time, i.e., on the first beat of the next measure. Of course, the consequent which is actually forthcoming, though it must be possible within the style, need not be the one which was specifically expected. Nor is it necessary that the consequent arrive at the expected time. It may arrive too soon or it may be delayed. But no matter which of these forms the consequent actually takes, the crucial point to be noted is that the ultimate and particular effect of the total pattern is clearly conditioned by the specificity of the original expectation.6

Example 1: A cadential progression, reproduced here from Example 1 of Meyer’s Emotion and Meaning in Music (1956), 25

Hence, a cadence, or more precisely, the progression preceding cadential arrival, elicits very definite expectations concerning the melodic scale-degree, the harmony, and the metric position of the goal event. The moment of cadential arrival, on the contrary, elicits no further expectations with respect to these parameters.7 This absence 5. 6. 7.

Koch, Versuch II (1787), 342–349 (= Introductory Essay [1983], 1–3). Meyer, Emotion and Meaning in Music (1956), 25f. Depending on the formal or generic context, however, this point does not preclude the possibility that we may generate expectations for the initiation of subsequently new processes following a cadential goal, such as the prolongation of dominant harmony following a half cadence or the onset of codettas following a perfect authentic cadence. I employ the term ‘expectation’ rather narrowly in this instance to refer to the musical parameters that characterize a cadential goal, but I acknowledge that the possible types of expectation experienced during music listening are wide-ranging. For a discussion of the diverse applications of the term in music discourse, see Margulis, “Surprise and Listening Ahead” (2007), 197–217.

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of expectancy following cadential arrival led Eugene Narmour to describe cadential arrival as a “nonimplicative context,” or, to use Elizabeth Margulis’s expression, as an event that suppresses expectancy.8 These authors might therefore suggest that terms like rest, finality, and repose result from a desire to characterize the cessation of expectancy following cadential arrival. David Huron summarizes this point nicely: “When there cease to be expectations about what may happen next, it makes sense for brains to experience a sense of the loss of forward continuation—a loss of momentum, of will, determination or goal. In short, it makes sense for brains to experience a sense of repose or quiescence whenever the implications cease.”9 But how do such expectations form? The most frequent answer given by theorists and psychologists infers a causal relationship between a statistically probable event and an expected event.10 Because cadences appear frequently and their underlying harmonic and melodic characteristics remain fairly consistent, listeners learn over repeated exposure to expect these endings. A theory of expectation is therefore appealing to the study of cadence because it provides a direct, causal link between events on the musical surface and the behavioral and neurophysiological responses of the listening subject. Yet since listeners often differ in how they experience a given musical excerpt, the study of closure may benefit from a hybrid approach in which both the music and the listener represent the objects of study. Although the term ‘cadence’ appears frequently in the music psychology literature as a perceptually-relevant concept, little experimental research explicitly investigates the perception of cadential closure. Instead, a vast number of studies employ cadences and other ending formulæ as stimuli under the assumption that the experience of closure during music listening is simply a by-product of more general cognitive processes. Questions as to how listeners store cognitive representations of harmonic, tonal, and rhythmic structure in long-term memory, as well as to how these mental representations affect various aspects of music perception (e.g., the formation of expectations during music listening, the perception of dynamic variations in tension, etc.), continue to resonate with music psychologists, resulting in considerably fewer studies devoted to the perception of closure itself.11 8.

Margulis, “Melodic Expectation” (2003), 263. If I may echo Margulis’ sentiment, Narmour’s concept of closure is complex, but his claim is essentially that non-closural events, such as the leading tone, elicit intense and very specific implications, while closural events, such as the moment of cadential arrival, suppress further implications. Narmour, “Analyzing Form and Measuring Perceptual Content in Mozart’s Sonata K. 282” (1996), 265–318. 9. Huron, Sweet Anticipation (2006), 157. 10. Although many authors have demonstrated the applicability of invoking statistical thinking in modeling musical expectancy, the relationship is by no means one-to-one. For an apt discussion of the issue, see Meyer, “Meaning in Music and Information Theory” (1957), 412–424. 11. To study expectations in music, researchers typically employ a priming paradigm, which assumes that the processing of incoming events is affected by the context in which they appear. Related events are primed, thus facilitating processing. Harmonic priming studies often employ an authentic cadence

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Nonetheless, closure often plays a prominent role in studies otherwise concerned with other aspects of music perception and cognition. Indeed, Bret Aarden has suggested that Carol Krumhansl’s highly influential probe tone studies reflect a cognitive representation of the tonal hierarchy that only pertains to phrase endings. In her initial experiment with Edward Kessler, Krumhansl asked participants to rate the goodness-of-fit of each of the twelve members of the chromatic scale following a tonal context.12 The resulting major and minor key profiles they obtained led the authors to propose that listeners possess a cognitive representation of the tonal hierarchy. Moreover, a comparison of the goodness-of-fit ratings with the frequency-ofoccurrence of these scale-degrees in various corpora from Western music revealed a significant correlation, with scale-degrees that occur more frequently receiving higher “fit” ratings,13 thus leading Krumhansl to suggest that listeners form an internal representation of the tonal hierarchy by internalizing the distribution properties of Western tonal music.14 Publications over the past two decades of numerous key-finding algorithms incorporating Krumhansl and Kessler’s major and minor key profiles provide convincing evidence for the psychological reality of the tonal hierarchy.15 Yet a number of authors have since raised several objections both to Krumhansl’s probe-tone method and to her interpretation of the results.16 Aarden, noting a disparity between the distribution of the goodness-of-fit ratings with the scale-degree distributions from tonal music, conducted a reaction-time study in which participants responded to the contour of each event in a short tonal melody.17 His first experiment was designed to test the assumption that scale-degrees receiving a higher “fit” rating in Krumhansl’s tonal hierarchy

12.

13. 14. 15.

16. 17.

in the expected condition and then recompose the moment of cadential arrival in order to consider the effect of an expectancy violation on response accuracy and reaction time. For an example, see Loui and Wessel, “Harmonic Expectation and Affect in Western Music” (2007), 1084–1092. Many of these studies, however, neglect to discuss harmonic and melodic closure per se. Krumhansl and Kessler, “Tracing the Dynamic Changes in Perceived Tonal Organization in a Spatial Representation of Musical Keys” (1982), 334–368. The profile for the major key is the average rating given to each of the 12 tones of the chromatic scale following either a major chord or one of three progressions (IV–V–I, II–V–I, and VI–V–I); the minor-key profile is the average rating for each of the 12 tones of the chromatic scale following a minor chord or one of the same three progressions. Krumhansl, Cognitive Foundations of Musical Pitch (1990), 68f. Ibid., 286. The first model incorporating the Krumhansl-Kessler key profiles was proposed by Krumhansl herself, in collaboration with Mark Schmuckler. For a discussion of the model, see Krumhansl, Cognitive Foundations of Musical Pitch (1990), 77–110. Huron and Parncutt have since suggested methods for incorporating effects of echoic memory and pitch salience on tonality perception (Huron and Parncutt, “An Improved Model of Tonality Perception,” [1993], 154–171), and Temperley has provided numerous revisions to the Krumhansl-Schmuckler model that improve the mathematical efficiency of the algorithm and address issues related to modulation (Temperley, “What’s Key for Key?” [1999], 65–100). For a succinct summary and critique of Krumhansl’s methodology and the interpretation of her results, see Aarden, “Dynamic Melodic Expectancy” (2003), 11–26. Although the correlations between the scale-degree distributions of various corpora with Krumhansl’s goodness-of-fit ratings are quite high (r > .80), several discrepancies remain unexplained, the most

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would lead to faster reaction times, yet the results did not support this hypothesis. However, when he asked participants to respond only to the contour of the final event of each melody in a second experiment, he observed a close correspondence between participant reaction times and the “fit” ratings of the final events,18 leading him to conclude that the probe-tone method employed by Krumhansl and Kessler actually encouraged listeners to treat the probe tone as a phrase-final event. Thus, Aarden claimed, Krumhansl and Kessler’s major and minor key profiles reflect a cognitive representation of the tonal hierarchy that pertains specifically to endings.19 That an internal representation of the tonal hierarchy affects the perception of melodic closure is by no means contentious, though it remains far less clear whether such a representation pertains only to the final event of a phrase, or instead, whether it may pertain to a series of events, thereby suggesting that listeners possess schematic representations of various melodic closing formulæ. Marilyn Boltz and David Butler have reported effects of serial order on both the perception of melodic closure and the identification of tonal center respectively,20 but the issue as to whether listeners store melodic closing patterns in long-term memory remains open. For bass line motion, however, the serial position of the events preceding a phrase ending is fundamental to current definitions of cadential closure; the cadential status of the final tonic in an authentic cadence, for example, is crucially determined by the harmony of the preceding event. Thus, music scholars frequently treat harmonic closure as a temporal process, an idea that has gained acceptance in the experimental literature. To consider the effect of a number of musical parameters on the perception of harmonic closure, Burton Rosner and Eugene Narmour asked participants to judge which of a pair of two-chord progressions seemed more closed; they then quantified variables relating to the position of the soprano and bass voices with respect to the root of each chord, the number of common tones shared between the two chords, and the motion of the soprano voice.21 In addition to these parameters, they also considered style-specific variables that corresponded to music-theoretic notions of cadential closure, such as the root progression of each stimulus and the position of the final melodic event within the tonal hierarchy. To their surprise, parametric variables such as the soprano position, bass inversion, and the number of shared common tones did not affect the closure preference ratings. Instead, schematic representations of root progressions common to known cadences appeared to play the most prominent role, leading the

18. 19. 20. 21.

noteworthy example being that 5^ normally appears more frequently than 1^ in the various corpora, yet in Krumhansl and Kessler’s key profiles, the tonic receives the highest “fit” rating. Aarden, “Dynamic Melodic Expectancy” (2003), 75. Ibid., 25f. Boltz, “Perceiving the End” (1989), 754; Butler, “Describing the Perception of Tonality in Music” (1989), 234–236. Rosner and Narmour, “Harmonic Closure” (1992), 383–411.

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authors to claim that the various harmonic formulæ located at phrase endings result in the formation of schematic representations of harmonic closure. They explain, “when evaluating closure, listeners presumably invoke learned harmonic structures as stylistic schemata. Such schemata come into play when the stimulus displays a sufficient number of featured properties to activate them. This process relies on previously learned stylistic patterns and should be central to closural evaluation.”22 That listeners may possess both melodic and harmonic “closing” schemata might also explain why cadences play a prominent role in the perception of tension, a topic that has received a great deal of attention over the past two decades. In a study initially investigating Lerdahl and Jackendoff’s model of tonal tension, Emmanuel Bigand and Richard Parncutt asked listeners to rate their perception of musical tension for each pair of successive chords in Chopin’s Prelude in E major.23 Although they expected Lerdahl and Jackendoff’s model to perform best, they were surprised to find that the simple encoding of authentic and half cadences best explained listener ratings of tension, leading them to conclude that cadences provide important reference points for the perception of tension during music listening.24 From an examination of the experimental literature, it appears that cadences play a vital role in the perception of tonal music. Furthermore, that listeners may possess cognitive representations for various ending patterns seems intuitive. But what remains absolutely essential to such a claim is that the strength of the schematic representation depends on a listener’s exposure to the musical style. Unfortunately, the effect either of explicit musical training or passive exposure on the perception of closure remains unclear, with many studies reporting contradictory findings. Boltz asked both musicians and nonmusicians to provide melodic completion ratings on a 10-point scale for several ending patterns, yet she failed to observe a difference between the two groups, leading her to claim that implicit exposure, rather than explicit training, accounts for the perception of melodic completion.25 Barbara Tillman et al. also reported a similar finding using cadential patterns, in which musicians and nonmusicians provided com22. Ibid., 397f. 23. Bigand and Parncutt, “Perceiving Musical Tension in Long Chord Sequences” (1999), 237–254. 24. Ibid., 254. In a related and pertinent finding to this research, the authors also suggest that listeners perceive tension from within a short temporal window. Accordingly, they claim tension ratings for a given harmonic event remain more or less independent of non-adjacent events. The effect of hierarchy on the perception of both closure and tension is, however, very much in dispute. Lerdahl has since proposed that the results obtained by Bigand and Parncutt reflect a conflation of stability/instability (terms Lerdahl associates with tonal tension) with closure/non-closure. He rightly points out that a highly stable event, such as the tonic initiating a phrase, may nonetheless imply continuation, and thus, non-closure (see Lerdahl, “Modeling Tonal Tension” [2007], 357). The results provided by these studies therefore suggest that the relationship between the concepts of tension and closure crucially depend upon how we define and operationalize these often loaded terms. 25. Boltz, “Perceiving the End” (1989), 753. Like Aarden, Boltz also considered how cognitive representations of tonal structure affect music perception, but in her case she employed an explicit rating task rather than a reaction-time task.

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pletion ratings for both half cadences and authentic cadences (in the context of 16-m. minuets).26 Tillman therefore proposed that participants apply the same perceptual principles when assessing musical closure, regardless of expertise, though nonmusicians may be less efficient than musicians. Other scholars, however, have noted significant effects of musical expertise on the perception of closure. Michel Vallières et al. asked participants to categorize a series of short excerpts from Mozart’s keyboard sonatas as beginnings, middles, or ends; and for the ending excerpts, Vallières selected only perfect authentic cadences. The results revealed a significant difference between musicians and nonmusicians, as the musician group correctly identified these cadences as “ends” with nearly perfect accuracy, while nonmusicians were considerably less accurate, correctly identifying ends roughly 80% of the time.27 Margaret Weiser also reported an effect of expertise for two-chord cadences (authentic, half, plagal, and deceptive), in which participants were asked to rate the stability of the final chord on a 5-point scale. The results led her to suggest that musical training facilitates flexible voice-tracking, while the absence of such training results in an attentional bias toward the soprano voice.28 Finally, the findings obtained over a series of experiments investigating the perception of harmonic and melodic cadential patterns led Roland Eberlein and Jobst Fricke to theorize that experienced listeners of tonal music form schematic representations for frequently occurring cadential formulæ. Differences of expertise during the perception of closure therefore result from differences in familiarity with the tonal idiom.29 Such contradictory reports as to the role of explicit formal training or implicit exposure on the perception of closure may reflect differences either in the choice of experimental task or in the use of stimuli, as researchers often prefer to use homorhythmic, four-part chorale representations of cadential progressions rather than attempt to find examples of cadences from genuine musical literature. And there are certainly very good reasons for doing so; by eliminating variations in dynamics, tempo, and rhythm, as well as disregarding a number of features that appear fre26. Tillman, Bigand, and Madurell, “Local versus Global Processing of Harmonic Cadences in the Solution of Musical Puzzles” (1998), 168. 27. Vallières, Tan, Caplin, and McAdams, “Perception of Intrinsic Formal Functionality” (2009), 23. The correct identification of 80%, of course, is still significantly better than chance, but as Vallières’s analysis later revealed, this effect of expertise could not be attributed simply to greater variability between subjects in the nonmusician group, but rather to explicit differences in the way the two groups perceived cadential patterns. 28. Weiser, “Rating Cadence Stability” (1992), 40–46. There has been some empirical support for the claim that nonmusicians appear to privilege parameters related to melodic motion, such as pitch proximity and contour, while musicians attend principally to harmonic factors, such as the size of the interval between two events (see Vos and Pasveer, “Goodness Ratings of Melodic Openings and Closures” [2002], 631–639), a claim that will be pertinent to the results presented here. 29. Eberlein and Fricke, Kadenzwahrnehmung und Kadenzgeschichte (1992), 258. Eberlein has also succinctly summarized his theory and proposed a rough model for the effect of familiarity on the perception of closure (see Eberlein, “A Method of Analysing Harmony” [1997], 232f.).

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quently in compositional practice (e.g., a trill at the cadential dominant, the cadential six-four, the suspension dissonance at cadential arrival), such abstract paradigms provide greater experimental control and are much easier to alter to satisfy specific experimental needs. But these paradigms also misrepresent the ways in which composers often articulate phrase endings in tonal music (and consequently the ways in which listeners might actually perceive these endings), as they disregard many of the features of cadences that might contribute to the perception of closure. Perhaps worse, such an approach often leads researchers to generalize the behavioral responses elicited by these simple melodic and harmonic formulæ to all tonal music, though the characteristics of closure present in Prokofiev’s piano sonatas might differ markedly from those found in Mozart’s symphonies.30 To be sure, the goal of many of the experimental studies employing cadential stimuli is to determine how listeners represent tonal structure in long-term memory. As a result, the examples that they employ serve to probe the various cognitive representations of tonal patterns listeners have abstracted from previous experience. Whether or not a given musical example could actually appear in the repertoire might therefore seem largely irrelevant. But the precision with which we may examine these various representations ultimately depends on a careful understanding of the music to which listeners are consistently exposed. In comparing a listener competent in Mozart’s keyboard style with a diverse group of participants, for example, we might find very similar ratings for rhythmically isochronous, harmonic formulæ (and indeed, as a few of the previous studies I have just mentioned can attest, we sometimes do), yet when presented with an excerpt written in that keyboard style, our listener may possess distinctions of a much finer grain than those possessed by the wider group. The recent revival of interest in the Formenlehre tradition has also largely gone unnoticed in the music psychology community, as those studies explicitly examining the perception of closure rarely employ the wider variety of cadential types found in the “common practice” period. Techniques for cadential deviation, in particular, serve an important formal and expressive function in the classical style, but they have yet to be considered in an experimental setting. Indeed, the experimental study of cadential failure could serve to explore rich areas of inquiry in music psychology—the perception of closure, the processing of harmonic syntax, and the generation and violation of expectations—using musical examples that remain ecologically valid. The study I will summarize here attempted to address these issues directly. While an exploration of the underlying sensory and cognitive mechanisms responsible for the perception of closure in tonal music is the ultimate aim of this research, our initial

30. Indeed, Courtenay Harter has outlined some of the characteristic differences of cadential articulation found between Prokofiev and composers of the common practice (see Harter, “Bridging Common Practice and the Twentieth Century” [2009], 57–77).

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approach was more limited in scope, concentrating as it does on a closing pattern that appears frequently in tonal music: the classical cadence. Limiting the initial investigation to cadential closure also afforded the opportunity to consider issues germane to music theory. In the analysis of musical form, the capacity to discern amongst various cadential categories is paramount to the identification of the function of a specific musical passage,31 and this study provides evidence as to whether expert and non-expert listeners can make such distinctions in real time, without the aid of the score. Furthermore, analysts frequently appeal to a hierarchy of cadential closure, and a few authors have proposed preliminary models of cadential strength (e.g., Janet Schmalfeldt, William Caplin, and, more recently, Edward Latham),32 though it remains unclear how various cadential categories—perfect authentic, imperfect authentic, half, etc.—may be positioned within the hierarchy, or how the various musical parameters—melody, harmony, rhythm, etc.—contribute to the perception of closure (an issue to which I will return later in the chapter). As the methods by which composers articulate cadences also vary dramatically both from style to style and from composer to composer, we restricted the selection of stimuli to excerpts from Mozart’s keyboard sonatas, which comprise a stylistically unified repertory composed over a period of just 15 years (1774–1789). Due to the lack of experimental evidence concerning the potential effect of musical expertise on the perception of cadential closure, we also considered the impact of explicit formal training. To that end, we recruited 20 participants with musical training equivalent, or superior, to second-year-university level, which comprised the musicians group, and 20 participants with less than one year of training, which comprised the nonmusicians group. The experimental task was fairly straightforward. Participants were instructed to rate the degree of completion for each excerpt on a 7-point continuous scale. Completion was defined as “the expectation that the music will not continue. A value of 1 indicates that the excerpt would certainly continue, while a value of 7 indicates that the excerpt could end at that moment without the need for anything further.” By adopting the more neutral term “completion,” we hoped to sidestep any reference to theoretically loaded terms (e.g., cadence, closure) that might complicate the task for nonmusicians and unintentionally bias musicians toward consciously categorizing the excerpts. In addition to the completion judgment, participants also rated both the confidence of their completion rating along with their familiarity with the excerpt on 7-point scales. Finally, to distinguish between those potentially ambiguous excerpts that participants might rate in the center of the completion scale, we also included two 31. In Caplin’s theory, a formal function refers to the capacity of a given time span to express its own location in musical time, and he offers five such formal functions: before-the-beginning, beginning, middle, end, and after-the-end (Caplin, “What are Formal Functions?,” [2009], 23). 32. Schmalfeldt, “Cadential Processes” (1992), 1–52; Caplin, Classical Form (1998), 101–111; Latham, “Drei Nebensonnen” (2009), 308f.

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statements to which the participants would respond on a 4-point Likert scale labeled from strongly agree to strongly disagree: “this excerpt could complete an entire work or movement,” and “this excerpt could complete a phrase or short passage of music.”33

Characterizing the excerpts— Caplin’s theory of cadential closure Although the “high classical style” refers to a fairly limited period of music history (ca. 1770–1810), the compendium of cadential terms associated with the music of this period is still enormous. This fact reflects profound disagreement, appearing both in contemporaneous treatises and in recent research, as to the impact of a large number of musical parameters (e.g., melody, harmony, the presence and treatment of dissonance, inversion, texture, dynamics, tempo, timbre, and orchestration) on the perception of endings of varying strengths and for various levels of the structural hierarchy. Thus coming to a consensus as to the procedure by which endings may be identified and categorized remains a tremendous challenge. Attempting to clarify some of these issues, William Caplin classifies every possible cadential category according to two fundamental types: those for which the goal of the cadential progression is tonic (the authentic cadence and its variants), and those for which the goal is dominant (the half cadence and its variants).34 To these two types he finally adds the IAC, a melodic deviant of the PAC. He refers to these three cadential categories as “the only genuine cadences in music in the classical style.”35 Borrowing from Kofi Agawu, Caplin further classifies the parameters articulating cadential closure under two headings, syntax and rhetoric: “in its syntactical aspect, a given cadence represents a particular cadential type on the basis of its harmonicmelodic content exclusively. In its rhetorical aspect, that cadence has a unique compositional realization entailing the entire range of musical parameters, including rhythm, meter, texture, intensity, and instrumentation.”36 Thus, Caplin differentiates between the cadential categories common in music-theoretical discourse—perfect authentic, imperfect, deceptive, and so on—strictly according to the syntactic param33. A Likert scale is a common psychometric scale typically used in survey research to measure the level of agreement with a given statement. By providing only four possible responses, participants in this study were forced either to agree or disagree with the statement. 34. Ibid., 43. Caplin distinguishes between cadential progressions that feature a final dominant triad in root position—a half cadence—from a final dominant that is inverted or contains a dissonant seventh, which he terms a dominant arrival (see Caplin, Classical Form [1998], 79–81). 35. Ibid., 43. 36. Caplin, “The Classical Cadence” (2004), 107. On the rhetorical aspects of closure, see Agawu, “Concepts of Closure and Chopin’s Opus 28” (1987), 3–5.

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eters specific to each category. Indeed, few scholars have questioned the important role accorded to melodic and harmonic content in establishing cadential closure, particularly for music from the classical style.37 Distinguishing cadential categories according to their syntactic content therefore provides a suitable starting point for an experimental investigation of cadences. Moreover, the choice to examine cadential categories determined only on the basis of these syntactic parameters greatly reduces the number of potential categories we might study. Nevertheless, by selecting excerpts from the literature (rather than composing stimuli that reflect simple cadential paradigms), the musical examples also differ as a result of the rhetorical content unique to each excerpt. It was therefore necessary to explicitly include these parameters in the design of the experiment. We presented the participants with 50 short excerpts (average 9 seconds) from Mozart’s keyboard sonatas that contained an equal number of perfect authentic (PAC), imperfect authentic (IAC), half (HC), deceptive (DC), and evaded cadences (EV). These categories were chosen both on the basis of their frequency in Mozart’s style and on their assumed relevance to scholarship in music theory and music perception. Each excerpt contained at least the entire cadential progression, with some excerpts including music preceding the onset of that progression.38 Thus, each cadential category differs at the moment of the cadential arrival, which represents the crucial variable distinguishing each excerpt.39 Finally, to limit the number of variables under consideration, we neutralized performance features such as dynamics and rubato and selected a tempo for each excerpt that followed conventional performance practice. In order to take into account syntactic and rhetorical features not embraced by cadence category membership that occur frequently in Mozart’s cadences, we further subdivided each cadential category into two subtypes to consider issues of formal context (in the case of the PAC and HC), the presence of a melodic dissonance at cadential arrival (for the IAC and HC), as well as the melodic scale-degree and harmony at cadential arrival (for the DC and EV, respectively).40 Table 1 displays the 37. However, many scholars have questioned the subordinate status traditionally accorded to nonsyntactic parameters in the perception of closure, in particular for music following the classical period. For an example, see the second analysis of the first movement of Schubert’s D. 46 in Hyland, “Rhetorical Closure in the First Movement of Schubert’s Quartet in C Major, D. 46” (2009), 120–123. 38. We included additional material preceding the onset of the cadential progression in instances in which we felt the duration of the excerpt was too short to provide a sufficient tonal context. 39. Of course, a number of other parameters within the cadential progression itself might necessarily imply a given cadential category. For example, metrical placement and duration serve to distinguish a dominant harmony in a half cadence from a dominant in an authentic cadence. But for the purposes of the experimental design it was useful to differentiate each cadential category according to a specific temporal event, in this instance the moment of cadential arrival. 40. We also considered a number of other parameters for inclusion as subtypes in the experiment, such as the presence of a surface dissonance at cadential arrival in the perfect authentic cadence category, but the time constraints imposed by the experimental session precluded a design examining more than two subtypes for each category. Moreover, our intent was to select subtypes that reflect the most

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cadential categories, the subtypes, and a brief description of the characteristics that define each category. Table 1: Provides the cadence categories, syntactic characteristics, subtypes, and the number of excerpts for each subtype. a ECP refers to an expanded cadential progression; b CA refers to cadential arrival.

Cadence Categories

Characteristics

Subtypes

Perfect Authentic

- V and I in root position - Soprano 1^

Main Theme

Number 5

Subordinate Theme (ECP)a

5

b

5

Imperfect Authentic

- V and I in root position - Soprano 3^

Melodic Dissonance at CA

No Melodic Dissonance at CA

5

Half

- V in root position - No 7th

Main Theme

4

Transition

6

- Ends grouping structure - Typically on vi

Failed PAC at CA

7

Failed IAC at CA

3

- Melody leaps up - Provides no resolution

Tonic Harmony at CA

5

Non-Tonic Harmony at CA

5

Deceptive Evaded

The category of perfect authentic cadences was subdivided according to formal location, selected either from the main theme or the subordinate theme. The excerpts chosen from subordinate themes feature an expanded cadential progression (ECP) (see Example 2a), which, in addition to its longer duration (compared to those cadences selected from main themes), is characterized by a dramatic increase in surface activity, usually resulting from an Alberti bass in the left hand and the appearance of a cadential trill above the penultimate dominant.41 Indeed, that surface activity may affect the perception of closure has been suggested by Michel Vallières, as he found that higher average event density as well as the sudden decrease in event density at cadential arrival significantly affected the categorization of endings by nonmusicians.42 Example 3 displays the average event density, calculated as the total number of notes per second, for each of the last five seconds of the two subtypes of the PAC category, the EV category, and finally the other categories aggregated together. Both the PAC subordinate-theme subtype and the EV category feature a significant increase in surface activity in the last moments before cadential arrival, at which point the prevalent features of Mozart’s compositional style. However, in doing so, it should be acknowledged that whereas the features reflected in each subtype may play a prominent role in phrase endings from a number of different style periods, they may also be idiomatic to Mozart. 41. For a discussion of the ECP, see Caplin, “The ‘Expanded Cadential Progression’” (1987), 215–257. 42. Vallières, “Beginnings, Middles, and Ends” (2011), 106.

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                         

        (a)

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               



                                 

                                                                 

 

(b)



(c)

   

-

  



    





      

       















 











        

              

   



(e)

-

       



            

     

       

       



(d)

-

   











               







 

        

                 

  

Example 2: Five excerpts representing the five cadential categories. (a) PAC category, Subordinate Theme subtype: K. 309/i, mm. 48–54. (b) IAC category, Melodic Dissonance subtype: K. 330/iii, mm. 39–43. (c) HC category, Main Theme subtype: K. 284/iii, mm. 1–4. (d) DC category, Failed PAC subtype: K. 281/ii, mm. 32–35. EV category, Non-Tonic subtype: K. 279/ii, mm. 1–4

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activity ceases almost entirely, while for the other categories, surface activity does not vary within the cadential progression. We therefore hypothesized that PAC excerpts selected from subordinate themes might yield significantly higher completion ratings than excerpts from the other categories.

Example 3: Time Series Plot of the mean event density calculated in a window of 1 second for the two subtypes of the PAC category, the EV category, and the other categories aggregated together

The IAC category was subdivided according to the presence or absence of a melodic dissonance at cadential arrival (Example 2b displays the former case, an accented passing tone embellishing the melodic goal). Although a number of other features might serve to differentiate imperfect authentic cadences, such as the metric placement of cadential arrival (i.e., “masculine” vs. “feminine” endings) or the contour of the melody preceding cadential arrival (ascending vs. descending), etc., the presence of a surface dissonance in the melody at the moment of cadential arrival (defined by the appearance of the final tonic harmony) is a prominent attribute of Mozart’s imperfect authentic cadences.43 As with the PAC category, half cadences were subdivided according to their formal location, selected either from the main theme (as in Example 2c) or from the end of the transition.44 As the material within the transition in sonata form typically modulates to the subordinate key, the passages preceding cadential arrival for the

43. Imperfect authentic cadences featuring a surface dissonance typically include ©2^ at cadential arrival (see K. 330/i, m. 8; K. 311/ii, m. 32). To prolong the dissonance at cadential arrival, 2^ also sometimes appears in the soprano as an upward resolving suspension to 3^, with a chromatic passing tone inserted in between (see K. 498a/iv, m. 36; K. 533/iii, m. 26). 44. Unfortunately, the formal location subtypes for the HC category do not contain an equal number of excerpts: the main theme subtype contains four, whereas the transition subtype contains six. However, the surface dissonance subtypes for the HC category contain an equal number of excerpts.

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transition subtype are frequently characterized by increased energy (relative to the main theme) and tonal instability.45 These features serve dramatically to differentiate transition half cadences from those appearing in the main theme. In addition, the ten excerpts from the HC category were also separately classified according to the presence or absence of a melodic dissonance at the moment of cadential arrival. Whereas imperfect authentic and half cadences remain categorically distinct from the perfect authentic cadence, deceptive and evaded cadences generally do not, as they initially promise a perfect authentic cadence, yet fundamentally deviate from the goal harmony of the cadential progression only at the moment of cadential arrival. The deceptive cadence closes with a non-tonic harmony, usually vi, thus leaving harmonic closure somewhat open, but the melodic line resolves to a stable scale-degree at cadential arrival, thereby providing a provisional sense of ending for the ongoing thematic process.46 Depending upon the degree of melodic closure, this cadence category has been further subdivided according to whether the melody arrives on the tonic degree (1^), which I will refer to as a failed perfect authentic cadence (as in Example 2d) or on the third degree (3^), which I will refer to as a failed imperfect authentic cadence.47 Finally, the evaded cadence is characterized by a sudden interruption in the projected resolution of the melodic line; instead of resolving to 1^, the melody leaps up, often to 5^, thereby replacing the expected ending with material that clearly initiates the subsequent phrase. Thus, the evaded cadence projects no sense of ending whatsoever, as the event located at the point of expected cadential arrival, which should group backward by ending the preceding thematic process, instead groups forward by initiating the subsequent process. In order to consider issues of harmonic context associated with the evaded cadence, the category has been subdivided according to which harmony appears at the moment of expected cadential arrival—tonic harmony (which is typically inverted, but may sometimes be in root position), or non-tonic harmony (as in Example 2e).

45. Caplin, Classical Form (1998), 125; Hepokoski and Darcy, Elements (2006), 93. 46. Caplin does not define a deceptive cadence strictly by the presence of the submediant at cadential arrival, but rather by the appearance of a non-tonic harmony that nonetheless ends the grouping structure, thereby providing a provisional sense of ending. Thus, although deceptive cadences in Caplin’s typology typically feature vi at cadential arrival, other harmonies may also appear instead, such as I6 or vii6/V. Of the excerpts employed in the study, only one did not feature vi at cadential arrival. For more information on the physiognomy of the deceptive cadence and the history of the concept, see the contribution by Neuwirth in this volume. 47. Because deceptive cadences occur less frequently in Mozart’s keyboard sonatas than the other cadence categories selected for this study, the two subtypes do not contain an equal number of excerpts: the failed perfect authentic cadence subtype contains seven while the failed imperfect authentic cadence subtype contains three.

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Example 4: EV category, Tonic Harmony subtype: K. 281/iii, mm. 30–35. Top: From score. Bottom: Recomposed

Unfortunately, the extraction of each excerpt from its surrounding material introduced a number of factors at the moment of cadential arrival that might confound the experimental outcome. To eliminate these unwanted effects while preserving the stylistic integrity of each excerpt, it was necessary to impose a few constraints on the materials appearing at the cadential arrival. First, any chord tones appearing after cadential arrival (e.g., an Alberti bass pattern) were verticalized to the moment of cadential arrival and all subsequent material was removed. This alteration was necessary in order to eliminate differences in surface activity among excerpts, in particular for instances in which the absence of the third of the triad at the point of arrival would have resulted in an unstylistic open octave. Second, we recomposed the duration of the cadential arrival to one full tactus to ensure that differences in duration would not affect the perception of closure. This change still resulted in small variations in the duration of the final event for each excerpt, but these differences were assumed to be too small to significantly affect the completion ratings. Third, because we did not wish to consider the effect of cadential absence—such as when a rest replaces the expected tonic at cadential arrival—in two instances the events following the rest were shifted back to cadential arrival (see Example 4). Finally, any melodic dissonances appearing at the cadential arrival were retained so as not to fundamentally alter the excerpt (for example, in evaded cadences the melodic line frequently features an appoggiatura at the point of the expected cadential arrival).

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Results of the experiment I will first describe the results as they relate to the cadential categories and then discuss differences arising between the various subtypes.48 The left figure in Example 5 displays the completion ratings in a bar plot for each of the five cadential categories for musicians and nonmusicians.49 As expected, the musician ratings revealed significant differences between each adjacent pair of categories (PAC–IAC, IAC–HC, etc.), descending from PAC to EV. The membership of each excerpt to a cadential category would therefore seem to significantly affect the completion ratings. Moreover, the descending linear trend from PAC to EV demonstrated in the mean musician ratings suggests a kind of ordinal ranking of the categories according to their perceived strengths, a point I will return to later.

Example 5: Left: Bar plot of the completion ratings for each cadential category for musicians and nonmusicians. Right: Bar plot of the familiarity ratings for each cadential category for musicians and nonmusicians

Like musicians, nonmusicians fully distinguished between the PAC, IAC, and HC categories, which replicates a finding by Tillman et al., in which musicians and nonmusicians did not differ in their ratings of either perfect authentic or half cadences.50 However, nonmusicians provided much higher completion ratings for both deceptive and evaded cadences than musicians. They also rated deceptive cadences as more complete than half cadences, and surprisingly, their ratings of half cadences 48. For the present purposes, a discussion of the statistical procedures involved in analyzing the participant ratings might obscure a clear presentation of many of the theoretical issues this experiment sought to explore. For a full discussion of the methods and the experimental results, please see Sears, Caplin, and McAdams, “Perceiving the Classical Cadence” (2014), 397–417. 49. A bar plot simply displays the mean responses across all of the participants of each group for each category. The error bars (the vertical lines bounded by short horizontal lines) represent confidence intervals around the mean. Without going into too much detail, a large interval for this error bar indicates that the variability around the mean is quite large, which gives us less confidence that the mean we actually observed will substitute for the mean we would expect to find if we could sample the entire population. 50. Tillman, Bigand, and Madurell, “Local versus Global Processing of Harmonic Cadences” (1998), 166.

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and evaded cadences did not differ significantly. Differences in ratings of deceptive cadences might indicate that nonmusicians privileged the soprano voice in determining the completion of a given excerpt, but differences for the evaded cadence category are more difficult to interpret. There are three possible explanations for this result: first, the completion ratings of the half cadence and evaded cadence categories did not differ significantly for nonmusicians because half and evaded cadences represent the weakest cadential categories for these listeners; second, nonmusicians were simply less comfortable using the entire range of the scale, resulting in considerably higher ratings for evaded cadences; third, this bump in the completion ratings for the evaded category might result from a flaw in the design of the stimuli. Indeed, that each stimulus ends directly following the cadential arrival may have induced an artificial impression of closure, particularly for nonmusicians.51 To assess the perception of closure for evaded cadences without imposing an artificial boundary would therefore necessitate a new approach to the stimuli, one in which the material directly following the cadential arrival is retained.52 The familiarity ratings indicate that both groups rated perfect authentic cadences as somewhat familiar, while the IAC, DC, and EV categories received very low ratings, near the bottom of the scale. Shown in the right figure in Example 5, the familiarity ratings also revealed a surprising effect of expertise. While both groups provided higher familiarity ratings for the PAC category than for the other cadence categories, musicians also rated excerpts from the HC category as somewhat familiar. This effect was specific to musicians, however, as the nonmusician ratings for half cadences did not differ from those of the other cadence categories. The intention behind providing a familiarity scale was simply to determine if previous exposure to a particular excerpt might affect completion ratings. Our assumption was that knowledge of the material following the end of a given excerpt might alter the interpretation of that excerpt’s ending, thus affecting the completion rating and confounding the experimental outcome. This effect of expertise on the familiarity ratings of half cadences instead suggests a difference in the degree of exposure to, and subsequent knowledge of, half cadences in general, a particularly compelling finding that we did not observe in the completion data. So perhaps an explicit completion task alone cannot account for effects of expertise on the perception of half cadences. To resolve this issue, we also asked participants to respond to the statement, “this excerpt could complete a phrase or short passage of music,” on a 4-point Likert scale. Example 6 displays a bar plot of the distribution of the percentage of responses for each cadential category, with musician ratings above the x-axis and nonmusician ratings below. The dotted lines represent the minimum threshold necessary to reach significant agreement. Thus, for the 200 51. My reasoning as to why these artificial boundaries only affected nonmusicians will become clear later. 52. My dissertation examines this issue in a subsequent study.

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responses provided for each cadential category (20 participants in each group x 10 excerpts in each cadence category), a minimum of 68 identical responses (or 34%) was necessary to reach significant agreement.53

Example 6: Bar plot of the distribution of the percentage of responses for each cadential category for the statement, “this excerpt could complete a phrase or short passage of music,” with musician ratings above and nonmusician ratings below the x-axis. The dotted line indicates the minimum threshold necessary to reach significant agreement.

Reading from left to right, the first column in the PAC category for the musician group indicates that in 85% of all cases musicians strongly agreed that excerpts from this category could complete a phrase or short passage of music. Musicians generally agreed with this statement for the IAC and HC categories, while they generally disagreed for excerpts from the EV category. The results for the DC category are less clear, as both musicians and nonmusicians appeared to hover between agree (40%) and disagree (37.5%). Indeed, with the exception of the HC category, the general shape of each distribution appears fairly similar between the two groups, though the nonmusicians were more variable in their responses. However, in 43% of their responses nonmusicians disagreed that a half cadence could complete a phrase, whereas musicians agreed with the statement in over 50% of their responses. Thus, while the completion ratings did not reveal an effect of expertise for the perception of half cadences, the Likert-scale ratings suggest that nonmusicians generally did not consider a half cadence to be a satisfactory goal.

53. To determine if participants significantly agree in their judgments for a specific category, we compared the distribution of responses for a given category with a flat distribution, in which each of the four possible judgments is equally likely (i.e., 50 responses that strongly agree, agree, disagree, and strongly disagree for each category).

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Example 7: Bar plots of the completion ratings for each of the ten subtypes for musicians and nonmusicians

The completion ratings for the ten cadential subtypes, provided in Example 7, reveal significant effects of formal location and surface dissonance as well as the melodic scale-degree and final harmony of the various cadential excerpts. Beginning with the PAC subtypes, the inclusion of formal context significantly affected the perception of completion, with both groups providing higher ratings for excerpts from the subordinate theme. These excerpts exhibit a number of unique characteristics that might explain this result: the expanded temporal duration of the cadential progression resulting from a decrease in harmonic rhythm, the increased surface activity, and the appearance of a trill above the cadential dominant. Without further study, however, it remains unclear precisely how each of these characteristics might contribute to this result. With respect to the IAC, DC, and EV categories, it appears that on the one hand, nonmusicians attend predominantly to the melody when assessing the completion of a given excerpt, as they provided much higher ratings than did musicians for deceptive

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cadences, a cadential category that always provides a certain degree of melodic closure. Nonmusicians also appear to be more sensitive to variations in the melody, as evidenced by their lower ratings for imperfect authentic cadences featuring a surface dissonance at cadential arrival. Moreover, differences in the melodic scale-degree in the DC category significantly affected the ratings of the nonmusician group, with melodies featuring 1^ receiving higher ratings than those featuring 3^, a result that was not replicated by the musician group. On the other hand, musicians appeared to be more sensitive to variations in harmony, as they provided much lower ratings for deceptive cadences, and the harmony replacing the cadential arrival in the evaded cadence category also significantly affected their ratings, with excerpts featuring non-tonic harmony receiving lower ratings. These results might therefore suggest that expertise influences the attending strategy employed by the listener, with melody playing a more prominent role for nonmusicians.

Modeling attention: Melody and harmony

Closure

Closure

The purpose of this study is to demonstrate the extent to which various cadential categories contribute to the perception of closure. To that end, five distinct categories were selected on the basis of their melodic-harmonic content. But the claim that strategies of attention may differ as a result of musical training necessitates a statistical approach that may determine how melody and harmony independently affect the perception of closure. By encoding the melodic and harmonic information of each excerpt separately, we may model the completion ratings of both musicians and nonmusicians exclusively on the basis of the harmonic and melodic content specific to each excerpt, thus permitting us to abandon the cadential categories proper.

Melodic Scale-Degree

Melodic Scale-Degree

Example 8: Scatter plots of melodic scale-degree and closure. Left: E = .96, R2 = .90. Right: E = -.21, R2 = .04

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Before going further, a brief explanation of the statistical approach might be useful here. Let us imagine that the melodic scale-degree at cadential arrival for each excerpt will perfectly predict the completion ratings of our participants. Thus, for every excerpt we may calculate a mean completion rating from both our musician and nonmusician groups, and then quantify our melodic predictor according to a set of pre-determined criteria. We may finally place these two variables on a Cartesian plane, assigning our melodic predictor to the x-axis and the completion scale to the y-axis, and then determine the location of each excerpt in the space using the melody and completion values for each excerpt as xy coordinates (called a scatter plot). Shown in Example 8, if the relationship between our predictor and our outcome appears to be linear, we may model the relationship using linear regression, in which we calculate a best-fit line that minimizes the error between the predicted position of each excerpt on the line with its actual position in Cartesian space. To understand the regression estimates I will describe in the models that follow, R2 refers to the fit of the model, where a value of 1 indicates that the model accounts for all of the variance in the outcome variable (i.e., a perfectly linear relationship between the predictor and the outcome), and a value of 0 indicates that the model fails to account for any of the variance. In a multiple regression model, in which we may wish to determine the role of a number of predictors on the perception of completion, the slope of the line measured for each predictor, denoted by E, is also a useful estimate for the relationship between the predictor and the outcome, as it will indicate the degree to which the predictor covaries with the outcome variable. The value of E simply represents the change in the outcome resulting from a unit change in the predictor: the larger the value of E, the greater the role of the predictor within the regression model.54 Hence, the figure on the left in Example 8 presents a best-fit line that significantly predicts closure, while in the figure on the right, the best-fit line provides a very poor fit for the data. In order to account for the participant ratings of completion, we must quantify each predictor according to a set of criteria. First, a simple and fairly intuitive method might be to evaluate the melodic and harmonic content of each excerpt according to concepts of closure derived from music theory. For the purposes of this experiment, the harmony of each excerpt was assigned a value of 2 for a tonic triad in root position at the cadential arrival, 1 for a dominant triad in root position, and 0 for any other harmony in any inversion.55 The melody of each excerpt was assigned a value of 2 for

54. In a multiple regression model, each predictor (e.g., harmony, melody, metric position, etc.) may be quantified according to entirely difference scales, so it is important to standardize the β values of each predictor so that we can determine the relative contribution of each predictor in the final model. In the models that follow, one unit of change has been standardized to one standard deviation. 55. Bigand and Parncutt employed precisely this rating system to assess the effect of cadential patterns on tension ratings. See Bigand and Parncutt, “Perceiving Musical Tension in Long Chord Sequences” (1999), 250.

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1^ at cadential arrival, 1 for 3^, and 0 for any other scale-degree; henceforth I will refer to the estimates obtained from these variables as the syntax model. While this approach is certainly intuitive, it is also glaringly imprecise, as it fails to consider the effect of all of the possible scale-degrees that might appear at the end of each excerpt. In a second approach I assigned the mean goodness-of-fit ratings obtained from Krumhansl and Kessler’s major and minor key profiles to the scaledegrees appearing in the soprano and bass line of each excerpt at cadential arrival under the assumption that their profiles signify a cognitive representation of the tonal hierarchy pertaining specifically to endings; I will refer to the estimates obtained from these variables as the KK model. Table 2: Estimates from a stepwise linear regression analysis predicting the mean completion ratings of each excerpt using the Syntax and KK models. Musicians: Syntax R2 = .42 for Step 1; 'R2 = .22 for Step 2. KK R2 = .48 for Step 1; 'R2 = .24 for Step 2. Nonmusicians: Syntax R2 = .47 for Step 1; 'R2 = .18 for Step 2. KK R2 = .37 for Step 1; 'R2 = .35 for Step 2

Model Musicians

E

Syntax Harmony

.61

Melody

.47

Bass

.73

Soprano

.49

KK

Nonmusicians

Syntax Melody

.65

Harmony

.43

Soprano

.65

Bass

.60

KK

Table 2 displays the estimates of the syntax and KK models for both musicians and nonmusicians. For the musician group, the syntax model selected harmony, with a E of .61, in the first step, accounting for about 42% of the variance in their ratings. The selection of melody in the second step, with a E of .47, significantly improved the fit of the model, which produced a final R2 of .64. Stepwise selection therefore indicated that the harmony predictor played the most substantial role in accounting

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for musicians’ ratings of completion.56 Applying the KK predictors improved the fit of the regression model, with the two predictors accounting for 72% of the variance in musicians’ ratings. The KK model also produced similar standardized E weights, with the bass-line scale-degree again playing the more prominent role. Thus, as predicted, musicians placed greater emphasis on the bass voice at cadential arrival. For the nonmusician group, the estimates of the syntax model were a near mirror image to those found for the musicians, with the parameters of melody and harmony accounting for 65% of the variance in their ratings, but with melody, with a standardized E of .65, playing a more prominent role than harmony. However, with the addition of the goodness-of-fit ratings in the KK model, the lopsided influence of the soprano voice diminished somewhat, with the bass-line scale-degree playing a more significant role. Thus, it appears that harmonic and melodic content can predict the completion ratings of both groups, and both models indicate unequivocally that musicians privilege the bass voice. With nonmusicians, however, the relative contribution of the two parameters is less clear-cut. In the syntax model, melody accounted for a greater proportion of the variance, while in the KK model, regression estimates for the two parameters were nearly identical. These models support the claim that, in the perception of cadential closure, musicians appear to privilege the bass voice while nonmusicians are more sensitive to subtle differences in the soprano voice. That musical training may indeed influence attention in the perception of closure supports Weiser’s claim that training facilitates flexible voice-tracking.57 Furthermore, a recent study conducted by Psyche Loui and David Wessel showed that, even when presented with a task that explicitly directed participants to attend to the contour of the melody, violations in harmonic expectancy still influenced the behavioral responses of musicians.58 And because this effect was not observed for nonmusicians, the authors claimed repeated exposure to Western music results in the formation of automatic expectations to harmonic progressions that musicians simply cannot ignore, even when asked to attend to other features of the stimulus. It remains unclear, however, whether attention to bass-line motion in cadential contexts reflects a flexible voice-tracking strategy promoted during explicit 56. Stepwise selection refers to a method for determining the order of input for the predictors. In the first step, the algorithm inputs the predictor that accounts for the highest proportion of the variance in the outcome, then in the second step, the algorithm inputs the next predictor that accounts for the highest proportion of the residual variance (i.e., the variance not already accounted for by the first predictor). Depending on the number of predictors, this process continues either until no predictors remain, or until the remaining predictors no longer significantly improve the fit of the model. 57. Weiser, “Rating Cadence Stability” (1992), 40–46. 58. Loui and Wessel, “Harmonic Expectation and Affect in Western Music” (2007), 1084–1092. In a selective attention task, the authors asked participants to respond to the contour of a melody as they were presented with harmonic progressions that were either highly expected, slightly unexpected, or extremely unexpected. They found that the expectancy condition affected the speed and accuracy of the contour judgment for musicians, but had no effect on nonmusicians.

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formal training (i.e., in a pedagogical setting), or an attentional bias formed simply through implicit exposure to Western music. The distinction between explicit learning through training and implicit learning through passive exposure is admittedly a slippery one. The literature concerning the effect of expertise on musical experience is certainly vast, but it is fair to say both from behavioral and neurophysiological studies that explicit training fundamentally affects aspects of perception and cognition, such as attention, learning, and memory.59 Yet investigating the potential effects of expertise in an experimental setting crucially depends on the experimenter’s sensitive treatment of every aspect of the experimental design (the question(s) of the experimenter, the selection and creation of stimuli, the participant’s tasks, etc.). When experimenters employ stimuli with which a trained participant might be highly familiar, for example, the observed results may not reflect differences in expertise, but rather differences in familiarity.60 To be sure, perceiving and comprehending an auditory stimulus as rich and complex as music places a significant cognitive burden on listeners, and though exposure alone may not account for all of the reported differences between musicians and nonmusicians, the implicit knowledge gained from exposure nevertheless plays a significant role in music listening.

Modeling cadential strength The previous analysis sought to explain effects of expertise by appealing to differences in the attentional strategies employed during music listening. But perhaps differences in the completion ratings of musicians and nonmusicians might also be explained by taking another approach altogether, one in which we retain the cadential categories and propose a general model of hierarchical cadential closure. Unfortunately, the small number of excerpts employed for this study (50) prohibits a multiple regression model embracing the vast number of musical parameters implicated in the

59. To give two examples, researchers treating musicians as a special population have found differences between the morphology of the musician and nonmusician brains, which suggests that the development of musical expertise, particularly during early childhood, provides a good model for the study of brain plasticity (see Münte, Altenmüller, and Jäncke, “The Musician’s Brain as a Model of Neuroplasticity” [2002], 473f.). When expert musicians listen to music played on their own instrument, Margulis et al. also found increased activity in brain regions implicated in the processing of musical syntax, timbre, and sound-motor interactions, suggesting that explicit expertise subsequently affects music listening (see Margulis et al., “Selective Neurophysiologic Responses to Music” [2009], 267–275). 60. Such a conflation of formal training and passive exposure has led Emmanuel Bigand to propose a methodological distinction between tasks intended to investigate explicit formal training and tasks that explore how, simply through exposure to Western music, listeners acquire implicit knowledge of a given style (see Bigand, “More About the Musical Expertise of Musically Untrained Listeners” [2003], 304f.).

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articulation of cadences. Nevertheless, the cadential categories themselves provide a starting point for considering a model of perceived cadential strength that might lead to hypotheses to be examined in future studies. In a model of cadential strength, the perfect authentic cadence represents a good place to begin. From even a cursory glance at the literature, it occupies a central position in music theory, as it clearly represents the locus classicus for establishing thematic closure in the high classical period. Indeed, we may speculate that listeners versed in tonal music not only possess a cognitive representation of the tonal hierarchy, but perhaps for those listeners especially familiar with the classical style, a schematic representation explicitly for authentic cadential closure.61 During music listening, a number of parameters located within the cadential progression may activate our schematic representation of closure in real time, allowing listeners to generate harmonic and melodic expectations concerning the moment of cadential arrival. Accordingly, any deviation on the musical surface would naturally result in a violation of listener expectations, and thus would be experienced as a decrease in the cadential strength of a given excerpt. Deviations in melodic scale-degree and harmony at the cadential arrival thereby result in cadential categories of diminished strength.62 In this view, the half cadence represents the weakest cadential category; it is marked not by a deviation in the melodic and harmonic content at cadential arrival, but rather by the absence of that content. Thus, the half cadence is, as the term suggests, an incomplete cadence.63 So according to this view, every cadential context is compared to one essential prototype: the perfect authentic cadence. Henceforth I will refer to this model of cadential closure as the 1-Schema model. Indeed, this model has received some support from music theorists. Lamenting that “a well-defined hierarchical theory of cadence-types has simply not become established,” Janet Schmalfeldt outlined the five cadential types that achieve what she termed distinct closure,64 and of these types, she regarded

61. By this I mean not only a representation for harmonic closure, though such a claim has already been made by Rosner and Narmour (“Harmonic Closure” [1992], 397f.), but rather for a number of potential characteristics—both syntactic and rhetorical—that appear within the cadential progression. However, the question as to whether listeners actually possess such a representation remains open. 62. But such deviations need not only pertain to harmonic and melodic expectations. Hepokoski and Darcy’s attenuated PAC, in which the moment of cadential arrival is marked by a sudden drop in dynamics or an unexpected shift to the minor mode, provides one such example (see Hepokoski and Darcy, Elements [2006], 170). 63. See also the contributions by Poundie Burstein as well as Nathan Martin and Julie PedneaultDeslauriers in this volume. 64. Schmalfeldt, “Cadential Processes” (1992), 11f. In her model she distinguishes between three essential categories of closure: (1) distinct closure, in which the goal event closes a preceding process, (2) elision, in which the goal event both closes the preceding process and initiates the subsequent process, and (3) evasion, in which the goal event provides no ending whatsoever. She then situates the cadential types—PAC, IAC, HC, and so on—within these three categories.

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the half cadence as weakest.65 Citing Schmalfeldt’s hierarchical model of cadential closure, Edward Latham recently proposed a model that identifies and subsequently weighs the criteria deemed necessary for establishing cadential closure on a 10-point scale.66 He assigns 5 points to tonic harmony and 5 points to the preceding dominant, and he derives these scores from the scale-degrees present in the bass (1.5) and soprano (0.5), from whether the sonority is in root position (1.5), and finally from the presence of particular chord members (0.5) and a contextual feature: whether each sonority serves as a harmonic and melodic goal (1.0). Latham then scores each of Schmalfeldt’s cadential types and places them along the scale. According to his criteria, the PAC category receives between 9 and 10 points (depending on whether the cadential tonic is elided), followed by IAC (8.5–9.5), DC (6.5–8.5), EV (3.5–8.5), and finally HC (3.5–5.0), positioned near the bottom of the scale.67 His model therefore conceptualizes a half cadence as an incomplete authentic cadence. At the heart of the half-cadence issue is an inherent contradiction: that a dominant, which is the penultimate harmony in an authentic cadential progression, can serve as a satisfactory goal. Indeed, many scholars besides Latham envision the half cadence as an incomplete cadence, one in which the expected resolution to tonic simply never appears.68 And perhaps the results of our experiment reflect this contradiction. Recall that while the two groups did not differ in their completion ratings for the HC category, musicians provided much higher familiarity ratings than nonmusicians. In contrast to musicians, nonmusicians also generally disagreed that half cadences could complete a phrase or short passage of music. Thus, the effect of expertise on the perception of half cadences remains patently unclear. Certainly the very notion of half cadence is a paradoxical one, an instance of what Leonard Meyer famously called “parametric noncongruence,” in which a dominant harmony—an active, unstable sonority—achieves the status of a cadential goal not by virtue of its melodic-harmonic content alone, but by means of metrical, textural, and rhythmic reinforcement.69 William Caplin has posited another view of half cadence, in which a dominant, merely by virtue of its melodic-harmonic content, can represent a harmonic end: “In the half-cadential progression, the dominant itself becomes the goal harmony and so occupies the ultimate position. To be sure, this dominant usually resolves to tonic, one that normally initiates a new harmonic progression, but within the boundaries 65. Ibid., 7. At no point, however, does Schmalfeldt explicitly compare the strength of the half cadence with modifications of the perfect authentic cadence, such as the deceptive cadence. Thus her view of the half cadence within the general hierarchy of cadential categories remains unclear. 66. Latham, “Drei Nebensonnen” (2009), 308f. 67. His model also positions plagal and abandoned cadences on the scale, and it considers the effect of cadential elision, an issue that has received very little treatment in experimental studies of closure. 68. See, for example, Hepokoski and Darcy, Elements (2006). They describe the half cadential dominant as an active dominant (24), one that necessarily implies resolution to an existing or implied tonic (xxv). 69. Meyer, Explaining Music (1973), 85.

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of the half-cadential progression itself, the dominant possesses enough stability to represent a harmonic end.”70 Moreover, recall that Caplin distinguishes the half cadence—one of the genuine cadence categories—from the deceptive and evaded cadences, which represent failed attempts to achieve authentic cadential closure. We may therefore postulate an alternative to the 1-Schema model, in which listeners may possess schematic representations for each of the genuine cadences, which I will call the Genuine Cadence model. Accordingly, we may rank the strength of cadential closure beginning with the PAC category, followed by IAC and HC, followed by the syntactically weaker cadential categories: the DC and EV categories. Table 3: Estimates from a linear regression analysis predicting the average completion ratings for each excerpt using the Genuine Cadence, 1-Schema, and Latham models as predictors

Musicians

Model

Cadential Strength

Genuine Cadence

PAC>IAC>HC>DC>EV

1-Schema Latham Nonmusicians

Genuine Cadence 1-Schema Latham

PAC>IAC>DC>EV>HC PAC>IAC>HC>DC>EV PAC>IAC>DC>EV>HC

E

Model R2

.84

.84

.76

.56

.77

.59

.74

.53

.80

.63

.79

.61

By ranking each cadential category, we may compare the two models with the completion ratings. Given that Latham has provided a method for quantifying closure, I have also calculated the strength of closure for each excerpt using Latham’s criteria, which I will refer to as the Latham model. Table 3 provides the estimates for each model. For the musicians, the Genuine Cadence model accounts for 84% of the variance in their ratings, while the 1-Schema and Latham models were less successful, accounting for between 55-60% of the ratings. However, for the nonmusicians, the 1-Schema model provided the best fit, accounting for approximately 63% of the variance in their ratings. What are we to make of this result? The 1-Schema model assumes that, when presented with a cadential excerpt, listeners have no knowledge of the future, and thus, of the material that may follow cadential arrival. Yet for a listener familiar with the classical style, the material that follows instances of cadential failure often differs considerably from the material following genuine cadential closure. By thwarting the expected moment of cadential arrival, theorists typically conceptualize cadential deception and evasion as a kind of derailment. And in order to attain the cadential closure initially promised, the subsequent passage typically features a continuation 70. Caplin, Classical Form (1998), 29 (emphasis in original).

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of an earlier process, sometimes even a direct repetition of the previous cadential progression itself, a compositional procedure Schmalfeldt refers to as the “one more time” technique.71 Thus, Caplin refers to the PAC, IAC, and HC categories as genuine specifically because they are the only categories that can achieve thematic closure. What these results may suggest, however, is that the PAC, IAC, and HC categories also achieve genuine status by virtue of the material following cadential arrival. A genuine cadence therefore not only provides sufficient closure to permit the introduction of new initiating material, but the perceived strength of such a cadence is also crucially influenced by the function of the material following cadential arrival; or more generally put, the surrounding context may be crucial to determining the strength of a given cadence.72 So perhaps during music listening (and particularly during a first listening), the 1-Schema model is the default for determining the strength of closure of a given ending, but the material following each cadence subsequently compels listeners to retrospectively re-evaluate their earlier impression, and thus, to adopt a model that embraces a theory of genuine cadential closure. Given enough exposure to the style, however, listeners may apply a model of genuine cadential closure even to excerpts presented out of context, which would explain why musicians and nonmusicians disagreed as to whether a half cadence could complete a phrase or short passage of music. But to consider this claim in an experimental setting would nevertheless require stimuli that include the material following cadential arrival, an approach that our experimental design did not permit. Furthermore, many aspects of the perception of closure—the effect of cadential elision, variations in timing and dynamics surrounding cadential arrival, schematic representations of closure for other style periods—remain largely unexplored in music psychology.

71. Schmalfeldt, “Cadential Processes” (1992), 1–52. 72. This claim is, in fact, essential to Hepokoski and Darcy’s concept of essential expositional closure (EEC), the moment when the subordinate theme attains the first satisfactory PAC in the new key that proceeds onward to differing material (Hepokoski and Darcy, Elements [2006], 120). And it is precisely this “differing material” that distinguishes the EEC from any other PACs appearing in the subordinate theme. Indeed, if what follows the PAC is immediate thematic repetition or variation, then the EEC is deferred to the next PAC in the subordinate theme (123). The authors emphasize, however, that the EEC should not be psychologically privileged as the strongest cadence in the exposition; stronger cadences (i.e., cadences featuring expanded cadential progressions, trills above the cadential dominant, etc.) very often occur in the closing section as reinforcement-work: “One should not determine an EEC on the basis of what one imagines an EEC should ‘feel’ like in terms of force or unassailably conclusive implication. […] The first PAC closing the essential exposition is primarily an attainment of an important generic requirement—nothing more and nothing less” (124).

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Concluding remarks As a first step, this particular study took a deductive path, beginning with the categories identified in Caplin’s theory of cadential closure and then working down to the parameters at the musical surface that characterize those categories. But this is not to say one could not have taken an inductive approach, whereby the musical parameters dictate the number and position of the categories within the hierarchy. Indeed, my choice here was to engage experimental methods with models of cadential strength advanced in music theory to examine whether, and to what degree, these models might be consistent with the behavioural ratings of participants. But in doing so, this study did not consider those musical passages that defy ready categorization in traditional theories of cadential closure, but that nevertheless elicit an ending percept. By abandoning the cadential categories entirely, we might therefore consider the entire range of musical parameters responsible for the perception of closure without recourse to theories of cadence that attempt to reveal the procedures by which composers articulated closing patterns in the classical style, but which do not always directly correspond with the listening habits, attending strategies, and behavioral responses of listeners. Indeed, what is essential for a theory of cadence may not always be tenable for a psychological theory of closure.73 Certainly, empiricism provides a method for applying constraints to our theoretical models, weeding out the impossible from the possible, but the concept of closure advanced in theories of cadential closure need not dispense with an examination of compositional procedures in favor of exclusively explaining how listeners perceive and process closing patterns. However, the desire to explain or clarify how we experience musical endings can provide common ground for further cross-disciplinary work. To be sure, terms relating to closure may have a long history in music theory, but closure has emerged only recently in music-psychological research as a relevant perceptual and cognitive concept.74 The application of experimental methods in future studies may therefore offer researchers the opportunity to gain a more complete understanding of the underlying sensory and cognitive mechanisms responsible for the perception of closure in music.

73. Nicholas Cook makes the same point in reference to the perception of tonal closure (Cook, “The Perception of Large-Scale Tonal Closure” [1987], 205). 74. It is difficult to determine the precise origins of the term in the history of psychology, but Wertheimer’s application of closure in visual perception provides one well-known early example (Wertheimer, “Laws of Organization in Perceptual Forms” [1938], 83).

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Bibliography Aarden, Bret (2003), “Dynamic Melodic Expectancy,” Ph.D. diss., The Ohio State University. Agawu, Kofi (1991), Playing with Signs: A Semiotic Interpretation of Classic Music, Princeton: Princeton University Press. Anson-Cartwright, Mark (2007), “Concepts of Closure in Tonal Music: A Critical Study,” Theory and Practice 32, 1–18. Bigand, Emmanuel (2003), “More About the Musical Expertise of Musically Untrained Listeners,” Annals of the New York Academy of Sciences 999, 304–312. Bigand, Emmanuel and Richard Parncutt (1999), “Perceiving Musical Tension in Long Chord Sequences,” Psychological Research 62, 237–254. Blombach, Ann (1987), “Phrase and Cadence: A Study of Terminology and Definition,” Journal of Music Theory Pedagogy 1, 225–251. Boltz, Marilyn (1989), “Perceiving the End: Effects of Tonal Relationships on Melodic Completion,” Journal of Experimental Psychology: Human Perception and Performance 15/4, 749–761. Butler, David (1989), “Describing the Perception of Tonality in Music: A Critique of the Tonal Hierarchy Theory and a Proposal for a Theory of Intervallic Rivalry,” Music Perception 6/3, 219–242. Caplin, William E. (1998), Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, New York: Oxford University Press. ——— (1987), “The ‘Expanded Cadential Progression’: A Category for the Analysis of Classical Form,” Journal of Musicological Research 7/2-3, 215–257. ——— (2004), “The Classical Cadence: Conceptions and Misconceptions,” Journal of the American Musicological Society 57/1, 51–118. ——— (2009), “What are Formal Functions?,” in: Musical Form, Forms, and Formenlehre: Three Methodological Reflections, ed. Pieter Bergé, Leuven: Leuven University Press, 21–40. Cook, Nicholas (1987), “The Perception of Large-Scale Tonal Closure,” Music Perception 5/2, 197–206. Eberlein, Roland (1997), “A Method of Analysing Harmony, Based on Interval Patterns or ‘Gestalten’,” in: Music, Gestalt, and Computing, ed. Marc Leman, Springer: Berlin and Heidelberg, 225–236. Eberlein, Roland and Jobst Fricke (1992), Kadenzwahrnehmung und Kadenzgeschichte: Ein Beitrag zu einer Grammatik der Musik, Frankfurt: P. Lang. Gjerdingen, Robert O. (2007), Music in the Galant Style, New York: Oxford University Press. Harter, Courtenay (2009), “Bridging Common Practice and the Twentieth Century: Cadences in Prokofiev’s Piano Sonatas,” Journal of Music Theory Pedagogy 23, 57–77. Hatten, Robert (1992), “Interpreting Deception in Music,” In Theory Only 12/5, 31–50. Hepokoski, James and Warren Darcy (2006), Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata, New York: Oxford University Press. Huron, David (2007), Sweet Anticipation: Music and the Psychology of Expectation, Cambridge, MA: MIT Press. Huron, David and Richard Parncutt (1993), “An Improved Model of Tonality Perception Incorporating Pitch Salience and Echoic Memory,” Psychomusicology 12/2, 154–171.

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Hyland, Anne (2009), “Rhetorical Closure in the First Movement of Schubert’s Quartet in C Major: A Dialogue with Deformation,” Music Analysis 28/1, 111–142. Koch, Heinrich Christoph (1782–1787–1793), Versuch einer Anleitung zur Composition, 3 vols., Leipzig: Böhme. Reprint, Hildesheim: Olms, 1969. Selections trans. Nancy Kovaleff Baker as Introductory Essay on Musical Composition, New Haven, CT: Yale University Press, 1983. Krumhansl, Carol (1990), Cognitive Foundations of Musical Pitch, New York: Oxford University Press. Krumhansl, Carol and Edward Kessler (1982), “Tracing the Dynamic Changes in Perceived Tonal Organization in a Spatial Representation of Musical Keys,” Psychological Review 89/4, 334–368. Latham, Edward (2009), “Drei Nebensonnen: Forte’s Linear-Motivic Analysis, Korngold’s Die Tote Stadt, and Schubert’s Winterreise as Visions of Closure,” Gamut 2/1, 299–345. Lerdahl, Fred and Carol Krumhansl (2007), “Modeling Tonal Tension,” Music Perception 24/4, 329–366. Loui, Psyche and David Wessel (2007), “Harmonic Expectation and Affect in Western Music: Effects of Attention and Training,” Perception & Psychophysics 69/7, 1084–1092. Margulis, Elizabeth (2003), “Melodic Expectation: A Discussion and Model,” Ph.D. diss., Columbia University. ——— (2007), “Surprise and Listening Ahead: Analytic Engagements with Musical Tendencies,” Music Theory Spectrum 29/2, 197–217. Margulis, Elizabeth, Lauren Mlsna, Ajith Uppunda, Todd Parrish, and Patrick Wong (2009), “Selective Neurophysiologic Responses to Music in Instrumentalists with Different Listening Biographies,” Human Brain Mapping 30, 267–275. Meyer, Leonard (1956), Emotion and Meaning in Music, Chicago: The University of Chicago Press. ——— (1973), Explaining Music: Essays and Explorations, Berkeley: University of California Press. ——— (1957), “Meaning in Music and Information Theory,” The Journal of Aesthetics and Art Criticism 15/4, 412–424. Münte, Thomas, Eckart Altenmüller, and Lutz Jäncke (2002), “The Musician’s Brain as a Model of Neuroplasticity,” Nature Reviews Neuroscience 3, 473–478. Narmour, Eugene (1996), “Analyzing Form and Measuring Perceptual Content in Mozart’s Sonata K. 282: A New Theory of Parametric Analogues,” Music Perception 13/3, 265–318. Rosner, Burton and Eugene Narmour (1992), “Harmonic Closure: Music Theory and Perception,” Music Perception 9/4, 383–412. Schmalfeldt, Janet (1992), “Cadential Processes: The Evaded Cadence and the ‘One More Time’ Technique,” Journal of Musicological Research 12/1, 1–52. Sears, David, William E. Caplin, and Stephen McAdams (2014), “Perceiving the Classical Cadence,” Music Perception 31/5, 397–417. Temperley, David (1999), “What’s Key for Key? The Krumhansl-Schmuckler Key-Finding Algorithm Reconsidered,” Music Perception 17/1, 65–100. Tillman, Barbara, Emmanuel Bigand, and Francois Madurell (1998), “Local Versus Global Processing of Harmonic Cadences in the Solution of Musical Puzzles,” Psychological Research 61, 157–174. Vallières, Michel (2011), “Beginnings, Middles, and Ends: Perception of Intrinsic Formal Functionality in the Piano Sonatas of W. A. Mozart,” Ph.D. diss., McGill University.

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Vallières, Michel, Daphne Tan, William E. Caplin, and Stephen McAdams (2009), “Perception of Intrinsic Formal Functionality: An Empirical Investigation of Mozart’s Materials,” Journal of Interdisciplinary Music Studies 3/1-2, 17–43. Vos, Piet and Dennis Pasveer (2002), “Goodness Ratings of Melodic Openings and Closures,” Perception & Psychophysics 64/4, 631–639. Weiser, Margaret (1992), “Rating Cadence Stability: The Effects of Chord Structure, Tonal Context, and Musical Training,” Ph.D. diss., McMaster University. Wertheimer, Max (1938), “Laws of Organization in Perceptual Forms,” in: A Source Book of Gestalt Psychology, ed. Willis Ellis, London: Kegan Paul, Trench, Trubner & Company, 71–88.

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TOWARDS A SYNTAX OF THE CLASSICAL CADENCE* Martin Rohrmeier and Markus Neuwirth

“The idea that there is a grammar of music is probably as old as the idea of a grammar itself”1

I. Theoretical foundations 1. The cadence: Essence or family resemblance?

A

crucial aspect of our listening experience is the formation of expectations and predictions.2 No matter what kind of music we are listening to, we have a predisposition towards expecting certain continuations of what we have heard before. In Leonard B. Meyer’s words, a given musical event “implies” another and at the same time may “realize” the implications set up by earlier events.3 The cadence is often cited as one of the most prototypical patterns in Western tonal music, creating and ultimately fulfilling highly specific expectations.4 It has frequently been suggested that cadential contexts differ systematically from non-cadential ones with respect to their expectancy profile. Cadences articulate phrase boundaries at which there is a highly contrastive change in predictability from high to low.

*

1. 2. 3. 4.

Financial support for the research presented in this chapter has been generously provided to the first author by the MIT I2 Intelligence Initiative, the MIT Department of Linguistics and Philosophy, as well as the Zukunftskonzept at TU Dresden funded by the Exzellenzinitiative of the Deutsche Forschungsgemeinschaft. The work by M.R. was conducted under the affiliation of MIT as well as TU Dresden. M.N.’s research has been funded by The Research Foundation – Flanders. We would like to thank Taiga Abe and Sophia Stuhr for their kind assistance in preparing the figures included in this chapter. Steedman, “The Blues and the Abstract Truth” (1996), 1. Rohrmeier and Koelsch, “Predictive Information Processing” (2012); Rohrmeier, “Musical Expectancy: Bridging Music Theory, Cognitive and Computational Approaches” (2013). Meyer, Explaining Music (1973). See Meyer, Emotion and Meaning in Music (1956).

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Although cadences are often described as a stock pattern, the variety of cadential structures is in fact enormous, exceeding by far the simple characterizations in terms of “I–IV–V–I” or “I–ii(6)–V–I” found in numerous modern music-theory textbooks and used in typical experimental settings in music psychology.5 This variability of cadences clearly defies music-theoretical attempts to provide an unequivocal and all-encompassing definition. As Robert Gjerdingen polemically points out, a chordcentered definition of the cadence is dubious, as it “highlights only what Locatelli has in common with Rimsky-Korsakov.”6 This type of “lowest common denominator” approach adopted by many theorists may single out V–I as the essence of an authentic cadence,7 although this feature is hardly sufficient to allow a clear-cut distinction between cadential and non-cadential (prolongational or sequential) progressions.8 In other words, the bare harmonic essence may not be capable of providing the differentia specifica to other (non-cadential) types of progressions. Because non-cadential phrases may likewise feature V–I, this element (the alleged “essence”) is too unspecific a requirement for a cadential progression. As shown elsewhere in this volume, the characterization of half cadences is even less straightforward, especially due to the variety of possible predominant chords.9 Conversely, the four-stage prototype of the cadence,10 embracing an initial tonic, predominant, dominant, and final tonic, does not cover all possible instances of the cadence concept, as not all of these stages must necessarily be present: Not only might the initial tonic be omitted, but the predominant as well.11 Even a dominant in root position, sometimes considered an absolute requirement for “the authentic cadential progression” to have “sufficient harmonic strength to confirm tonality,”12 may not be strictly necessary, as (pre-classical) cadences featuring an inverted dominant demonstrate.13 This might suggest that one of the crucial problems in defining cadences seems to be the lack of an “essence”: It appears to be difficult, if not downright impossible, to identify the necessary and sufficient criteria underlying the definition of a cadence,

5.

This is hardly surprising, as cadences have evolved over a remarkably long period of time; thus, the ways in which cadences materialize depend to a large extent on the historical style in which they appear. 6. Gjerdingen, Music in the Galant Style (2007), 140. 7. See Temperley, The Cognition of Basic Musical Structures (2001), 336ff. 8. On these types of harmonic progressions, see Caplin, Classical Form (1998), 23ff. 9. Specifically on the problems surrounding a robust definition of half cadences, see, for instance, the contributions by Martin and Pedneault-Deslauriers as well as by Burstein in this volume. 10. Caplin, “The Classical Cadence” (2004). 11. E.g., Mozart, K. 330/i, mm. 5–8. In his discussion of such “incomplete cadential progressions,” William Caplin hypothesizes that “the initial tonic is left out more often than the pre-dominant is, for eliminating the latter results in the loss of a fundamental harmonic function. Excluding both of these harmonies occurs infrequently in the literature” (Caplin, Classical Form [1998], 27). 12. Caplin, Classical Form (1998), 27; see also Caplin, “The Classical Cadence” (2004). 13. See Caplin in this volume.

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a fact that might indicate that there is no such thing as “the” cadence. Rather, one could argue, the various forms of cadences are related to one another by way of a Wittgensteinian “family resemblance.”14 Nonetheless, considering other disciplines such as evolutionary biology, linguistics, and economics, the complexity and diversity of real-world phenomena should not prevent us from developing concise analytic characterizations with the aid of formal methods. In this chapter, we seek to account for the combinatorial complexity inherent in the classical cadence by taking advantage of the flexibility of a generative grammar approach.

2. Formal modeling and music theory Music theory seeks to provide a concise description of the principles governing a musical system or a specific, historically bound style. Despite the field’s ambitions with regard to accuracy and conciseness, at present formal models of music description are the exception rather than the rule. Although the notion of (linguistic) syntax has been repeatedly invoked in theoretical writings since the eighteenth century,15 only a few theorists have taken this analogy seriously, among them Aldwell and Schachter: One way that music resembles language is that the order of things is crucial in both. “I went to the concert” is an English sentence, whereas “I concert went the to” is not. Similarly, I-VII6-I6-II6-V7-I [...] is a coherent progression of chords, whereas I-I6-VII6-II6-I-V7 [...] is not, as you can hear if you play through the two examples. In the study of language the word syntax is used to refer to the arrangement of words to form sentences; word order is a very important component of syntax. In studying music, we can use the term harmonic syntax to refer to the arrangement of chords to form progressions; the order of chords within these progressions is at least as important as the order of words in language.16

Despite their explicit reference to linguistic syntax, Aldwell and Schachter do not go on to employ formal tools and their powerful potential in music-theoretical descriptions, although most of the rules in their textbook would lend themselves to formal modeling. However, in the 1980s and over the last decade, a number of theorists have taken advantage of the power of formal grammars for the characterization of music and computational music analysis.17 14. On the notion of “family resemblance,” see Wittgenstein, Philosophical Investigations (1953/2001), 65–68. 15. Most famously by Koch, Versuch I–III (1782–1793). For modern sources, see Albersheim, “Die Tonsprache” (1980) and Kostka and Payne, Tonal Harmony (1984). 16. Aldwell and Schachter, Harmony and Voice Leading (2003), 139 (emphasis in original). 17. Winograd, “Linguistics and the Computer Analysis of Tonal Harmony” (1968); Keiler, “Bernstein’s ‘The Unanswered Question’ and the Problem of Musical Competence” (1978); Steedman, “A Generative Grammar for Jazz Chord Sequences” (1984) and “The Blues and the Abstract Truth” (1996); Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983); Rohrmeier, “A Generative Grammar Approach to Diatonic Harmonic Structure” (2007) and “Towards a Generative Syntax of

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Formal models are particularly well-suited to music-theoretical purposes, as they (1) contribute to the specificity and conceptual clarity of a given theory, (2) offer precise evaluation criteria, truth conditions, and empirically testable predictions, and (3) allow differentiation between regular and irregular (or grammatical and non-grammatical) musical utterances as well as between general and style-specific features. In addition, it should be noted that a generative grammar approach not only describes the structure implied in the musical pseudo-surface (e.g., chord representation), but also captures functional and dependency relationships between elements in the deep structure (weak vs. strong generativity). Such a formal characterization additionally allows us to make predictions with respect to the corresponding cognitive processes and constraints. More specifically, it makes it possible to model the generalized competence of a well-informed expert listener/composer/performer with regard to the tonal language, deliberately sidelining style-specific, piece-specific, composerspecific, and idiosyncratic aspects.18 Another important (and cognitively informed) theoretical approach addressing the classical cadence embraces the families of schema and prototype theories.19 From a formal perspective, schema or prototype theories and grammar approaches may be construed as the opposite ends of a complexity spectrum. Their primary difference involves a tradeoff in terms of compression: If a pattern evinces both regularity and combinatorial freedom, grammars will be more suitable to describe it; however, if a musical structure exhibits more standardization and less variability, schema-theoretical (and exemplar-based) approaches will be more appropriate. However, the boundaries between schemata and generative grammars may be fuzzy, since the ways in which prototypes can be modified can approximate the ways in which generative rules specify the modification of strings; conversely, building blocks and rules may incorporate fixed block sequences.20 Although, as noted above, the classical cadence appears to be relatively formulaic, closer inspection reveals a high degree of variety, flexibility, and freedom. This flexibility may lend itself in particular to the use of a generative grammar focusing on small building blocks and rule-based generative mechanisms, rather than the schemata employed in music theory. Tonal Harmony” (2011); Katz and Pesetsky, “The Identity Thesis for Language and Music” (2010); De Haas et al., “Modeling Harmonic Similarity Using a Generative Grammar of Tonal Harmony” (2009); De Haas, “Music Information Retrieval Based on Tonal Harmony” (2012); and De Haas et al. “Automatic Functional Harmonic Analysis” (2013). 18. For an earlier attempt, see Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), 3; Jackendoff and Lerdahl, “The Capacity for Music” (2006). 19. E.g., Gjerdingen, Music in the Galant Style (2007). For a schema-theoretical approach to cadences, see Byros in this volume. 20. See also Temperley, The Cognition of Basic Musical Structures (2001), 336ff. If a schema-based description employs rules to recursively adapt, modify, and recombine schemata, this converges to a syntactic approach with building blocks of different sizes. For an attempt to transform schemata into a grammar, see Lerdahl, Tonal Pitch Space (2001), 233–248.

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3. Formal grammars: A brief introduction The concept of formal grammars and rewrite systems dates back to Chomsky’s early approaches in the 1950s.21 A crucial motivation for such systems is the insight that infinite or very large sets of sequences can be efficiently and concisely characterized by a small number of rules operating in conjunction with combinatorial principles, rather than listing each of these sequences individually. The formalism requires the following definitions: A language is a finite or infinite set of sequences (or strings) over a predefined repertory of symbols that are commonly referred to as terminal symbols. In the case of music, one may, for instance, decide to choose tones, drumbeats, chords, or bass notes for the set of terminal symbols. A language distinguishes grammatical (regular, licit) sequences from ungrammatical (irregular, illicit) ones generated by the same terminal symbols. A finite number of sequences could simply be described by listing all of the sequences, whereas an infinite set of sequences requires an indirect definition to characterize it, a definition that specifies the generating mechanism.22 A formal grammar (generative grammar) is a way of characterizing an (infinite) set of sequences by means of construction (generation), defined through its terminal symbols, nonterminal symbols (variables that represent a deep structure not observable in the surface sequence; for instance, relationships between grammatical categories), rewrite rules for grammatical production, and one special nonterminal start symbol defining the beginning of production.23 The production process defines strings by beginning with the start symbol and iteratively replacing nonterminals in the current string until the string consists only of terminals. The set of all strings generated by the start symbol using all possible combinations of rule applications defines the language expressed by the grammar. The set of productions derived from one nonterminal is called the yield of the nonterminal; in particular, the language expressed by the grammar corresponds to the yield of the start symbol. The derivation process results in a parse tree that expresses the derivation steps that produce a given sequence. If there is more than one nonequivalent parse tree (the order of the single derivations does not matter), the sequence is referred to as ambiguous. For instance, a toy grammar G = (6, V, R, S) may be defined with the terminals 6 = {a,b,c,d}, the nonterminals V = {U,V,W,X}, the start symbol S = {U}, and the following rules in R: U o bV V o cW

21. See, e.g., Chomsky, “Three Models for the Description of Language” (1956). 22. Note also that a finite set of sequences might be more easily or comprehensively described by characterizing it by its underlying structure rather than listing all instances without taking into account a generalizing structure; in other words, a grammatical description is a means of compression by generation. 23. Note that “production” here does not refer to a temporal process or a cognitive model; rather, it characterizes a mathematical (atemporal) construction principle for sequences.

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V o aW W o dV W o bW W o dX X o b

Our simple grammar G now generates strings by successive rewrite steps, beginning from the start sequence “U” until any sequence is reached that lacks a nonterminal symbol. One sample generation process could involve the following steps: U Ÿ b V ŸbaWŸbadVŸbadcWŸbadcbWŸbadcbbWŸbadcbbbWŸ b a d c b b b d V Ÿ b a d c b b b d a W Ÿ b a d c b b b d a d X Ÿ b a d c b b b d a d b. The final string contains no more nonterminals and therefore the generation stops, resulting in a terminal string. This grammar is recursive because the yield of the symbol W (and V) generates another instance of this symbol, resulting in strings of unbounded lengths. Based on the way the rules for this toy grammar are defined, it is straightforward to conclude that (1) each sequence must begin with a single ‘b’, (2) each sequence must end with ‘d b’, and (3) the possible middle sections include repetitions of the sequence ‘c’ or ‘a’ followed by any number of ‘b’s (including no ‘b’) and ‘d’. Furthermore, one can easily see that no string with a different structure can be produced. Note that the definition of the start symbol is crucial here, since defining ‘V’ or ‘W’ as the start symbol would result in somewhat different structures. The process of reconstructing the possible underlying generation paths that resulted in an observed terminal sequence (and deciding whether a sequence is grammatical) is referred to as parsing (structural listening or language perception would involve a form of parsing). Each class of formal grammars (see below) requires a specific associated parsing process (or automaton) to parse strings. The automata associated with formal grammars differ in terms of the types of memory representation they use—a distinction that is cognitively highly relevant for processing and learning.24 Chomsky’s work on formal languages led to what has come to be known as the Chomsky Hierarchy,25 which differentiates various complexity classes of grammars. In its most well-known form, it encompasses four different types of formal grammars. A grammar in which all rules take the abstract forms of either A o b C or A o C b (not both!) and A o b is referred to as a regular grammar (sometimes also a finite-state grammar). Grammars of this complexity (type 3 in the Chomsky Hierarchy) correspond to a sequence model analogous to a flow-diagram. Relaxing the restrictions of regular 24. See Hauser, Chomsky, and Fitch, “The Faculty of Language: What is It, Who Has It, and How Did It Evolve?” (2002); Fitch, Hauser, and Chomsky, “The Evolution of the Language Faculty: Clarifications and Implications” (2005); Rohrmeier and Rebuschat, “Implicit Learning and Acquisition of Music” (2012); Rohrmeier et al., “Implicit Learning and Recursion” (2014). 25. Chomsky and Schützenberger, “The Algebraic Theory of Context Free Languages” (1963).

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grammars, rules of the more general form A o b1 b2 b3 … bn, in which each bi is either a terminal or a nonterminal, characterize context-free grammars (type 2 in the Chomsky Hierarchy). Such grammars famously have as one of their distinctive features the power to generate sequences with center-embedding, such as “seq1 – seq2 – continuation of seq1,” or “seq1 – seq2 – seq3 – continuation of seq2 – continuation of seq1” as the simplest examples. Such center-embedding structures cannot be expressed by regular grammars (or lower complexity subregular grammars). Grammars in which all rules are of the general form c A o b1 b2 b3 … bn (a nonterminal A rewrites to any sequence of terminals and nonterminals b1, b2, b3 … bn only when it occurs in the context of c; the left-hand side is not longer than the right-hand side) are referred to as context-sensitive grammars (type 1 in the Chomsky Hierarchy). They can model centerembedding recursion, cross-serial dependencies, and other varieties of complex structure. The set of unrestricted grammars has no restrictions on rewrite rules (type 0). The four types of grammar are ordered in terms of increasing complexity in such a way that a higher-order language contains as a subset all languages of lower complexity (e.g., due to its less restrictive rules, every context-free grammar includes the expressive power of regular grammars). The types of formal languages in increasing order of complexity are: regular languages (type 3), context-free languages (type 2), contextsensitive languages (type 1), and unrestricted languages (type 0). It is important to note that there are other types of formal models apart from the traditional Chomsky Hierarchy (e.g., subregular, multiple context-free, and mildly context-sensitive grammars) as well as Hidden Markov Models and Dynamic Bayesian Networks that have been employed in both linguistics26 and music theory27.

26. See, e.g., Clark, “An Introduction to Multiple Context Free Grammars for Linguists” (2014); Seki et al., “On Multiple Context-free Grammars” (1991); and Jäger and Rogers, “Formal Language Theory: Refining the Chomsky Hierarchy” (2012). Furthermore, it is important to note that the Chomsky Hierarchy does not represent the only way to characterize formal languages of different complexity. 27. There are ongoing debates over the type of complexity required for the characterization of music. Some theorists argue for context-free complexity: see Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983); Rohrmeier, “Towards a Generative Syntax of Tonal Harmony” (2011); Steedman, “A Generative Grammar for Jazz Chord Sequences” (1984) and “The Blues and the Abstract Truth” (1996). Other theorists argue for lower complexity: Temperley, “Composition, Perception, and Schenkerian Theory” (2011); Tymoczko, “Function Theories: A Statistical Approach” (2003). Still other theorists argue for higher mildly context-sensitive complexity: Katz and Pesetsky, “The Identity Thesis for Music and Language” (submitted draft). Note that it is crucial to bear in mind for this debate that, due to the fact that higher-order models by definition include lower complexity models, converging evidence of regular grammar structure in music cannot decide the debate, since the existence of one non-regular (context-free or context-sensitive) feature would obligate a requirement of higher grammatical complexity.

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II. Towards a grammatical model of the cadence 1. Dependency relations Following the music-theoretical consensus, we conceive of a cadence as a stagebased process. We understand cadential progressions not as a linear or (Markovian) forward process, in the manner of “B follows A,” “C follows B,”28 but instead propose to represent the logical structure through implicative dependencies: A prepares (= implies) B, B in turn implies C. This view is consistent with the one outlined in Rohrmeier’s Generative Syntax Model (GSM),29 according to which tonal language can to a large degree be expressed in terms of a series of nested implication-realization relationships.30 Accordingly, the hypothesized principles that motivate our tree analyses of cadences are twofold:31 (A) Two elements can have an implication-realization relationship. For example, the straightforward implications of tonal functions are: Dominants imply (or prepare) the tonic, predominants imply the dominant, embellishments imply their goal event (and only that event). (B) Two elements can establish a prolongational relationship: Two instances with the same tonal function can form a prolonged higher-order region or unit.

Cadential patterns involve a recursive, left-branching, and right-headed structure. The syntactic organization of cadential phenomena can be represented in tree structures that depict this type of implicative and prolongational relationships. The dependency structures that govern such syntactic trees may also be expressed in terms of a dependency graph (see Fig. 1).

28. See, e.g., the approaches by Temperley, “Composition, Perception, and Schenkerian Theory” (2011); Tymoczko, “Function Theories: A Statistical Approach” (2003); Tymoczko, A Geometry of Music (2011). 29. Rohrmeier, “Towards a Generative Syntax of Tonal Harmony” (2011). 30. The core difference between the present approach and a Markovian approach is that preparations and embellishments may be nested in multiple (hierarchical) ways, rather than being restricted to a linear order. 31. We assume that cadences are constituents in tonal phrases that may be modelled using the standard set of generative rules of Western tonality. In other words, cadences are nothing special in the sense that there are no special cadential rules. Rather, cadences are special constituents in which common tonal rules that hold for any other part of a given piece are applied in a particular configuration to achieve a powerful drive towards closure. While cadences may be conceptualized in terms of different stages (predominant, dominant, final tonic), these stages are neither structural parts of the music itself (they have no ontological status) nor of the grammatical model. These stages are reflected in the trees in terms of subordination relationships. Lerdahl proposes a similar view in Tonal Pitch Space (2001).

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Figure 1: An example of a syntactic parse tree and the corresponding dependency graph

The dependency graph visualizes all dependency relationships between the harmonies involved in the cadential process in terms of implication (imp) or prolongation (prl). The dependency structures as implied by the tree and visualized in the dependency graph are identical in the sense that one can easily be transformed into the other.32 Moreover, the syntax tree inherently represents the rewrite rules that were used to generate the structure; for instance, I o V I (second highest branch) or IV o V65/IV IV in the example given above. Every parent node in any branch of the tree or subtree corresponds to the left-hand side of a rewrite rule, and every immediate child of that node corresponds to the right-hand side of the rewrite rule. The syntax (or parse) tree expresses the structure generated by specific applications of rewrite rules to the nonterminals.

32. It is important to note that there are significant differences between dependency grammars and phrase-structure grammars, for instance, with regard to the notion of constituency (see also Kuhlmann, Dependency Structures and Lexicalized Grammars [2010]). The complex issues concerning the evaluation of the use of constituency in musical structures (cf. Rohrmeier, “Towards a Generative Syntax of Tonal Music” [2011]) will be considered in future work.

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2. Level of representation While the syntactic formalism and its complexity are independent of the building blocks involved, the right choice of the level of representation is crucial for the formalism’s expressive power, specificity, and generality. However, in the case of tonal music, the right choice of building blocks is not self-evident; prima facie, there are several candidates on which the syntactic model could be built: the bass line, harmony on scale degrees, harmony with inversion, functional harmony, outer voices, and full four-part blocks. To begin with, a model of the cadence (and of tonal music in general) grounded in the bass line alone is clearly insufficient. Consider, for instance, the following harmonization: 3–4–6–©4–5–1 :=: iii–vii°64–iv6–V/VII–iii6–vi6. This example illustrates the fact that there are possible harmonic realizations of a well-formed bass line that are clearly irregular in common-practice tonal language. Perhaps more importantly, the bass line cited above demonstrates that categorizing cadential events based only on the bass gives rise to representations of harmonically non-interchangeable events (e.g., i6, iii, vi64; IV, IV64/IV, vii°64, etc.). In other words, although a well-formed bass line is fundamental, crucial constraints stem from factors other than the bass line. Another approach, one based on the outer voices, is more constrained, since already two notes of a given harmony are specified. However, choosing outer voices as the building blocks is only useful when a difference in the top voice makes a categorical difference for the syntactic progression. Generally speaking, two chordal tones are still too unspecific (or ambiguous) with respect to the harmony they serve to express. Because the interchangeability of surface elements falling under the same building-block category is crucial for the choice of building blocks, it is necessary to consider a third approach here, namely modeling the harmonic structure.33 As powerful as such a fully generalized approach may be, a model based solely on harmony may result in irregular bass lines and hence be incapable of distinguishing cadential from non-cadential progressions.34 In opposition to an account of harmonic building blocks (as proposed by Keiler), Lerdahl and Jackendoff in their Generative Theory of Tonal Music (GTTM) argue that such harmonic syntax trees would not be able to (1) assign structure to non-harmonic tones or (2) account for Schenkerian interruption.35 This

33. Alan Keiler proposes an elegant generative syntax analysis based on scale degree harmony that expresses generalized musical structure in a manner that is formally more precise and efficient than the one put forth by the “Generative Theory of Tonal Music” (GTTM). See Keiler, “Bernstein’s ‘The Unanswered Question’ and the Problem of Musical Competence” (1978); Keiler, “Two Views of Musical Semiotics” (1981). 34. This discussion is based on the implicit assumption that the core structure has to be modelled within a single system. It may also be viable, however, to model harmonic structure and the bass line separately and relate the sequences by means of constraints or interfaces. 35. Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), 338 (n. 4).

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criticism appears to be misguided: First, a syntactic theory is indeed able to account for interruption. Second, including additional detail is only useful as long as it does not undermine the expressive power and compression by abstraction that is achieved by a generative grammar approach. Again, the question is whether it is worthwhile to enrich the representation to account for voice leading, outer voices, or full texture, despite the fact that this implies eliminating generalization over elements that should be grouped together because they are related in analogous ways. On the other hand, if the building blocks were full four-part harmony textures, it would be possible to distinguish a large number of different cases, but generalization, compression, and abstraction (all of which are the purpose of describing a structure by rules) would no longer be possible. For example, two instances of a ii6–V7 progression should be regarded as identical with respect to syntactic structure, regardless of whether or not the inner voices are exchanged. This aspect may lend itself to a critique of the level of representation chosen by the GTTM. Despite the problems of defining “the” musical “surface”36 by modeling at the note-level, Lerdahl and Jackendoff pay the price for giving up concrete generative rules37 and end up proposing a generative theory without any generative rules. Thus, their proposal is not, and cannot easily be amended to be, a theory of competence or of (tonal) syntax.38 Although models improve with increasing levels of detail, the generalizations drawn from these models may grow weaker. This makes it clear that generality is an important criterion with regard to the choice of building blocks. Functional categories provide a further tool for generalization, allowing us to subsume V7, V, vii° and ii, IV, (vi) under the same categories, and suggesting that categorial constituent heads be employed rather than encoding the bare dependency structure. To be sure, it is not immediately clear whether modeling cadences in terms of functional regions (such as tonic, dominant, and subdominant) is useful; however, if one intends to draw generalizations from categorization by functions, it is certainly possible to express the rules we are outlining here in terms of the functional regions used by the GSM.39 36. For various problems of defining and identifying the “musical surface,” see Cambouropoulos, “The Musical Surface” (2010). 37. Designing a model that generates the entire musical surface is very difficult and is equivalent to creating a generative model of the entire composition (which is unlikely to simultaneously be a good, cognitively adequate model of processing or listening). 38. The GTTM is a theory of parsing that excludes core processing aspects of parsers, such as the use of a stack, online backtracking, and revision. Rather than being a model of musical syntactic competence, GTTM turns out to provide an (incomplete) theory of performative aspects of musical parsing, whereas Keiler proposes a view of modeling tonal syntactic structure at the right level of abstraction. 39. A purely functional approach such as the one advocated by Riemann and his followers might prove insufficient here because it enforces the interchangeability of certain chords belonging to the same functional category, a restriction that our approach does not endorse. Rather, we would argue that there are certain limitations to the arbitrariness with which seemingly functionally equivalent chords can be used to replace one another. For instance, a ii6 chord has a stronger implication of moving to V than a IV chord, as the latter chord may also be used as a neighboring sonority and hence as a means

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Although we are entirely aware of the problem that arises from abstracting from voice-leading characteristics, we opt to concentrate almost exclusively on functional harmony in order to considerably reduce the complexity inherent in cadential patterns. For the reasons outlined in this section, we build our model on scale-degree harmonic representations, including inversions and some common features of voiceleading patterns.40 However, generally speaking, it is important to bear in mind that the chosen level of representation can never be perfect.41

3. The structure of the perfect authentic cadence 3.1. The head of the cadence constituent: The initial tonic, the final tonic, and its preparation (and extension)

Constituents feature a head element upon which the other parts of the constituent depend. The head of a cadence is the final tonic, which at the same time functions as the head of the entire overarching phrase. Furthermore, the tonic chords involved in the cadence are all connected in specific ways. The phrase-initiating tonic and the final tonic constitute the overarching head for the whole phrase, whereas the I(6) chord initiating the cadence may best be modelled as subordinate to the final tonic. Alternatively, the I(6) can be analyzed as preparatory with regard to the (adjacent) predominant chord over 4^. This would imply, however, that the I(6) could not appear without this chord over 4^, which is not necessarily the case: In fact, both elements can appear independently of one another (e.g., I6–V64–V7–I, ii6–V64–V7–I).42 Figure 2 illustrates both interpretive possibilities.

of prolonging a tonic harmony. ii6 and IV are more likely to occur in a cadential context than a rootposition ii chord, due to the fact that both share scale degree 4 in the bass. 40. It is important to note that the challenge in this musical modeling endeavor results from the fact that the formalism is fundamentally required to account for both adequate harmonic dependency relationships and a coherent bass line. This formal correspondence is far from trivial, since a coherent bass line involves certain linear aspects that run counter to harmonic hierarchical dependency relationships. Ultimately, this may require a specifically amended type of formalism. 41. As Temperley cogently argues, “[a]n immediate problem with this model is that its predictions do not always hold: sometimes predominants move to tonics, for example, as in a plagal cadence. Admittedly, such exceptions show that functional harmonic theory is imperfect as a model of tonal harmony; but they do not show that it is useless. A theory whose predictions hold true most of the time can still be of great value; we use such theories all the time in our daily lives. Imperfect though it may be, functional harmonic theory represents a powerful and valid generalization about tonal harmony, better than many conceivable alternatives—for example, a theory that posited that chords are chosen at random without regard for the previous chord, or that predominants move to tonics and dominants move to predominants. On this basis, I would argue, we are justified in positing functional harmony as part of the knowledge that common-practice composers brought to bear in their compositional process” (Temperley, “Composition, Perception, and Schenkerian Theory” [2011], 148). 42. Another way of resolving this problem is to derive the I6 chord in both ways when it precedes a 4^ and to analyze it in terms of a double function. Cf. double functions of pivot elements in the GSM; Rohrmeier, “Towards a Generative Syntax of Tonal Harmony” (2011).

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Figure 2: The tonic frame. The cadence is marked by the box. The overarching frame of the cadence constituent is headed by the tonic (I), which in turn merges with the phraseinitiating tonic to constitute the overarching head of the phrase. The I(6) chord that initiates the cadence could either be modelled as subordinate to the final tonic or to the predominant function.

With regard to the first solution (I(6) subordinate to the final tonic), the following rules establish the tonic frame (bear in mind that the rules are represented as branches in the tree diagram): (1) I o I(6) I (2) I o V I

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These rules define both the head of the entire cadential constituent and the tonic seed.43 In this abstract form, rules (1) and (2) hold for both major and minor modes. It is important to note that we construct our syntactic model of the cadence largely independent of mode. Most rules and generalizations apply to both modes, and most diatonic scale degrees can be employed with the respective mode-specific adaptations. Rule (1) generates the final tonic as well as the initial I(6) chord and, in so doing, defines the overarching link between the I(6) and the final tonic. Note that the cadenceinitiating I(6) chord is optional and not necessary for the formation of a cadence constituent. As for the final tonic, a perfect authentic cadence requires that tonic to appear in root position, whereas an evaded cadence typically (but not exclusively) uses I6.44 The way in which the final tonic is realized in terms of voice leading and grouping defines in part the type of cadence (PAC, IAC, or deceptive/evaded cadence). Crucially, this implies that part of the cadential structure is not definable purely by syntactic tree structure (using harmonic building blocks). The penultimate dominant (V(7)) is necessary for the structure to be a cadence. This is expressed by rule (2). If there were no dominant, a given phrase might be regular in the sense of being in accordance with the rules of tonal harmony, but it would not be considered a cadence. For instance, a dominant harmony cannot be replaced by a diminished (seventh) chord (vii°(7)) on 7^ without the progression losing its cadential capacity. In other words, if the root of a V chord is missing, the resulting harmony cannot express a genuine cadence.45 Within the tonic frame, rule (2) defines the seed for the dominant group and its further recursive elaborations. It should be clear that, in a cadential context, there are naturally no options other than the dominant to immediately precede (and be subordinate to) the final tonic.46 In other words, rule (2) alone demands, and is sufficient to ensure, that the dominant is string-adjacent to I. 3.1.1 The plagal progression as a means of tonic prolongation Opposing a widespread view, we follow the assertion of Caplin and other theorists that plagal progressions (IV–I) do not act as genuine cadences in the classical style. Rather, they are better understood as post-cadential codettas, serving to prolong and consolidate a preceding cadential tonic (e.g., I–IV–I).47 In other words, by the time the 43. Our general analysis (see Fig. 2) is similar to the normative prolongational structure proposed in the GTTM; it differs, however, with respect to the intent to avoid right-branching derivations. 44. Methods of modeling cadences that avoid tonic closure are discussed below. 45. One exception may be the Prinner cadence (IV–I6–ii7–vii°6–I or IV–I6–vii°(7–6)–I), which, however, might also be described as projecting a prolongational progression in Caplin’s sense. See the discussion in Caplin’s contribution to this volume. 46. Compare the formalization by Rohrmeier, “Towards a Generative Syntax of Tonal Harmony” (2011). 47. See Aldwell and Schachter, Harmony and Voice Leading (2003), 193; Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), 134; Caplin, Classical Form (1998), 43; and Caplin, “Conceptions and

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plagal progression enters in a given piece, a sense of closure has already been imparted to the listener by means of an authentic cadential progression. This view underpins the approach employed by the GSM, which does not treat the plagal cadence as a strong constituent at a functional level, but rather as a mere appendix at the surface level.48 However, this interpretation is not meant to preclude the possibility that plagal progressions functioned as cadences in historical periods prior to the “classical” era (e.g., the Amen cadence in a Baroque composition) or in contemporary popular music.49 3.2. Preparing the preparation (of the preparation of the preparation)

Having discussed the tonic frame and its corresponding dominant seed, we now consider the remaining elements of the cadence, which essentially function as preparations of V and as potential recursive preparations of such preparations. We distinguish between generalizable and non-generalizable preparations, i.e., those generalizing across different harmonies and those that apply only to specific harmonies. 3.2.1. Preparations of the dominant Non-generalizable preparations of the dominant include versions of IV (IV, IV6), ii (ii, ii43, ii64, ii6, ii6(5)), vi, V64, and N6. Each of these preparations may be modelled using a rule in the following form: (3) V o V-Prep V

One example would be V o ii6(5) V. There are as many specific V-preparation rules as there are chords that can prepare a cadential dominant. These rules are largely identical for major and minor modes (potentially adapted to match the diatonic counterpart, e.g., ii° instead of ii, iv instead of IV). Note that the chords involved in these rules imply specific bass notes: ii implies 2^; ii6(5), IV, and N6 imply 4^; IV6, ii43, ii64, and vi imply 6^. On the surface, V may be realized as either V or V7, or as a combination of the two. Some dominant preparations, in particular the Neapolitan chord and the various augmented sixth chords on ¨6 (see below) hint at the minor mode. 3.2.2. Embellishing the dominant Let us now briefly consider the cadential 64 as the primary means of embellishing the penultimate dominant. After having reached a dominant 64 in the context of a cadential progression, the most frequently used option is to resolve the double-suspension to a V53 (or V7) chord. However, the composer may alternatively choose to add chords at the expected point of resolution that are normally used to lead to (or prepare) the

Misconceptions” (2004), 71f. 48. See Rohrmeier, “Towards a Generative Syntax of Tonal Harmony” (2011). 49. See also the discussion in De Clercq and Temperley, “A Corpus Analysis of Rock Harmony” (2011).

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cadential 64, namely either vii°7/V, vii°6/V, or a German augmented sixth chord, as though stepping backwards in time within the multi-stage process. Consequently, these chords cannot be understood as mere insertions between a cadential 64 and its resolution, but may instead be analyzed as a means of embellishing (and thus, in a way, prolonging) the cadential 64 itself. In other words, they seem to act as a means of embellishing the embellishment. Two examples from Mozart’s oeuvre can be cited in support of this interpretation. Towards the end of the reprise in the first movement of his D-major Piano Sonata, K. 576 (see Figure 3), Mozart launches a normative cadential progression, starting with a tonic harmony in m. 148, proceeding to a ii6 (m. 149), and finally arriving at a cadential 64, which is extended for two measures (mm. 151f.). At the moment one expects the resolution of the 64 suspension, a fully diminished seventh chord suddenly enters, likewise sustained for two measures. But rather than entirely abandon the attempt to complete the cadence, the progression reverts to the cadential 64 (m. 154), this time resolving the suspension properly, ultimately arriving at the final tonic (m. 155).

            

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

Figure 3: Mozart, Piano Sonata in D major, K. 576/i, mm. 148–155

In Mozart’s F-major Piano Sonata, K. 533/i, the exposition is about to close with a PAC but avoids closure by means of a deceptive harmony (vii°6/V) at the progression’s ultimate stage (m. 82), the cadential resolution being delayed until m. 89. However, before the cadential 64 is resolved, it is prolonged by various embellishing chords, including vii°7/V (m. 84) and an augmented German sixth (m. 86), both of which subsequently return to the cadential 64, which ultimately gives way to a root-position V in m. 88. This suggests that chords that are normally employed to prolong a predominant harmony, connecting it to the cadential dominant, can also be used (even within the same temporal sequence) to extend in time a particular dominant embellishment, namely the cadential 64.

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Figure 4: Mozart, Piano Sonata in F major, K. 533/i, mm. 80–89

Alternatively, the situation described in the two Mozart sonatas may also be interpreted as a form of dominant prolongation. This would help avoid an increase in complexity resulting from additional rules. In addition, it would explain the fact that both of the embellishing chords (vii°7/V and the augmented sixth chord) can easily be followed by a plain dominant sonority. The fact that another cadential 64 is inserted, thus framing the appearance of these embellishing chords, might simply be regarded as a coincidental surface event, one that lacks any deeper-level structural significance. 3.2.3. Predominant preparations There are several non-generalizable preparations for different predominant chords. (4) IV o iii IV (5) ii6 o vi ii6 (6) vi o iii(6) vi

Rule (4) expresses the somewhat less frequent case in which IV is prepared by iii in the major mode. Rules (5) and (6) express diatonic fifth relationships that apply in the context of both major and minor modes (given diatonic adaptations of the respective harmonies). 3.2.4. General preparations: Applied dominants Several preparations of dominants, predominants, and other chords appearing in a cadential context result from the general flexibility with regard to preparing chords

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with applied implicative chords. Analogous to the formalization of dominant preparations, all the general preparations discussed here follow the same abstract rule pattern (note the similarity to the general rule (3) above): (7) X o X-Prep X

In this context, V6(5) and vii°(7) may function as chord preparations from a semitone below (for instance, in a rule such as X o V6(5)/X X). Ger6, Fr6, It6, and V42/X6 can function as preparations from a semitone above, and V/X as a preparation from a fourth below. In particular, chords on IV and ii are often approached via their own secondary dominants (either V6(5) or vii°(7)).50 IV6 may be prepared by its applied V42. Specifically, the cadence-initiating tonic (I or I6) may also be embellished from above by an applied dominant (e.g., V43, V42, vii°6). Augmented sixth chords on ¨6^ constitute a common way to prepare the dominant in minor cadences. It is important to note that it is possible (although rare) for some of these preparatory embellishments to themselves be recursively embellished—for instance, a prepared Neapolitan, as found in Mozart’s Piano Concerto in D minor, K. 466 (mm. 347f.; see the discussion below). However, this list of embellishments is not exhaustive, as further examples may be discovered (e.g., the harmonically flexible diminished chord and its variants). Further note that for the sake of simplicity, this list of rules does not imply an explicit ranking of different preparations with respect to their order.51 3.2.5. Sample analysis A sample analysis will illustrate the formalism of the cadential structure developed in the previous sections (see Fig. 5). This example shows that the multiple predominants are characterized by the fact that they are all dependent on V. For instance, there is no rule that vii°7/V may follow ii6; rather, both chords are dependent on V. Further, it is important to note that V65/IV (or vii°/IV) is very similar to I6, yet it fulfills a different function: Instead of serving as an initial tonic, it acts as the subordinate applied dominant preparation of IV (compare the discussion above regarding the tonic frame). Note that this tree diagram (like all syntax trees) contains all rules that were applied to generate or parse the tree structure. From the top, some of the rules involved are I o I I, I o V I, V o IV V, IV o V65/IV IV, etc. The tree represents the (atemporal) dependency relationships between the elements and does not have direct implications regarding the order of rule applications when generating or parsing such a sequence.

50. Note that in Caplin’s theory, V65/IV is considered an initial tonic embellishment, rather than a predominant embellishment; see Caplin, Classical Form (1998), 29. 51. Such an encoding could be achieved by using different symbols for V that represent different stages of preparations (such that preparations on 4^ would precede preparations on ©4^).

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Figure 5: Analysis of an elaborated PAC with the sequence I–V65/IV–IV(5–6)–ii6–vii°7/V–V64–V7–I

3.3. The order of dominant and predominant embellishments

There is considerable variety in the ways in which dominants and predominants may be prepared in a cadential environment. It is by no means a simple task to define the specific constraints governing the temporal order of these elements, as there is a remarkable combinatorial power inherent in cadences and their underlying syntax. However, it is possible to state several general constraints. First, predominant and dominant elements establish their own order in straightforward ways: One or more dominants may be used to prepare the tonic; none, one, or more diatonic predominant elements may precede each dominant. Within diatonic predominants, IV (when present) usually precedes ii or ii6, whereas the order that chords over 6^ take is more flexible. Second, within this diatonic frame, chromatic embellishments may enter the cadential pattern, creating additional implications. For instance, embellishing chords on ©4^ (such as V65/V or vii°7/V) may be inserted between 4^ and 5^. The same holds for embellishing chords on (¨)6^ (either V43/V or vii°6/V) or ¨6^ in minor mode (e.g., Ger6). Both of these elements— chords based on ©4^ and on 6^—may be present, the order being interchangeable. Once scale degree 5^ is reached, a cadential V64 may be introduced to delay the entrance of V(7). These rules indirectly control the sequential order of the cadential constituents. The table below summarizes the different components that affect the order of the elements involved. In this context, it is important to bear in mind, as mentioned above, that the difficulties arising from the attempt to bring cadential elements into a linear order stem from the fact that two structures, linearity in the bass line and hierarchical harmonic dependency, are closely linked, and linear order is sought where the structure arises from hierarchical organization. Note that because the generation process

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is recursive, a number of complex chord progressions can be generated as a result of coordination and recursive expansion (see Section 5.1 below). Table 1: Overview of the order of different dominant embellishments and dominant or predominant preparations

V64, V54

Dominant embellishments Order of dominant preparations Order of predominant preparations

diatonic

ii6(5), IV, ii, IV6, VI, ii43, ii64

other

V/V, V/V6(5), vii°/V(7), Ger6/V, It6/V, Fr6/V, N6

diatonic

IV: I, iii, V6(5)/IV, I6, vii°6/IV ii(6): vi, V42/ii, vii°6/ii vi: iii(6)

other

X: V/X, V6(5)/X, vii°(7)/X, Ger6/X, It6/X, Fr6/X, N6/X, V42/X6

4. Ways of avoiding (perfect) cadential closure In the history of music, composers have used numerous devices to play with the strong patterns of expectancy conveyed by the cadence, manipulating them by means of delaying, replacing, or omitting the final tonic. Naturally, these cases are far more difficult to systematize than authentic cadential closure, since breaking an established formulaic structure is a creative act that is open to all kinds of possibilities. Nonetheless, there are some underlying syntactic structures common to all of these cases, in particular the usage of operations such as replacement, coordination, and elision, all elements known from linguistics. 4.1. The imperfect authentic cadence

The so-called “imperfect authentic cadence” (IAC) does not differ from the PAC in terms of its syntactic parse or its harmonic structure; rather, it differs with respect to voice leading. An IAC is generated such that the final tonic does not support the first scale degree in the soprano (as is the case with a PAC), but rather scale degree 3^, which may represent the genuine goal of a descending linear motion, as is the case with the Prinner cadence (see the example given in Fig. 6).52 A sense of closure is imparted to the listener because the final chord is a tonic (a fact also reflected in the tree); only the voice-leading treatment weakens the sense of closure. For this reason, a purely harmonic interpretation may prove insufficient for a proper char-

52. See Caplin in this volume.

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acterization of the IAC, as it does not include the treatment of the upper voice—the very criterion that sets the IAC apart from the PAC. Although this difference is not reflected in the tree at the chosen level of representation, it informs the interface between the syntactic dependency, constituency structure, and voice leading and thus disambiguates the parsing process. Allegro moderato       :  :  :      :    :   :      :   : mf  p  :                  

Figure 6: Cadential closure reached by a Prinner cadence, see Haydn, Keyboard Sonata in D major, Hob. XVI:14/i, mm. 1–4

While in some situations, scale degree 3^ may indeed be the proper melodic goal, in other situations perfect cadential closure is purposefully avoided by disappointing the expected voice-leading motion: Rather than completing the melodic line by moving down to 1^ (as shown in (a)), this pattern is interrupted, leading back to 3^ (potentially with a ©2 preparation, as shown in (b)) and thus creating a deceptive effect. (a) 5–4–3–2–1 (b) 5–4–3–2–[©2]–3

This structure ensures that the phrase context remains open and implies further continuation. In other words, the imperfect authentic cadence may trigger a subsequent phrase structure (most typically by using a “one-more-time” strategy53) upon which the preceding phrase is syntactically dependent. In this case, it is advantageous to model the syntactic structure of the overarching phrase structure in terms of a recursively embedded phrase that is inserted between the tonic (supporting 1^) bringing about perfect cadential closure and the original V (supporting 2^). The following example by Mozart illustrates this (see Figure 7).

53. Schmalfeldt, “Cadential Processes” (1992).

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            



    

   



     

 

         

   



   





                          

   f



 

 

  

 

 

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  





  

 sf

 

   

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

  

                          f p                   p

                           f



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            

 

     

 

 

    

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sf

 

 

  



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309

vii /vi

vii64 vii7 /vi

vi

vii64

IV

I

I

V7

vi

V

vi

I

ii6

V

V

I

I

IV

I

I

I

V7

vi

V

ii

6

ii

6

V

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V64

V

V

iii

vi

I

ii6

vi

ii6

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iii

vi

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7

vi

ii6

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ii6

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V64

V

I

V

I

I context

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Figure 7: Mozart, Piano Sonata in F major, K. 332/i, mm. 71–93. IAC as a deferral of perfect authentic closure through the recursive embedding of another phrase. This structure is combined with a one-more-time pattern.

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4.2. The half cadence

4.2.1. Distinctive features of half cadences Half cadences are often described as incomplete forms of authentic cadences, lacking the final tonic and hence the necessary requirement for an authentic cadence. However, half cadences also seem to be special in the way they function. Several contextual features distinguish half cadences from authentic cadences. Some of these features help to weaken the tonic-implications of the dominant, stabilizing the latter in such a way that the degree of closure conveyed by a given phrase is partial rather than perfect. One of these features concerns the surface realization of the dominant: Whereas authentic cadences often use V7 to approach the final tonic, a dissonant V chord has been regarded as irregular when it functions as the final moment in a half cadence.54 However, Poundie Burstein argues that half cadences can likewise end on a V7 sonority, a notion previously rejected by theorists, as this chord had been considered too unstable a harmony to act as a true (local) goal.55 In addition, half cadences seem to make occasional use of a dominant sonority in first inversion (e.g., Mozart, Piano Sonata in C major, K. 309/i, mm. 106–108), an option that is irregular in the context of authentic cadences. Irrespective of these distinctions, it is important to note that a (phrase-initiating) I immediately following the halfcadential V is merely a coincidental surface adjacency resulting from the juxtaposition of two phrases, rather than a structural V–I relation. Another difference between half and authentic cadences is derived from metrical criteria: Whereas the concluding V in a half cadence typically arrives on a strong beat, in an authentic cadence, V more frequently occurs on a relatively weak beat. This suffices to make it clear that the generation of half cadences also differs from the generation of authentic cadences in the ways non-harmonic factors are affected. This concerns in particular factors that help determine grouping boundaries (such as pitch proximity, rests, articulation, texture, register, dynamics, and relative lengthening, factors that have been formalized in the grouping preference rules 2 and 3 in the GTTM). The generation of such grouping boundaries, in conjunction with the cadence type, strongly contributes to the recognition of the half cadence in the reverse-engineering (i.e., parsing/listening) process, since the mere harmonic structure generated by the syntactic core can frequently result in ambiguities that may, e.g., arise from an unrelated phrase-initiating tonic following a half-cadential dominant.56

54. See Burstein in this volume. 55. Ibid. 56. Lerdahl and Jackendoff note: “If a grouping boundary intervenes between the two chords, the V does not resolve into the I; instead the V ends a group and is heard as a half cadence, and the I is heard as launching a new phrase. Metrical structure alone cannot account for these discriminations, precisely

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Grouping boundaries are an essential factor in disambiguating parses that would be ambiguous based on the harmonic structure alone, and they make it possible to determine whether the surface has been generated by the underlying form (phrase type) of a half cadence or an authentic cadence. In cases in which harmonies other than the tonic follow a half cadence, such ambiguities are clearly avoided, reinforcing the half cadence parse. Half cadences and authentic cadences might also differ statistically from each other with respect to both the functional sonorities used as predominants and the bassline. Phrygian half cadences often approach their goal by a descending bass melody, unlike the majority of authentic cadences. Furthermore, in authentic cadences, it is generally rare to have a 6–5 tenor clausula in the bass before arriving at the final tonic (e.g., Beethoven, Piano Sonata op. 7/ii, mm. 22–24). Consequently, authentic cadences seldom use an augmented-sixth chord as a predominant (they may rarely use this chord prior to a V64), whereas this is the defining feature of a Phrygian half cadence. In half cadences, by contrast, the final dominant is frequently approached by a 6–5 motion in the bass. For instance, the half-cadential progression over a (¨)6–5 line in the bass (clausula tenorizans) can best be understood as achieving a sense of local stability with the arrival on V. This V represents a genuine goal harmony, rather than interrupting an authentic cadential progression. 4.2.2. Revisiting the syntax of the half cadence: Where on earth is the missing tonic? The points outlined above highlight the fact that there are striking differences between half cadences and authentic cadences in terms of stability, metrical structure, and voice leading, all features that help disambiguate grouping structure. Notably, in all forms of half cadences, the chord progression lacks a tonic implied by V within the confines of the phrase. One challenge for a generative approach is to explain how to reconcile the missing tonic with the core of the cadential tonic frame. The reason why the missing tonic creates a problem for the generative approach is that the dominant can only be generated with reference to its implied tonic (or as the goal of a tonicization), otherwise it would be “left hanging” in empty space, violating the dependency principle. One core test for the investigation of the syntactic structure of the missing tonic consists of tonic completion: It is possible for almost all types of half cadences to transform their harmonic sequence into an authentic cadence by adding the missing tonic and by adjusting nonsyntactic parameters such as the meter, rhythm, melody, and other features that are affected by the syntactic structure when generating the surface. The example of Mozart’s Piano Sonata in A major, K. 331 (see Figure 9, below), may serve as a useful illustration of a composed version of such a tonic because it has no inherent grouping. Both components are needed” (Lerdahl and Jackendoff, A Generative Theory of Tonal Music [1983], 29).

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completion test. The fact that tonic completion is possible in a large number of cases motivates solutions that explain half cadences in terms of manipulated authentic cadential progressions. Such solutions are likely to end up being more parsimonious than transformation-free approaches because they avoid adding inelegant rules that generate V as the stable, reference-free end of a phrase and might interfere in problematic ways in non-cadential contexts. The fact that there are some forms of half cadences (such as Phrygian half cadences or simple half cadences such as V65– I–V) that cannot easily be completed (or transformed) in such a way could suggest that there may be additional factors determining the type of half cadence. However, this does not necessarily diminish the general power of our proposed analysis or the usefulness of the completion test for a significant number of cases. Overall, there are several options for dealing with the problem of the missing tonic: (a) proposing a different tree analysis in which V is not subordinated to the final I (but instead, for instance, to the initial tonic; see Fig. 8a), (b) using an empty (hidden) element of a I that is present in the analysis but does appear on the musical surface (see Fig. 8b), (c) modeling V as dependent on the final I of the subsequent phrase context (see Fig. 8c), and (d) assuming that the I upon which V depends was moved away, either to an earlier or a later position (see Fig. 8d). Options (c) and (d) are similar; one of the main differences is that (d) maintains the parallelism and coordination between the two analogous phrases, whereas (c) models the second phrase as subordinate to the first phrase at the final tonic position.

Figure 8a: Departure analysis of V as subordinate to the preceding I (tonic departure). The GTTM prefers this analysis. This solution models the V as not having any implications of the phrase-final I.

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Figure 8b: Empty element analysis. The tonic I first generates V and is then rendered empty. The epsilon symbol represents the empty element.

Figure 8c: Subordination analysis of the half cadence. The consequent (or one-more-time) phrase is subordinate to the antecedent phrase, and the final tonic of the consequent phrase terminates the tonic implication of the V of the initial half cadence. Note that because the initial and final tonic nodes of the consequent phrase are joined at a higher level, both the string-adjacent and the sequence-final tonic relate to the open V of the half cadence. This analysis models the open structure of the underlying (Schenkerian) interruption as well as its continuity.

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Figure 8d: Movement analysis of the half cadence. This analysis is similar to 6b (empty element) and 6c (subordination). In contrast to the previous analyses, however, both the antecedent and consequent phrases are arranged in a paratactic (not hypotactic) way. The tonic implication regarding the phrase-final tonic is achieved through a rightwards movement operation: Beginning from a perfect cadence in the antecedent phrase, the final tonic I is moved to the right and merged with the tonic seed of the consequent phrase. In this way, the analysis manages to retain the paratactic order of both sequences while still maintaining the implication of the half cadence to the final V.57

It is important to bear in mind that previous syntactic approaches have faced considerable difficulties in making sense of the half cadence, which may perhaps best be exemplified by Lerdahl and Jackendoff’s account (analogous to the option depicted in Figure 8a): In order to explain the counterintuitive result that the phrase-concluding V is subordinate to the preceding tonic in their prolongational reduction, the authors propose to think of “cadences as signs, or conventional formulas, that mark and articulate the ends of groups from phrase levels to the most global levels of musical structure.”58 Rather than invoking the heavy baggage of a concept that is external to one’s theory, such as the semiotic notion of a musical sign, the present approach addresses the issue of cadence with the help of syntactic methods only. The final analysis, depicted in Figure 8d, involves a structure that expresses a dependency relationship between the two tonic elements that exceeds what 57. It is important to note that this movement operation cannot be achieved by means of a contextfree grammar (i.e., a tree-structured analysis); it requires a more complex mildly context-sensitive grammar that in turn entails remarkably greater complexity in terms of parsing, processing, and learning the grammatical structure. 58. Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), 134.

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a context-free grammar is capable of expressing. While there are historical precedents,59 the analysis of the half cadence constitutes a promising candidate for analogies with complex syntactic structure in linguistics.60 The open dominant at the end of the first phrase may be analyzed such that the final tonic node of the first phrase is associated with the final tonic of the second (or final) phrase. This can be understood as the first tonic “moving” to the end of the second phrase or the first dominant selecting the final tonic of the second phrase. The final tonic of the first authentic cadence form is not moved to a position before the V but rather to the end of the following phrase, forming the overarching structural head for both phrases (for instance, within the antecedent-consequent structure of a period). Thus, the second analysis emphasizes the view that the V of the half cadence may be locally stable (despite the lack of a directly adjacent tonic and without any immediate need for resolution), yet in an overarching hierarchical context, it is closely linked to the higher-order superordinate tonic. This view is also reflected in the Schenkerian concept of interruption: As Cadwallader and Gagné note, the I immediately following a half cadence may not necessarily be regarded as providing a moment of tonic closure.61 According to a Schenkerian analysis, periods are viewed as a bipartite structure resulting from an interrupted (or divided) structural motion from the primary note (3, 5, or 8) to the first scale degree. Since the first attempt at completing the fundamental line fails because of the interruption on 2^ (supported by V), this motivates a repetition of the

59. One historical example of an explanation by transformation accounts for the half cadence by means of a V–I inversion thus: x V I o x I V. This analysis makes use of an operation that reverses the sequence V–I from an authentic cadence to I–V. This view is found in Koch’s Handbuch bey dem Studium der Harmonie, in which the half cadence is regarded as the inverted form of the authentic cadence in harmonic as well as metrical terms: “With regard to the underlying harmony, the original form of the half cadence is the reversed form of the Kadenz [authentic cadence], that is, in the half cadence, the tonic triad precedes the dominant triad on a weak beat [...]” (Koch, Handbuch [1811], 378 [our translation]). Today, this explanation is commonly considered incorrect, and the argument can be countered in the following way: Half-cadential subtypes such as the converging or the Phrygian half cadences do not feature a tonic preceding the concluding dominant sonority. In these progressions that feature a I at their very beginning, this I is structurally identical to those found at the beginning of authentic cadences. Accordingly, there are cases in which there are no positions where the I could move if it were required to move towards the left. Hence, the reversal explanation is only partial and requires another significant addition to the formalism to explain other variants of the half cadence (that may ultimately render this form of reversal unnecessary). If one assumed a combination of reversal and empty element (i.e., moving to an empty element position), this solution would be inelegant because the empty element could be directly positioned after the V without requiring any movement at all. 60. At present, it remains an open question whether or not forms of transformations and movements known from linguistics occur in music or are meaningfully necessary in music analysis. For a discussion of cadential V–I locality as another potential phenomenon requiring movement, see Katz and Pesetsky, “The Identity Thesis for Language and Music” (submitted manuscript). 61. Cadwallader and Gagné, Analysis of Tonal Music (2011), 119f.

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whole phrase,62 this time completing the line by moving further to 1^/I: I–V || I–V–I. According to the Schenkerian interpretation, the half cadential V is a higher-order event that remains active across the phrase boundary between antecedent and consequent, aiming at the theme-concluding tonic. However, the structural dominant that resolves the tension is that of the consequent phrase, not the half-cadential V concluding the antecedent.63 In this respect, there is an important structural similarity between the half cadence and the deceptive (or evaded) cadence, both of which imply the use a one-more-time technique. From a syntactic perspective, the analysis of interruption outlined in Fig. 8d may be regarded as analogous to the linguistic phenomenon of right node raising as seen in the following example: Mary likes ___ and John hates tomatoes.

In brief, the two verbs “likes” and “hates” can be analyzed as being coordinated and jointly selecting the noun “tomatoes.” Alternatively, one may wish to employ the concept of rightward across-the-board movement, analyzing the noun “tomato” as having been moved to the end of the sentence.64 Which of the pre-existing linguistic approaches (e.g., rightward across-the-board movement or type-raising, as is typical in categorial grammar65) the musical analysis adopts need not concern us at this (early) stage in building a syntactic theory of the cadence. What matters is that the movement analysis outlined above indeed proposes a structure that is capable of reflecting the unrealized forward implication of the interruption, the sense of local completion, and the parallelism and paratactic arrangement of the two phrases. This movement-based solution must be compared to other possible accounts that do not use movement. First, an empty element solution (lacking the first tonic; see Fig. 8b) cannot explain the open implication of an interruption and hence the syntactic motivation for the second phrase. It would further predict that phrases in general could end on a missing empty tonic, which is problematic in cases in which there must be a final tonic (e.g., phrases that conclude entire sections or pieces). Second, a solution in which V is dependent on the initial tonic (see Fig. 8a), as proposed by the GTTM, faces the same problem as the empty element solution and is inconsistent with the interpretation of the trees and strong generativity (V as a forward implication to a final tonic, not as a departure from the initial tonic), as well as the other rules for V (it would require a specific rule on its own). Third, a solution such as that proposed

62. Note that the present syntactic formalism does not enforce the parallelism that both phrases are built identically. 63. Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), 140. 64. Across-the-board movement constitutes a problematic example in generative linguistics, since one of the core tenets requires movement to be only left-directed (i.e., against the direction of speech). 65. See Steedman, The Syntactic Process (2000).

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by Fig. 8c is consistent with the unrealized V-implication and the one-more-time pattern. The only issue is that the two phrases are not paratactic, but instead hypotactically arranged. It is clearly possible to model interruptions in this way.66 One final problem with considering the half cadence as an instance of movement is that the dissonant V7 chord very rarely (if at all) occurs in half cadences, whereas it frequently occurs in perfect cadences (see above). Pure movement of the tonic to a different position may not account for this phenomenon, and this may mean that only the late surface realization of the subsequent tonic in fact licenses the appearance of the seventh in the subsequent generation process. Overall, whether the lack of paratactic analogous phrase structure truly necessitates the introduction of a new syntactic mechanism that massively increases the formal complexity of the syntactic mechanism (beyond context-free) is unclear and remains questionable. Future research may shed more light on this point. Nonetheless, two syntactic mechanisms manage to account for interruption, which is impossible under Lerdahl and Jackendoff’s system, even in their analysis of Schenkerian interruption. An excerpt from Mozart’s A-major Piano Sonata, K. 331 (see Fig. 9), illustrates the above point, showing that it is possible to model interruption with the help of a syntactic approach. Andante grazioso    :      :                     p                   :  :        :  

   :    :              :  :

                  

     ::     

sf

p

     ::  

66. This has been previously proposed by Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), and Rohrmeier, “Towards a Generative Syntax of Tonal Harmony” (2011), and employed in Koelsch et al., “Processing of Hierarchical Syntactic Structure in Music” (2013).

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I

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tonic context

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V64

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Figure 9: Analysis of the theme (mm. 1–8) from Mozart’s Piano Sonata in A major, K. 331, using the movement analysis of half cadences

4.3. The deceptive cadence as coordination and recursive embedding

The deceptive cadence constitutes a more radical way of avoiding cadential closure than the half cadence.67 Rather than leaving the V-implication unrealized and establishing the V chord as the ultimate goal, the deceptive cadence builds up a “normal” cadential framework, one that raises but ultimately frustrates strong tonic expectations by introducing a non-tonic chord (or a first-inversion tonic) at the final stage of the cadential progression. In the classical style, a variety of non-tonic chords have been employed to break the expected pattern. Some of these chords may be viewed as acting as tonic replacements (such as vi or ¨VI), others less so (e.g., vii°6/V or viio7/vi). The latter situation can be illustrated by the following two examples: (a) I–viio6–viio/IV–IV–iv–V–It6–V64–V–viio7/vi–vi (b) I6–IV–V64–V7–viio7/vi–vi

In both (a) and (b), a strong cadential context sets up a drive towards I that is (temporarily) suspended by vii°7/vi, which itself leads to vi (thus acting as an embellishment of the submediant). While music theorists have primarily devoted attention to the local surprise effect conveyed by the deceptive cadence, linguistically minded attempts at modeling the syntactic structure of the deceptive cadence must take the overarching phrase context into account. If we understand the vi chord as a tonic substitute, as has often been proposed in the literature,68 the tree structure of the cadence would be almost 67. See also Neuwirth in this volume. 68. Aldwell and Schachter, Harmony and Voice Leading (2003), 197; Caplin, Classical Form (1998), 25.

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the same as for an authentic cadence: The tonic head that governs the entire phrase would be rewritten as a tonic replacement with the unary rule “I o vi” after the V chord is derived (maintaining that V does not prepare vi, but rather I). The tree resulting from this interpretation would suggest a structure that is completely closed at the moment of arrival on the tonic replacement. While this reading may be adequate for some cases (especially in which there is a sense of redirected closure), in many cases the overarching phrase context is different: The deceptive tonic replacement vi does not act as a completion of the preceding phrase, although it may convey a local sense of rest; instead, it functions as the setup to a subsequent phrase that promises cadential closure. Often this second attempt at closure is a repetition of the previous phrase, in the manner of a one-more-time pattern. This yields a different interpretation of the syntactic structure: Rather than being a tonic replacement, the non-tonic chord at the end of the deceptive cadence functions as a preparation of another harmonic sequence that finally leads to the previously suspended tonic. Expressed in formal terms, the deceptive cadence effects the recursive embedding of another, longer phrase into a cadential context. Therefore, the deceptive chord itself represents a far left-branching subordinate dependency of a second final tonic phrase. This understanding further predicts that other chords (or almost any chord) may occur in a deceptive cadential context, or more precisely: Any chord that occurs in the left-hand corner of a V constituent may function as a deceptive sonority. The following examples illustrate this point as well as the empirical occurrence of the predicted flexibility. The first example is by Haydn (see Fig. 10) and exemplifies several quite complex aspects: (c) vii°6/V–V7–I7 == V7/IV–IV–I6–ii6–V–vii°6/V–V7–I7 == V7/IV–IV–I6–ii6–V–I– I6–ii6–I6–ii6–V–I

This example combines the avoidance of cadential closure through deceptive strategies with several nested one-more-time patterns. What is remarkable about this excerpt is that cadential closure is denied no fewer than three times, with each deceptive cadence followed by a further attempt at a complete cadence. The first cadential progression replaces the expected tonic not by a stable submediant sonority, but by a much more active secondary dominant function, vii°6/V. The deceptive harmony sets up an expectation for another attempt at completing the cadence.69 This expectation is indeed fulfilled: A second cadential goal is approached in mm. 47–48. Here, again, the soprano carries out its expected, typical concluding formula (1^–2^–1^, featuring a trill on the penultimate 2^), but once more the bass denies closure by moving from 69. Note that here we indeed have a context in which I6 is subordinate to ii6, since otherwise the tree lines would cross if ii6 were linked to its related I (the same holds for the two subsequent one-moretime patterns). The phrase continues with a repetition of the same deceptive patterns before cadential closure is reached via another two (simpler) embedded one-more-time patterns.

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3–4–5 to 6, the latter again harmonized as vii°6/V. The preceding unit is now repeated in its entirety (mm. 48–52 ~ 43–47). However, this time, the roles of the soprano and bass are exchanged: Whereas the bass provides its expected clausula 5–1, the soprano violates expectations by moving from 2^ to 3^ (rather than repeating its previous 1^–2^–1^ pattern). This cadence may be heard as an imperfect authentic cadence, but because a perfect authentic cadence is truly expected at this point, and this expectation is disappointed, we can refer to this pattern as a melodically deceptive cadence. The unsatisfactory character of the IAC is also revealed by the fact that a two-bar unit is attached to this cadence, closing the exposition as a whole by completing the previously denied 1^–2^–1^ pattern (mm. 54–55).

       

                        p mf                                                                                                                                    

f

                                                        p                             

V7 /IV

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viio6 /V

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Figure 10: Haydn, Keyboard Sonata in G major, Hob. XVI:27/i, mm. 38–57. Modeling the deceptive cadence as a pattern of recursive embedding. The deceptive context vii°/ii illustrates the fact that the deceptive cadence forms part of a one-more-time pattern in which the deceptive chord initiates the phrase. The parse tree shows that the second phrase constitutes a copy of the first phrase that is recursively embedded within the V–I concluding the first phrase.

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I

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(I)

(I)

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6

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V V64

V

7

IV6

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ii6

I V

V64

V7

Figure 11: Mozart, Piano Sonata in F major, K. 279/ii, mm. 1–6: An example of a deceptive cadence based on a IV6 chord within the context of a one-more-time pattern

Another example by Mozart further illustrates the proposed analysis of the deceptive cadence (see Fig. 11). In this example, which contains another one-more-time pattern, it is a IV6 chord that denies cadential closure—that is, a chord that cannot function as a tonic replacement.70 In what follows, this chord initiates a second subsequent embedded cadential preparation. This embedded deferral ensures that a level of tension is maintained from the previous phrase and increased with the new subsequent cadential context. This analysis shows that the syntactic tree can express the fact that the tonic chords in mm. 2 and 4 serve a double function: They close the preceding constituent and initiate the subsequent constituent (analogous to an elision; see below). It further represents both the disruption of the expected cadential closure by IV6 as well as its overarching embeddedness in the surrounding dependency relation-

70. At times, however, IV6 is characterized as a variant of vi produced by a 5–6 motion over a sustained bass note (6^).

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ships. This example, like the previous one, illustrates how closely connected methods of deferring cadential closure are to the general syntactic principle of coordination and embedding (as discussed in detail in Section 5.1. below). A third example exhibits a context in which a diminished chord fulfills the deceptive function (see Fig. 12). This example further shows that in terms of an embedded tonic deferral, the deceptive cadence is independent of the use of a one-more-time pattern; it may or may not be found in conjunction with it.

Figure 12: Haydn, Keyboard Sonata in F major, Hob. XVI:21/ii, mm. 13–26: An example of a deceptive cadence based on a diminished chord

A fourth example (see Fig. 13) demonstrates that even a Neapolitan chord can follow V in a deceptive cadential context and may nonetheless give rise to a regular, syntactically well-formed structure.71 The syntactic analysis shows that V and N6, although 71. Note that this situation could also be analyzed as involving a cadence evasion (see below), since the Neapolitan sonority does not articulate the goal of the preceding phrase, but rather launches a new one. This relates to the discussion on interpreting the neurocognitive ERAN patterns of Neapolitans after a cadential context (as presented by Koelsch, Brain and Music [2012]). The interpretation of such

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string-adjacent on the surface, are in fact not dependent in the deep structure; the two chords belong to different branches of the tree.

    

                                            ::   :::  :: :

    

          

3

3

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3

3 3 3 3                                    3

3

    

 

 3

 

 

3

3 3 3 3                       :      p decresc.              

Figure 13: Haydn, Keyboard Sonata in E-flat major, Hob. XVI:28/i, mm. 82–89. An example of a deceptive cadence based on a Neapolitan chord that follows V and initiates a subsequent phrase with a tonic continuation (no one-more-time pattern in this case). Note that the sequence is syntactically regular and well-formed despite the Neapolitan following V.

Any attempt at understanding the V–N6 chord succession as a direct progression would render the structure ungrammatical, as this succession itself is highly unlikely (or implausible), especially with the Neapolitan occurring on a strong beat. Rules such as ii prepares V, V prepares I, etc., are hierarchical rules (V o ii V) rather than simple Markovian progressions. Therefore, a context-free grammar approach need not consider rules such as V o V N6 or N6 o V N6, whereas a strictly local or Markovian approach would be obliged to. In contrast, V(7) o N6 V(7) would be an appropriate rule that would license the example as grammatical, with reference to a (remote) second V chord. After all, merely sequential or strictly local rules (such as those used in a Markov model or a Piston progression table) cannot both adequately describe this harmonic structure and at the same time characterize irregular V–N6 progressions. structures should not be based on the distinction between regular and irregular sequences but instead on “completion vs. revision” in musical processing (as suggested by Koelsch, ibid.).

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However, not all deceptive cadences are explicable in terms of embedded phrases ultimately leading to the previously withheld tonic (“delayed realization”). Although it is crucial to understand the syntax of the deceptive cadence from the perspective of the overarching musical context, this context may not necessarily be the preceding prolonged tonic but also the subsequent (novel) musical segment. An example by Haydn, the first movement from his D-major Keyboard Sonata, Hob. XVI:37/i, illustrates this case (see Fig. 14). In this example, the deceptive chord (V7/iv in the key of vi) serves a double function, not only concluding the development section but also initiating the modulation back to the home key by means of a brief descending-fifths sequence, with the return to the tonic coinciding with the entrance of the primary theme that launches the recapitulatory rotation (i.e., an instance of denied realization). From a syntactic perspective, this example can be modelled by two different analyses: If one prefers the consistency of syntactic embeddings, this example forces an analysis that treats the entire B-minor section as a subordinate preparation of the subsequent tonic; that is, (part of) the development section would be syntactically subordinate to (and preparatory of) the subsequent head tonic of the recapitulation. However, there is a second interpretive option, one that is analogous to the (linguistic) notion of “elision” as used by Lerdahl and Jackendoff.72 As the example shows, it is not a remote non-tonic harmony that replaces the expected B-minor tonic, but rather the right tonic root (B) upon which a major seventh (dominant) rather than a minor tonic chord is built, thus transforming the expected minor tonic into a secondary dominant. In other words, we hear the expected tonic root at the end of the cadence, but its function has been transformed. This interpretation can be reframed using the linguistic concept of elision: Instead of saying that the tonic is transformed, the example can be analyzed such that the final tonic and the subsequent dominant-seventh chord that share the same root and fifth are merged into one sonority. Instead of two chords that link different ends of branches in the tree (as in the Neapolitan example above), the surface adjacency and similarity of the two chords permits them to be merged into one item that fulfils two different functions in the tree. This analysis does not require (as the first subordination analysis does) that the development section as a whole be understood as subordinate to the recapitulation. In addition, it emphasizes the implicative density inherent in the classical style and links it to the notion of elision.

72. In linguistics, elision refers to the omission of an expected sound in such a way that the resulting sequence is easier to pronounce or to produce. In English, for instance, “vegetable” is pronounced like “vegtable,” and in German “teuerer” becomes “teurer.” Lerdahl and Jackendoff (A Generative Theory of Tonal Music [1983], Chapters 3 and 4) discuss elision in the context of two overlapping groups in a grouping structure and beat overlaps in a metrical structure.

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Figure 14: Deceptive cadence with denied realization rather than delayed realization, from Haydn, Keyboard Sonata in D major, Hob. XVI:37/i, mm. 54–64

4.4. Evaded cadence

Another important strategy of avoiding cadential closure must also be mentioned here: the evaded cadence.73 Unlike a deceptive cadence, in which the deceptive harmony groups backwards, the evaded cadence is characterized by the fact that the harmony following the penultimate cadential dominant is cut off from the preceding phrase, initiating a new formal unit. Whereas the deceptive cadence features a goal harmony (although a deceptive one) on the level of mere surface relationships of metrical and phrase structure, the evaded cadence does not. Cadential evasion is typically generated by means of secondary parameters (most importantly, texture and register). The harmony most commonly used to launch a new phrase is I6, but other harmonies can be chosen here as well (e.g., V7/IV); the decisive criterion for differentiating an evaded cadence from a deceptive one is not the identity of the chord following the dominant (since almost any chord can initiate the one-more-time pattern), but the location of the grouping boundary. A special (and frequently used) variant of the evaded cadence 73. Schmalfeldt, “Cadential Processes” (1992).

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even allows for the inversion of the penultimate dominant74: At the moment when the proper resolution of a cadential 64 is expected, the bass starts moving downwards (5–4), thus giving rise to a V42 sonority moving to I6 (typically initiating a new group). In this sense, one can conceive of this variant as a possible means of embellishing the I6 chord. Despite the surface differences with respect to the deceptive cadence, it can be argued that the deep structural relationships underlying the evaded cadence are fundamentally analogous to those modeling the deceptive cadence. For both types of cadences, cadential deferral is achieved via a recursive insertion of a chord progression between V and the final I.

5. The generative power of syntactic formalisms 5.1. Coordination

The formalism outlined above characterizes the different elements of the cadential progression and their embellishments. However, another aspect must be addressed here as well, namely the coordination and expansion of cadential elements, as this will allow us to account for some more extravagant examples that occur in actual compositional practice. The following list displays some of these examples: (a) V64–V–V64–V–I (b) I–V64–V7–V64–V7–V64–V7–I (c) I–V7–vi–ii6–V64–V–I (d) i–iv65–ii65–V7–I65–IV7–VI7–ii°6–V64–V7–i (e) I–IV–ii–V–V7–V64–viio43/ii–ii6–V64–V7–I (f ) I–ii6–V–viio7/vi–vi–ii6–V64–V7–I (g) V64–V7–V64–V7/V–V–V7–V64–V7–vii°7/vi–vii°7/V–V64–V7–i (h) I6–ii6–ii65–V7–vi–ii6–V64–V–I

In each of these cases, either there are multiple V harmonies, or the V harmony is extended through an insertion that sets up a sequence of implications to another subsequent V. However, in the latter case, the inserted second sequence is not necessarily implied by the preceding V (e.g., V–viio7/vi in example (f )). This pattern is structurally similar to, and may indeed be combined with, a deceptive cadence. To account for this phenomenon, one must find a way to make sense of these multiple instances of V. There are several ways to achieve this. First, one could regard these different instances of V as separate left-branching derivations from I, or as coordinated instances of an overarching V group. In the case of coordination, a second possible distinction concerns whether more than two instances are simultaneously derived 74. Note that this is the only form of cadence that allows a V42 chord.

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from the same parent node (referred to as “n-ary branching”), or whether branching is restricted to binary branching, forcing a binary hierarchical structure in different V nodes.75 Moreover, coordination may be applied at the highest level or below, depending on whether predominants such as IV prepare a single instance of V within the dominant group or the entire group. Although there is a practical limit imposed on the number of coordination instances of V, this limit is not a theoretical one and should not be incorporated at the level of this rule (since we are able to correctly perceive or generate an even larger number of coordinations). Figure 15 illustrates the different ways of modeling multiple V harmonies.

Figure 15: Different methods of accounting for multiple V nodes

The derivation of the first example in Fig. 15 (left) does not require any additional rules, since it follows from multiple applications of the I o V I rule. The second case (middle) requires a rule such as (8), which coordinates multiple instances of V in a single derivation from their V parent. In contrast, the third option (right) enforces binary branching, employing a rule such as (9) multiple times to create internal structure in the different V nodes. (8) V o V+ (that is: V o V | V V | V V V | …) (9) V o V V

Of course, the coordination principle is not restricted to the V chord; there are other relevant instances that do not concern V. For example, the very end of the first movement of Mozart’s D-minor Piano Concerto, K. 466, features a repeated alternation between V6/iv and iv (mm. 390–393) that prolongs the subdominant harmony and

75. This point is also discussed in detail in the GTTM; see Lerdahl and Jackendoff, A Generative Theory of Tonal Music (1983), e.g. 326–328.

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thus represents an instance of subdominant coordination. Other situations of alternating harmonies cannot be easily explained in terms of coordination and must be analyzed more carefully. Consider, for example, the following harmonic sequence: (i) I6–ii65–V64–iv6–V64–iv6–V64–vii°7/V–V

In this case, we do not want to model the multiple instances of V64 and/or iv6 via coordination, since this would only make sense if, for instance, iv6 were subordinated to V64 or vice versa. Otherwise, the derivation would involve crossing branches, which cannot be expressed with context-free grammars (instead requiring a context-sensitive grammar). Because both iv6 and V64 are in fact themselves subordinate to V, the preferable analysis in this case is to regard the entire harmonic sequence (except for I6) as multiple subordinate derivations from the final V at the end of the sequence. In contrast, the case exemplified in (j–l) may be better understood in terms of coordination of several instances of predominant chords. However, as above, it is equally possible and plausible to analyze this example in terms of derivation (iv being derived twice from V). It is again a matter of choice on the part of the analyst whether such cases should be regarded as one extended predominant subtree or as several individual predominant derivations. (j) i–V43/iv–iv–V65/iv–iv–iio6–V64–V–i (k) I–V7/vi–IV–vii°43/ii–ii6–vii°65/ii–ii6–vii°65/ii–ii6–V65/V–V (l) I–vii°64/IV–IV6–IV–V64–V7–I

In summary, it can be seen that from a structural syntactic perspective, coordination and methods of avoiding or delaying cadential closure employ very similar structures of recursive embedding. 5.2. Generalizations regarding the order of implicative elements

A second generalization concerns the order of elements with the same tonal implication. Multiple instances of the same tonal function (1) each carry their own tonal implication (multiple implications instead of multiple replications of a single implicative function) and (2) typically appear in increasing order of implicative strength (see (a) and (b*)). For instance, IV has a weaker implication of V than ii. Therefore, the coordination of IV–V and ii–V results in the order IV ii(6) V rather than ii IV V. (a)

IV–ii(6)–V

(b*) ii(6)–IV–V

V has a weaker implication of I than V7. By analogy, this predicts a predominance of the order V–V7–I (as opposed to V7–V–I). In general, the dependency structure of these examples is (IV (ii–V)) and (V (V7–I)) and not ((IV–ii) V) and ((V–V7) I), since the latter parallelization of “ii, IV” and “V, V7” would not predict the restriction in the order.

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5.3. Tonicization, key borrowing, and modulation as forms of recursion

A fundamental strength of the combinatorial complexity of generative grammars involves recursion as well as the power to express multiply embedded structures. This recursive combinatorial power is particularly useful for modeling multiple applied embellishments, coordination, and prolongation, as well as the derivation of multiple embellishments from other keys and tonicizations.76 The GSM formalizes the idea of modulation and tonicization as center-embedding recursion within a concise framework. (a) I–It6/ii–V/ii–vii°43/ii–ii6–V64–V7–vii°7/vi–vi (b) i [...] ii6–V64/iv–iv–V6/iv–iv–V6/iv–iv–V6/iv–iv–V6/iv–i6–V7/V–V7–I–V/N6– N6–vii°7/V–V64 [...] V7–i (c) I6–vii°65/ii–VI6/ii–vii°43/ii–ii6–V64–V7–I (d) I6–ii65–ii43–V64–V42/IV–IV6–IV–V65/IV–V7/IV–IV–ii6–V64–V (e) I6–vii°65/V–V43/V–V–IV6–V7–I

Example (a) illustrates the possibility of temporarily borrowing harmonic elements from keys other than the tonic, especially those keys in which the constituent elements of a cadential progression act as a new tonic. This allows us to derive one or even multiple subordinate implicative harmonies. This change in our point of reference precisely defines an instance of recursion in tonal music. The slash “/” symbol in standard notation represents a functional switch to a different tonal space and can be logically applied in a recursive manner, e.g., V/V/ii. However, instead of notating the sequence given above as It6/ii–V/ii–vii°43/ii–ii6, it is more parsimonious to reflect the underlying regular structure by choosing ii as the new point of reference or as a local point of tonicization: (It6–V–vii°43–i6)/ii. Otherwise, the rules of tonality would be represented in a very redundant and unsatisfactory manner (see, for instance, It6/ ii–V/ii, It6/iii–V/iii, etc.). Recursion and coordination challenge the adequacy of local grammars, Markov models, and schema-based approaches, all of which lack the power to express these aspects (see also 5.5.). A generative hierarchical approach, by contrast, is capable of representing the underlying structure in a parsimonious fashion. Figure 16 provides an example of how such a recursive embedding analysis of key borrowing/tonicization/modulation is modelled following the formalism of the GSM. Note that such recursive generation generalizes to any part of a phrase (or, here, a cadence), not only to key relationships between phrases and modulations.

76. The use of recursion to capture tonicization and key embedding has already been suggested by Douglas Hofstadter in his Gödel, Escher, Bach (1979).

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Figure 16: Tree analysis of the sequence I–It6/ii–V/ii–vii°43/ii–ii6–V64–V7–I. The tree illustrates recursive embedding using a local change of key reference based on the modulation mechanism proposed by the GSM.

Another example of the power of recursion in the generative mechanism is given above in example (b) from the end of the first movement of Mozart’s Piano Concerto in D minor, K. 466 (mm. 338–356). The cadential pattern considered here starts with an initial tonic (after a preceding cadence) and features a tonic extension by means of a onemore-time pattern. After recursively extending the area around iv via coordination, the sequence reaches the major tonic via the secondary and the home-key dominant recursively borrowed from the corresponding major key. It then diverges to the Neapolitan, which is itself prepared by its applied dominant. The “grand cadence” ends with an extended V64 (preceded by a V preparation with a diminished chord based on ©4^), inviting the soloist to deliver a cadenza ending with a trill on 2^ over V7 and the final tonic. A final example, the end of the second movement of Mozart’s Piano Sonata in F major, K. 280, demonstrates the generative power of recursion in music and the way it is modelled in our grammar (see Fig. 17). The dramatic effect conveyed by this ending results from the various steps employed to extend and delay cadential closure. First, a simple conventional cadential context is established by the first four chords, using the standard pattern i6–IV–V64–V7. The concluding sonority (i) is avoided by means of a i6 chord, which provides only partial closure. At the same time, i6 serves two further functions: It embellishes the subsequent IV and initiates a (subordinate) one-moretime repetition of the cadence in an attempt to complete the phrase. In other words, i6 represents an example of elision here. In the following measures, the cadence-final dominant is delayed until after the cadential V64 with several subsequent embellishments that each imply the cadential

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V: Ger6, vii°43/V, and again Ger6. The first Ger6 is in turn recursively embellished with a relative diminished chord (preparing VI, iv, and the Ger6). This delay of the cadencefinal V creates a strong momentum towards V, such that V is extended and split over an entire bar into V and V7. What follows is a brief and harmonically incomplete tonic (represented by its root only), immediately followed by a V7/iv in first inversion, in a manner that almost provides another case of elision (although here the two chords are separate). This again recursively triggers a one-more-time pattern, this time serving to prolong tonal closure for the cadence and the entire movement. This one-more time pattern is repeated once more (initiated by a stronger subdominant preparation by means of a diminished chord) before the final closure is finally achieved. These one-more-time patterns establish a tonic extension via overarching coordination. The tonic concluding this movement is itself delayed by a dominant overhang. Altogether, all of these recursive embellishments and extensions create a cadential progression that is longer than 13 chords.

      















  





 f

    



       

   



p



   f



  



     

   p

  

       f

                         

                             p f p                        



               f            

     f

 :    :     :: 

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Figure 17: Mozart, Piano Sonata in F major, K. 280/ii, mm. 51–60. The end of this piece provides an example of an extensively elaborated and embellished cadence using multiple parallel recursive embellishments and several applications of coordination (one-more-time technique).

5.4. The combinatorial power of a recursive grammar

Another powerful characteristic of a generative grammar is that it models strong assumptions about conditional independence and is effective at modeling combinatorial flexibility. For instance, it formalizes the intuition that the application of one or more secondary dominants is independent of whether or not there is coordination and whether or not the cadence is deceptive or perfect authentic. Example (a) illustrates this point: It combines several preparatory implicative dependents of V (one with a recursive secondary dominant, viio), coordination of dominants, and a deceptive cadence framework in which vi is itself recursively prepared by viio7. Note in this context that predominant chords are themselves combined with dominant preparations, as seen in examples (a)–(d). (a) I–viio6–viio/IV–IV–iv–V–It6–V64–V–viio7/vi–vi […] (b) I6–IV6–V64–IV–viio65/ii–ii6–V64–V7–I (c) I6–ii65–V64–iv6–V64–iv6–V64–viio7/V–viio64–viio65/ii–ii6–V7–I (d) I–V7–V43/V–V7–vii°7/vi–vi–V64–IV–V7–I

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Cadences can potentially be enriched and expanded to a very large extent. One example of this is found in the famous C-major Prelude from J. S. Bach’s Well-Tempered Clavier I, the second half of which can be analyzed as one greatly extended cadence-like pattern.77 The strong combinatorial power of a generative grammatical approach such as the one proposed here makes it possible to plausibly express complex cases such as (a)–(d) as well as the examples given in the previous sections; however, if the rules are stated in a probabilistic form, they would predict that such complex cases will be rare and will appear much less frequently than simple, (seemingly) prototypical cases. 5.5. Inadequacy of local grammars and forward or Markov models

One may further note that the combination of different elements in a generative grammar is enormously flexible. However, this means that it is difficult to express the syntax of the cadence purely in terms of a forward model (such as a Markov model). As mentioned repeatedly in this chapter, if one modelled cadential progressions solely in terms of what can be followed by what (i.e., I–vi, vi–ii6, ii6–V, V–I), each forward step would have to incorporate all possible forms of recursive insertions (e.g., I–It6/ ii, I–V/ii, IV–It6/ii, IV–V/ii, etc.), which would result in a model containing hundreds of redundant multiple representations of the same structure. Furthermore, recursive insertions that generate and permit seemingly irregular surface progressions (such as V–N6 or many of the forms found in deceptive cadences or transitions at boundaries between separate subtrees) cannot be modelled as regular or irregular by strictly local grammars that neglect the hierarchical context. Because a syntactic approach aims at the characterization of structure in the sense of strong rather than weak generative capacity (capturing the internal logic of relationships between elements rather than merely their surface sequence), a Markovian representation would be a possible and computationally powerful model of the musical surface, but would fail to meet the criterion of a parsimonious and concise representation of the internal logic of a given sequence.

Conclusion As the title of this chapter indicates, we do not claim to provide a comprehensive or exhaustive theory of the syntax of the classical cadence; rather, our aim is to demonstrate the manifold advantages of adopting a generative grammar approach (such as those devised more than half a century ago in the field of linguistics by Noam Chomsky 77. See Schoenberg’s assertion that “[i]n a general way every piece of music resembles a cadence, of which each phrase will be a more or less elaborate part” (Schoenberg, Musical Composition [1967], 16).

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and his followers) in music theory. Although generative linguistics inspired Lerdahl and Jackendoff to develop an enormously powerful generative theory of tonal music, we believe that adhering more closely to formal language theory and well-defined generative rules than the GTTM did could be rewarding, allowing us to account for both the linearity and the hierarchical (and recursive) nature of the classical cadence and tonal music in general. As pointed out in the introduction to this chapter, one of the main challenges in addressing the classical cadence is the almost infinite variety of cadential patterns, even when we consider the harmonic level in isolation. This variety seems to be difficult to capture using an exemplar-based or chunk-based approach. Rather, the representation of the internal logic of the tonal dependency structures inherent in cadences requires a hierarchical approach, as opposed to a linear or Markovian model. A syntax approach such as the one proposed in this chapter (1) accounts for the underlying deep structural dependencies in the main cadence types found in the classical repertoire and described by music-theoretical approaches, and (2) models sequential structures based on a small set of rules that generate temporal sequences through their multiple independent combinations. Such an approach allows us to generate embellishments, insertions, coordination, and functional relationships independently for each event in the sequence. In other words, it provides combinatorial power and predicts a great variety of cadential phenomena (with divergent frequencies of occurrence). We suggest that the empirical variety of cadences found in the classical repertoire, along with the very frequent occurrence of a few very common cases, can be successfully predicted by (potentially probabilistic) generative mechanisms. The family of formal approaches subsumed under the umbrella of formal and generative syntax provides precise, explicit, empirically testable, and computationally implementable ways to characterize hierarchically organized sequential structures in music. At present, our proposed formalization is limited by the selected level of representation (scale-degree harmony and bass line); it does not yet address the interface between metrical and grouping structure on the one hand and the cadential progression on the other. The mathematical formalization of such relationships remains to be addressed in future work. Furthermore, we regard the rules proposed in this chapter as merely a (potentially suitable) starting point for further studies. The development of a more refined apparatus of generative rules and their empirical examination by means of corpus research must await future studies.

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LIST OF CONTRIBUTORS

PIETER BERGÉ is Professor of Music History, Analysis, and Music Theory at the University of Leuven, Belgium. His main research areas are the formal analysis of classical and early romantic music, German opera in the first half of the twentieth century, and music analysis and performance. He has published two monographs on the operas of Arnold Schoenberg, and is the editor of Musical Form, Forms & Formenlehre: Three Methodological Reflections (co-authored by William E. Caplin, James Hepokoski, and James Webster; Leuven University Press, 2009). He has been the President of the Dutch-Flemish Society for Music Theory since 2006. L. POUNDIE BURSTEIN is Professor of Music Theory at Hunter College and the Graduate Center of the City University of New York. He also has taught at Mannes College of Music and Columbia University. His essay “The Off-Tonic Return in Beethoven’s Piano Concerto No. 4 in G Major, Op. 58, and Other Works,” published in Music Analysis 24, received the 2008 Outstanding Publication Award of the Society for Music Theory. He is currently the President of the Society for Music Theory. VASILI BYROS is Assistant Professor of Music Theory and Cognition at Northwestern University, having received his Ph.D. in Music Theory at Yale in 2009. He researches the compositional and listening practices of the long eighteenth century as an ethnographic pursuit, drawing on frameworks in music theory, history, cognitive and social psychology, and anthropology in order to reconstruct “native” perspectives on music of the period. This research has appeared in Music Analysis, Eighteenth-Century Music, Musica Humana, and is forthcoming in the Oxford Handbook of Topic Theory (ed. Danuta Mirka). WILLIAM CAPLIN is James McGill Professor of Music Theory at the Schulich School of Music, McGill University, specializing in the theory of musical form and the history of harmonic and rhythmic theory in the modern era. His textbook Analyzing Classical Form has been published in November 2013 by Oxford University Press. A former president of the Society for Music Theory, he has presented many keynote addresses, guest lectures, and workshops in North American and Europe. He recently completed a twoyear leave supported by a Killam Research Fellowship from the Canada Council of the Arts on the project “Cadence: A Study of Closure in Tonal Music.”

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List of Contributors

FELIX DIERGARTEN is Professor of Music Theory at the Schola Cantorum Basiliensis. He obtained diplomas in conducting and music theory in Dresden, where he studied with Ludwig Holtmeier and Clemens Kühn, and went on to study with Markus Jans in Basel. He has been active as repetiteur, assistant-conductor, and conductor at various theaters, and received his Ph.D. in Music Theory with a study on form in Haydn’s symphonies (2009). In addition, he has published a book on Renaissance Music (2014) and is currently preparing a study on French fourteenth-century song. NATHAN JOHN MARTIN holds a Marie Curie Pegasus Fellowship (Fonds Wetenschappelijk Onderzoek Vlaanderen) at the Katholieke Universiteit, Leuven. His interests are in the history of music theory, historically informed analysis, and musical analysis more generally. He received his Ph.D. from McGill University in 2009 and has held postdoctoral positions at Columbia and Harvard. He is the assistant editor of the Leuven Cadence Compendium and a reviews editor for the Dutch Journal of Music Theory. His articles appear in such journals as Studies on Voltaire and the Eighteenth Century, Recherches sur Diderot et sur l’Encyclopédie, and the Journal of Music Theory. DANUTA MIRKA is Reader in Music at the University of Southampton. She is the coeditor, with Kofi Agawu, of Communication in Eighteenth-Century Music (2008) and the editor of The Oxford Handbook of Topic Theory. Her books include The Sonoristic Structuralism of Krzysztof Penderecki (1997) and Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791 (2009), which won the 2011 Wallace Berry Award from the Society for Music Theory. Her articles have appeared in many publications, including The Journal of Musicology, Journal of Music Theory, The American Journal of Semiotics, Musical Quarterly, and Eighteenth-Century Music. MARKUS NEUWIRTH holds a Postdoctoral Fellowship from the Fonds Wetenschappelijk Onderzoek Vlaanderen (FWO) at Leuven University. He received his Ph.D. from Leuven University in 2013. He is guest editor of the Zeitschrift der Gesellschaft für Musiktheorie as well as the assistant editor of the Leuven Cadence Compendium. He has published a number of articles and book chapters on various sonata-form issues in the works of Haydn and his contemporaries, on cognitively oriented music analysis, on the relationship between hypermetric analysis and music performance, and on Helmut Lachenmann’s music. JULIE PEDNEAULT-DESLAURIERS is Assistant Professor of Music Theory at the University of Ottawa. Her research centers on the late tonal and atonal works of the Second Viennese School, and she is also interested in theories of musical form and in French music theory before Rameau. Her work has appeared or is forthcoming in the

List of Contributors

341

Journal of the American Musicological Society, the Journal of Musicology, and the Journal of Seventeenth-Century Music. She is currently working on a co-edited volume on the theory of formal functions. MARTIN ROHRMEIER is Professor of Systematic Musicology and Music Cognition at the Technische Universität, Dresden. Previously, he was a Postdoctoral Fellow at the I2 Intelligence Initiative and the Department of Linguistics at MIT, as well as at the “Languages of Emotions” cluster at the Freie Universität, Berlin. He studied in Bonn and received his MPhil and PhD degrees from the University of Cambridge under the supervision of Ian Cross. His research lies in the areas of music cognition and perception, and he intends to strengthen interdisciplinary connections between music cognition, music theory, psychology, computer science, and linguistics. Recent publications include a coedited issue on music cognition in Topics in Cognitive Science (with Patrick Rebuschat), and articles on syntactic approaches to music theory, predictive processing, and implicit acquisition of music. DAVID SEARS is currently a Ph.D. Candidate in Music Theory at McGill University, having obtained Bachelor’s degrees in Music Theory and English Literature at the University of Arkansas. His dissertation examines the perception of closure in music of the classical style, using both experimental and corpus-analytic methods, and drawing from theories of implicit (statistical) learning, schema theory, and expectation. His other research interests include emotion and psychophysiology, empirical aesthetics, computational approaches to music theory, and the analysis of popular music. He won the Grand prize for student research at the 2011 meeting of the Society of Music Perception and Cognition (SMPC 2011), and has presented several papers at international conferences in North America and Europe.

Index

343

INDEX

Cadence-related Terminology Abandoned cadence 76, 122, 199 (n. 24) Absatz 93, 124, 129, 225ff. Aenderungsabsatz 90, 94 Grundabsatz 129, 226f., 229, 232, 234, 240 (n. 95) Quintabsatz 90, 94f., 98f., 104 (n. 34), 226f., 234ff., 240 Anhang 178 (n. 44), 216, 227, 238 (n. 90), 239ff. Ausfliehen der Cadenz 118 Cadence attendante 121 evitée 118 imparfaite 90, 121 (n. 24) parfaite 92 (n. 16), 119 (n. 13), 121, 125 rompue 118, 121, 125 Cadentia altizans 124 ficta 118 (minor) ligata 11, 66, 81, 126 (maior) perfecta 68, 81 (maior) simplex 11, 66, 81, 126 Cadenza composta 65f., 231 di grado 68 diminuita 64f., 126 d’inganno 118 di salto 68 doppia 63 (n. 18), 67ff., 81, 193ff., 201 finta 118 lunga (long cadence) 216, 221ff., 230, 233f., 236, 239f., 244, 246 maggiore 69 maior 81 major 66f. minima 69 minor 81 minore 69

sfuggita 118 semplice 64, 81, 229ff. Clausula altizans 123f. basizans 123 cantizans 11, 123, 126f. explementalis 124 formalis 126 formalis minus perfecta 124 imperfecta 91 imperfecte ascendens 123 (n. 35) imperfecte descendens 123 (n. 35) ligata 126 ordinata ascendens imperfectior 124 ornata 126 perfectissima 20 principalis 123, 126 pura 126 saltiva imperfectior 123 simplex 126 tenorizans 11, 31 (n. 26), 123, 126, 190 (n. 13), 311 vera 17 (n. 4), 31 (n. 26), 126 (n. 49) Codetta 33f., 36, 46 (n. 43), 76 (n. 53), 157, 178, 231f., 254 (n. 7), 300 Colon 93 Comma 93, 124, 216, 230f., Contrapuntal cadence 11, 226 (n. 59) Cudworth cadence 139 Deceptive cadence 9f., 12, 63 (n. 21), 70, 118ff., 122ff., 127ff., 139f., 142ff., 151f., 173, 175f., 178 (n. 44), 232, 235, 267, 269f., 273, 279 (n. 65), 318ff., 333f. Dissecta desiderans 90, 92 (n. 16) Einschnitt (incise) 73, 93, 123 (n. 35), 225, 228, 240 (n. 95), 243

344

Index

Essential expositional closure (EEC) 31 (n. 27), 78, 126, 136 (n. 83), 139, 226, 229, 231, 281 (n. 72) Essential structural closure (ESC) 126, 226 Evaded cadence 120f., 127, 132, 134f., 139, 143, 146f., 178, 235, 263, 267f., 269f., 273, 280, 300, 316, 326f. Expanded cadential progression (ECP) 222 (n. 35), 240, 264, 281 (n. 72) Falsche Cadenz 129 Fliehender Tonschluß 118 Grand cadence 127, 139, 331 Halbkadenz (or Halbcadenz) 90, 94, 98, 226f., 229, 234f., 237, 241ff., 246 Halbschluss 90 Half close 68, 70, 90 Imperfect cadence 90, 121, 129, 132 Improper cadence 121 Indugio 20, 24f., 49, 230f., Interpunctische Form (punctuation form) 215, 224, 247 Klausellehre 120, 123 Klauselverwechselung 123, 127 Medial caesura (MC) 77, 94f., 226f., 229, 236, 240f., 243, 245f. One-more-time technique 132ff., 138f., 178 (n. 44), 281, 316, 333

Periode (H. Chr. Koch) 93ff., 225f. Plagal cadence 8 (n. 8), 68, 70, 91, 259, 279 (n. 67), 298 (n. 41), 301 Post-cadential 46 (n. 43), 78, 86 (n. 3), 178, 216, 239, 242, 244, 300 Prinner cadence 10, 31ff., 36ff., 41ff., 45f., 50, 52f., 55ff. Quiescenza 20, 230 Ruhepunct (des Geistes) 215, 224ff., 232f., 235f., 240ff. Satz (H. Chr. Koch) 225ff., 229 Schlußsatz 93 (n. 19), 145 (n. 97), 178 (n. 44), 225ff. Semicadence 90 Semi-colon 93 Standing on the dominant 49f., 85, 86 (n. 3), 233, 238f., 243 Trugschluß 118, 144 Unterbrochene Cadenz (interrupted cadence) 144 Verdopplung der Cadenzen (doubling of cadences) 178 (n. 44) Vervielfältigung der Cadenzen (multiplication of cadences) 178 (n. 44) Überhang (overhang) 46 (n. 43) Unison cadence 142, 145 (n. 97) Unvollkommener Tonschluss 90

Music Theorists (up to the early twentieth century) Adlgasser, Anton Cajetan 62, 81 Agricola, Johann Friedrich 90 (n. 7), 113 Ahle, Johann Georg 159 Albrechtsberger, Johann Georg 143f., 147, 152f., 179 (n. 46) Artusi, Giovanni Maria 65 (n. 29), 81 Bach, Carl Philipp Emanuel 160, 173 (n. 37), 181 Berardi, Angelo 122, 153 Bononcini, Giovanni Maria 65, 81 Calvisius, Sethus 126 (n. 52), 153 Campion, François 173 (n. 37), 181 Crotch, William 98 (n. 31), 114 Crüger, Johann 170 (n. 32), 182

Czerny, Carl 98 (n. 31), 114 Daube, Johann Friedrich 132, 143f., 147, 153 Descartes, René 126, 153 Deysinger, Johann Franz Peter 63, 82 Eberlin, Johann Ernst 62, 64, 68, 82 Ebner, Wolfgang 61 Faisst, Immanuel 98 (n. 31), 114 Fux, Johann Joseph 165f. Gasparini, Francesco 65, 69, 81 (n. 60), 82, 173 (n. 37), 182 Goetschius, Percy 98 (n. 31), 114 Gugl, Matthäus 60, 62, 82, 91 (n. 10), 114, 160, 166

Index

345

Haydn, Michael 60, 62f., 82, 160 Heinichen, Johann David 160, 166, 170 (n. 32), 173 (n. 37), 180, 182 Herbst, Johann Andreas 61, 82, 91f., 114 Holden, John 91 (n. 11), 114 Jones, William 98, 114 Kellner, David 123 (n. 33), 154, 166, 173 (n. 37), 182 Kessel, Johann 98, 114 Kirnberger, Johann Philipp 13, 34f., 57, 98, 114, 119f., 147, 154, 161ff., 174 (n. 39), 180ff., 224, 249 Koch, Heinrich Christoph 14, 46 (n. 43), 89f., 92ff., 97ff., 104f., 114, 127ff., 145 (n. 97), 154, 178 (n. 44), 183, 215, 224ff., 231f., 235f., 238 (n. 90), 240, 242ff., 249, 253f., 284, 289 (n. 15), 315 (n. 59), 337 La Voye-Mignot, de 91f., 114, 121, 154 Lippius, Johannes 159 Lipsius, Justus 124 Marpurg, Friedrich Wilhelm 92 (n. 18), 94 (n. 22), 98, 114, 124, 127, 154, 160, 166, 183, 224, 249 Marx, Adolph Bernhard 98 (n. 31), 114, 224 Masson, Charles 121, 154 Matthaei, Conrad 91, 115 Mattheson, Johann 123 (n. 35), 124, 154, 159f., 165f., 173 (n. 37), 180f., 183, 223f., 249 Mozart, Wolfgang Amadé 63, 166 (n. 25) Muffat, Georg 59, 61ff., 66f., 69, 81f., 91 (n. 10), 115, 160 Nauß, Johann Xaver 63, 82 Nivers, Guillaume-Gabriel 121 (n. 23), 154 Poglietti, Alessandro 60f., 82 Prinner, Johann Jacob 10, 17 (n. 2), 60 (n. 5), 61, 82

Printz, Wolfgang Caspar 92 (n. 16), 115, 123f., 154, 159 Rameau, Jean-Philippe 119, 125, 155, 160, 173 (n. 37), 184 Reicha, Antonin 91 (n. 9), 115, 143f., 155 Reinhard, Leonhard 63, 83 Riemann, Hugo 9, 119, 155, 297 (n. 38) Riepel, Joseph 92 (n. 18), 115, 128ff., 132, 136, 139, 148 (n. 104), 155, 178 (n. 44), 184, 224, 228, 236, 238, 250 Samber, Johann Baptist 62, 83, 160 Scheibe, Johann Adolf 119, 144, 155, 223f., 250 Schenker, Heinrich 7 (n. 1), 9, 16, 98 (n. 31), 104, 111 (n. 43), 115, 117 (n. 1), 118 (n. 7), 130ff., 138, 155, 168 (n. 31), 186 (n. 7), 205f., 296, 313, 315ff. Schoenberg, Arnold 9, 16, 334 (n. 77), 338 Schulz, Johann Abraham Peter 165 (n. 17), 167, 184 Sorge, Georg Andreas 170 (n. 32), 184 Spieß, Meinrad 8 (n. 5), 16, 123f., 155 Sulzer, Johann Georg 98, 115, 130, 147, 155, 161, 165 (n. 17), 170, 224, 242, 250 Tigrini, Oratio 69 (n. 37), 83 Tovey, Donald Francis 115 Türk, Daniel Gottlob 128, 155, 161 (n. 13), 184, 250 Viadana, Lodovico 60 Vogler, Georg Joseph 174 (n. 39) Walther, Johann Gottfried 65 (n. 32), 83, 121ff., 155, 159 Werckmeister, Andreas 123, 155, 159 Wiedeburg, Michael Johann Friedrich 91 (n. 10), 115 Wolf, Georg Friedrich 92 (n. 18), 116 Zarlino, Gioseffo 64f., 83, 120f., 126 (n. 52), 155, 159f., 184

Composers Alberti, Domenico 99f. Albrechtsberger, Johann Georg 142 Allegri, Gregorio 79f. Aubert, Jacques 25f.

Bach, Carl Philipp Emanuel 26f., 42, 99f., 106f., 166 (n. 24), 241 Bach, Johann Christian 97, 241 Bach, Johann Sebastian 334

346

Beethoven, Ludwig van 86f., 95, 97 (n. 27), 99f., 104 (n. 35), 113 (n. 45), 133 (n. 74), 196 (n. 20), 215ff., 224, 229f., 232f., 236, 239, 241ff., 311 Benda, Georg 97 Brahms, Johannes 55 (n. 54) Castrucci, Pietro 37 Cimarosa, Domenico 240f. Corelli, Arcangelo 59, 61, 69, 160 (n. 12) Eckard, Johann Gottfried 241 Ferrari, Domenico 30, 46f. Gallo, Domenico 32 Galuppi, Baldassare 22, 33ff., 241, Gaviniès, Pierre 28f. Graun, Carl Heinrich 23 Haydn, Joseph 13, 23f., 38ff., 43ff., 62, 68, 98 (n. 30), 99f., 102f., 108 (n. 41), 126f., 129 (n. 63), 133ff., 145ff., 157ff., 165ff., 204, 221, 234ff., 241, 253, 307, 319, 325f. Haydn, Michael 99, 101 Kozˇeluch, Leopold 101, 146 (n. 98) Marcello, Benedetto 32f. Mendelssohn, Felix 52ff. Mozart, Leopold 63, 67, 79, 81, 101, 180 (n. 51), 241

Index

Mozart, Wolfgang Amadé 11, 13, 35f., 38 (n. 35), 48ff., 62ff., 68, 70ff., 75ff., 81, 88, 97, 99f., 102f., 106f., 109ff., 129f., 133f., 136 (n. 84), 147 (n. 100), 148 (n. 104), 150ff., 173 (n. 38), 179 (n. 45), 185ff., 241, 246 (n. 112), 253, 259ff., 263f., 266f., 288 (n. 11), 302ff., 307, 309ff., 317f., 322, 328, 331ff. Muffat, Georg 59, 61f., 81 Myslivecˇek, Josef 101, 241 Neefe, Christian Gottlob 99, 101 Pasquini, Bernardo 59, 61, 69, 81 Peroti, Fulgentius 46ff. Pichl, Wenzel 99, 101 Pleyel, Ignaz 101, 140 (n. 90) Prokofiev, Sergei 260 Scarlatti, Alessandro 59 Schobert, Johann 241 Schubert, Franz 99 (n. 32), 263 (n. 37) Schumann, Robert 54f. Stamitz, Johann 35 Sˇteˇpán, Josef Antonin 241 Stravinsky, Igor 32 Vanhal, Jan Krˇtitel 24f., 101 Vogler, Georg Joseph 101f.