How Sonata Forms: A Bottom-Up Approach to Musical Form

when the new Formenlehre emerged about three decades ago as a prominent subfield of American music theory, its landmark texts centered the canonical works of the First Viennese School. By explicit denomination or preponderance of examples, William Caplin (1987, 1998, and 2004), James Hepokoski and Warren Darcy (1997, 2007), Janet Schmalfeldt (1991, 1992), and James Webster (1991a, 1991b) all gave pride of place to the music of Haydn, Mozart, and Beethoven. Since then, although study of those composers continues, the subfield has owed its extraordinary fertility largely to the application of its methods to an expanding array of other repertoires, generally ones that are more recent.1 The 2020s have seen major works begin to cast an eye back to earlier music: first L. Poundie Burstein's Journeys Through Galant Expositions (2020) and then Yoel Greenberg's How Sonata Forms: A Bottom-Up Approach to Musical Form (2022), both of which treat pieces from earlier in the eighteenth century that can be interpreted as predecessors to the Classical sonata form.2 From a distance, this turn further back into the past might be taken for just another expansion of the sphere of works in the purview of form scholarship. For both Burstein and Greenberg, however, it represents something more: a chance to reexamine the conceptual foundations of the new Formenlehre by excavating its stylistic roots. Greenberg's study also represents another, more fundamental shift: away from form theory as the groundwork for analysis of individual works toward analyses as the raw material for a new history of musical style.At the heart of How Sonata Forms lies an interest in the interplay between two perspectives on sonata form: the synchronic and the diachronic. The synchronic perspective considers the form as a system existing in a steady state during a snapshot of historical time, while the diachronic one considers the questions of how and when the form evolved. Greenberg situates his work in relation to earlier scholarship by suggesting that previous theories have tended to overemphasize the synchronic perspective. A primarily synchronic view, he argues, will always leave theories of sonata form on shaky footing, because synchronic theories are inherently incapable of solving the familiar problem of categorization: When does a piece belong to the taxon of sonata form? Sonata form is not a classical category, definable in terms of necessary and sufficient criteria, but a fuzzy Wittgensteinian one with no clear boundaries or simple essence.3 The form's existence can thus only be understood through the history of how its individual features coalesced into a single concept. In short, Greenberg's thesis is that “the synchronic question of what sonata form is becomes inseparable from the diachronic, evolutionary question of how it came to be” (8).The lightness and clarity with which Greenberg develops this thesis make for a book whose brevity, at under two hundred and fifty pages, understates the heft of its argument. Blending thought from a wide variety of domains, from literature to evolutionary biology, the primary conceptual tool of the book is a statistical model backed up by data drawn from a corpus of works spanning the eighteenth century. Defying the propensity of statistics to be complex and obscure, Greenberg marshals the facts of the corpus to make a case that should invite all form scholars to rethink what they know about the history of sonata form. I offer an overview of the nature of this rethinking in the first part of this review, though given the deftness of the book's prose, I can only aspire to offer a shorter, not clearer, exposition of it.In the second part of the review, I discuss some limitations of the argument it presents. In particular, I suggest that while the diachronic argument on its own terms is compelling, it overlooks some of the achievements of synchronic theories. The problems of categorization are not new to music theory, and I am not convinced that the diachronic explanation can provide a satisfactory resolution of them on its own.4 Focusing on Hepokoski and Darcy's Sonata Theory as a representative of the kinds of synchronic theories that Greenberg criticizes, I argue that its ability to offer rich analytical interpretations of individual works is an essential complement to the diachronic model. In particular, the principle of dialogic form invites us to understand pieces in terms of the expressive and social functions for which musical features, including large-scale forms, are used. Such an understanding is necessary for a full explanation of the forces that drive diachronic change.In Greenberg's account, previous theories of sonata form suffer a chicken-and-egg problem: Which comes first, the form as a whole or the parts that make it up? The whole surely cannot exist without the parts, but the parts are only defined in relation to the whole (and moreover it is notoriously hard to find an ideal example of the whole in which all the textbook parts are as they should be). The problem is at once theoretical and historical, plaguing attempts both to identify early historical instances of the form and to fashion an airtight definition of exactly what the form is.How Sonata Forms proposes that the chicken is only a byproduct of the egg. That is, the definitional conundrum arises from too strong an attachment to a “holistic” or “top-down” conception of sonata form as a self-evident entity (3–8, 36–42). Especially as a matter of diachronic development, this attachment problematically presumes an evolutionary teleology that could not have actually shaped the composition of pieces that we now in retrospect identify as predecessors of sonata form. Instead, Greenberg advocates for a theory that prioritizes the individual elements of a piece, understood independently. These elements each have their own microhistories that began separately and only eventually came together to assemble sonata form, which is therefore best understood as an emergent feature of musical style.5 This is the “bottom-up approach” of the book's subtitle, which Greenberg also characterizes as a “reductionist” theory (50–53). Evolutionary biology serves as a key inspiration for this approach, as Greenberg likens the individual elements from which sonata form emerges to Richard Dawkins's account of genes competing for perpetuation in the population of a species, going so far as to suggest that, “continuing the Selfish Gene analogy, there is much to gain by considering musical forms as temporary survival machines for their much more enduring constituent elements—a favorable environment within which each one of these elements would thrive” (52).6Chapters 1 and 2 of the book pose these problems, the former focusing on the issue of fuzziness, or the vague boundaries inherent to the definition of sonata form. It outlines three general strategies that it suggests have dominated previous scholarship's attempts to solve that problem (replacement, refinement, and relaxation), none of which are judged to be satisfactory. Chapter 2 identifies holism as the culprit, to which chapter 3 proposes reductionism as the remedy. Here, Greenberg introduces the most important concepts of the book in the form of an abstract statistical model, which will be connected to real musical details in the remaining chapters.The essence of the model is to assume that a form is defined, from the bottom up, by a set of distinct musical features, each of which has some probability of occurring in any given piece. Those probabilities are initially assumed to be independent of one another: Every piece is essentially a combination of dice rolls determining which properties it will have. If early in the evolution of a form the dice are weighted against each feature occurring, the chance of all the features turning up together in one piece will be even lower. Hence few pieces from that time will appear to be a typical instance of the form. On the other hand, if later each individual probability is quite high, then some pieces will have all the typical features of the form by happenstance, and many others will have most of them but lack one or two. Thus, as musical tastes change and individual elements go in and out of fashion, the confluence of features that we recognize as a large-scale form can seem to crystallize out of nowhere—not as the result of conscious intent to achieve precisely this form but simply as a by-product of the individual elements successfully replicating themselves.In an actual musical repertoire, individual features may not always be strictly independent. (For instance, if we suppose that a piece from the eighteenth century has an only 50 percent chance of including a part for violin and 25 percent for a viola, I would guess that having a viola part makes a piece almost certain to include a violin part too: These probabilities are not independent of each other.) Greenberg begins with the assumption of independence to show how a form can evolve even without any interaction between its elements. A theory of form thus need not—indeed should not—assume that the features are dependent on one another. Instead, the existence of statistical correlation between elements is a factual claim that should be based on data from a corpus study. In the remaining chapters of the book, Greenberg turns to exactly such a study to develop a diachronic model of sonata form, testing the extent to which the form does or does not reveal correlations between its elements.The goal of How Sonata Forms is to present a proof of concept for this perspective rather than to exhaustively itemize every facet of the Classical sonata, so Greenberg develops his model of sonata form around just three important musical events: the medial repeat, the double return, and the end rhyme, which are introduced in chapter 4. The medial repeat, probably the least familiar element today, is “a repeat of the opening idea at the double bar, usually in a nontonic key” (64).7 The double return, borrowed from Webster 2001, marks the simultaneous return of the global tonic and the opening idea, in what would eventually become the launch of a conventional recapitulation. The end rhyme encompasses any “significant matching between the endings of the two halves” of the form (64).Greenberg assembles and analyzes a corpus of “732 fast or moderately paced binary instrumental works dated 1650–1769, by 84 composers born and active in Germany, Austria, and Italy” (195).8 Since the diachronic development of sonata form is the book's principal focus, the works in the corpus are grouped by decade to track the probabilities of each element across time. Chapter 4 discusses some preliminary results: From the late 1600s to the 1760s, the end rhyme and the double return grow more common decade by decade. The medial repeat, meanwhile, is the most common feature in the earliest parts of the corpus but begins to become less common around the middle of the eighteenth century. More striking are the chapter's results on independence between the elements, which are summarized in Table 4.2 (89): There is on the whole very little indication of correlations between them.9 This is a startling result. As late as the 1760s, the double return and end rhyme are nearly completely uncorrelated. Since a recapitulation depends on the confluence of those two features, in a certain sense this suggests that recapitulations did not exist during the first decade of Haydn's career, except as the chance coincidence of smaller features.10 (As we shall see, though, Greenberg nuances this picture in chapter 5.) This is a compelling demonstration of the value of corpus studies in general and Greenberg's bottom-up approach in particular, especially as a check on our propensity to anachronistically import formal ideas developed in historical hindsight into the present moment of a given piece.11The book's next three chapters investigate interactions between formal elements in more detail. Chapter 5 discusses the possibility of positive interaction between two bottom-up elements: Instances where two elements that occur frequently together, at first by chance, may eventually come to reinforce one another because of emergent effects that result from their conjunction. This is proposed as the likely origin of the sonata recapitulation. 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