The title What Is a Cadence? won't have immediate appeal for all readers. The prospect of exhuming that obligatory stalwart of the undergraduate curriculum and labouring over it once more with nitty-gritty technical detail and terminological hair-splitting is bound leave many cold. They might well ask what the point is, because we know perfectly well what cadences are. But it is precisely because cadences are so easy to take for granted that they are such worthy subject matter – especially for those interested in eighteenth-century music, in which they play such a vital role in creating variety and shape. If its cadences are familiar to us, it is because they are essentially formulaic and more or less accessible to listeners. On the one hand, standard use affirms the ‘rules of the game’, and on the other, deviations from expected cadential outcomes are measured against those norms, thereby reinscribing them as conventions. Cadences are therefore at the heart of this music's communicability, and a more deliberate and informed engagement with them cannot but enrich an appreciation of the repertory. In recent music-theoretical scholarship, much attention has been devoted to the subject, and especially to the role cadences play in shaping and dramatizing large-scale form, following landmark work by Janet Schmalfeldt (‘Cadential Processes: The Evaded Cadence and the “One More Time” Technique’, Journal of Musicological Research 12/1–2 (1992), 1–52) and William Caplin (Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven (New York: Oxford University Press, 1998); ‘The Classical Cadence: Conceptions and Misconceptions’, Journal of the American Musicological Society 57/1 (2004), 51–117). This volume reminds us again how much we stand to gain from developing our understanding of cadences.

Naturally, What Is a Cadence? does not seek to answer the eponymous question, but rather ‘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’ (10), reflecting the book's origin in papers delivered at a conference held in Rome in 2011. This multiplicity of perspectives naturally entails some opposing views. For example, in spite of some beautiful analytical explanations, Danuta Mirka's assertion that a cadential six-four chord had the potential to function as either a dissonant ${\rm V}{}^{\raise-1pt\hbox{$_{6}$}}_4$ or a consonant ${\rm I}{}^{\raise-1pt\hbox{$_{6}$}}_4$ in the eighteenth century will be hard to swallow for readers who only hear the chord as embellishing a dominant. The subjective experience of cadences is in fact directly addressed by David Sears, who discusses the results of a psychological experiment into the perception of closure. His findings reveal discrepancies between non-musicians and musicians, most notably in the degree of phrase completion ascribed to deceptive cadences. However, because the experiment was consciously premised on one set of theoretical assumptions, some of those expert listeners may find its results to be limited in scope – limited, that is, to the theory it was in effect testing.

A challenge to one of Sears's theoretical assumptions comes from Poundie Burstein's contribution to this volume (separate from his similarly titled article ‘The Half Cadence and Other Such Slippery Events’, Music Theory Spectrum 36/2 (2014), 203–227), in which Burstein refutes the common assertion that a half cadence must end with a root-position dominant triad. He provides ample evidence from a wide-ranging repertory that shows inverted dominants, dominant sevenths and even inverted dominant sevenths appearing in what, according to ‘other contextual features’ (98), clearly feel like half cadences. Yet in his very generous list of examples he cites alleged half cadences that appear in vastly different situations, so those ‘contextual features’ will be a locus of some disagreement – in part because the half cadence is probably the least well theorized of the major types. Thus it is very pleasing indeed to see it come under systematic scrutiny in this book.

Two other essays besides Burstein's focus on the half cadence. Nathan John Martin and Julie Pedneault-Deslauriers attempt to categorize different subtypes of half cadence in their corpus analysis of Mozart's piano sonatas, and Vasili Byros discusses the role of two galant schemata in marking half cadences of formal significance. Martin and Pedneault-Deslauriers identify four types according to the textural disposition of ‘clausulae’, or cadential voice-leading strands, thereby taking an important step towards clearing up the general murkiness surrounding the half cadence. These types are indeed recognizably different, yet the authors still attempt to link them all together in one single definition. This is a virtuosic display of analytical skill, with scale-degree substitutions and elliptical compressions permitted in the definition, as well as the omission of voices whereby ‘one, two, or even three of the abstract clausulae may be left implied’ (204). It is all completely defensible and rooted in the venerable tradition of speculative theory, but I feel a disconnect here from musical perception: if, say, a half cadence that ends the antecedent phrase of a period with a perfunctory I–V sounds like a separate proposition from one that labours a pre-dominant, tonicizes V and initiates a modulation to that key, then surely the differences in their respective contrapuntal structures are more telling than the purported kinships. The authors do suggest that an investigation into ‘the probable correlations between half-cadential type and formal location’ (205) would be an obvious next step, so they evidently anticipate that the findings of such a study would help further to distinguish between half-cadential subtypes. Yet in their conclusion they somewhat neglect the role of formal context.

This is where Byros's contribution has a lot to offer. Concentrating on the half cadence that ends a sonata-form exposition's transition section, he notes an impressive statistical preponderance of cases in music from the later eighteenth century in which that particular cadence is emphasized by the use of one or both of two common ‘phrase-level’ patterns (222): the cadence may be reached by what he has elsewhere named the le–sol–fi–sol schema on account of those pitches being present in the bass (‘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 dissertation, Yale University, 2009)); and it may also be prolonged by a variant of Robert Gjerdingen's Fenaroli schema (Music in the Galant Style (New York: Oxford University Press, 2007)). The latter is typically a canonic or quasi-canonic pairing of $\hat{7}\hbox{$-$}\hat{1}\hbox{$-$}\hat{2}\hbox{$-$}\hat{3}$ in the bass and $\hat{2}\hbox{$-$}\hat{3}\hbox{$-$}\hat{7}\hbox{$-$}\hat{1}$ or $\hat{4}\hbox{$-$}\hat{3}\hbox{$-$}\hat{7}\hbox{$-$}\hat{1}$ in the treble, usually repeated, and featuring a dominant pedal in an inner voice – or in Byros's variant, in the bass. In observing that this combination of schemata is most likely to occur at the end of a sonata-form transition section (and presumably in analogous modulating sections in other forms), Byros gives us reason to assume that the half cadence found there is often of an altogether different type – in terms of its rhythm, counterpoint, pre-dominant harmonies and so forth – from one used, for instance, within an opening theme. Interestingly, Gjerdingen has claimed that the Fenaroli was often used in earlier sonatas in positions that would later be occupied by the second theme (462), so if the Fenaroli was also often used as a transition-suffix, then the connection between these two subtly but significantly different scenarios would be worth investigating.

The particularities of context can complicate even the most elegant definition, so it is in an admirable spirit of open discourse that all three essays on half cadences have appended long lists of musical examples not printed in the book. The reader should take these as an invitation to engage the subject matter head-on, and, indeed, this is where a lot of the fun lies. Martin and Pedneault-Deslauriers's ‘simple I–V half cadence’ (192), for example, appears not to be so simple after all. What comes before the cadence in such cases surely merits further research, for in many of the passages they cite the penultimate tonic is prolonged by another of Gjerdingen's galant schemata, such as the Prinner (see below), Fenaroli or even the Fonte (a short sequence typically manifested as [ ${\rm V}{}^{\raise-1pt\hbox{$_{6}$}}_5$ ]–ii– ${\rm V}{}^{\raise-1pt\hbox{$_{6}$}}_5$ –I). This produces a far faster pre-cadential harmonic rhythm than is found in Byros's le–sol–fi–sol, or in half cadences featuring an Indugio schema that dwells on $\hat{4}$ before the bass rises through ♯ $\hat{4}$ to $\hat{5}$ .

Burstein's list raises the question of tonal context, as several of his examples feature a dominant (seventh) that has little or no diatonic connection to the immediately preceding material (such as moving straight from i to ${\rm V}{}^{\raise-1pt\hbox{$_{6}$}}_5$ /III]. For him, a half cadence marks a ‘phrase endpoint’ (89), as determined by the congruence of various musical elements – but the mere presence of some form of dominant chord at the end of a phrase, irrespective of what key that chord implies and whether the ensuing music is in that key, is surely not enough to make that ending a half cadence. Caplin would call this a ‘dominant arrival’ (Classical Form, 75) and in such instances this seems the better choice, notwithstanding Burstein's valid objections to the term in certain other cases (104, note 35). Surely some kind of set harmonic progression must precede the half-cadential goal, but how many chords are required? If a cadence is a musical event that relies on expectations, then those expectations will logically need to be set up by more than the final chord alone. Byros, in one of his lists, cites keyboard sonatas by Domenico Cimarosa as instances of his Fenaroli variant, but the majority of these feature only parallel motion in the upper voices, not the schema's characteristic imitation. I would argue that is not enough to claim those passages are closely related to the Fenaroli, even though they are definitely schematic: rising and falling through ${}^{\raise-1pt\hbox{$_{5}$}}_3$ , ${}^{\raise-1pt\hbox{$_{6}$}}_4$ and ${}^{\raise-1pt\hbox{$_{7}$}}_5$ sonorities over a held bass is a procedure familiar from baroque solo string writing, in which an open string provides the sustained or ostinato dominant pedal. Martin Rohrmeier and Markus Neuwirth, whose principal aim is to sketch a model of cadential syntax in the manner of a Chomskian generative grammar, also add to the discussion on half cadences. Printed last, their essay offers a number of common-sense observations that I had hoped the preceding authors would make (at least as more than a passing remark), such as that the metrical accent on the dominant in a half cadence is typically stronger than in an authentic one (to stay with North American terminology) and that a $\hat{6}\hbox{$-$}\hat{5}$ bass motion is generally reserved for half cadences (310–311).

Of course, further cadence types also appear in the book. In particular, a number of authors argue for a more nuanced view of authentic cadences. Drawing on treatises from eighteenth-century Salzburg, Felix Diergarten insightfully observes that relative strength among different instantiations of a perfect authentic cadence can be determined by the presence or absence of suspended dissonances, notably over the dominant scale degree. A modern notion of the cadence that operates on the ‘reduction of an alleged “surface”’ (79) to harmonic verticalities will overlook this contrapuntal difference. Diergarten illustrates his point with thematic constructions that contain a perfect authentic cadence at both midpoint and end – a conundrum for those who maintain a theme can only have one such cadence – and shows that what in prevailing thinking would be classified as two instances of the same cadential type may in fact be quite distinct if the first contains no suspended dissonances but the second does.

William Caplin considers the conditions under which Robert Gjerdingen's Prinner schema can be said to effect authentic cadential closure. (In essence, the Prinner is a string of descending tenths featuring $\hat{6}\hbox{$-$}\hat{5}\hbox{$-$}\hat{4}\hbox{$-$}\hat{3}$ in the melody and $\hat{4}\hbox{$-$}\hat{3}\hbox{$-$}\hat{2}\hbox{$-$}\hat{1}$ in the bass, and is often used to end a phrase.) He contrasts those conditions with instances in which the bass makes the schema prolongational or sequential, or when it produces the special case that he calls the ‘Prinner cadence’ (31). This essay, like Byros's, enriches our understanding of galant schemata by systematically demonstrating the different formal functions that a schema can take on, which in turn opens new doors to analysis. For instance, the contrapuntal similarity that can sometimes be noted between the prolongational Prinner and the Fenaroli (also prolongational) is perhaps more than superficial, not least because in the nineteenth century Schumann and other composers appear to have exploited that connection. Finally, Markus Neuwirth's essay, though primarily about deceptive cadences and their structural functions, also addresses authentic cadences, as he considers that these, too, should be regarded as deceptive when their expected melodic goal is averted. He prefers to regard deceptive cadences as strategies rather than as harmonic formulas such as V–vi: thus when the melodic line of an expected perfect authentic cadence deviates to $\hat{3}$ at the moment of cadential arrival, he would speak of a ‘deceptive PAC’ (129), as distinct from an imperfect authentic cadence where $\hat{3}$ was actually set up as the melodic goal. Neuwirth's point is well observed, but unless he proposes to theorize conventionalized usages of such tactics in the future, it is not evident that the ‘deceptive PAC’ really needs to be treated as its own conceptual entity when the narrative thread of cadential expectation, evasion and eventual fulfilment can be described perfectly well in other words.

This occasions some reflection on the coining of new terminology, which can easily lead to an unwieldy lexicon. We have seen this in the at times mathematical taxonomy of schemes and structures in recent theories of form (especially Caplin, Classical Form, and James Hepokoski and Warren Darcy, Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata (New York: Oxford University Press, 2006)), and in the quasi-anthropomorphic monikers given to the schemata in Gjerdingen's Music in the Galant Style. It does take an effort to familiarize oneself with so many names, but discussing music quickly becomes laborious without them and they doubtless aid conceptualization. One needs to strike a balance, however, for an increasing proliferation of highly specific terms can only lead to their being more narrowly interpreted. By contrast, if we accept that music can conform in diverse ways to a smaller number of models, then it becomes clearer how variety in instantiation reinforces the salience, and therefore conventionality, of those models.

Such engagement with convention is central to artistic creation and reception, especially in the eighteenth century. It is therefore not always necessary to divide larger concepts into distinct subcategories. Burstein, for instance, does not argue that half cadences ending with V⁷ or V⁶ should be treated as categories of their own, but that in determining half-cadential status we should take multiple factors into consideration rather than ruling an instance out on the basis of harmony alone. He also makes a salutary call for us to recognize that cadential status can be ambiguous, something that is often integral to the artistic transaction between composer and player/listener/analyst. In keeping with Burstein's approach, schema theory may be helpful in refining some aspects of cadential theories, whereby realizations are measured in terms of typicality rather than by whether or not they meet definite criteria. Byros champions this idea when he points out that ‘nothing in the epistemology of the schema concept would belie a schema-theoretic understanding of a harmonic cadence’ (219). And Sears, in comparing different models of cadential strength, suggests that listeners may possess either ‘a schematic representation explicitly for authentic cadential closure’ (278) that other cadential activity is heard to deviate from, or else ‘schematic representations of each of the genuine cadences [PAC, IAC, HC]’ (280). To whichever theoretical end one sees fit to apply it, the schema concept obviates the need for doctrinaire decisions on cadential status and highlights the reciprocal relationship between a given schema and its individual realizations, however varied.

For the same reason, however, we might query the necessity of Byros's new name for his Fenaroli variant: the ‘Fenaroli-Ponte’, so called because it holds a dominant pedal in the bass, like the Ponte schema. The term does reflect its form-functional role, but to invoke formal function is to invite harmonic function to the table as well, and there is functionally no difference between a Fenaroli that has the dominant pedal in the bass and one that has it in another voice. Gjerdingen had in fact already pointed out that the Fenaroli ‘was most often introduced following a modulation to the dominant key’ (Music in the Galant Style, 462), so one with a pedal bass is only a minimal departure from the schema as it is generally understood. But at least Byros works with Gjerdingen's established terminology. Martin and Pedneault-Deslauriers adopt Gjerdingen's ‘Converging Cadence’ for one of their half-cadential categories and then co-opt it for a form that does not feature the characteristic ♯ $\hat{4}$ in the bass (186–189). They also make no mention of Byros's le–sol–fi–sol cadence (despite listing three of his works in their bibliography), even though it has much in common with their ‘Doppia Half Cadence’ − a name of their own devising whose link to the Cadenza Doppia (an authentic cadence with the dominant elaborated over four beats, as in ${\rm V}{}^{\raise-1pt\hbox{$_{5}$}}_3\hbox{$-$}{}^{\raise-1pt\hbox{$_{6}$}}_4\hbox{$-$}{}^{\raise-1pt\hbox{$_{5}$}}_4\hbox{$-$}{}^{\raise-1pt\hbox{$_{5}$}}_3\hbox{$-$}{\rm I}$ or ${\rm V}{}^{\raise-1pt\hbox{$_{7}$}}_3\hbox{$-$}{}^{\raise-1pt\hbox{$_{6}$}}_4\hbox{$-$}{}^{\raise-1pt\hbox{$_{5}$}}_4\hbox{$-$}{}^{\raise-1pt\hbox{$_{5}$}}_3\hbox{$-$}{\rm I}$ ) is eloquently explained, but which may not sit well with readers who would rather those categories remained separate. Additionally, for all their good sense, Caplin's ‘Prinner cadence’ and ‘IAC (Prinner type)’ are nuanced concepts that may overcomplicate existing terminology, and one suspects readers may fail to retain their precise meanings, not least because one of the terms is used elsewhere in this volume without the same fine-grained discrimination (300, note 45).

Nevertheless, Caplin's insistence on detail reflects an engagement with the messiness of history and the small but ultimately significant changes that successive generations of composers wrought on musical language. He and Burstein are really the only ones fully to address the historical contingency of the musical phenomena they describe. Although the book's title indicates it deals only with ‘the Classical repertoire’, many of the essays seem tacitly to ascribe a little too much stylistic stability to that body of music. This can certainly be justified in the context of relatively short essays, but a more general awareness of the stylistic disunities within the period would have generally enriched the volume, as would wider consideration of the fact that the cadential strategies favoured at that time originated in earlier practices and continued, varied or unvaried, into later ones. Naturally, for pure theory to have total explanatory power it needs a precisely defined and stylistically consistent repertorial scope, but the choice of music in many of these essays also appears to reflect a predilection for music from the analytical canon. Indeed, the only really disappointing thing in this volume is how often the authors have looked no further than the Big Three, especially instrumental first movements, and it is a shame there is such an unimaginative overreliance on Mozart's piano sonatas (two essays theorize exclusively on the basis of those pieces). Nevertheless, each of the essays makes thought-provoking arguments and offers stimulating observations, and ones hopes that this important book will encourage a wider engagement with this cornerstone of tonal music.