TY - JOUR
AU1 - Ng, Samuel
AB - Abstract For centuries, theorists have debated whether musical phrases are normatively beginning-accented or end-accented. The last two decades of the twentieth century gave beginning-accented rhythm the upper hand; yet, recent work on end-accented phrases has reinvigorated the debate. I contribute to this discussion in two ways. First, I aim to rehabilitate a central position of end-accented rhythm by drawing attention to phrase-rhythmic tendencies in classical sentence structure. My analyses show that end-accented sentential schemas are well-established compositional options in various action spaces—including Primary and Secondary Themes—in late eighteenth- and early nineteenth-century instrumental music. Moreover, integral roles of end-accented sentential themes are substantiated by their production—in tandem with their beginning-accented counterparts—of large-scale progressions analogous to tonal and formal ones. Awareness of these sentential themes re-energizes the century-old debate and deepens our understanding of phrase rhythm as a source of musical meaning. Second, in order to achieve the first goal, I develop a theory of phrase-rhythmic progression for categorizing phrase-rhythmic types and mapping their trajectories. This theory fills a gap in current spatial representations of rhythm and meter, which focus on metric dissonances and hierarchies without considerations of phrase–meter interaction. INTRODUCTION In his in-depth dissection of the intellectual history behind three centuries of metrical theories, Roger Mathew Grant highlights a far-reaching repercussion of eighteenth-century reconceptualization of metrical accent that is still keenly felt today: “The tug between beginning accentuation and end accentuation … has haunted writings on meter since Kirnberger’s time.”1 While several influential theories from the 1980s have given beginning-accented rhythm an indisputable advantage in contemporary scholarship,2 more recent publications by David Temperley and myself have reinvigorated the debate by revealing integral roles of end-accented phrases in certain formal locales.3 William Rothstein has added yet another layer to the discussion by associating beginning- and end-accented rhythms with national styles.4 He examines the practice of what he calls the German and Franco-Italian meters in eighteenth-century music. In the former, hypermetrical downbeats are normatively aligned with the beginning of phrases; contrastingly, the latter employs either linguistic or phenomenal cues to schematically position the strongest hyperbeats at the end of phrases.5 This divergence demonstrates the highly complex history of metrical theories, which are often entangled with a wide array of issues, including national styles and their linguistic features, cognitive theories of time and performance, and the constantly evolving notions of “accent” and “meter”—terms that are notoriously difficult to define in theoretical discourse. In this article, I further the debate in two ways. First, I aim to rehabilitate a central position of end-accented rhythm. I challenge contemporary modes of hypermetrical interpretation that systematically privilege beginning-accented rhythm and propose an alternative view that recognizes a larger spectrum of rhythmic types than current theories of phrase rhythm. Analyses based on this view reveal end-accented propensities in the presentation function of sentences in late eighteenth- and early nineteenth-century instrumental music. Significantly, in tandem with their beginning-accented counterparts, these sentential themes often produce large-scale progressions that are analogous to tonal and formal ones. End-accented rhythm identified across national styles and formal zones re-energizes the centuries-old “tug” that Grant observes, on the one hand, and deepens our understanding of phrase rhythm as a source of musical tension and narrative, on the other. Second, in order to achieve the first goal, I develop a theory of phrase-rhythmic progression for categorizing phrase-rhythmic types and mapping their trajectories. DEFINITIONS AND TAXONOMY: BEGINNING-ACCENTED, END-ACCENTED, AND MIXED RHYTHMS Inspired by David Lewin’s seminal essay on Brahms’s Capriccio, Op. 76, No. 8, Richard Cohn, Daphne Leong, and Scott Murphy have proposed various versions of Zeitnetz as temporal analogs for the Tonnetz.6 A limitation in their utility, however, is that these spaces are primarily designed to model metric dissonance relationships (especially between duple and triple), and are therefore ineffectual for passages that are metrically consonant.7 Furthermore, metric states in these spaces are defined exclusively by the hierarchical organization of time spans without consideration of group–meter interaction; in other words, these spaces are fundamentally metric, not phrase-rhythmic. In response, I propose (1) a taxonomy of phrase-rhythmic types and (2) geometric spaces that model the relationships among these types in order to remedy the current lack of theoretical tools for tracing large-scale phrase-rhythmic progressions. While most studies categorize phrase-rhythmic types into binaries (e.g., “in phase” versus “out of phase”; “beginning-accented” versus “end-accented”; “German” versus “Franco-Italian”),8 I propose a tripartite taxonomy by adding a category I call “mixed rhythm” to beginning-accented and end-accented rhythms. The last two have been sufficiently defined in current research, with Temperley offering the most detailed formulation.9 The newly proposed “mixed rhythm” encompasses phrase-rhythmic constructions that contain both beginning- and end-accented characteristics. This mixture results from a variety of factors, as will be discussed below. Example 1 presents the most common scenarios of all three categories. The nomenclature requires some preliminary explanation. To most readers, the use of Arabic numbers evokes the analytical tradition of scholars such as Eric McKee and Rothstein; their numbers represent configurations of hyperbeats within melodic groups.10 In this tradition, hyperbeats are intrinsic to the musical structure and conform to a cyclic ordinal sequence (i.e., beat 1 is always followed by 2, 2 by 3, 3 by 4, and 4 by 1), although any given beat may be durationally expanded or contracted to create surface irregularities. In contrast, John Paul Ito offers an approach that aims to bridge the gap between analytical and cognitive approaches:11 he uses Arabic numbers to denote heard hyperbeats within what he calls “hypermetrical schemas,” which are essentially “cognitive template[s] against which new inputs can be matched and … comprehended.”12 His “1–2–3–4” and “2–3–4–1” schemas are thus mental constructs that help to process and evaluate individual hypermetrical stimuli. Using his approach, Ito is able to describe (hyper)beats at any level of the metric hierarchy in the form of X/Y: the first number X specifying the beat function (position), the second number Y the size (cardinality) of the (hyper)measure. For example, a hyperbeat may be designated 3/4, which denotes the third beat of a four-beat hypermetrical pattern. Compared with both the analytical and cognitive approaches as he defines them, Ito’s system is more tolerant of various hypermetrical hiccups caused by the incongruence between an irregular grouping structure (e.g., a 2 + 4 + 2 grouping of an eight-measure phrase) and a hypermetrical schema (e.g., 1–2–3–4). EXAMPLE 1. Open in new tabDownload slide A tripartite taxonomy of phrase-rhythmic types EXAMPLE 1. Open in new tabDownload slide A tripartite taxonomy of phrase-rhythmic types My use of Arabic numbers in Example 1 essentially follows Ito’s formulation based on heard hypermeasures and hyperbeats, but with three main differences. First, whereas Ito focuses on three main schemas that correspond to my rhythms (a), (a'), and (f)—he calls them the 1–2–3–4, 2–3–4–1, and hybrid schemas, respectively, I include other schematic possibilities in hypermeter-grouping alignment, notably the 4–1–2–3 and 3–4–1–2 rotations that are absent from his discussion.13 Second, while Ito’s templates are more akin to Candace Brower’s “metrical grouping”—a concept of hypermeter based on counting—my sense of hypermeter is more aligned with Brower’s accentual meter—a concept of hypermeter predicated on a sense of accented downbeat due to phenomenal cues.14 Finally, I account for the embedment of a lower-level schema within a higher-level one. For example, scenario (b) is distinct from scenario (a) because of the embedment of the 1–2 schema within the 1–2–3–4 due to reasons that I will explain later. In Ito’s terms, I imagine in these nested schemas the concurrent activation of multiple “metric windows.”15 The taxonomy in Example 1 consists of several distinctive features that set it apart from its precursors, such as those by Temperley and McKee.16 First, original to my taxonomy is the division of both beginning- and end-accented rhythms into “strong” and “moderate” types. Strongly beginning- and end-accented rhythms are so-called because the most accented beats occur at the extremities (as the first and last beats in the group respectively). Scenario (a), equivalent to Ito’s 1–2–3–4 schema, represents the most prototypical of the strongly beginning-accented type. In this type, the four-beat pattern is maximally in phase with its formal grouping. As mentioned earlier, I consider scenario (b) to be distinct from (a): the presence of a lower-level 1–2 schema in (b) is usually promoted by heavy group boundary and melodic parallelism,17 both factors engendering a lower level strong beat in the middle of the higher-level 1–2–3–4 schema. These elements are particularly pertinent to sentential forms, where a four-measure presentation function and its two-measure components (the basic idea and its repetition) support four-beat and two-beat patterns simultaneously. Another important feature of the taxonomy is its underlying symmetry. Strongly end-accented scenarios (a') and (b') may be understood as the opposites of strongly beginning-accented scenarios (a) and (b). By “opposites,” I do not mean a retrograde of beat functions (i.e., 4–3–2–1). In metrical theories, beat functions are of course non-retrogradeable; however, they are permutable as they interact with group boundaries. In this sense, (a') and (b') are the opposites of (a) and (b) because of the diametrical locations of the downbeats. This principle implies that 1–2–3–4 and 2–3–4–1 are opposites at the four-beat level, while 1–2 and 2–1 are opposites at the two-beat level. The antithetical relationship between (a)/(b) and (a')/(b') is similarly present between the moderately beginning-accented (c)/(d) and moderately end-accented (c')/(d'). Compared to the “strong” category, the “moderate” designation denotes a less distinctive flavor of rhythmic characters, although the fundamental difference between beginning- and end-accented rhythms remains evident. One factor that causes the attenuation of beginning- or end-accentedness is the positioning of the downbeat at an internal beat location. This can be seen in scenario (c), where the metrical accent is found on the second position instead of the first. According to Temperley’s second definition, this rotation of the four-beat pattern is still considered beginning-accented, although the beginning-accentedness is relatively less pronounced than cases (a) and (b).18 Scenarios (d) and (e) are considered moderately beginning-accented for a different reason: only two beat functions are present in these scenarios,19 implying that there is less metric content to distinguish the downbeats from the rest of the group. Opposite constructions may again be identified in the end-accented category, where scenarios (c'), (d'), and (e') constitute the counterparts to (c), (d), and (e) in the same way as (a') and (b') are to (a) and (b). The third category in the taxonomy comprises cases of mixed rhythm in the middle column of Example 1. Mixed rhythms are those that contain both beginning- and end-accented characteristics due to either a group extension (hereafter the “extension” type), or the presence of groups of different rhythmic types at different metrical levels (hereafter the “incongruent” type). The arrows in Example 1 show how the mixed types combine specific characteristics of beginning-accented and end-accented categories. Scenario (f), an extension type, often appears with group (phrase) overlap at a major formal juncture.20 Although the group begins with the 1–2–3–4 schema (scenario [a]), it also closes with the 2–3–4–1 schema (scenario [a']), rendering it both beginning- and end-accented.21 Similar to (f), scenario (g) also involves extension, but only at the level of duple groups derived from (d) and (d'). Scenarios (h) and (i) are examples of the incongruent type, in which groups at different levels contradict one another in their rhythmic characteristics. In (h), the four-beat pattern is identical to (c) and is therefore moderately beginning-accented. However, the subgroups here project an embedded end-accented 2–1 schema, similar to that in (b'). The entire structure is therefore beginning-accented on one level, but end-accented on another. Finally, in scenario (i), a moderately end-accented schema (c') contains beginning-accented groups from (b). The resulting structure is the opposite of (h). Example 2 provides a spatial map that helps relate the rhythmic types in the taxonomy. The five main categories—strongly beginning-accented, moderately beginning-accented, mixed, moderately end-accented, and strongly end-accented—are arranged horizontally from strong beginning-accentedness on the left to strong end-accentedness on the right. Within each category, subtypes are strategically positioned to demonstrate two sets of symmetrical relationships: types connected by the solid lines are opposites as defined above, while the dotted lines show derivations of mixed types from the other two categories also described in the preceding discussion. The whole diagram provides a map for tracking the overall phrase-rhythmic progression of a passage. On the one hand, the horizontal plane traces fluctuations in beginning- and end-accentedness; on the other hand, the vertical columns keep record of the utilized rhythmic types in each category, providing a kind of “heatmap” to show the level of participation in various locations of the horizontal spectrum. EXAMPLE 2. Open in new tabDownload slide A linear phrase-rhythmic space EXAMPLE 2. Open in new tabDownload slide A linear phrase-rhythmic space While I have set forth categorical distinctions between duple and quadruple schemas (to differentiate between moderate and strong subtypes) as well as between single-level and multi-level schemas (e.g., [a] and [b]), measurements based on my taxonomy will likely be more experientially driven than those of conceptual distances in formalistic spaces, such as in Cohn’s ski-hill graph and Zeitnetz, where ski-hill paths and metric nodes represent precise complexes of beat subdivisions objectively verifiable both visually and sonically.22 Scholars have by and large agreed that phrase-rhythmic analysis is inherently subjective, as groups and hypermeasures are often permeable to different interpretations and revisions.23 In this light, the types in Example 2 are necessarily interpretive representations based on perception (“heard” hypermeasures and groups) rather than intrinsic and fixed properties. Phrase-rhythmic progressions on the map should thus be considered not just as states traversed, but also as contours outlined. Depending on performance tempi and listening habits, two analysts reading the same passage may possibly be attending to different levels of the metric hierarchy and hence starting at different points on the map. Nonetheless, disparate shapes of phrase-rhythmic paths derived from different interpretations could well find common hinge points and foci even if their content may not be precisely identical. Example 3(a) shows the Secondary-Theme and Closing zones of the first movement of Beethoven’s Piano Sonata in C major, Op. 53 to demonstrate the utility of the map in Example 2. I have formerly argued that the cadence in m. 74 is a much stronger candidate for the Essential Expositional Closure than the previous two PACs in m. 42 and m. 50 because of the marked change from beginning-accented to end-accented rhythm at m. 74.24 The diagram shown in Example 3(b) refines my previous analysis by charting a teleological progression from beginning- to end-accented types. As Example 3(a) shows, the Secondary Theme begins with strongly beginning-accented rhythm (a) in mm. 35–49 (the score begins in m. 43). Beginning in m. 50, however, grouping structure tightens from four-measure to two-measure units; at the same time, motivic parallelism between the two-measure groups in mm. 50–51 and 52–53 suggests a reduction from four-beat to two-beat schemas, implying a change from rhythm (a) to (d).25 The following passage from m. 54ff continues to privilege rhythm (d), as hypermetrical accents are implied by various phenomenal changes at two-measure intervals.26 Rhythm (d) persists through what James Hepokoski and Warren Darcy call the “excursus” passage27 until mm. 70–74, where the last group before the cadence—anchored by the dominant harmony and uniform in texture and rhythm—articulates the expansion type of mixed rhythm (f). The closing zone ensues in m. 74ff, and carries the phrase-rhythmic progression to strongly end-accented rhythm (a')—the opposite of (a) where the whole passage began.28 Most interestingly, the codetta in mm. 82–85 briefly passes through rhythm (d'); not only is (d') the opposite of (d) in the excursus, but it also “completes the aggregate” by involving the lone remaining phrase-rhythmic category before the journey returns to beginning-accented rhythm (at either the repeat of the Exposition or beginning of the Development). EXAMPLE 3. Open in new tabDownload slide (a) Beethoven, Piano Sonata in C major, Op. 53, first movement, mm. 43–86. (b) Phrase-rhythmic progression EXAMPLE 3. Open in new tabDownload slide (a) Beethoven, Piano Sonata in C major, Op. 53, first movement, mm. 43–86. (b) Phrase-rhythmic progression EXAMPLE 3. Open in new tabDownload slide [continued] EXAMPLE 3. Open in new tabDownload slide [continued] Although the linear arrangement of rhythmic types in Example 2 makes intuitive sense, it nevertheless undermines a potentially significant theoretical relationship within a subset of rhythmic types in Example 1. Example 4 extracts this subset—the four basic rotations of the four-beat pattern from Example 1 (rhythms [a], [a'], [c], and [c'])—and puts them in a hyper-cycle.29 A clockwise move on the hyper-cycle shifts the beat functions “to the left” by one position, while a counterclockwise on the hyper-cycle shifts the beat functions “to the right” by the same degree. A feature of the hyper-cycle not represented in the linear space in Example 2 is a direct connection between (a) and (a'), and by the same token, a direct connection between (c) and (c'). Despite sitting at the extremes of the linear spectrum, (a) and (a') are nevertheless related by a single shift in Example 4. This close relationship between (a) and (a') reveals a contradiction between the linear and cyclic spaces in Examples 2 and 4: the distance between (a) and (a') is smaller in the hyper-cycle than that between (a) and (c') or that between (a') and (c), while the opposite is true in the linear space, where the distance between (a) and (a') is the maximum distance possible between two rhythms. The two models suggest complementary ways of conceptualizing the relationship between beginning- and end-accented rhythms, and both models find their relevance in passages analyzed below. EXAMPLE 4. Open in new tabDownload slide An alternative space of strongly beginning- and end-accented rhythms EXAMPLE 4. Open in new tabDownload slide An alternative space of strongly beginning- and end-accented rhythms METHODOLOGY: PHENOMENAL ACCENTS AND THE “STRONG BEAT EARLY RULE” As already noted, analysis of phrase rhythm—especially when hypermetrical levels are involved—has inevitably admitted a high degree of subjectivity, even when analysts appeal to formalistic rule systems. Identifying hypermetrical downbeats entails making many cognitive and analytical decisions regarding perceived and internalized accents and patterns. Contemporary studies tend to view beginning-accented rhythms as normative and end-accented ones as ad hoc, animated by national styles or form-functional schemas. This trend seems to have been, at least to some extent, a result of the broad rejection of Hugo Riemman’s metrical theory and its offshoots, which are often adjudged dogmatic and outdated.30 Yet, another significant impetus may have originated from one of Fred Lerdahl and Ray Jackendoff’s preference rules—their “strong beat early rule”—which Temperley renames “grouping rule” and Rothstein calls “rule of congruence.”31 The essence of the rule may be summarized as follows: the downbeat (i.e., beginning) of a metrical unit is preferably positioned as close to the beginning of a melodic group as possible so that the melodic group and the metrical unit are as congruent (i.e., temporally in phase) as possible. This rule has given the most significant support for beginning-accented rhythms in contemporary research, its perceptual reality, and prescriptive weight often presumed without further contextual interrogation from case to case.32 Yet, there are good reasons to re-evaluate our collective confidence in the rule when applied to hypermetrical analysis. First, rarely considered is the fact that Lerdahl and Jackendoff conceive of this rule as a “weak” one, and have only demonstrated its application at a local metrical level.33 In an earlier chapter of their book, where they discuss the hypermeter of a four-measure phrase, they state that “a dogmatic preference for either [beginning-accented rhythm] or [end-accented rhythm] would distort the flexible nature of the situation.”34 Application of the strong beat early rule in subsequent analytical literature to categorically privilege beginning-accented phrases seems therefore an overreach in light of the original intent of the rule. Second, there is a general lack of clarity as to how the rule is able to systematically overrule other factors. Carl Schachter’s explanation of why he views beginning-accented rhythm as normative may shed some light on this confusion: In my earlier essay, I discussed the rather prevalent view [of Riemann, Komar, and Cone] that phrases are normally end-accented, that the final cadential chord falls on an accent or downbeat. I disagree with this view and follow Schenker in assuming that the final tonic of a phrase does not normally receive an accent. I see no reason to believe that the metrical organization of a group of measures differs in principle from that of a single measure and assume that both are beginning- rather than end-accented.35 The problem with this explanation hinges on the ambiguous meaning of “a group of measures.” From the preceding context, it is clear that Schachter initially uses the expression to denote a phrase. However, when he later compares the same group of measures with a single measure, the expression becomes equated with a hypermeasure. Inadvertently, the explanation exemplifies the common conflation between phrases and hypermeasures, making the axiomatically beginning-accented hypermeasure an uncomfortable bulwark for axiomatically beginning-accented phrases. To consider this further, the current acceptance of the strong beat early rule is also motivated by certain cognitive expediencies. One of these stems from the way we learn and perform conducting patterns beginning on the downbeat. As the basic four-beat pattern (down–in–out–up) is familiar both mentally and physically, conducting the hypermeter of a phrase with an accented beginning simply feels the most natural. Yet, just as motives do not always begin on a downbeat, phrases ought not to start on a strong beat to accommodate a familiar conducting pattern. A second expediency has to do with the way we count with ordinal numbers the number of measures in a phrase when assessing its length.36 Oftentimes, assessment of the hypermeter becomes conflated with measuring the length of a (sub)phrase37; the habitual start from ordinal number “1” when counting measures thus unintentionally privileges beginning-accented rhythm as the default. My approach recaptures the essence of Lerdahl and Jackendoff’s strong beat early rule by limiting its prescriptive power in hypermetrical analysis, putting instead a higher premium on contextual evidence. I propose that when locating the first hypermetrical downbeat, the strong beat early rule serves as an auxiliary principle or tie-breaker. Only when phenomenal accents are inconclusive will the strong beat early rule be invoked to prefer beginning-accented rhythm for the cognitive reasons stated in the previous paragraph. When phenomenal accents are clearly concentrated in the second half of groups, however, the strong beat early rule yields contextual input and makes room for end-accented readings.38 Admittedly, these changes to the theoretical system will generate hypermetrical readings that may seem implausible to listeners familiar with the beginning-accented orientation in contemporary practice. I maintain, however, that my analytical decisions are rigorously predicated on the methodology presented here; the ostensible idiosyncrasies of the results find precedents in various historical methods (such as Riemann’s) prior to the solidification of current trends in American scholarship on the one hand, and receive support through newfound “hypermetrical economies” within the composition on the other. To put it another way, my aim is not to provide a descriptive account of the intuition of contemporary expert listeners, but to envision a theory that blends considerations of phenomenal input with explanation of individual compositional strategies and designs. Example 5 provides an illustration of how these changes help reimagine the phrase rhythm of two sentential openings in Beethoven’s Piano Sonatas, both of which have been presumed to be beginning-accented in the literature.39 In Example 5(a), the basic idea opens with an initial attack that is durationally marked, texturally and harmonically robust. The dominant chord in m. 2 presents no conspicuous intensification of phenomenal accents; only the bass note provides a slightly stronger registral emphasis. Without an unequivocal differential in accentual weight between m. 1 and m. 2, the strong beat early rule is applied to prescribe a preference for m. 1 to be hypermetrically strong. The opening of Example 5(b), however, presents a different scenario. The downbeat at m. 1 receives tenuous durational, textural, and harmonic emphasis.40 Even though the opening leap of a minor sixth subtly accentuates the B♭, the leap to the C in m. 2 is comparatively more weighted, harmonically, texturally, and durationally. The holistically stronger emphasis of m. 2 gives the basic idea in mm. 1–2 a Riemannian anacrustic shape.41 This rhythmic profile persists through the rest of the sentential Primary Theme and Transition, as phenomenal accents continue to populate even-numbered measures.42 EXAMPLE 5. Open in new tabDownload slide Two Primary Themes from Beethoven’s Piano Sonatas. (a) Op. 2, No. 3, mm. 1–8. (b) Op. 49, No. 1, mm. 1–15 EXAMPLE 5. Open in new tabDownload slide Two Primary Themes from Beethoven’s Piano Sonatas. (a) Op. 2, No. 3, mm. 1–8. (b) Op. 49, No. 1, mm. 1–15 A fundamental methodological question may be raised about my reading of Example 5(b): instead of taking the phenomenal cues in m. 2 as downbeat-affirming, would it not be more profitable to preserve beginning-accented rhythm (by invoking again Lerdahl and Jackendoff’s strong beat early rule), hearing m. 2 in this context as a counterstress or syncopation instead?43 In fact, there may still be other related possibilities, such as hearing the even-numbered measures as projecting either a “shadow meter,” to use Frank Samarotto’s celebrated term, or Harald Krebs’s concept of a displaced metrical layer, against the primary hypermeter.44 Similar alternatives are arguably conceivable for the remaining analyses in this article; potential feasibility of any of these alternatives would seem to cast doubts on the necessity of my readings. In response, I offer the following observations. First, the alternatives listed above share one commonality: they involve hearing some degree of rhythmic and/or metric conflict. This implication contradicts the character of the opening of Example 5(b) and many other similar instances, which contains minimal suggestion of (hyper)metrical instability. My methodology thus stands apart from the alternatives in that it allows end-accented configurations to be referential (or, more simply, “metric” instead of “antimetric,” to borrow Schenker’s term).45 Second, while I acknowledge that choosing among these analytical options may still be contingent on personal preferences and habits, I will demonstrate that my end-accented readings bring with them an additional hermeneutical layer not accessible through the antimetric alternatives. Example 6(a), which shows a contrapuntal reduction and hypermetric rendering of Op. 49, No. 1, illuminates this point. A significant interest of this interpretation concerns the hypermetrical position of a recurring descending-second motive in the middleground (boxed in the example) and its expressive role in the Primary Theme. As shown in the reduction, the motive is characterized by stepwise resolutions of 4̂ and 6̂ to tonic-triad members 3̂ and 5̂ respectively; an end-accented hearing of the passage underscores the poignancy of these descending gestures by conferring on them the character of an accented sigh motive.46 Another point of interest is the fact that the end-accented reading in Example 6(a) finds a rhythmic companion in the Primary Theme of the last movement, shown in Example 6(b). According to William Caplin’s paradigmatic eight-measure sentence, the four-measure sentences in mm. 1–4 and mm. 5–8 may be more appropriately understood as eight-measure sentences in 38 ⁠.47 Beethoven’s barlines are in this light de facto barlines of a two-measure hypermeter—the same “even-strong” hypermeter as the one I posit for the beginning of the first movement. The alternative barring I show in Example 6(c) “normalizes” the subphrases to a beginning-accented orientation. This reading (barring), while in line with the beginning-accented view, contradicts the conspicuous difference in phenomenal (textural, contour, and harmonic) weights between the second and the fifth eighth notes. That Beethoven expressly employs end-accented rhythm in the last movement lends further credence to an end-accented reading of the Primary Theme in the first movement. EXAMPLE 6. Open in new tabDownload slide Beethoven, Piano Sonata in G minor, Op. 49, No. 1, first movement. (a) Contrapuntal reduction and hypermetrical grouping. (b) Opening of the third movement, mm. 1–8. (c) Opening of the third movement (renotated) EXAMPLE 6. Open in new tabDownload slide Beethoven, Piano Sonata in G minor, Op. 49, No. 1, first movement. (a) Contrapuntal reduction and hypermetrical grouping. (b) Opening of the third movement, mm. 1–8. (c) Opening of the third movement (renotated) BASIC IDEA WITH AN ACCENTED MIDDLE: THE RHYTHMIC PROBLEM The above discussion of Example 5(b) reveals an important source of end-accented rhythm in an opening sentential theme: a basic idea that grows from a relatively restrained beginning to a phenomenally emphatic middle. Excerpts in Example 7 summarize the various dimensions in which this growth may occur. It must be noted that even though these themes exhibit some form of growth to the middle of the basic idea, they do not all immediately exude irrefutable end-accentedness, nor do the following materials always track identifiable rhythmic paths spawned by the opening theme. Nonetheless, sensitivity to an accented middle in the basic idea could potentially help explain later phrase-rhythmic features of the passage. EXAMPLE 7. Open in new tabDownload slide Various phenomenal accents in the middle of the sentential basic idea. (a) Melodic contour, Beethoven, Piano Sonata, Op. 2, No. 1, first movement, mm. 1–2. (b) Dissonance, Mozart, Piano Sonata, K. 310, first movement, mm. 1–2. (c) Texture, Mozart, Symphony No. 41, K. 551, third movement, mm. 1–4. (d) Dynamics, Beethoven, Piano Sonata, Op. 7, third movement, mm. 1–4. (e) Duration and bass register, Haydn, Symphony No. 98, first movement, mm. 1–2. (f) Beethoven, Piano Sonata, Op. 7, third movement, mm. 106–141, durational reduction EXAMPLE 7. Open in new tabDownload slide Various phenomenal accents in the middle of the sentential basic idea. (a) Melodic contour, Beethoven, Piano Sonata, Op. 2, No. 1, first movement, mm. 1–2. (b) Dissonance, Mozart, Piano Sonata, K. 310, first movement, mm. 1–2. (c) Texture, Mozart, Symphony No. 41, K. 551, third movement, mm. 1–4. (d) Dynamics, Beethoven, Piano Sonata, Op. 7, third movement, mm. 1–4. (e) Duration and bass register, Haydn, Symphony No. 98, first movement, mm. 1–2. (f) Beethoven, Piano Sonata, Op. 7, third movement, mm. 106–141, durational reduction One telling instance here is Example 7(e), which shows a reduction of the beginning of the last movement of Haydn’s Symphony No. 98. In many sonata-form movements in Haydn’s late symphonies, the Primary Theme elides with the tutti onset of the Transition, causing what Rothstein calls a metrical reinterpretation.48 The need for this adjustment is eliminated, however, if we allow the growth to the middle in Example 7(e) to reorient the opening theme hypermetrically, thus altering the following phrase-rhythmic trajectory.49 A similar outcome can be obtained when studying the larger context of Example 7(d), taken from the third movement of Beethoven’s Piano Sonata in E♭ major, Op. 7. In this case, an end-accented reading of the Minore is supported by at least three other elements, as shown in the durational reduction in Example 7(f): (1) the codetta of the Minuet clearly concludes with half of a four-bar hypermeasure in mm. 94–95, setting up the entry of the Minore at hyperbeat 3; (2) the Minore culminates in a structural downbeat at m. 138, where the climactic arrival at the only PAC of the section ascertains a hypermetrical downbeat as well; and (3) the downbeat heard in m. 138 sets up end-accented 2–3–4–1 segments in the coda in mm. 139–146, with mm. 146–149 supplying a smooth hypermetrical transition back to 1–2–3–4 at the repeat of the Minuet. In many other sentential themes (including the rest of the themes in Ex. 7), sustenance of end-accented rhythm faces difficulties at the continuation function, where liquidation of the basic idea problematizes the end-accented shape suggested earlier. The continuation unit in this situation is phrase-rhythmically ambiguous; in a Schoenbergian sense, this ambiguity poses a rhythmic problem with further ramifications. Example 7(a) presents such a scenario, as an end-accented reading of the presentation function is confronted by a strong suggestion of hypermetric downbeat at the beginning of the continuation at m. 5 (not shown). Subsequent phrase-rhythmic developments in this movement may be related back to the tension between these mixed signals in the opening sentence.50 The Primary Theme of the first movement of Mendelssohn’s Piano Trio No. 1, Op. 49 illustrates how an elaborate rhythmic problem unravels through various stages. As shown in Example 8, a 3–4–1–2 pattern may be heard in the sentential P1.1 (mm. 1–16). This end-accented rhythm is first suggested in the initial four-measure basic idea by the dynamic, agogic, and contour accents in m. 3. It appears even more strongly in the repeated basic idea (mm. 5–8) through contour (both in the melody and the bass) and harmonic support of the downbeat at m. 7. In the continuation unit in mm. 9–16, the same rhythm remains palpable; despite the weaker contour, agogic emphases, and removal of dynamic accents, the accented 64 chord in m. 11 and dominant arrival in m. 15 reinforce these accented measures. Overall, four-measure groups in mm. 1–16 are characterized by an accented middle; consequently, the 3–4–1–2 schema may be heard as the referential rhythmic state of the opening. EXAMPLE 8. Open in new tabDownload slide Mendelssohn, Piano Trio No. 1 in D minor, Op. 49, first movement, mm. 1–71 EXAMPLE 8. Open in new tabDownload slide Mendelssohn, Piano Trio No. 1 in D minor, Op. 49, first movement, mm. 1–71 EXAMPLE 8. Open in new tabDownload slide [continued] EXAMPLE 8. Open in new tabDownload slide [continued] EXAMPLE 8. Open in new tabDownload slide [continued] EXAMPLE 8. Open in new tabDownload slide [continued] EXAMPLE 8. Open in new tabDownload slide [continued] EXAMPLE 8. Open in new tabDownload slide [continued] The phrase rhythm begins to shift, however, in the expanded consequent phrase in mm. 17–39. Although the basic idea in mm. 17–20 and its repetition in mm. 21–24 maintain features that support the 3–4–1–2 schema, the continuation unit in mm. 25–39 immediately subverts it. At the downbeat of m. 25, the hitherto most unequivocal root-position tonic triad, highest melodic point, and strongest dynamic level all converge at the onset of the continuation unit, shifting the rhythm emphatically to the beginning-accented 1–2–3–4. After an evaded cadence in m. 32, the repeated continuation unit delivers the same phenomenal accents in m. 33, even more strongly than before, to cement the change. The entire P1 thus epitomizes the inherent dialectic between an end-accented basic idea and a beginning-accented continuation. This tension forms the kernel of the rhythmic essay in the rest of the Primary Theme. The central rhythmic problem begins to unravel at the PAC in m. 39 and the subsequent entry of a new sentential theme, P2. As the PAC in m. 39 falls on a relatively strong hyperbeat, the two-measure basic idea of the following P2 must enter at a hypermetrically weak position and end at a stronger one.51 While the two-measure rhythm has thus returned to end-accentedness, four-measure rhythms have become less defined. Example 8 shows two parallel solutions to this ambivalence; these opposing possibilities reveal a continuing dialectic through which a meta-solution to the rhythmic problem emerges. To begin, solution A maintains the hypermeter from the end of P1, and renders the subphrases of P2 rhythmically 4–1–2–3. While this interpretation preserves beginning-accentedness secured at the end of P1, it encounters difficulty at m. 45, where the IV chord embedded in the middle of a series of parallel tenths seems too feeble to support a hypermetrical downbeat. Moreover, this solution receives progressively less support in the extended continuation in mm. 52ff. In other words, while viable at the onset of P2, solution A gradually loses steam and disintegrates. Running parallel to A is solution B, which begins with a hypermetrical downbeat at m. 39 via a metrical reinterpretation of the cadential arrival. As Temperley has pointed out, this type of reinterpretation is particularly common following an expanded cadential progression,52 exemplified here by the last eight measures of P1. The resetting of the four-bar hypermeter at m. 39 shifts the subphrases of P2 to a 2–3–4–1 pattern, implying a radical change from strongly beginning-accented to strongly end-accented rhythms across P1 and P2. This reading receives initial phenomenal support through the tonic triads in mm. 43, 47, and 51, gains traction in mm. 55 and 59 through agogic and registral accents in the top melodic line, and culminates in the strongest structural arrival hitherto in m. 67. In short, as solution A weakens progressively, solution B strengthens at the same time. These concurrent processes continue until m. 67, where an elided P-based Transition brings the tension-building process to its climatic close. Most significantly, the reappearance of the opening incipit at m. 67 has become strongly beginning-accented due to the indisputable downbeats at mm. 67 and 71. The refashioning of the main motive bestows on it a conspicuously different rhythmic character from its initial appearance, where m. 1 and 5 lack the phenomenal strength that m. 67 and 71 possess. The opening dialectic in P1 has found its synthesis at the conclusion of the P-zone. Example 9 maps the entire phrase-rhythmic progression of the Primary Theme onto the hyper-cycle in Example 4. As detailed above, the journey begins with the “home state” 3–4–1–2 in P1, which, as we have seen, concludes with an apparent shift to 1–2–3–4. This beginning-accented state may be short-lived; nonetheless, it introduces an “imbalance” (to use Schoenberg’s imagery53) to the home state, setting the phrase rhythm in motion. The trajectory proceeds with a “split” from the home state into its adjacent states 4–1–2–3 and 2–3–4–1 at P2, with the former gradually dissolving as the latter strengthens. Finally, 2–3–4–1 (as the main state of P2) resolves to 1–2–3–4 at the onset of the Transition. The path taken from 3–4–1–2 through 2–3–4–1 to 1–2–3–4 completes a counterclockwise rotation through three of the four states on the hyper-cycle, revealing a strongly directional rhythmic motion from an end-accented state to a beginning-accented one. Seen this way, the rhythmic journey may be further construed as an analog to the tonal trajectory between P1 and P2. Just as 2–3–4–1 of P2 appears in Example 9 as a transitional state between the home state 3–4–1–2 and the goal state 1–2–3–4, the tonally more dissonant P2 (characterized by the preponderance of fully diminished-seventh chords) is analogously an intermediary between the initial presentation of the tonic at P1 and its confirmation at the conclusion of the P-zone. EXAMPLE 9. Open in new tabDownload slide Mendelssohn, Piano Trio No. 1 in D minor, Op. 49, first movement, mm. 1–71, phrase-rhythmic progression EXAMPLE 9. Open in new tabDownload slide Mendelssohn, Piano Trio No. 1 in D minor, Op. 49, first movement, mm. 1–71, phrase-rhythmic progression BASIC IDEA FOLLOWING AN “INTRODUCTORY” DOWNBEAT GESTURE While the previous section demonstrates that attention to phenomenal accents loosens our subconscious grip on the strong beat early rule, recent research has also shown that conventionalized metrical schemas constitute another common generator of end-accented phrases. As mentioned at the beginning of the essay, the research of Ng, Rothstein, and Temperley has drawn attention to metrical schemas that induce end-accented rhythm at the closing zone of sonata form, on the one hand, and at the beginning of Italian operatic numbers, on the other. In both scenarios, an initial downbeat—articulated by a strong phenomenal accent—establishes the hypermetrical context in which ensuing phrases (or subphrases), lagging behind the hypermeasures, enter on a weak hyperbeat and conclude on a strong one. In this section, I explore a similar mechanism at the beginning of sentential themes that produces end-accented subphrases. This mechanism involves a forceful gesture at the presumed onset of a sentential function, while subsequent melodic groups—having been displaced from the initial downbeat—retroactively render the forceful gesture a pre-sentence event. The opening of Beethoven’s Piano Trio in E♭, Op. 1, No. 1, shown in Example 10, is a locus classicus of this category. A telling feature of the example is that the length of the opening sentence exceeds the normative eight measures by an extra beat in m. 9. To be sure, the addition of a beat to the standard eight-measure phrase is by no means uncommon: it often appears at the end of the Primary Theme, for instance, as a result of phrase expansion to create an overlap with the Transition section. The situation in Example 10, however, contains three anomalies: (1) the use of irregular phrase length in an opening, not concluding, statement of the Primary Theme; (2) the absence of clear internal expansions (through harmonic deceleration, internal repetition, etc.) that typically account for irregular phrase lengths; and (3) unclear subgroup boundaries due to apparent elisions, as indicated by the dotted slurs below the staff. On the last point, the irregular sentence seems to be a variant of what Hepokoski and Darcy call a “Mozartian loop.”54 A weakness of this interpretation, however, is that the opening chord and its corresponding gesture on the downbeat of m. 3 are, according to Lerdahl and Jackendoff’s GPR2b,55 weak onsets of groups due to the gap between them and the arpeggios that follow. In fact, the chord on the downbeat of m. 3, preceded by two quarter-note chords in m. 2, sounds more like the end of a group. EXAMPLE 10. Open in new tabDownload slide Beethoven, Piano Trio No. 1 in E♭ major, Op. 1, first movement, mm. 1–13 EXAMPLE 10. Open in new tabDownload slide Beethoven, Piano Trio No. 1 in E♭ major, Op. 1, first movement, mm. 1–13 A preferable reading of the subgroups is indicated by the brackets above the staff, which show the basic idea containing two motivic elements: an opening ascending arpeggio, and three staccato quarter-note chords. In this reading, the opening chord in m. 1 becomes an introductory metric and tonal marker rather than part of a proper group.56 Beethoven’s dynamic marking encourages this hearing, as the forte of opening chord is clearly distinguished from the piano of rest of the phrase. The grouping structure thus understood, the basic idea, its repetition, and the continuation are all end-accented at the two-bar hypermetrical level (as indicated by the lower brackets). This phrase-rhythmic interpretation sheds light on the eight-measure length of the phrase: the extra beat is added not at the end, but at the beginning as a sort of prefix. The upper brackets in Example 10 show the presence of four-bar hypermeasures and their corresponding four-measure subphrases in the 2–3–4–1 configuration. This level of hypermeter is tightly coordinated with the tonal middleground of the passage, as I demonstrate in the reduction of the opening theme in Example 11. In the harmonic middleground I–IV–V–I, downbeats of four-bar hypermeasures coincide with the onset of tonic and pre-dominant functions. The dominant function, tonally the most anticipatory, appears on a hyperbeat that similarly anticipates an imminent resolution. EXAMPLE 11. Open in new tabDownload slide Beethoven, Piano Trio No. 1 in E♭ major, Op. 1, first movement, mm. 1–9, Schenkerian reduction EXAMPLE 11. Open in new tabDownload slide Beethoven, Piano Trio No. 1 in E♭ major, Op. 1, first movement, mm. 1–9, Schenkerian reduction Example 12 presents a durational reduction of the entire Primary Theme and Transition (mm. 1–32) to evaluate the overall metrical progression. The first stage of the Transition in mm. 13–21 prolongs the tonic key with four-measure harmonic loops (see dotted slurs), which help keep the same four-bar hypermeter and end-accented 2–3–4–1 rhythm as in the Primary Theme. The second stage of the Transition in mm. 22–32, moving toward (and eventually arriving at) the dominant of the secondary key, gradually dissolves the 2–3–4–1 rhythm through subtle changes in both grouping and hypermeter. The first change occurs when the subgroup that begins in m. 22 is extended by a measure to m. 26, where the harmonic progression first arrives at the dominant of the secondary key. While this dominant arrival often triggers the onset of a cadential extension (what Hepokoski and Darcy call the “V-lock”), Beethoven opts instead for a motivic repetition of mm. 25–26 in mm. 27–28, problematizing both the precise location of the cadential goal and the integrity of the hypermeter. It is not until the last three measures of the Transition that we understand retrospectively that the V-lock has been reached in m. 26. In sum, the dominance of 2–3–4–1 is challenged in the last stage of the Transition through dissolving hypermeasures and subgroup boundaries, setting the stage for beginning-accented rhythm in the Secondary-Theme zone. The overall contrasting expressive qualities of the Primary and Secondary Themes suggest and complement an antithetical relationship between 2–3–4–1 and 1–2–3–4, captured at the opposite ends of the linear space in Example 2. EXAMPLE 12. Open in new tabDownload slide Beethoven, Piano Trio No. 1 in E♭ major, Op. 1, first movement, mm. 1–33, durational reduction EXAMPLE 12. Open in new tabDownload slide Beethoven, Piano Trio No. 1 in E♭ major, Op. 1, first movement, mm. 1–33, durational reduction The opening theme of Mozart’s Piano Sonata in C minor, K. 457, shown in Example 13(a), provides another illustration of an introductory downbeat gesture setting up end-accented groups. A significant difference from Example 10 is that the end-accented groups in Example 13(a) occur not at the beginning of the sentence, but in the continuation function. With an assertive opening in octaves, the presentation function in mm. 1–8 is strongly beginning-accented. On the downbeat of m. 9, the onset of the continuation makes an apparent reference to the octave at m. 5; liquidation of the basic idea, such as that shown in my hypothesized version in Example 13(b), would typically have followed. Mozart’s continuation, however, takes an unexpected course. Failing to launch another ascending arpeggiation, the octave at m. 9 serves as an introductory downbeat gesture for a new motivic idea in mm. 10–11. First appearing as a descending tetrachord in the top voice, counterpointed by a chromatic alto a sixth below, the motive is then repeated in mm. 12–13 in inverted counterpoint, suggesting that a nested sentence within the continuation may be underway. The new motive and its repetition are both end-accented at the two-measure level—not only due to the preceding downbeat, but also supported by the dynamically accented middle of the motivic statements (in mm. 11 and 13). As a four-bar hypermeter from mm. 1 to 8 continues to be operative,57 the motivic statements and subsequent groups in mm. 13–17 become strongly end-accented even at the four-measure level. EXAMPLE 13. Open in new tabDownload slide Mozart, Piano Sonata in C minor, K. 457, first movement. (a) Phrase rhythm of mm. 1–19. (b) Hypothetical recomposition EXAMPLE 13. Open in new tabDownload slide Mozart, Piano Sonata in C minor, K. 457, first movement. (a) Phrase rhythm of mm. 1–19. (b) Hypothetical recomposition Shifting abruptly from strongly beginning-accented to strongly end-accented rhythm, the continuation represents an antithesis to the presentation in other dimensions. The recurring descending tetrachords in the continuation counteract the commanding ascents in the presentation; the deliberate diatonic and chromatic lines in the new motive contrast the impulsive arpeggiation of the opening idea. To complete the dialectic process, the cadential function in mm. 17–19 synthesizes various oppositions: counterpoint between the two hands combines descending and ascending contours; surface arpeggiation in the right hand elaborates an underlying stepwise motion; and a mixed 1–2–1 rhythm brings together beginning- and end-accented characteristics. The radical discursive shift introduced in m. 9 thus steers the progression toward the introduction and reconciliation of an array of contrastive factors. In this light, the study of phrase rhythm further enriches our assessment of Mozart’s prowess at weaving together eclectic elements to articulate a deeper level of meaning.58 I conclude this section by drawing attention to an intriguing theoretical property of the strongly end-accented 2–3–4–1 rhythm. In both Beethoven’s Op. 1 and Mozart’s K. 457 (Exx. 10 and 13[a]), the 2–1 groups following the initial downbeat (mm. 1–5 in Beethoven and mm. 9–13 in Mozart) may in fact be read as 2–3–4–1 groups by considering the next faster level of four-cycles. Indicated by the small numbers above the piano LH in the examples, these four-cycles are based on half of a notated measure as the beat unit. The significance of this observation lies in the recursivity: the 2–3–4–1 groups at the two-measure level are embedded in a larger version of 2–3–4–1 groups at the four-measure level. The mechanism and theoretical implications of this property are demonstrated in Example 14. The two levels of beats in each of the four scenarios represent two related four-cycles, with the lower level embedded in upper one and going twice as fast. Both the strongly beginning-accented 1–2–3–4 group in (a) and the strongly end-accented 2–3–4–1 group in (b) are recursive—that is, two groups in the lower level are embedded within one group in the higher level of the same rhythmic type. While the presence of this recursive property is well known for the 1–2–3–4 type, I am not aware of any theoretical discussion of this property as intrinsic also to the 2–3–4–1 type. That 2–3–4–1 is capable of this recursion is due to the possibility of hearing beat 2 at the lower level as an anacrusis to beat 2 at the higher one, implying that groups on both levels commence similarly at (or close to) beat 2 of the four-cycle.59 The potential significance of this property is especially noteworthy when we consider the two remaining cycles in (c) and (d): 3–4–1–2 and 4–1–2–3 are not capable of the same recursivity due to their violation of well-formedness requirements of grouping hierarchy.60 Awareness of this recursive property of 2–3–4–1 deepens our understanding of its hierarchical “depth” and further bolsters its status as a preferred compositional option.61 EXAMPLE 14. Open in new tabDownload slide Recursivity and non-recursivity of the four-beat schemas EXAMPLE 14. Open in new tabDownload slide Recursivity and non-recursivity of the four-beat schemas END-ACCENTED SENTENTIAL SECONDARY THEMES Thus far I have examined end-accented sentences in tight-knit Primary-Theme zones. In this section, I explore loose-knit sentential Secondary Themes, focusing on an idiosyncratic thematic design and its role in large-scale rhythmic development.62 I first consider briefly the Secondary Theme of the first movement of Beethoven’s Piano Sonata in C major, Op. 2, No. 3, shown in Example 15. Prior to the theme, a short P-based Transition arrives at a half cadence (in the secondary key) in m. 29 on a hypermetrical downbeat. The overlap with the Secondary Theme’s accompaniment ensures continuation of the hypermeter; hence, the basic idea enters in m. 30 on a weak hyperbeat and grows to an accented middle in m. 31. A defining feature of this idea—one that distinguishes it from tight-knight themes—is the reversal of the prototypical I–V opening to a V–I. This reversal paves the way for a curious sentential design: instead of two standard iterations of the basic idea (i.e., initial presentation and a single repetition), we find two-and-a-half iterations of the idea. The extra half iteration in m. 34 may be heard initially as a third iteration; yet, as the V7 resolves to I6, the iteration is curtailed by an encroachment of the continuation function at the downbeat of m. 35, which momentarily restores beginning accentedness. Significantly, the continuation unit is five measures long—the same length as that of the presentation function. This odd length allows the continuation module to conclude at a hypermetrical downbeat in m. 39 in order to set up the following end-accented restatement of the theme. As both the five-measure presentation and five-measure continuation serve integral roles in the theme’s phrase-rhythmic structure, the ten-measure theme may be seen as irreducible to a basic eight-measure phrase.63 EXAMPLE 15. Open in new tabDownload slide Beethoven, Piano Sonata in C major, Op. 2, No. 3, third movement, mm. 25–41 EXAMPLE 15. Open in new tabDownload slide Beethoven, Piano Sonata in C major, Op. 2, No. 3, third movement, mm. 25–41 The Secondary Theme of the first movement of Beethoven’s Piano Sonata in C minor, Op. 10, No. 1, shown in its larger context in Example 16, exemplifies a more globally coordinated phrase-rhythmic progression. The example starts from the codetta of the Primary-Theme zone, which concludes in m. 30 on a hypermetrical downbeat. Following a measure of rest in m. 31 and a harmonic lead-in in m. 32, the Transition Theme enters in m. 33 on a hypermetrical upbeat, its four-measure units articulating a 4–1–2–3 rhythm. The last of these four-measure units elides with the beginning of the Secondary Theme at m. 56; the last hypermetrical beat 3 of the Transition thus serves also as the first hypermetrical beat 3 of the Secondary Theme. EXAMPLE 16. Open in new tabDownload slide Beethoven, Piano Sonata in C minor, Op. 10, No. 1, first movement, mm. 22–105 EXAMPLE 16. Open in new tabDownload slide Beethoven, Piano Sonata in C minor, Op. 10, No. 1, first movement, mm. 22–105 EXAMPLE 16. Open in new tabDownload slide [continued] EXAMPLE 16. Open in new tabDownload slide [continued] The four-measure basic idea of the Secondary Theme in mm. 56–59 thus shifts the phrase rhythm from 4–1–2–3 to 3–4–1–2, the downbeat in m. 58 reinforced by a growth to the middle of the basic idea. The repetition of the basic idea in mm. 60–64 retains the melodic contour and the 3–4–1–2 rhythm. The entire eight-measure presentation is ostensibly repeated (with eighth-note elaboration) in mm. 64ff; however, the repetition falls two measures short, again due to the encroachment of the continuation unit and restoration of beginning-accentedness in m. 70. The repetition of the continuation (mm. 78–94) involves further complications. The first difficulty arises when m. 78 seems to have mistakenly returned to m. 71 instead of m. 70. This impression is rectified by the downbeat of m. 80. While four-bar hypermeasures continue unperturbed until the end of the exposition, the group boundaries (and therefore the rhythmic profile of groups) have become highly obscure. First, the lead-in in mm. 76–7 suggests an overlap with m. 78; then, the quarter-note rest in m. 78 further obscures the formal role of the preceding E♭: is it a part of the next group, or is it an “introductory downbeat” (as discussed in the previous section) setting up imminent end-accented groups? The immediate evidence remains somewhat unclear, and neither beginning- nor end-accented rhythm regains clarity until the Closing Theme in mm. 95–105, where 2–3–4–1 emerges from the extensive rhythmic liquidation as the last one standing.64 Example 17 summarizes the rhythmic odyssey of the entire Exposition, combining both the linear and cyclic spaces proposed in this article. The top of the diagram shows a linear progression from strongly beginning-accented to strongly end-accented rhythm within the Primary-Theme zone. This interpretation elaborates Temperley’s analysis of the same passage.65 The thrust of his reading is that the hypermeter in mm. 17–22 gradually shifts from even-strong to odd-strong, and he describes this shift as a hypermetrical transition. Omitted from his analysis, however, is an interpretation of the melodic groups, transformed amidst the hypermetrical transition from beginning-accented to end-accented groups across the Primary Theme. The progression from (a) through (d) and (d′) to (a′) not only parallels simultaneous changes in formal functions, but the complete traversal of the linear phrase-rhythmic space also reinforces the tonally determined character of the Primary Theme.66 EXAMPLE 17. Open in new tabDownload slide Beethoven, Piano Sonata in C minor, Op. 10, No. 1, first movement, mm. 1–105, phrase-rhythmic progression EXAMPLE 17. Open in new tabDownload slide Beethoven, Piano Sonata in C minor, Op. 10, No. 1, first movement, mm. 1–105, phrase-rhythmic progression From there, the progression from 4–1–2–3 in the Transition, to 3–4–1–2 in the Secondary Theme and 2–3–4–1 in the Closing Theme partakes in a global counterclockwise motion on the cyclic rhythmic space. As stated above, instability in grouping boundaries momentarily unsettles 3–4–1–2 in the Secondary Theme and threatens to revert to beginning accentedness. Premature return is averted when the Closing Theme affirms the 2–3–4–1 schema, the last rhythmic state in the cycle. Finally, an incomplete rhythm 2–3–4 in mm. 103–5 helps transition back to 1–2–3–4 at the beginning of the P-based development. In its entirety, the Exposition completes not only a full formal rotation,67 but also expeditions across both phrase-rhythmic spaces proposed in this article. In this remarkable Beethovenian essay, E. T. Cone’s provocative edict “form is rhythmic” finds another compelling testimony.68 FINALE: PAUL BALOCHE’S “OFFERING” In his article on beginning- and end-accented themes, Temperley concludes with an analysis of Schubert’s “An die Musik” to show that the scope of his theory extends from large eighteenth-century instrumental forms to nineteenth-century vocal miniatures.69 I venture even further in historical period and genre with an analysis of a contemporary American Christian worship song, a genre that is beginning to gain more analytical attention in music scholarship.70 In closing, this brief analysis demonstrates the applicability of my theory in non-canonic and non-sentential environments, and illumines the artistic creativity in a popular Christian song. Example 18 shows a transcription of Paul Baloche’s “Offering” with my analytical annotations.71 I begin with a brief summary of the three divisions of the text. Lines 1–4 of the verse summarize the fundamental human predicament according to Christian theology: the mortal person has no standing before the throne of the glorious and holy God. The last line (line 5) of the verse pronounces the very heart of the Christian gospel: the blood and mercy of Jesus open the way for humankind to approach God. Finally, the chorus changes the focus yet again to the response of humankind upon receiving the gift of salvation: the singer now brings an offering of worship to the Lord and King. This tripartite structure of the text outlines several main threads of the Christian faith: irreconcilability between God’s holiness and human’s mortality (sinfulness), Christ’s redemptive work as the only means to reconcile the irreconcilable, and the radical response and ultimate purpose of the redeemed person having received the gift of salvation. EXAMPLE 18. Open in new tabDownload slide Baloche, “Offering,” mm. 1–24 EXAMPLE 18. Open in new tabDownload slide Baloche, “Offering,” mm. 1–24 My analysis of subphrases and hypermeasures shows that the three main sections of the text are delineated not only by their different melodic/harmonic materials, but also by their disparate phrase-rhythmic characters. To set the metrical context for the entire song, the instrumental introduction establishes a two-bar hypermeter that is in phase with its two two-measure melodic-harmonic units. Given the rather slow tempo at quarter note = 66, the two-bar hypermeasures are more aptly heard in quadruple than duple time, with each notated half-measure serving as a hyperbeat. The first four lines (mm. 5–12) of the verse follow a melodic scheme of abab, with each ab comprising a phrase that ends on a half cadence. Each subphrase (i.e., each of the four lines) appears to coincide roughly with a single quadruple hypermeasure, except that the subphrase begins slightly after a hypermetric downbeat and finishes before the next one. Temperley calls this kind of (sub)phrase “unaccented,” a category which he identifies at the beginning of “An die Musik.”72 The last line of the verse (mm. 13–16), which I have proposed to be the site of the first theological transition, introduces a new melodic phrase that drives the verse to the first conclusive cadence.73 At the same time, this line also marks the first conspicuous departure from the foregoing “unaccented” rhythm of the first four lines. Instead of entering after the downbeat, the line begins with an upbeat to m. 13, subsequently articulating a hypermetrical downbeat at m. 13 on the word “only.” Preceded by four lines of “unaccented” rhythm, the fifth line thus categorically shifts to an accented—or more precisely, a beginning-accented—one. As the fifth line unfolds, however, we encounter complications with the hypermeter (which has hitherto been straightforward) as well as with the beginning-accented rhythm suggested at m. 13. The entire phrase is expanded from two measures (the length of the previous subphrases) by half a measure and a downbeat. Baloche notates the expansion with an added 24 measure in m. 15, which contains a cadential gesture V–IV setting up the resolution to I at m. 16. This expansion is motivated both musically and textually. First, an inserted IV6– V56 progression in m. 13 displaces the opening I chord by half a measure; an added half measure (i.e., the 24 measure) is thus required for the progression to return to I at m. 16. Textually, the line contains seventeen syllables; the three additional syllables compared to line 1 are accommodated precisely by the added 24 measure. As I show in the top row of numbers in mm. 13–16, the expansion transforms the anticipated downbeat at m. 15 to an expanded beat 4. The phrase eventually concludes at m. 16, at which point line 5 is completed as an expanded version (1–2–3–4–[expansion]–1) of mixed rhythm. Coming from four lines of unaccented rhythm, the fifth line thus compensates for the lack of hypermetrical anchors in the vocal materials by catching hypermetrical accents at both ends. This shift to mixed rhythm involves a calculated process of transformation from a beginning-accented to an end-accented state. Recall that the beginning of the fifth line contains a delay of the appearance of the tonic by half a measure. Although the consistency of two-bar hypermeasures has ensured the perception of a strong hyperbeat at m. 13, that all previous hypermetrical downbeats in the song have been supported by the tonic chord suggests the hearing of the second half of m. 13 also as strong. As a result, a shadow meter may be heard at m. 13.5. A remarkable result of this shadow meter is that the subphrase “and it’s only through Your mercy, Lord I come” may be heard in this metrical context as an instance of the end-accented 2–3–4–1 rhythm. In other words, the fifth line begins with a beginning-accented 1–2–3–4 in the predominant meter, while the shadow meter carries the line forward with an end-accented 2–3–4–1. In this light, the expansion (the added 24 measure) serves yet another function: it negotiates the transition from one rhythmic type to the other, ensuring that the two metrical strands converge on a structural and hypermetrical downbeat at m. 16. The textual line that depicts Jesus’ role as the mediator between humankind and God turns out to contain a unique measure that serves a mediatory metrical role. Bringing the song’s theological trajectory to its final stage, the chorus in mm. 16–24 presents yet again new melodic and harmonic materials. Central to our discussion is the prominence in this section of the end-accented 2–3–4–1, the emergence of which, as we have seen, was carefully prepared by the last line of the verse. Departing from a deafening absence of hypermetrical downbeats in lines 1–4, and having moved through the prominent beginning- and end-accents in line 5, the song has finally found its rhythmic destiny in the new prevalence of end-accented phrases. Example 19 summarizes the phrase-rhythmic path and its textual correspondences. The precise choice of the phrase-rhythmic type for each of the three sections exhibits a kind of parabolic illustration of each theological point. The omission of a downbeat—the critical foundation from which all things metrical arise—in the opening vocal lines seems to be a commentary on the fundamental inability of humankind—not just created and dependent, but also fallen and condemned—to attain existential certainty before the transcendental and immutable God. The appearance of the hypermetrical downbeat on “only” the first, and in fact the only word set to a hypermetrical downbeat at the beginning of a vocal phrase, thus underscores the absoluteness of God’s nature and the salvific work of Christ.74 When the same line transitions to end-accentedness, which dominates the entire chorus, the shift of metric weight to the end of phrases encapsulates the anticipation of the future weight of glory,75 as the redeemed offer of their continual worship to the King. The story that the song tells is not only located in the text or a musical style that appeals to the lay congregation; it is also encoded deeply in its phrase-rhythmic intricacies, the significance of which as a source of musical structure and meaning is what I have argued for in this article. EXAMPLE 19. Open in new tabDownload slide Baloche, “Offering,” phrase-rhythmic progression and textual association EXAMPLE 19. Open in new tabDownload slide Baloche, “Offering,” phrase-rhythmic progression and textual association Footnotes 1 Grant (2014, 213) cites the theories of Gottfried Weber and Jérôme-Joseph de Momigny as early representatives of the two views. Initial explorations of this issue date back to the eighteenth century when theorists wrestled with the proper placement of bar lines on the one hand, and grew in awareness of hypermetrical organizations (even without explicitly using the term “hypermeter” or its equivalents) on the other. For other helpful discussions of the connection between these two issues in eighteenth- and nineteenth-century theoretical writings, see Grave (1985), Caplin (2006), Rothstein (2008 and 2011), and Mirka (2009). 2 Early advocates in contemporary research of beginning-accented rhythm include Schachter (1976, 1980, and 1987), Berry (1976), and Rothstein (1989). Other theorists who support similar views include Burkhart (1991), Kamien (1993), Samarotto (1999), and McClelland (2006). Many of their hypermetrical analyses are informed by the Schenkerian notion of Dehnung and rhythmic middlegrounds based on four-measure constructions. More recently, Love (2015) conjectures a cognitive view of hypermeter based on a cyclic model that privileges beginning-accented rhythm. Applications of phrase-rhythmic concepts in analyses of non-canonic repertories have similarly privileged beginning-accented rhythm. See Biamonte (2014), for example. 3 See particularly Temperley (2003) and Ng (2012). Temperley’s main argument is that end-accented rhythm, while overall less common than beginning-accented rhythm, is nevertheless pervasive in closing themes due to a specific schema at the juncture between the Secondary-Theme and Closing zones. Ng imports Temperley’s thesis into the purview of Sonata Theory and constructs a phrase-rhythmic interpretation of sonata form. 4 Rothstein (2008 and 2011). 5 Wilson (2016, 36) has proposed renaming these meter types “departure” and “arrival” meters, noting that their occurrence in practice is not strictly confined to particular national styles. 6 See Lewin (1981), Cohn (1992a, 1992b, 2001), Leong (2007), and Murphy (2009, 2018). 7 Compositions cited to illustrate their theories invariably contain a high degree of direct and indirect grouping dissonance. Famous examples include Beethoven’s Symphony No. 9, second movement (Cohn [1992a]), Mozart’s Symphony No. 40, third movement (Cohn [1992b]), excerpts from Wagner’s Parsifal (Leong [2007]) and numerous passages from Brahms’s oeuvre (Lewin [1981], Cohn [2001], and Murphy [2009 and 2018]). 8 These three binaries frame the theoretical discussions of Lerdahl and Jackendoff (1983), Temperley (2003), and Rothstein (2008 and 2011) respectively. 9 Temperley (2003, 129–131 and 150) offers two complementary methods to assess whether a phrase is beginning- or end-accented: (1) comparing the metrical weight between the first and the last beats of the phrase; and (2) comparing the distances of the strongest hyperbeat from the beginning of the phrase and from the end of the phrase. In either case, the level of meter and grouping must be specified, as it is possible that a phrase is beginning-accented on one level and end-accented on another according to these criteria. 10 McKee (2004) and Rothstein (2011). 11 Ito (2013, 48) broadly describes Rothstein’s approach as representative of the analytical traditional of hypermetrical analysis, while Lerdahl and Jackendoff’s as representative of the cognitive tradition. Ito aims to bridge the gap between these two through his concept of metric orientation, which is “a mental construct akin to a notated measure that is a salient framework for temporal orientation.” 12 Ibid., 50. 13 Although I include other schemas into my taxonomy, I will show later in this article that 1–2–3–4 and 2–3–4–1—the two schemas that Ito highlights—enjoy a special theoretical status due to their recursivity (see Ex. 14). 14 In her oft-cited article, Brower (1993, 26–28) proposes a dichotomy between the concepts of “accentual meter” and “metric grouping” to differentiate between the mechanisms of perceiving lower and higher levels of the metrical hierarchy. In short, accentual meter deals with levels of metric hierarchy where beat durations are short enough for echoic memory to differentiate between “strong” and “weak” events, while metric grouping concerns higher levels of the hierarchy in which longer beat separations exceed the limit of echoic memory and thus necessitate “a counting strategy, in which we count off measures and hypermeasures of groups of twos and threes” (27). Brower does not address directly whether this principle implies normalcy of beginning-accented rhythms at higher levels, although her postulation certainly suggests it. What remains uncertain, however, is exactly where in the metric hierarchy the switch between accentual meter and metric grouping takes place. It may not be assumed that hypermetrical levels necessarily fall into Brower’s metric grouping category, even if this seems to be implied by her use of the terms “high-level” and “hypermeasure.” I maintain that if hypermeters are to have any perceptual reality, then they should be felt experientially and not just prescribed theoretically. On this point, Justin London (2012) goes even further by asserting that there is no such thing as “hypermeter” as a categorically distinct concept from meter. Although I agree with the perceptual premium London puts on hypermeter to render it but part of the general phenomenon of metrical entrainment, I maintain a categorical difference between meter and hypermeter because hypermeters are in practice much more flexible and unpredictable than notated meters. 15 Ito (2013, 57). In cases where I believe that two windows are operative concurrently, I admit that usually one of them is much stronger than the other. In the case of a 1–2 schema embedded within a 1–2–3–4, for instance, my sense is that usually one of the two windows takes the primary position, while the other is “lurking.” To illustrate this, I would argue that Ito’s analysis of the first eight measures of Beethoven’s Piano Sonata, Op. 31, No. 3, first movement (in which he reads an irregular patterning of the 1–2–3–4 schema based on the 2 + 4+2 grouping structure) may be complemented by a 1–2 schema throughout, given the very conspicuous grouping boundaries every two measures. In fact, I believe that the 1–2 schema is in this case primary, while Ito’s particular reading of the 1–2–3–4 schema resides more in the background of this hypermetrical perception. I contend that it is precisely this tension between the two schemas that makes the passage rhythmically fascinating. 16 Temperley (2003, 130–31) presents nine different phrase-rhythmic scenarios using Lerdahl and Jackendoff’s dots and brackets. His scenarios A through E correspond to my (b), (b′), (e), (e′), and (h); his H combines my (d) and (e), while his I combines my (d′) and (e′). His F and G are too abstract to be accounted for in my taxonomy. McKee (2004) presents four basic rotations of hyperbeats and labels them [1234], [4123], [3412], and [2341], the equivalents of my (a), (c), (c′), and (a′). Neither Temperley nor McKee, however, devises spatial representations of conceptual distances among their types. 17 See Temperley and Bartlette (2002) for an insightful discussion of the impact of melodic parallelism on (hyper)metrical perception. 18 Temperley (2003, 131) describes rhythm (c) as extremely rare. Both Temperley and Ito (year, page number) highlight the 1–2–3–4 and 2–3–4–1 schemas (those I call the strong types) as primary, while the relevance of the other two rotations (what I call the moderate ones) is downplayed. I will demonstrate in this article composers’ resourcefulness in using a variety of rotations to create large-scale trajectories, taking advantage of their different rhythmic characters to articulate teleological processes. As far as rhythm (c) is concerned, Rothstein’s (1989) celebrated analysis of the main theme from Johann Strauss’ An der schönen blauen Donau is a famous example. See also McKee’s (2004) analysis of the Trios from Mozart’s divertimenti, K. 563 and 439. 19 These duple hypermetrical patterns feature regularly in phrase-rhythmic analyses and theoretical systems (such as in Temperley 2003). While they may sometimes combine to suggest quadruple patterns at a higher level, tempo and grouping can help secure duple patterns and resist assimilation into larger quadruple ones. 20 I examine the appearance of this rhythmic type at the juncture between the Primary-Theme and Transition zones in Ng (2012, 66). 21 In Ng (2012), I categorize scenario (f) as beginning-accented because the appearance of a hypermetrical accent at the beginning of the phrase is a defining characteristic of beginning-accented groups. In this article, in order to construct a taxonomy that accounts for the difference between rhythms (a) and (f), I follow Temperley’s (2003) suggestion that scenario (f) be considered end-accented as well because the defining characteristic of end-accented groups is indeed present, even if it must appear later in time. 22 Cohn (2001). 23 See Temperley (2003, 128–29). He summarizes: “The disagreement on the issue of normative meter-grouping alignment should serve as a warning: the perception of meter and grouping can be quite subjective.” The difficulty is further explored in Grant (2014, chapter 8). 24 Ng (2012, 57–61). 25 It seems possible to maintain a four-beat schema here, implying a move from rhythm (a) not to (d), but to (b). I will argue, however, that the four-beat level will nonetheless be weak (due to the conspicuous two-measure groups); its perception will require much assistance from performance tempo and phrasing. Even if an analyst prefers (b) over (d), the overall shape of the phrase-rhythmic path on the map is not significantly altered. 26 The phenomenal changes here include registral in m. 56; beat subdivision in m. 58; dynamic and registral (LH) in m. 60; dynamic, harmonic, textural, and motivic in m. 62; harmonic in m. 64; dynamic, harmonic, and motivic in m. 66; dynamic and motivic in m. 68; and harmonic in m. 70. 27 Hepokoski and Darcy (2006, 152). 28 Recall from Example 2 that type (f) (found here in mm. 70–74) may be seen as derived from combining (a) (found here in mm. 35–49) and (a') (found here in mm. 74–86). In Hegelian terms, (f) may be regarded as the synthesis of the antithetical pair (a) and (a'). One could perhaps extend this dialectic view of the entire paragraph from phrase rhythm to formal functions: the beginning-accented presentation function in mm. 35–49 and the end-accented post-cadential function in mm. 74–86 find their synthesis in the mixed rhythm and cadential function in mm. 70–74. 29 I call the overall cyclic construct a “hyper-cycle” because each of the four-beat patterns is in itself a cyclic pattern of beats. In fact, Rothstein (2011) calls these patterns “4-cycles.” The four patterns here form the kernel of the analyses in McKee (2004), although he does not explicitly relate them within a larger cyclic pattern. 30 Representative works cited as offshoots of Riemann’s anacrustic prototype include Cooper and Meyer (1960), Cone (1968), and Komar (1971). Schachter (1976) critiques all three. While Schachter raises many valid points about their theories (mostly regarding the conflation between rhythmic and metrical phenomena), he rejects all three on the grounds that their end-accented paradigms of phrases contradict Schenker’s beginning-accented view. 31 Temperley (2001, 357) and Rothstein (1995, 173). Rothstein asserts at one point that his “rule of congruence” is derived from Lerdahl and Jackendoff’s time-span reduction rule. However, from his description of the rule, it is clear that the rule is in fact an extension of the strong beat early rule to cover hypermetrical levels: “If a four-measure phrase is subdivided, melodically, either as 2 + 2 or as 1 + 1+2, a listener should infer a metrical pattern in which the first downbeat in each two-measure group is also the downbeat of a two-bar hypermeasure. The first downbeat in the first two-measure group will be the downbeat of a four-bar hypermeasure. In plain English, a four-measure phrase is, generally, also a four-bar hypermeasure …” The time-span reduction rule, which prefers metrical readings that put structural harmonies at stronger metrical positions, has no direct connection to this explanation. 32 Both prescriptive and descriptive (perceptual) theories on hypermeter have regularly cited this rule to support the primacy of beginning-accented rhythm. Love (2015, 3.1), for instance, while proposing a hypermetrical model based on recent developments in perception theories, provides but a passing mention of Lerdahl and Jackendoff (1983) to ascertain the idea that a “new phrase or group” constitutes “[one of the two] most common signals for a four-bar hyperdownbeat” (the other being a harmonic change). His analyses often require hypermetrical adjustments to ensure a strong subgroup beginning, effectively minimizing opportunities to hear subgroups as anacrustic or end-accented. 33 Lerdahl and Jackendoff (1983, 76): “Weakly prefer a metrical structure in which the strongest beat in a group appears relatively early in the group.” 34 Lerdahl and Jackendoff (1983, 32–33). They cite the opening of Mozart’s Piano Sonata, K. 331 and the third movement of Beethoven’s Symphony No. 5 as examples of beginning-accented and end-accented rhythms (which they call “in-phase” and “out-of-phase” respectively). 35 Schachter (1980, 205). 36 See Brower (1993, 26–28). 37 In the introduction of his seminal book on phrase rhythm, Rothstein (1989, 14) cautions against this simplistic enumeration of phrase lengths without de facto hypermetrical interpretations. I would argue that this warning is equally germane to an uninterrogated subscription to beginning-accented rhythm when a hypermeasure is automatically imparted on a group in the most visually congruent way. 38 It is interesting to note that theorists who generally subscribe to the beginning-accented view have indeed presented end-accented readings of passages in which phenomenal accents are prominent at the end of (sub)phrases. Schachter (1987, 9–13) proposes an end-accented reading of phrases and subphrases in the Allegro molto vivace from Beethoven’s Piano Sonata, Op. 27, No. 1, although he apparently avoids framing his discussion in those terms by focusing on the location of the hypermetrical downbeats at higher metrical levels. Kramer (1988, 91–93) explicitly identifies end-accented phrases in mm. 1–20 of the third movement of Mendelssohn’s Symphony No. 4. He argues that the lack of harmonic support in mm. 1–2 and harmonic change in m. 3 compels the listener to equate the “rhythmic accent” at m. 4—created by the tonal discharge of the cadence—with a hypermetrical accent. 39 Rothstein (1989, 44 and 59). 40 Although space here does not allow me to present a detailed diagrammatic demonstration of my methodology, it can easily been seen that my approach to hypermetrical analysis overlaps considerably with Mirka’s (2009) dynamic model of meter, which combines aspects of Jackendoff’s (1991) “parallel multiple-analysis model” and Hasty’s (1997) theory of projection. The most significant similarity is the premium on moment-by-moment evaluation of various phenomenal accents and the realization of their projective potentials, which characterizes a cognitive and processual approach to meter (and hypermeter) recognition. 41 See Riemann (1918–19, 480–87) for his end-accented reading of the theme. Interestingly, Riemann also considers (but rejects) a beginning-accented interpretation of the passage. Anecdotally, one of my former colleagues, who was musically educated in Europe and not conversant with contemporary American phrase-rhythmic theories, asserted that he heard m. 2 as hypermetrically stronger than m. 1. To further support an end-accented view of this excerpt, I will add that the (presumably) more stable tonic chord in m. 1 does not always provide sufficient phenomenal weight to maintain beginning-accented rhythm. As is well known, tonal-functional schemas, such as the I–V–V–I sentential opening, may well prescribe a hypermetrically weak position for the second tonic chord. For a detailed survey of historical views on this issue, see Caplin (1983). See also Mirka (2009, 52–57) on common scenarios in Haydn’s string quartets of incongruence between tonal and metric points of stability. 42 “Even-strong” hearing (an expression borrowed from Temperley [2008] to refer to the hearing of even-numbered measures as hypermetrically strong) faces some opposition at the continuation function in m. 6, which, according to Tetzel’s rule (which prescribes a stronger metric position for a motive than its subsequent imitations or reiterations; see explanation in Rothstein (2011, 96)), should be weaker than m. 5. However, I would argue that dissonant harmony and registral emphasis make it possible to hear m. 6 as strong. Commencing as a dissolving consequent to the Primary Theme, the Transition zone retains many of the same phenomenal accents to maintain end-accented rhythm at the two-measure level. 43 For an application of the counterstress idea in analysis, see Willner (1998). In Willner’s system, the phenomenal accents I discuss are considered counterstresses, which are rhythmic accents attached to weak beats or hyperbeats. 44 See Samarotto (1999) and Krebs (1999). 45 Schenker (1979, 122). 46 A potential argument against my reading of the C–B♭ and E♭–D as manifestations of the sigh motive is that a slur is usually considered an essential component of the motive (see Hatten [2004, 140–2]), while no such slurs exist in the opening of Op. 49 No. 1. Further, as an anonymous reviewer of the article points out, these alleged sigh motives are cleaved into two by the grouping boundaries. I would argue, however, that the clarity of middleground voice-leading connections 4̂–3̂ and 6̂–5̂ implies that the effect of a slur can be heard even when it is not expressly notated. This potential is further buttressed by Beethoven’s dynamic design: the accents on the C and E♭ make their connection to the B♭ and D quite audible. 47 Caplin (1998, 35). 48 Rothstein (1989, 52–56). 49 Space prevents me from giving a detailed account of this passage, but I contend that an even-strong hypermeter, as suggested by the opening theme, clearly persists to the end of the Exposition. This metrical interpretation “correctly” locates en route important hypermetrical downbeats, such as the one at the dominant arrival before the medial caesura in m. 32, and many later ones supported by phenomenal factors and grouping. 50 For example, consider the Secondary Theme of Op. 2 No. 1 (mm. 21–41). While the basic idea is similarly characterized by an accented middle, the hypermetrical downbeat at the beginning of the continuation in m. 26 nevertheless follows seamlessly from the foregoing end-accented rhythm due to an added half repetition of the basic idea in m. 25. The Secondary Theme thus provides phrase-rhythmic relief to the tension in the Primary Theme. Later in this article, I explore the rhythmic impact of a half repetition of the basic idea found in other Secondary Themes. For representative studies on the impact of an opening rhythm on later formal developments, see Headlam (1985) and Ng (2006). 51 This design is reminiscent of Temperley’s end-accented closing-theme schema, the relevance of which will be further explored in the following section. 52 Temperley (2003, 152). 53 Schoenberg (1984, 123). 54 Hepokoski and Darcy (2006, 80). 55 Lerdahl and Jackendoff (1983, 46). 56 It would seem that there are at least two alternative options to putting the opening chord outside of a proper group: (1) the chord makes its own group; and (2) the chord combines with the following group to make a mixed-rhythm group from the downbeat of m. 1 to the downbeat of m. 3. I would argue that both of these alternatives are problematic. Alternative (1) is rejected by Lerdahl and Jackendoff’s GPR 1, which “strongly avoid groups containing a single event” (1983, 43). Alternative (2) is undesirable because it fundamentally disregards the strong parallelism between the first two two-measure groups I have marked in the example. 57 Dynamic, agogic, and registral accents at the downbeats of m. 1, 5, and 9 clearly establish and project four-measure periodicity. Changes in accompaniment pattern at m. 13 and harmony at m. 17 continue to maintain four-bar hypermeasures. 58 Hatten (2014, 524) cites the opening of this sonata as an example of troping between Tempesta and empfindsamer Styl by juxtaposing the topical extremes of heroic and tragic, resulting in a style type that Beethoven explores further in his C-minor Piano Sonata and Piano Concerto, Op. 10, No. 1 and Op. 37. As my analysis shows, the juxtaposition of seemingly incongruent ideas goes beyond contrasting topics to other domains, including phrase rhythm. 59 This recursion is admittedly clearer in Beethoven’s Op. 1, No. 1 (Ex. 10) than in Mozart’s K. 475 (Ex. 13[a]), where the lower-level groups begin slightly after beat 2. That is, the groups enter in what Rothstein (1989, 29) calls afterbeats. 60 Lerdahl and Jackendoff (1983, 38) state in their Grouping Well-formedness Rule 4 (GWFR 4): “If a group G1 contains part of a group G2, it must contain all of G2.” 61 I am not aware of other scholars making the same point about the correlation between recursivity of a particular phrase-rhythmic cycle and its preferred status in practice. However, a different but certainly related issue is raised by Samarotto (2000, 3.4) when he evaluates the independence of an anti-metric layer from the primary layer, and therefore its strength in projecting a sense of metric dissonance. He believes that a genuinely dissonant anti-metric layer should demonstrate “potential for a nested metric hierarchy.” In other words, the thicker the hierarchies of the conflicting meters, the stronger the sense of metric dissonance. The depth of a metrical (or in my case, phrase-rhythmic) construct is thus crucial to its utility in practice to define a compositional element. 62 In his dissertation, Siu (2020) conducts a detailed corpus study on phrase-rhythmic norms in all the sonata-form first movements by Haydn and Mozart. His main findings concern the different proportions of what he calls regular and irregular phrase rhythms between Haydn’s and Mozart’s output. In his theory, end-accented rhythm is considered irregular in the Primary and Secondary Themes, but regular in the Closing zone. It is interesting to note that while his understanding of hypermeter is mostly in line with current practice (which prioritizes beginning-accented groups), his statistics show that Mozart incorporates end-accented rhythm at a much higher percentage than Haydn, especially in the Transition, Secondary-Theme, and Closing zones. This result provides preliminary empirical evidence for the significance of end-accented rhythm at least in the oeuvre of particular composers, while in my discussion I argue more broadly for the schematic relevance of end-accented rhythm to all formal zones and their large-scale phrase-rhythmic connections. 63 Murphy (2012) and Ng (2018) have explored irreducible phrases of odd-number lengths in the music of Haydn and Brahms. While their analyses rely primarily on tonal or formal-rhetorical factors in determining the basic length of the phrases, my analysis here is based solely on phrase-rhythmic considerations. 64 I purposely use the term “liquidation” here to divulge an interesting difference between two contrasting scenarios of phrase-rhythmic ambiguity. While it is well known that Schoenberg (1967, 58) uses the term “liquidation” to describe combinations of melodic manipulations, such as fragmentation and sequential repetition, as a source of motivic development, both Temperley (2008, 316) and I use the term “liquidation” within a phrase-rhythmic context. The phenomenon Temperley describes with the term is, however, virtually the opposite of what I aim to capture here. Temperley uses the term as a synonym for “transition” in his article; thus he calls a passage where hypermeter becomes progressively unclear a “hypermetric liquidation.” The scenario I describe here, however, involves a largely stable hypermeter interacting with progressively fuzzier group boundaries. Both modes of group-metric interaction lead to ambiguous phrase rhythm, but the source of the ambiguity is clearly different. 65 Temperley (2008, 307–309). 66 It is also possible to read m. 22 with an overlap between the Primary Theme and the codetta, given that the melodic-rhythmic motive here clearly mirrors the opening of the movement. The inclusion of an overlap changes at least the first instance of rhythm (a′) into (f). However, the sense of overlap is much weaker by m. 26, for otherwise m. 24 would have been heard as an overlap also. Without a strong overlap at m. 26, the Primary Theme does definitively close with rhythm (a′). 67 Hepokoski and Darcy (2006, 611) explain rotation as structures “that extend through musical space by recycling one or more times—with appropriate alterations and adjustments—a referential thematic pattern established as an ordered succession at the piece’s outset. In each case the implication is that once we have arrived at the end of the thematic pattern, the next step will bring us back to its opening, or to a variant thereof, in order to initiate another (often modified) move through the configuration. The end leads into the next beginning. This produces the impression of circularity or cycling in all formal types that we regard as rotational.” The large-scale phrase-rhythmic progression I show in my analysis reinforces this impression of rotation. 68 Cone (1968, 25). 69 Temperley (2003, 146–49). 70 Most studies on contemporary Christian music (often abbreviated as CCM) focus either on the cultural/sociological aspects of the phenomenon or on the theological content of the lyrics. Ingalls (2018) and Frame (1997) are two representatives of these approaches, respectively. A recent and rare instance of a music-analytical study of CCM is Burggraff (2018), in which the author presents a corpus study of 260 contemporary Christian songs, focusing on the harmonic language and melodic contour. Begbie’s (2000) monograph on theology and musical time touches on a variety of temporal issues in CCM. While he does not directly analyze phrase rhythm as I define it, he does go into the notion of hypermeter and its implications for understanding Christian theology. 71 Sheet music of the song may be downloaded at the composer’s website: https://leadworship.com/wp-content/uploads/2019/07/Offering_PC-min.pdf. 72 Temperley and Bartlette (2002, 146). 73 Temperley (2011) provides a taxonomy of plagal cadences in popular and rock music. The cadence at m. 16 in “Offering” illustrates Temperley’s “deceptive IV,” where the IV chord briefly substitutes for the I chord expected at the cadential close. 74 The use of “only” and the hypermetrical emphasis it receives reveal Baloche’s subscription to the doctrine of solus christus, one of the five solas of Protestant theology. I thank one of the anonymous reviewers for pointing out this theological element of the text. 75 The connection between Parousia (second coming of Christ) and Christian worship is treated in copious literature on topics of worship and eschatology. One classic example is Russell (1983). WORKS CITED Begbie Jeremy. 2000 . Theology, Music, and Time . Cambridge : Cambridge University Press . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Berry Wallace. 1976 . Structural Functions in Music . Englewood Cliffs, NJ : Prentice-Hall . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Biamonte Nicole. 2014 . “Formal Functions of Metric Dissonance in Rock Music.” Music Theory Online 20 ( 2 ). https://www.mtosmt.org/issues/mto.14.20.2/mto.14.20.2.biamonte.html. Google Scholar OpenURL Placeholder Text WorldCat Brower Candace. 1993 . “Memory and the Perception of Rhythm.” Music Theory Spectrum 15 ( 1 ): 19 – 35 . 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TI - End-Accented Sentences: Towards a Theory of Phrase-Rhythmic Progression
JF - Music Theory Spectrum
DO - 10.1093/mts/mtaa018
DA - 2021-01-06
UR - https://www.deepdyve.com/lp/oxford-university-press/end-accented-sentences-towards-a-theory-of-phrase-rhythmic-progression-I5AtNj5ol2
SP - 1
EP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -