TY - JOUR
AU - Sullivan, James
AB - Abstract This article explores the continued use of eighteenth-century metric manipulations by composers of the twentieth and twenty-first centuries. These manipulations, called imbroglio, close imitation, and imitative imbroglio, are motive-driven and involve the perceptual interaction of meter, motivic parallelism, and perceptual streaming. Their defining features and local perceptual effects, which primarily involve metrical dissonance, are demonstrated in short passages by Schoenberg, Penderecki, Britten, Debussy, Webern, Barber, and Adès. Their larger form-functional and text-expressive potential is demonstrated in analyses of longer passages by Schoenberg, Webern, and Barber. In an insightful formulation of metric irregularity in Stravinsky’s music, Gretchen Horlacher demonstrates how motive can prompt a shift in meter.1 “By repeating a melodic fragment previously associated with a stable metric identity,” she argues, “Stravinsky enables the listener to make a metric adjustment, to reinterpret locally a fragment in light of its earlier metrical associations.”2 In other words, mere repetition may force a motive to take its earlier metric profile, even when that metric profile is at odds with the meter of the immediately preceding music. This account of motive-driven meter captures not only Stravinsky’s “melodic-rhythmic stutter,” as Horlacher convincingly argues, but also the metric vitality of much twentieth- and twenty-first-century music. For instance, Lewin points to a handful of atonal vocal works by Schoenberg in which vocal meter, at odds with the notated meter, arises from the “motivic inertia” associated with a series of rhythmic parallelisms, and Temperley hears the opening of Bartók’s “Syncopation” as projecting a non-isochronous series of strong beats, based primarily upon motivic parallelism.3 In all cases, motivic repetition generates meter. There are, of course, alternative approaches to meter in this music. Van den Toorn prefers to frame the kinds of motivic irregularity discussed by Horlacher against a non-shifting background periodicity, and Roeder reads “Syncopation” as articulating a variety of isochronous pulse streams.4 Even so, both authors acknowledge the importance of motive in projecting meter. For Roeder, motivic parallelism is a principal factor determining which pulse streams come to the fore over a given span of music.5 For van den Toorn, motivic displacement plays expressively against background periodicity. In extreme cases, such as “Evocation” from The Rite of Spring, where background periodicity is attenuated by its inability to arrive back “on target” with a motive’s “fixed metric identity,” fixed identity comes to the perceptual fore: “the listener is more apt to readjust his/her metrical bearings than to persevere with the diminishing traces of a prevailing periodicity.”6 The influence of motivic parallelism (also called melodic parallelism) on perceived meter is well-documented in tonal contexts. Lerdahl and Jackendoff, as well as Temperley, formalize this influence as a metrical preference rule, and Temperley and Bartlette incorporate it into a computational model of meter perception.7 More recently, Danuta Mirka identifies motivic parallelism as the preferred manner by which eighteenth-century composers manipulated listeners’ perception of meter.8 Specifically, she pinpoints three eighteenth-century metric manipulations, discussed earlier by Floyd Grave, which normatively feature motivic parallelism: imbroglio, imitatio per thesin et arsin (hereafter close imitation), and free fall (hereafter imitative imbroglio).9 Each manipulation employs a particular configuration of parallel melodic segments so as to induce a new, temporary meter that is at odds with the established meter. This manner of drawing the listener into a meter that is dissonant with its prior context is what Mirka means by the term metric manipulation.10 Despite obvious differences between the music of Stravinsky, Schoenberg, and Bartok, on the one hand, and the music of Mozart and Haydn, on the other, the motive-driven irregularities described by Horlacher, Lewin, and Temperley manipulate perceived meter in much the same way as do the techniques discussed by Mirka and Grave. In that sense, any motive-driven metric irregularity or reinterpretation might be characterized as a metric manipulation. Yet, the three manipulations discussed by Mirka are theoretically special. They represent three paradigmatic ways in which meter, melodic parallelism, and perceptual streaming interact.11 As such, they are schemata, broadly available to any musical style that features melodic parallelism and meter.12 In this article, I show that they have continued to serve as compositional tools for manipulating meter in the twentieth and twenty-first centuries and in a variety of post-tonal styles. To that end, I begin by defining imbroglio, close imitation, and imitative imbroglio in a generalized manner. I introduce them with straightforward eighteenth-century examples and discuss their relationship to Krebs’s metrical dissonances, before turning to twentieth- and twenty-first-century adaptations. I then expand Mirka’s taxonomy by considering examples in which metric manipulations are placed at the beginning of pieces. After this broad survey, I consider the special schematic nature of motive-driven metric manipulations and present three extended analyses: one of “Valse de Chopin” from Schoenberg’s Pierrot Lunaire, one of Webern’s Piano Variations, Op. 27, No. 1, and one of “The Praises of God” from Samuel Barber’s Hermit Songs. These analyses demonstrate how each piece’s metric manipulations function structurally and expressively in conjunction with pitch, form, and text. Finally, I conclude by showing how motive-driven metric manipulations have been adapted to rhythmic environments that are more intensely irregular than those of prior examples. Due to limitations of space, I do not include examples of metric manipulations from the nineteenth century, though any number of beautifully text-expressive and form-functional examples could have been mentioned. For instance, several passages of metrical dissonance discussed by Krebs are coordinated with motivic parallelism and are therefore properly examples of metric manipulation.13 These and other nineteenth-century passages, in conjunction with the examples in this article and in the work of Mirka and Grave, suggest a larger historical continuity from the eighteenth century to the present that deserves further study. METER, MELODIC PARALLELISM, AND MODULARITY Before we survey twentieth- and twenty-first-century adaptations of eighteenth-century metric manipulations, it is worth getting a precise handle on what is meant by meter and motivic or melodic parallelism. I take meter to be a perception of strong and weak beats that is “inferred from but not identical to the patterns of accentuation at the musical surface.”14 Meter is thus a mental construct or, as London puts it, “a perceptually emergent property of a musical sound, that is, an aspect of our engagement with the production and perception of tones in time.”15 Although meter may be reflected in musical notation, we will be concerned with meter as an aspect of perception, as a structure that arises in the mind of the listener in response to a musical stimulus. At times, perceived meter will match the notated meter. At other times, specifically in cases of metric manipulation, the two will differ. Perceived meter will be modeled after Lerdahl and Jackendoff. A beat or pulse is a durationless but perceptually marked point in time that is represented with a dot. Beats stand out perceptually from other time points through the mind’s attempt to establish meter in the first place. Relative beat strength is modeled as a hierarchy of beats, represented visually as multiple levels of dots. Specifically, “if a beat is felt to be strong at a particular level, it is also a beat at the next larger level.”16 A full hierarchy of beat strength is thereby represented with a metric grid, of the sort presented in Example 1(a). EXAMPLE 1. Open in new tabDownload slide Summary of annotations for meter and melodic parallelism. (a) Some metric grids. (b) Change of meter through melodic parallelism. (c) Some metric reinterpretations. (d) Meters in multiple perceptual streams and with different phases EXAMPLE 1. Open in new tabDownload slide Summary of annotations for meter and melodic parallelism. (a) Some metric grids. (b) Change of meter through melodic parallelism. (c) Some metric reinterpretations. (d) Meters in multiple perceptual streams and with different phases Meter is often defined to be periodic, with strong and weak beats alternating regularly. Periodicity is captured by the regular spacing of beats at each level in Example 1(a). The full extent to which meter must be periodic has been widely debated. For many, strict periodicity is essential, with aperiodicity arising at hypermetric levels through transformation rules.17 For others, meter can be aperiodic as long as it satisfies certain well-formedness constraints and is not more deeply irregular.18 Still others permit meter to be substantially irregular.19 The issue continues to be an active topic of investigation.20 From a perceptual standpoint, the question is: are the various percepts associated with periodic meter, as well as the mental processes giving rise to them, the same as those associated with ostensible aperiodic metric structures?21 This question is open and is well beyond the scope of the present article. Rather than attempting to address it here, I simply take for granted, based on intuition, that the aperiodic structures that appear in my examples are in fact properly metric. Such structures are generally limited to (1) changes of meter that are the consequence of motive-driven metric manipulations and (2) regularly recurring non-isochronous patterns, like 516 and 88 ⁠, which satisfy London’s well-formedness constraints. In the case of (1), there is still local periodicity, even when there are breaks in global periodicity. In the case of (2), a single aperiodic level is flanked above and below by strictly periodic levels. These outer levels satisfy Yeston’s definition of meter as, minimally, an interaction between two regular levels of motion, “a constant rate within a constant rate.”22 Perhaps this outer regularity perceptually mediates inner irregularity. Meter as a product of the listener’s real-time engagement with a musical stimulus has been modeled in several different ways by several different theorists. I do not attempt such fine-grained accounts of meter induction as are given by, say, Jackendoff, Hasty, and Mirka.23 Instead, I offer more course-grained descriptions of the changing meters associated with metric manipulation. I present meters as fully formed metric grids in the examples, though I allow them to change abruptly at moments of manipulation, as in Example 1(b). I do consider certain moment-to-moment reinterpretations, which I model in an ad hoc way using symbols like vertical dashed lines (to indicate an earlier-than-expected beat) and parentheses plus an arrow (to indicate the delay of an expected beat). Both situations are shown in Example 1(c). I also consider meters implied by multiple perceptual streams, which I model as multiple, simultaneously unfolding metric grids, as in Example 1(d). Finally, in order to define motive-driven metric manipulations precisely, two additional features of meter need to be clarified: metric period and metric phase. Period refers to the rate at which a particular metric level’s beats occur or, equivalently, the interval between a metric level’s successive beats. Thus formulated, meter is a hierarchy of periods or beat intervals. Period rate has to be measured with respect to something. When considering one meter alone, it is generally sufficient to measure according to the number of intervening beats at the next lower level or at the lowest musically significant level, sometimes called the pulse layer or unit pulse.24 When comparing multiple meters, this system of measurement suffices as long as there is a common pulse layer articulated by the music. In that case, one is able to refer unambiguously to the cardinality of different metric levels that interpret the unit pulse.25 However, when metric relationships are complex enough or when note onsets are sparse enough, there may be no musically relevant unit pulse. In that case, either some theoretical unit has to serve as the basis of measurement, or the measurement has to incorporate absolute length. Phase, on the other hand, is the placement of a meter or metric level relative to some point of reference. That point of reference can be a melodic segment or another meter or metric level. For instance, the half-note level of 24 meter in Example 1(b) occupies one of two possible phases relative to its quarter-note unit pulse. Similarly, the two 34 meters in Example 1(d) occupy two of three possible phases relative to their shared quarter-note unit pulse. The metric manipulations we will consider involve successions of meters with different periods, superimpositions of multiple phases of a single meter, or a combination of the two. These manipulations are driven by motivic or melodic parallelism, which I take to be the relatively immediate perception that two melodic segments are the same or similar. The qualifier “relatively immediate” is important. For metric manipulations to have their characteristically disruptive effect, the parallelisms that drive them must arise in a fast, spontaneous, reflex-like manner, rather than from conscious associations made through sustained effort.26 Such fast and automatic perceptions of parallelism are typical of modular processing and arise in cases of exact rhythmic repetition, tonal transposition, chromatic transposition, and contour repetition.27 While the theory of modularity has been hotly debated, and while I offer no further justification for it, two of its hallmark features—speed and spontaneity—make it a useful framework for thinking about melodic parallelism and meter.28 Furthermore, while I would argue that Temperley and Bartlette’s constraints are too restrictive to account for all fast and automatic perceptions of parallelism, they suffice for most of the examples in this article and will be modified only on a case-by-case basis. Melodic parallelism will be represented visually with brackets, as in Example 1(b). The reflex-like processing that underlies melodic parallelism also seems to underlie meter perception, and possibly music perception more generally.29 Thus, the fast and automatic processing of both parallelism and meter give metric manipulations their characteristic effect: to some extent, the listener cannot help but be pulled down the metric path cued by sustained motivic parallelism. A central premise of the modular view is that such processing is subconscious and operates independently from conscious reasoning. In other words, even if the listener consciously maintains the established meter in the face of a metric manipulation, some aspect of subconscious processing is still pulled away from it by melodic parallelism. This idea makes intuitive sense when couched in terms of metrical dissonance. Suppose the listener stubbornly clings to the established meter despite the cues associated with a metric manipulation, then the metric manipulation generates sustained metrical dissonance because subconscious processing is elaborating a meter that is at odds with the one to which the listener is consciously entraining. Suppose, on the other hand, that the listener consciously switches to the meter being cued by the manipulation, then metrical dissonance is briefer, lasting only until the listener has made the switch, because conscious entrainment and subconscious processing are at odds only over that short span. These two situations correspond to van den Toorn’s distinction between passages in which a motive’s “fixed metric identity” merely “counteracts” but does not supplant a background periodicity and passages in which “the listener is more apt to readjust his/her metrical bearings than to persevere with the diminishing traces of a prevailing periodicity.”30 As listening strategies, they also correspond to Imbrie’s distinction between “conservative” and “radical” hearings.31 The modular view of meter and melodic parallelism, in association with metrical dissonance, accounts for the perceptual difference between the two. In both situations, subconscious processing interacts with conscious listening strategy to produce a hearing of a passage. This distinction brings up an important methodological point. In the examples that follow, I do not claim to model one correct metric hearing of a passage. Rather, I attempt to account for meter and melodic parallelism as they are suggested by particular metric manipulations and as they are, according to the modular view, processed automatically and subconsciously. While this account is only part of the larger metrical experience, it is, at least in principle, a stable part and so, in conjunction with other variables like one’s conscious listening strategy, allows for predictable claims about how a passage can be heard.32 One might ask, how can I be certain that my analyses of metric manipulations actually correspond to subconscious processing? Certainly, the validity of introspection as a tool for making claims about subconscious processing has been called into question and debated.33 Ultimately, the modular view of meter and melodic parallelism awaits future experimental verification. In the meantime, it is still a useful introspective activity to adopt different listening strategies across several musical passages, to compare their perceptual effects, and to ask if there is some stable element that might be explained by subconscious processing.34 IMBROGLIO, CLOSE IMITATION, AND IMITATIVE IMBROGLIO Meter and melodic parallelism, as defined earlier, are the basic elements of imbroglio, close imitation, and imitative imbroglio, and reflex-like processing of these two elements underlies each manipulation’s perceptual effect. Thus, all three manipulations will be defined in terms of an interaction between meter and melodic parallelism or, more specifically, in terms of the way that a set of melodic parallelisms cuts against an established meter or a primary meter. The meter(s) induced by such parallelisms will be called false.35 In imbroglio, a series of parallel melodic segments induces a meter with at least one period that is different from any period of the established or primary meter.36 Example 2 diagrams the technique in its most characteristic instantiation: the hemiola.37 A clear example of imbroglio is the passage from the fourth movement of Beethoven’s String Quartet, Op. 59, No. 3, given in Example 3. After a 22 metric context, the first violin (top staff) spins out parallel three-eighth-note motivic segments. The quarter notes in the other strings (lower staff) that previously supported 22 meter suddenly drop from the texture, and the first violin’s parallelisms draw the listener into a false 68 meter. The perceptual confusion that results is what is meant by the term imbroglio.38 Temperley cites this passage as an example in which parallelisms that cut across an established meter are insistent enough to be readily perceived, in contrast to situations in which parallelisms that conflict with an established meter go by unnoticed.39 He supposes that “we create a secondary metrical pattern to go with [each parallelism], in which every third eighth-note beat is strong.”40 That is exactly the point of imbroglio—to force the listener to elaborate a false meter in place of the established one. The technique generates what Krebs calls indirect grouping dissonance.41 EXAMPLE 2. Open in new tabDownload slide Imbroglio EXAMPLE 2. Open in new tabDownload slide Imbroglio EXAMPLE 3. Open in new tabDownload slide Imbroglio in Beethoven , String Quartet, Op. 59, No. 3, fourth movement, mm. 57–64 EXAMPLE 3. Open in new tabDownload slide Imbroglio in Beethoven , String Quartet, Op. 59, No. 3, fourth movement, mm. 57–64 A straightforward twentieth-century example of imbroglio is the passage from Schoenberg’s “Valse de Chopin” from Pierrot Lunaire, given in Example 4. It establishes 24 meter through a series of dotted-quarter-plus-eighth rhythmic parallelisms that are passed between piano and voice. The imbroglio’s dotted rhythmic motive and false 24 meter motivate Krebs’s discussion of the movement’s recurring G 64 grouping dissonance, Malin’s reading of the movement as two energetic waves, Lewin’s association of the passage with the vocal meter of “Columbine,” and Dunsby’s association of the passage with the opening of Schoenberg’s Six Little Piano Pieces, Op. 19, No. 4.42 The passage is felt as dissonant against the notated 34 meter, which the preceding music cues through a set of stereotyped waltz features. These features, along with the passage’s form-functional and text-expressive roles, will be discussed in detail later (Analytical Application 1). EXAMPLE 4. Open in new tabDownload slide Imbroglio in Schoenberg, “Valse de Chopin,” Pierrot Lunaire, mm. 14–20 EXAMPLE 4. Open in new tabDownload slide Imbroglio in Schoenberg, “Valse de Chopin,” Pierrot Lunaire, mm. 14–20 A more recent example of imbroglio begins the Vivace section of Penderecki’s Duo Concertante for Violin and Double Bass, given in Example 5. Here, imbroglio arises through the dynamic interaction between the two instruments. First, the violin establishes the notated 34 meter through a two-fold repetition of its basic motive. The double bass then presents a variant of the violin’s motive, extended with a quarter-note pickup. This motive initially reinforces the violin’s meter, confirming a dotted-quarter metric level and the 34 meter as primary. However, through repetition, the motive produces conflicting half-note and whole-note metric levels, establishing a false 44 meter in the violin’s absence. Just as the double bass is completing its second motivic statement, the violin reenters in an attempt to thwart the double bass’s subversive metric intentions. It does so by again insisting on the notated 34 meter. The double bass persistently maintains its false 44 meter until its downbeat aligns with the violin’s, at which point the violin again drops from the texture and the double bass veers off with a chromatic and metrically ambiguous line (mm. 16–22, not shown). Because the violin intrudes directly against the double bass, the double bass’s imbroglio generates both indirect and direct grouping dissonance over the course of the passage. EXAMPLE 5. Open in new tabDownload slide Imbroglio in Penderecki, Duo Concertante for Violin and Double Bass, mm. 9–15 EXAMPLE 5. Open in new tabDownload slide Imbroglio in Penderecki, Duo Concertante for Violin and Double Bass, mm. 9–15 This imbroglio is the result of Penderecki’s creative approach to cyclic superimposition, a technique discussed by Horlacher in the context of Stravinsky’s music.43 The violin and double bass define two strata, whose 3:4 rhythmic relationship produces the larger 12-quarter-note cycle shown in Example 6. Unlike Stravinsky’s cyclic strata, which are usually motivically differentiated, Penderecki’s strata are motivic variants of one another. The resulting counterpoint initially creates parallel octaves, moves through a series of dissonant tritones, sevenths, and seconds that resolve to consonant thirds and sixths, and finally reapproaches the opening octave through contrary motion. Thus, the cycle has a dynamic contrapuntal trajectory: it is initially inert, becomes contrapuntally active as dissonance increases, and affects a sense of resolution at its end, where consonance again predominates. In coordination with this trajectory, the A-centricity of the violin’s basic motive is gradually challenged by F, which comes to function as a principal point of contrapuntal resolution (marked by * in Ex. 6). That the double bass opts to extend the violin’s motive with F, instead of maintaining A-centricity with, say, a dominant E, makes the imbroglio metaphor both metric and tonal in nature. Not only does the double bass challenge the violin’s meter, it also challenges the violin’s pitch center. EXAMPLE 6. Open in new tabDownload slide The cyclic and contrapuntal structure of Penderecki’s imbroglio EXAMPLE 6. Open in new tabDownload slide The cyclic and contrapuntal structure of Penderecki’s imbroglio The actual music of Example 5 shifts the violin’s first two motivic statements early, so that the continuous superimposition of Example 6 becomes a discontinuous one.44 The result is the metric imbroglio discussed earlier, as well as a heightened sense of interaction between the instruments. The shift also removes the counterpoint associated with the first half of the cycle, making the first full and direct statement of the violin’s motive against the bass tonally dissonant rather than consonant. In sum, the metric imbroglio of Example 5 is coordinated with both a subversive pitch center and dissonant, forward-driving counterpoint. It is therefore a highly active formal beginning, opening up a tense dialogue between instruments that keeps meter and tonal center in flux.45 Whereas imbroglio pits competing metric periods against one another in succession, close imitation pits competing metric phases against one another simultaneously. Specifically, in close imitation, a melodic segment or series of parallel segments imitates another segment or series of parallel segments at a short distance, supporting two different phases of the established or primary meter.46 Example 7 diagrams the technique’s manipulation of 34 meter.47 The minuet from Mozart’s String Quintet, K. 593, discussed at length by Mirka, offers a characteristic example.48 The minuet is a rounded binary form, and its thematic return, given in Example 8, presents the opening theme in its original metrical position (violin I) against a copy of itself displaced by a quarter note (viola I).49 The technique produces direct displacement dissonance. In this particular case, the displacement dissonance is all the more disorienting because the thematic return follows on the heels of a retransitional 24 imbroglio (not shown).50 EXAMPLE 7. Open in new tabDownload slide Close imitation EXAMPLE 7. Open in new tabDownload slide Close imitation EXAMPLE 8. Open in new tabDownload slide Close imitation in Mozart, String Quintet, K. 593, third movement, mm. 24–29 EXAMPLE 8. Open in new tabDownload slide Close imitation in Mozart, String Quintet, K. 593, third movement, mm. 24–29 Close imitation is a standard procedure in imitative genres throughout the history of western art music.51 It is also sometimes employed as a topical reference or dramatic device in genres that are not primarily imitative. In music with text, it often depicts textual conflict, be it inner turmoil, outward physical struggle, or, more specifically, chase.52 For instance, in the “Offertorium” of Britten’s War Requiem, which sets Wilfred Owen’s pacifist retelling of the biblical story of Abraham and Isaac, a series of short passages of close imitation depict Abraham closing in on and ultimately slaying his son Isaac. In the first such passage, given in Example 9, the baritone soloist (Abraham) continues the established 68 meter, while the tenor soloist (Isaac) imitates the baritone at the dotted-quarter note. In the fourth measure, the distance of imitation collapses to the eighth note, after which the two voices converge onto the notated downbeat. This collapsing distance of imitation depicts Abraham overcoming Isaac. The mounting metric tension conveys their physical struggle.53 EXAMPLE 9. Open in new tabDownload slide Close imitation in Britten, “Offertorium,” War Requiem, rehearsal 77 EXAMPLE 9. Open in new tabDownload slide Close imitation in Britten, “Offertorium,” War Requiem, rehearsal 77 Imitative imbroglio effectively combines imbroglio and close imitation. In this technique, a series of parallel melodic segments imitates another series of parallel segments at a short distance, supporting two different phases of a meter, which itself has at least one period that is different from any period of the established or primary meter. Example 10 diagrams the case where two displaced versions of 24 meter cut against an established 34 meter. This particular case, in which there is “imitation in virtual duple meter at the time interval of one beat, giving each beat the status of a downbeat in one part or another,” is what Grave, and Mirka after him, describes as “metrically dissonant free fall.”54 I use the term imitative imbroglio to generalize this particular situation as outlined in the definition and to highlight its connection to nonimitative imbroglio, which reflects eighteenth-century thinking.55 I reserve the term free fall as an evocative description of the technique’s metric effect: the imbroglio’s change of period knocks the listener off his or her feet, while the imitation’s competing phases bounce the listener back and forth between two plausible downbeats. The listener thus lacks a firm metrical footing. He or she is in metrical free fall. EXAMPLE 10. Open in new tabDownload slide Imitative imbroglio EXAMPLE 10. Open in new tabDownload slide Imitative imbroglio Example 11 gives a passage of imitative imbroglio from the second movement of Haydn’s Symphony No. 67, discussed by Grave.56 Here, the second violins (bottom staff) unfold a series of 38 melodic parallelisms, which cut against the primary 24 meter (not shown). The first violins (top staff) imitate the seconds at the interval of an eighth note. As with the imbroglio of Example 3, prior cues supporting the written meter disappear. Imitative imbroglio draws the listener away from the notated meter and into a pair of directly conflicting false meters. As a result, the passage produces both indirect grouping dissonance between the established 24 meter and the new 38 meters, as well as direct displacement dissonance between the two 38 meters. EXAMPLE 11. Open in new tabDownload slide Imitative imbroglio in Haydn, Symphony No. 67, second movement, mm. 56–63 EXAMPLE 11. Open in new tabDownload slide Imitative imbroglio in Haydn, Symphony No. 67, second movement, mm. 56–63 A form-functional twentieth-century example of imitative imbroglio is found in the opening piano solo of Schoenberg’s Concerto for Piano and Orchestra, Op. 42, given in Example 12. The passage is a 12-tone adaptation of a standard Classical hybrid phrase form, in which a periodic antecedent phrase is followed by a sentential continuation rather than a consequent phrase.57 The first four bars establish the notated 38 meter with the normative configuration of basic idea (mm. 1–2) followed by contrasting idea (mm. 3–4). This contrasting idea is in fact a motivic variation of the basic idea, in which the quarter-eighth rhythmic profile is elaborated as the dotted rhythmic pattern of m. 3 (dotted bracket).58 In the last measure of the antecedent phrase, the melody rests pseudo-cadentially on A♭, while the left hand imitates the right hand’s dotted rhythmic pattern. In the subsequent continuation, the two hands fragment a portion of the dotted pattern and subject it to close imitation (solid brackets). The result is 28 imitative imbroglio. Thus, normative sentential fragmentation is recast through imitation, and the momentum that usually comes with fragmentation is enhanced by metric free fall. The net effect is an especially strong rhythmic drive that intensifies over the course of the passage.59 EXAMPLE 12. Open in new tabDownload slide Imitative imbroglio in Schoenberg, Concerto for Piano and Orchestra, Op. 42, mm. 1–8 EXAMPLE 12. Open in new tabDownload slide Imitative imbroglio in Schoenberg, Concerto for Piano and Orchestra, Op. 42, mm. 1–8 At this point, readers familiar with Krebs’s work on metrical dissonance might pose the following criticism: given that imbroglio, close imitation, and imitative imbroglio always produce grouping or displacement dissonance, why bother to distinguish them from more general classes of metrical dissonance, which need not feature melodic parallelism? While such a solution might be, in some sense, theoretically cleaner, it misses key perceptual, analytical, and historical features of metric manipulation. First, from a perceptual standpoint, melodic parallelism is a privileged cue for meter. It directly facilitates the perception of meter by (1) determining the meter’s period and (2) transferring the meter’s phase, as established by other cues, onto parallel melodic segments.60 It also indirectly facilitates the perception of meter by facilitating the perception of grouping and streaming.61 Through these direct and indirect influences on meter, melodic parallelism in turn facilitates the perception of metrical dissonance. Second, from an analytical standpoint, I tend to experience meter and metrical dissonance in association with melodic material rather than as agential entities in and of themselves. For instance, in Penderecki’s Duo Concertante (Ex. 5), metric conflict arises from and in turn colors the dialog between violin and double bass, which is principally enacted by motivic manipulation and repetition. Competing motive lengths convey a sense of disagreement between the instruments, while metrical dissonance imparts the tension associated with such a disagreement. Imbroglio captures this combined effect. A similar situation holds for close imitation in Britten’s “Offertorium” (Ex. 9), where the competing forces are actual characters. The interaction is one of conflict rather than mere disagreement, owing to close imitation’s abrupt melodic interruption and its direct sustention of the leading melody against its transposition. Metrical dissonance makes that conflict feel violent. Of course, context matters. The imitative interaction in Mozart’s minuet (Ex. 8), though no less disruptive or metrically dissonant, comes across as playful rather than violent. The viola, realizing that the violin’s melody can harmonize itself at quarter-note displacement, enacts a witty melodic subversion. Metrical dissonance enlivens the viola’s deviance. And in Schoenberg’s Piano Concerto (Ex. 12), metric free fall creates a sense of being swept forward by the motivic process of fragmentation. In all cases, metrical dissonance is an expressive product of the actions of melody and of musical agents associated with melody.62 Melodic processes seem to define the nature and scope of a musical interaction, while metrical dissonance seems to shade, enhance, and make palpable the emotion associated with that interaction. Motive-driven metric manipulations are especially suited to capture this general paradigm in analysis. Finally, historical evidence suggests that motive-driven metric manipulations were well-defined techniques that composers implemented as schemata, even in the absence of specific terminology like imbroglio.63 In such cases, metrical dissonance may be the perceptual product, but the particular configurations of meter and melodic parallelism that define imbroglio, close imitation, and imitative imbroglio constitute the schemata. While it is certainly possible that composers also treated grouping and displacement dissonances without melodic parallelism as schemata (including those induced exclusively by dynamic accent or some other phenomenal accent), such use does not preclude motive-driven metric manipulations from functioning as schemata, too. OPENING METRIC MANIPULATIONS A special sub-case of each metric manipulation occurs when it is positioned at the beginning of a piece. I further qualify such instances of manipulation as opening imbroglio, opening close imitation, and opening imitative imbroglio. Just as each technique in its normative placement has a distinct effect, so does each opening placement. Eighteenth-century practice normatively begins imbroglio after the primary meter has been established, in order to intensify motion toward a cadence, to destabilize meter after a cadence has been achieved, or to mark a formal (re)transition in conjunction with a dominant pedal.64 In such cases, the false meter is experienced as a dissonant diversion away from the primary meter. In contrast, opening imbroglio positions the false meter first, before the primary meter is introduced. Since no cues yet support the primary meter, the false meter is initially experienced as primary. When the true primary meter finally appears, it is first experienced as false, generating dissonance and in need of correcting. Only with the primary meter’s sustained presence do we retrospectively recognize its primary status. Thus, opening imbroglio serves to mislead the listener by drawing him or her down the wrong metric path. The effect has been compared to the garden-path effect in linguistics.65 A classic example is the opening of the third movement of Beethoven’s Piano Sonata, Op. 14, No. 2, given in Example 13.66 Initially, no cues support the notated 38 meter. Instead, the opening parallelisms induce 28 meter. The listener has no reason to assume that the piece’s primary meter is anything other than 28 ⁠. Measures 3 and 4 briefly support the notated 38 meter, but the music quickly gives way again to 28 meter. A more emphatic statement supporting 38 meter follows in mm. 7 and 8, and the subsequent music (not shown) reveals that 38 is in fact the piece’s primary meter. As with normative imbroglio, the result is indirect grouping dissonance.67 However, because the listener is also forced to readjust his or her initial metric bearings, opening imbroglios often impart a greater degree of disorientation than do most normatively placed imbroglios. Example 13 is particularly complex because the opening motive returns after a brief suggestion of the primary meter, inviting the listener to hear that motive in two different metrical contexts, even before the true primary meter is firmly established. EXAMPLE 13. Open in new tabDownload slide Opening imbroglio in Beethoven, Piano Sonata, Op. 14, No. 2, third movement, mm. 1–8 EXAMPLE 13. Open in new tabDownload slide Opening imbroglio in Beethoven, Piano Sonata, Op. 14, No. 2, third movement, mm. 1–8 An early twentieth-century example of opening imbroglio that has large-scale metric implications is the beginning of the ninth prelude (“La sérénade interrompue”) from Debussy’s Preludes, Book 1, given in Example 14. The motivic parallelism of the opening chromatic neighbor figure establishes eighth- and quarter-note pulses. Before a larger level of meter has a chance to surface, the music abruptly stops. The descending and ascending scalar figures that follow are metrically ambiguous and so continue the established 28 pulses. In addition, a larger two-measure pattern emerges and groups these pulses into 34 meter. The first hint of the notated 38 meter comes in mm. 9–10 with the right hand’s descending leaps. This 38 motive is held in check by the left hand’s 28 leaping fifths. As with Example 13, this first intrusion of 38 meter is only temporary, and the music repeats the opening, this time without the pause of mm. 3–4 or the rising figure of mm. 7–8. This varied repetition further solidifies 34 meter. The right hand again pushes against this meter in mm. 15–16, while the left hand and the subsequent motivic parallelism hold it in force. Only with m. 19 is 38 established as the primary meter, revealing in retrospect that the opening 34 meter was false and part of an extended formal introduction. Tension between quarter and dotted-quarter pulses remains a part of the prelude’s metric fabric despite the dominating presence of 38 meter.68 The tension also plays out formally as a series of brief, contrasting 24 sections, which alternate with the principal 34 music in rapid succession (mm. 80–89, not shown). Such pervasive metric conflict, driven by short repetitive motives, gives the prelude a fragmented quality and is part of what makes it a “sérénade interrompue.”69 EXAMPLE 14. Open in new tabDownload slide Opening imbroglio in Debussy, “La sérénade interrompue,” Préludes, Book 1, mm. 1–20 EXAMPLE 14. Open in new tabDownload slide Opening imbroglio in Debussy, “La sérénade interrompue,” Préludes, Book 1, mm. 1–20 Whereas opening imbroglio misleads the listener into assuming that a false meter is primary, opening close imitation prevents the listener from determining which of two phases of a meter is primary. In the minuet of Haydn’s String Quartet, Op. 76, No. 2, given in Example 15, imitation at the notated measure obscures a sense of hypermetric downbeat and prevents the listener from establishing a clear pattern of strong and weak measures. In conjunction with triple hypermeter, which derives from each line’s three-bar harmonic rhythm, and irregular 6 + 5 phrase construction, opening close imitation obliterates the sense of balanced pacing that normally characterizes the Classical minuet. EXAMPLE 15. Open in new tabDownload slide Opening close imitation in Haydn, String Quartet, Op. 76, No. 2, third movement, mm. 1–11 EXAMPLE 15. Open in new tabDownload slide Opening close imitation in Haydn, String Quartet, Op. 76, No. 2, third movement, mm. 1–11 While close imitation at the beginning of a work is standard in imitative genres, Example 15 demonstrates that it can also serve as a topical reference or dramatic device in genres that are not primarily imitative. In music with text, close imitation’s association with tension and conflict apply to its opening placement as well. Especially evocative uses of the technique appear in the songs of Samuel Barber, two of which are given in Example 16.70 In the opening of “Despite and Still,” the piano’s left hand imitates the right hand a seventh below at the eighth note, producing two displaced versions of the notated 48 meter. The resulting metric (and tonal) instability conveys the emotional tension that exists between the text’s speaker and lover. The presence of close imitation throughout the song suggests that the two are engaged in a fight. Opening close imitation conveys that the fight is already underway when the song begins. In “The Praises of God,” the piano’s right hand imitates the left hand at the eighth note, initiating two displaced dotted-quarter pulses. After three iterations of leaping thirds, both hands enter an eighth note early and repeat the opening configuration. The move disrupts the prior dotted-quarter pulses and initiates a new set of competing pulses. These and other details to be discussed later (Analytical Application 3) convey the speaker’s inner excitement at praising God.71 EXAMPLE 16. Open in new tabDownload slide Opening close imitation in two songs by Barber. (a) “Despite and Still,” Despite and Still, Op. 41, No. 5, mm. 1–2. (b) “The Praises of God,” Hermit Songs, Op. 29, No. 9, mm. 1–4 EXAMPLE 16. Open in new tabDownload slide Opening close imitation in two songs by Barber. (a) “Despite and Still,” Despite and Still, Op. 41, No. 5, mm. 1–2. (b) “The Praises of God,” Hermit Songs, Op. 29, No. 9, mm. 1–4 Opening imitative imbroglio combines the effects of opening imbroglio and opening close imitation, drawing the listener into the wrong metric period and keeping the particular phase of that period ambiguous. The opening of Schoenberg’s “Nacht” from Pierrot Lunaire is well-known for its densely overlapping [014] motives.72 However, the passage’s metric implications are rarely discussed. Example 17 re-notates the opening three measures an octave higher and in a way that clarifies the motivic structure. Five motivic statements outline a series of rising minor thirds, with each successive statement proceeding from the second note of the immediately prior statement. When the first statement is replicated an octave higher, the process stops, and the motive is harmonized a perfect fifth below by a sixth statement that proceeds from the last note of the third statement. Were every statement perceived with equal immediacy, each one occupying its own stream, then the passage would be close imitation at the half note, with every phase of the motive’s 32 meter pitted against itself. Yet I do not perceive every statement with equal immediacy. Instead, I perceive odd-numbered statements more immediately than even-numbered statements.73 As a result, this passage becomes a series of imitations at the whole note, producing an apparent 42 opening imitative imbroglio. Example 17 shows both phases of 42 meter. However, because the tempo is slow, the double-whole-note pulse falls at or beyond the upper limit of metric entrainment.74 This pulse is therefore placed in parentheses in the example. As a result, the whole-note pulse that is common to both versions of 42 meter and that is shown in a separate staff becomes the perceptually salient upper level of meter. Opening 42 imitative imbroglio thus collapses to opening 22 imbroglio. EXAMPLE 17. Open in new tabDownload slide Opening imitative imbroglio in Schoenberg, “Nacht,” Pierrot Lunaire, mm. 1–10 EXAMPLE 17. Open in new tabDownload slide Opening imitative imbroglio in Schoenberg, “Nacht,” Pierrot Lunaire, mm. 1–10 After these opening measures, bass clarinet, cello, and piano present the [014] motive in imitation at the measure, revealing the song’s primary 32 meter. Example 17 gives a simplified version of the score from m. 4, in which only the primary imitative material is shown from the instrumental parts and in which instrumental staves associate material with the same octave register. Initially, the bass clarinet’s statement is perceived as metrically parallel to the opening statements. Once the cello and piano enter, the expanded dotted-whole-note distance of imitation gives rise to a corresponding dotted-whole-note pulse, also shown in a separate staff, which forces a reinterpretation of m. 4.75 Meanwhile, the rhythmic setting of the voice’s text stress continues the opening’s whole-note pulse. This 22 vocal meter is sustained in conflict against the instrumental 32 meter through the entirety of Example 17.76 The opening of “Nacht” thus has multiple functional roles. In addition to presenting the song’s basic motive, as is often recognized, opening imitative imbroglio introduces the song’s imitative texture and vocal meter. That the metric disruption associated with this vocal meter is nascent in the opening measures, prior to the voice’s entrance, mirrors the past tense of the opening lines of text, by which “Dark, black, giant moths / Killed the sunshine.”77 Moths have already blocked the sun, just as opening imitative imbroglio has already blocked the notated meter. THEORETICAL CONSIDERATIONS Imbroglio, close imitation, and imitative imbroglio turn out to be three paradigmatic ways in which melodic parallelism, meter, and perceptual streaming interact. First, a set of melodic parallelisms may exist (1) within a single stream or (2) between distinct streams (and displaced relative to one another). Second, the metric periods induced by the parallelisms (A) may be the same as those of the established or primary meter or (B) may include at least one period that is different from those of the established or primary meter. These two dichotomies intersect as shown in Example 18. Situation (1A) is entirely normative and is not a metric manipulation. (1B) is imbroglio. (2A) is imitation. When the distance of imitation is short, it is close imitation. (2B) is imitative imbroglio. This correspondence between historically derived techniques and ahistoric, music-cognitive categories is remarkably elegant. EXAMPLE 18. Open in new tabDownload slide Metric manipulations as paradigmatic interactions between melodic parallelism, meter, and streaming EXAMPLE 18. Open in new tabDownload slide Metric manipulations as paradigmatic interactions between melodic parallelism, meter, and streaming Within these paradigmatic interactions, the degree of metrical dissonance can vary, depending upon (1) the extent to which the listener entrains to the established or primary meter, (2) the degree to which a metric manipulation invites the listener to entrain to its false meter, and (3) certain relationships between the false meter and the established or primary meter. Both (1) and (2) are determined in large part by the strength and configuration of phenomenal accents before and during a metric manipulation. To that end, Krebs characterizes several factors that influence contextual intensity of metrical dissonance.78 Adapted to the language of metric manipulations, they include: the number, type, and consistency of type of accents that cue a metric manipulation’s false meter; the number and prominence of voices or streams involved in a metric manipulation; the number and persistence of dissonant attacks that cue a metric manipulation’s false meter; and, relatedly, the degree to which a metric manipulation’s competing meters are sustained in direct conflict with one another, particularly as concerns displaced meters in close imitation. Point (3) above is determined by several factors that influence inherent intensity of metrical dissonance.79 Again adapted to the language of metric manipulations, they include: the number of pairs of conflicting metrical levels between primary and false meters; the number of conflicting pulses within pairs of conflicting metrical levels, as measured between points of alignment in an imbroglio’s grouping dissonance or over a given span of time in a close imitation’s displacement dissonance; and distance of imitation, which determines the proximity to consonance of a close imitation’s displacement dissonance.80 Cohn uses the first of these factors—the number of pairs of conflicting metrical levels—as a measure of degree of dissonance.81 Finally, of paramount importance to (3) is the functional status of each conflicting level within its own metric hierarchy and relative to the temporal envelope described by London.82 Specifically, metrical conflicts that incorporate the tactus and other central levels will be more acutely felt than those that incorporate, say, only hypermetrical levels at the upper limits of metric entrainment. Thus, while imbroglio, close imitation, and imitative imbroglio are schemata with certain broad, characteristic perceptual effects, different instances of a particular schema can have different effects based on the numerous factors that influence degree of metrical dissonance. ANALYTICAL APPLICATION 1: SCHOENBERG, “VALSE DE CHOPIN,” PIERROT LUNAIRE, OP. 21, NO. 5 Having surveyed twentieth- and twenty-first-century adaptations of imbroglio, close imitation, and imitative imbroglio, I now present three extended analyses that demonstrate the text-expressive and form-functional potential of these manipulations within larger compositional contexts. We begin by returning to the passage of 24 imbroglio from Schoenberg’s “Valse de Chopin,” given earlier in Example 4. This passage is felt as dissonant against the notated 34 meter, which the preceding music cues through a set of stereotyped waltz features. The waltz topic, and its employment by Schoenberg, has been discussed by Frymoyer.83 General characteristics that signify a waltz include a melody-plus-accompaniment texture, an “oom-pah-pah” accompaniment, a set of melodic rhythmic motives, large ascending melodic leaps from beats one to two, hemiola effects, and other features.84 Schoenberg’s “Valse” includes but also complicates many of these features. The waltz’s melody is passed among flute, clarinet, and piano in rapid succession, as indicated by Hauptstimme brackets in Schoenberg’s score. The waltz’s “oom-pah-pah” accompaniment is similarly spread across the instrumental texture, and the same pattern is sometimes registrally inverted from low-high-high to high-low-low.85 Despite these complications, waltz features are prominent and pervasive enough to project 34 meter. Example 19 demonstrates this by isolating these features from the full texture of mm. 1–13 and reorganizing the score for visual simplicity. The top staff gives the piano’s introductory melodic material and the voice’s recitation, the middle staff groups together the Haupstimme melodies, and the grand staff shows the waltz accompaniment, condensing the music’s texturally diffuse “oom-pah-pah” patterns. As can be seen, waltz rhythms (marked by brackets) are pervasive in all staves, and the “oom-pah-pah” accompaniment is similarly pervasive in the grand staff.86 The grand staff also features several downbeat-oriented melodies that arise from simple pitch reductions (marked * in Ex. 19), melodic leaps into beat two (mm 3–7), and arpeggiated/arch accompaniment gestures (mm. 9–10, marked “arch”), which Frymoyer argues are specifically Chopin-esque.87 In sum, these cues project the notated 34 meter as the movement’s primary meter, even though certain isolated elements push against that hearing.88 EXAMPLE 19. Open in new tabDownload slide Waltz features in Schoenberg, “Valse de Chopin,” Pierrot Lunaire, mm. 1–14 EXAMPLE 19. Open in new tabDownload slide Waltz features in Schoenberg, “Valse de Chopin,” Pierrot Lunaire, mm. 1–14 As Example 19 comes to a close, the piano begins to undermine the 34 waltz meter with a repeating quarter-eighth-eighth rhythmic pattern and an inverted, hemiolic “oom-pah” accompaniment. Krebs points out that the rhythmic pattern inaugurates a half-note pulse, which the subsequent music—the imbroglio of Example 4—continues.89 While true, there are important qualitative differences between mm. 12–13 and the imbroglio that follows. First, the rhythmic parallelism and hemiolic accompaniment of mm. 12–13 are counteracted by waltz rhythms in other parts of the texture. Virtually no cues support the notated meter after the downbeat of m. 14.90 Second, the rhythmic parallelism of mm. 12–13 is different from and briefer than the one that structures the subsequent imbroglio. The former pattern is a fragment of a generic waltz rhythm heard in much of the prior music, while the latter pattern is more particularly a fragment of the waltz pattern just recited by the voice. Finally, Dunsby’s reading of the descending chromatic bass, D–G (marked with letter names below the grand staff in mm. 9–14), as a “substitute for functional harmony” is especially relevant.91 If the downbeat of m. 14 is a cadence on G, then the two measures leading into it are a cadential imbroglio, one that closes off the second vocal phrase. In contrast, the subsequent imbroglio of Example 4 is transitional. It spins out the voice’s motivic fragment as a means of intensifying motion into the third vocal phrase. Thus, even though the half-note pulse is common to both imbroglios, the rhythmic techniques underlying that continuity are functionally distinct. Schoenberg appears to be adapting two of the standard formal functions of imbroglio: cadence and transition.92 The third vocal phrase (Ex. 4) continues the transitional imbroglio’s rhythm to set “Wilder Lust Akkorde,” before passing the rhythm back to the piano. By setting these particular words in this particular way, the voice draws a direct, text-expressive connection between the transitional imbroglio that now extends into the new formal section and the music described by the text. The tonally and metrically dissonant chords that make up the imbroglio enact the text’s “Wilder Lust Akkord,” which disturb (“stören”) the established 34 metric context.93 Close imitation in the flute and clarinet (not shown) further enhance the music’s destructive tendencies. In addition to its local text-expressive function, the imbroglio of Example 4 also plays out a text-expressive metric tension that has been nascent since the voice’s opening phrase. The text of “Valse de Chopin,” given below, is trochaic tetrameter. Wie ein blasser Tropfen Bluts   As a pallid drop of blood Färbt die Lippen einer Kranken,  Colors the lips of a sick woman, Also ruht auf diesen Tönen    So there rests within these sounds Ein vernichtungssüchtiger Reiz.  An annihilative impulse. Wilder Lust Akkorde stören    Wild passion chords disturb Der Verzweiflung eisgen Traum— Despair’s icy dream— Wie ein blasser Tropfen Bluts   As a pallid drop of blood Färbt die Lippen einer Kranken.   Colors the lips of a sickwoman. Heiss und jauchzend, süss undschmachtend,   Hot and exultant, sweetand languid, Melancholisch düstrer Walzer,   Melancholic, sombre waltz, Kommst mir nimmer aus den Sinnen! You never leave my senses! Haftest mir an den Gedanken,   You cling to my thoughts, Wie ein blasser Tropfen Bluts!   Like a pallid drop of blood!94 Schoenberg’s rhythmic setting of the text’s opening lines fits uncomfortably with the 34 waltz meter. Example 20(a) demonstrates by marking strong syllables with accents. A more normative 34 setting might spread each tetrameter line across two measures, with two of the strong syllables falling on downbeats and the other two oriented as either upbeats (beat 3) or afterbeats (beat 2).95 Example 20(b) gives one such hypothetical setting, in which every measure is also a waltz rhythm. Relative to Example 20(b), Schoenberg’s setting shifts “Wie” early to beat 2, so that the first poetic foot mimics the accompanimental “pah-pah.” His setting also compresses “Lippen einer” to syncopate “Kranken.” These rhythmic manipulations cause text stress to support a half-note pulse over the bracketed segments of Example 20(a). The tenuousness of Schoenberg’s setting is revealed by Example 20(c), another hypothetical alternative that continues the half-note pulse implied at the phrase’s opening by repeating the bracketed “blasser” rhythm. The result is the rhythm of Example 4’s imbroglio. Thus, in addition to responding to the voice’s rhythmic patterning at the close of the second vocal phrase, the imbroglio of Example 4 also refers back to the nascent duple tendency in the rhythmic setting of the first line. By relinquishing 34 meter for 24 meter through a rhythmic fragment associated with that duple tendency, imbroglio lets loose the impulse for annihilation (“Ein vernichtungssücht’ger Reiz”) that the text tells us was already lurking in that earlier music (“Also ruht auf diesen Tönen”). EXAMPLE 20. Open in new tabDownload slide Text setting in the first vocal phrase of “Valse de Chopin.” (a) Actual setting of lines 1 and 2. (b) Hypothetical normative setting of lines 1 and 2. (c) Hypothetical imbroglio setting of lines 1 and 2 EXAMPLE 20. Open in new tabDownload slide Text setting in the first vocal phrase of “Valse de Chopin.” (a) Actual setting of lines 1 and 2. (b) Hypothetical normative setting of lines 1 and 2. (c) Hypothetical imbroglio setting of lines 1 and 2 A later passage of vocal imbroglio, also discussed by Krebs,96 is part of a varied reprise of the movement’s opening that begins at m. 23.97 As shown in Example 21, the voice enters on its original beat-two position (Example 20(a)), but with the rhythm of the earlier imbroglio (Example 4), thus playing out the potential of Example 20(c). While the voice sustains 24 imbroglio for several climactic measures, the instrumental music supports the 34 waltz meter. It does so in part by way of a series of fourth- (m. 27), whole-tone (m. 28), and fifth-progressions (mm. 29–30) in the bass, also shown in Example 21.98 The metric distinction between vocal and instrumental music mirrors the text’s sudden distinction between the speaker (“mir”) and the waltz music that haunts the speaker’s thoughts and senses (“… Walzer,” / “Kommst mir nimmer aus den Sinnen!” / “Haftest mir an den Gedanken, …!”). The speaker-singer, perseverating on the imbroglio motive, is ultimately overcome by the music’s impulse for annihilation. EXAMPLE 21. Open in new tabDownload slide Vocal imbroglio in Schoenberg, “Valse de Chopin,” Pierrot Lunaire, mm. 27–31 EXAMPLE 21. Open in new tabDownload slide Vocal imbroglio in Schoenberg, “Valse de Chopin,” Pierrot Lunaire, mm. 27–31 ANALYTICAL APPLICATION 2: WEBERN, PIANO VARIATIONS, OP. 27, NO. 1 The opening section of Webern’s Piano Variations, Op. 27, No. 1 is remarkable in that it consists entirely of opening imbroglio, close imitation, and imitative imbroglio. These metric manipulations are further coordinated with the passage’s row-based form. Example 22 gives the entire opening section and labels row-based phrases A, B, A′, and B′. Example 23 shows the specific row pairs that make up each phrase and how they are coordinated with metric manipulations.99 The motivic parallelisms that structure these metric manipulations are rhythmic and textural in nature. While much could be said about the ways in which pitch motive and harmony interact with rhythm and texture, pitch does not perceptually drive the passage’s metric manipulations. Therefore, this analysis is more narrowly focused on the piece’s adaptation of traditionally pitch-based metric manipulations to the non-pitch parameters of rhythm and textural density.100 EXAMPLE 22. Open in new tabDownload slide Metric manipulation and textural density in Webern, Piano Variations, Op. 27, No. 1, mm. 1–18 EXAMPLE 22. Open in new tabDownload slide Metric manipulation and textural density in Webern, Piano Variations, Op. 27, No. 1, mm. 1–18 EXAMPLE 23. Open in new tabDownload slide Row form and metric manipulation in Webern, Piano Variations, Op. 27, No. 1, mm. 1–18 EXAMPLE 23. Open in new tabDownload slide Row form and metric manipulation in Webern, Piano Variations, Op. 27, No. 1, mm. 1–18 The entirety of Example 22 consists of two-attack gestures, either chord-monad or monad-chord, each of which lies within one of the pianist’s two hands. Right-hand and left-hand gestures further couple and stand in various configurations. In mm. 1–7, the configuration is such that each two-event gesture in one hand lies between the two attacks of a gesture in the opposite hand. However, registral overlapping prevents the separate streaming of right- and left-hand material, which in turn prevents the parsing of individual two-attack gestures and the perception of parallelism at the level of individual gestures. Instead, parallelism arises at the level of composite pairings. Its basis is primarily rhythmic: each composite gesture consists of four sixteenth notes, followed by a sixteenth rest. A more fine-grained parallelism results from textural density, defined as the number of note onsets at a given moment and shown numerically above the staff in Example 22.101 Textural density parallelism cuts across the configuration of two-attack gestures. Within each of the first two composite gestures, the density pattern 2–1 repeats directly, establishing both an internal parallelism, as well as a larger 2–1–2–1 parallelism. The pattern then reverses, which establishes an internal 1–2 parallelism and a larger 1–2–1–2 parallelism across the third and fourth composite gestures. With no cues supporting the notated 316 meter, rhythmic and textural parallelisms draw the listener into 516 meter. Textural density favors a 2-plus-3 metric organization for the first two gestures, in alignment with the twos of the 2–1–2–1 profile. In contrast, durational accent favors a 3-plus-2 division as the last note of each composite gesture accrues greater length from the subsequent rest. This evening-out of metric cues makes the internal profile of 516 meter (i.e., the tactus), perceptually vague, though the placement of the 516 downbeat is relatively clear. The situation reverses with the third and fourth gestures. Textural density and durational accent now align, making the irregular tactus clearer. However, the coordination of these accents at the end of each gesture now conflicts with the preference for an early strong beat,102 making the downbeat perceptually vague.103 Measure 8 reconfigures the two-attack gestures so that they pair in close imitation, with portions of each gesture now sounding simultaneously. Individual gestures initially stream separately, so that their 2–1 density parallelism is easily heard. The parallelism of their composite pairing aligns with the notated 316 meter, which is established for the first time and reveals that the preceding music was an opening imbroglio. Yet, even though the music finally supports 316 meter, close imitation keeps the particular phase of that meter ambiguous. As the passage continues into mm. 9–10, rests between composite pairings are eliminated, removing rhythm as a factor of parallelism altogether. Textural density is all that is left. To complicate matters further, two-attack gestures again registrally intertwine, making it difficult to separate textural density within gestures from the density patterns of the entire texture. With respect to the full texture of mm. 8–10, the density patterns become quite varied: 2–3–1–3–4–1–1–3–2. However, a more abstract parallelism arises. If we define textural density contour against the thickest chord of a given span (designated m for more), with all thinner chords equated (designated l for less), then mm. 8–10 produce a consistent l–m–l contour parallelism that aligns with composite pairings and the notated 316 meter.104 Density contour seems to be the only factor contributing to a sense of parallelism in this passage and to the perception of 316 meter. The specific phase of 316 meter that controls the texture is kept somewhat ambiguous, though textural contour’s emphasis on more slightly favors the second notated sixteenth as metrically strong. Measure 11 begins another passage of close imitation, shifted a sixteenth note relative the preceding passage. As before, the first two-attack gestures stream separately but thereafter registrally intertwine. As they do, the textural density profile evens out, making this passage the most metrically ambiguous of the entire section. With respect to the full texture, the profile is 1–4–1–2–2–2–2–2–2–1–4–1. While the passage begins and ends with the l–m–l profile of the preceding phrase, its middle loses any density contour differentiation. Since density contour was already the primary cue to meter, parallelism and meter become completely attenuated. The passage reveals, through contrast, just how vital density parallelism was to the perception of meter in the earlier passages. Measure 15 initiates yet another rhythmic shift by sixteenth note. With it, the pitch material of m. 8 returns. As before, two-attack gestures initially stream separately but then registrally intertwine.105 This time, however, close imitation telescopes into imitative imbroglio, projecting 216 meter but keeping the particular phase ambiguous. This imbroglio cues the move toward an upcoming ending. That ending is the composite gesture from m. 10, reappearing in mm. 17–18 in the same displaced metrical position in which imitative imbroglio began. That position places the more accent of the less-more-less density contour on the notated downbeat for the first time. Thus, this gesture, which concludes the varied restatement of mm. 8–10 and the entire opening section, is metrically cadential. It expands 216 meter back to the primary 316 meter in coordination with formal closure. Webern thereby gives his imbroglio a traditional formal function—that of cadence—much like Schoenberg did in “Valse.” The coordination of metric manipulation with row-based form facilitates the perception of row structure as formal structure. Metric manipulations also help to articulate the movement’s larger ternary form, for which rhythmic organization is crucial. As a whole, Op. 27 has received a wide variety of formal interpretations, owing in large part to the obscurity of the piece’s title.106 I agree with Bailey that No. 1 is a ternary form, in dialog with sonata form.107 The reprise of mm. 1–18 in mm. 37–54, given in Example 24, is based not upon pitch—the reprise contains entirely new row forms—but upon rhythmic layout. Despite the reversed disposition of two-attack gestures relative to right and left hands, the composite pairings receive the same rhythmic profile and placement, and other than the last chord of the movement, the textural density profile is identical to that of the opening section. As a result, the techniques of opening imbroglio, close imitation, and imitative imbroglio all occur in the same relative position, recapitulating the metric and formal processes of the opening section. EXAMPLE 24. Open in new tabDownload slide Metric manipulation and recapitulation in Webern, Piano Variations, Op. 27, No. 1, mm. 37–54 EXAMPLE 24. Open in new tabDownload slide Metric manipulation and recapitulation in Webern, Piano Variations, Op. 27, No. 1, mm. 37–54 ANALYTICAL APPLICATION 3: BARBER, “THE PRAISES OF GOD,” HERMIT SONGS, OP. 29, NO. 9 Whereas many text settings use close imitation to depict outward conflict (see, for instance, Ex. 9), Samuel Barber’s songs frequently use close imitation to convey inner emotion. In “The Praises of God,” the ninth of the Hermit Songs, close imitation is sustained throughout as a primary component of the texture and conveys the speaker’s excitement at praising God. We will consider the song’s opening section, given in Example 25. EXAMPLE 25. Open in new tabDownload slide Metric manipulation in Barber, “The Praises of God,” Hermit Songs, Op. 29, No. 9, mm. 1–12 EXAMPLE 25. Open in new tabDownload slide Metric manipulation in Barber, “The Praises of God,” Hermit Songs, Op. 29, No. 9, mm. 1–12 The text is a translation of an eleventh-century Gaelic epigram that Barber commissioned from W. H. Auden specifically for the cycle.108 The text is singular in gesture, chastising him who fails to praise God with the effusiveness and spiritual lightness of singing birds. How foolish the man Who does not raise His voice and praise With joyful words, As he alone can, Heaven’s High King To whom the light birds With no soul but air, All day, everywhere Laudation sing.109 The speaker can hardly contain himself. The opening gambit runs into the image of singing birds in the single breath of a single sentence. In its delivery, the poem becomes the speaker’s own expression of praise. This excited, out-of-breath quality becomes especially obvious when compared to the paler translation of the same poem that Barber rejected: It is folly for any man in the world to cease from praising Him, when the bird does not cease and it without a soul but wind.110 Barber’s setting draws out exactly the feature of Auden’s translation that differs from Jackson’s: the speaker’s delivery. Barber conveys the speaker’s excitement through a flexible interplay between melodic parallelism, meter, and text stress. This interplay is structured around the piano’s close imitation and is coordinated with the textural separation of the voice, the piano’s right hand, and the piano’s left hand to such an extent that these three performative forces become distinct narrative agents.111 Part of the expressive impact of the song’s close imitation involves not just the manipulation of motivic parallelism and meter, as will be explored in detail momentarily, but also the manipulation of harmony and voice leading. The sparse staccato texture belies a thick, tangled counterpoint, and the motivic displacements arising from close imitation sometimes displace chord members to such an extent that their onsets align with a subsequent harmony. Example 26 clarifies these points in two stages. Stage (a) presents Example 25’s chord tones in their exact register but rhythmically normalized to a steady 68 meter. The dotted-quarter pulse is the song’s primary pulse. Stage (b) incorporates Example 25’s non-chord tones as contrapuntal embellishments to (a) and indicates them with figures. The actual music of Example 25 takes (b) and applies various rhythmic displacements and elisions. The most dramatic displacements include, for instance, the displacement of III7’s (V7/vi’s) chordal seventh (m. 4 and m. 8 in the reduction) to the subsequent downbeat (m. 5 and m. 9 in the score), in direct opposition to the root of the subsequent chord. The striking dissonances that result from such displacements, as well as those resulting from various non-chord tones, enliven the motivic and metric manipulations. EXAMPLE 26. Open in new tabDownload slide Harmonic reduction of “The Praises of God,” mm. 1–12. (a) Chord tones, rhythmically normalized. (b) Non-chord tones as contrapuntal embellishments of (a) EXAMPLE 26. Open in new tabDownload slide Harmonic reduction of “The Praises of God,” mm. 1–12. (a) Chord tones, rhythmically normalized. (b) Non-chord tones as contrapuntal embellishments of (a) The opening section of “Praises,” given in Example 25, sets Auden’s first six lines of text. The piano’s music consists entirely of close imitation, with the right hand imitating the left hand at the distance of the notated eighth note. In the piano’s introduction, the imitation is strict, with parallelisms consisting of leaping thirds (solid brackets), outlining harmonies I–iii–V. At the moment when the right hand leaps to a high B in m. 2, the left hand undercuts the established imitative process and reinitiates the opening C–E an eighth note early. This elision pits the right hand’s metrically weak B against the left hand’s metrically strong C. This tonal incongruity, together with the coinciding metrical incongruity and the juxtaposition of registral extremes, enhances the sense of playfulness already present in the leaping staccato gestures themselves. The right hand adjusts to maintain the imitative configuration of the opening, producing temporary imitative imbroglio. The entire process unfolds again, with the same jarring move of m. 2 returning at the downbeat of m. 4. In its totality, the piano introduction projects a non-isochronous 88 meter (3-plus-3-plus-2), but only after we have experienced metrically dissonant free fall. When the voice enters, the music becomes a whirlwind of shifting parallelisms, floating text stress, and metric manipulation. Such moment-to-moment instability can be heard as a product of the voice, the right hand, and the left hand destabilizing and influencing one another. This agential interplay infuses the music with a sense of motion, conveying the uncontrollable excitement bubbling up within the speaker. The voice begins by doubling the right hand, but its text stress immediately falls out of alignment with the metric stresses of both hands. Whereas the piano’s close imitation emphasizes the first and second eighth-notes of m. 4, the stress of “foolish” emphasizes the third eighth. The voice continues in rhythmic unison with the right hand, but the text stress becomes further delayed, shifting to the downbeat of m. 5 at “man.” This shift in turn forces a reinterpretation of the voice’s motivic parallelisms: C–E’s parallelism with B–D supplants its tentative parallelism with G♯–B. Relative to the left hand’s dotted-quarter pulse, B–D now occupies the third phase available to the ascending-third motive. Momentarily, all three parts of the texture are in close imitation with one another. The arrangement is short-lived. In mm. 4–5, the strictness of the opening’s close imitation begins to break down. The right hand’s thirds collapse onto seconds, and the opening progression becomes chromaticized and extended to I–III7–IV–V. These harmonic changes indirectly touch upon vi, a secondary harmonic region that becomes important at the end of the section. While the piano is modifying its harmony, the voice again alters its metric and melodic configuration. The rhythmic parallelism associated with “the man” and “Who does” is shortened with “not raise,” so that “raise” falls an eighth note early. Melodic contour reverses (dotted brackets), painting the text, and the component interval shrinks from a third to a second.112 Thus, rhythm, meter, contour, and interval all collapse together. It is as if the speaker is so excited that he musically trips over his own words. In order to make up for it, the voice reverses direction and moves more expansively upward in fourths. The voice’s motivic parallelisms now align with those of the right hand but continue to emphasize the third eighth note of the dotted-quarter beat. The voice’s tumble at the end of m. 5 thus has the fortunate consequence of regaining the motivic-metric composure of its entrance (“How foolish”). The sustained presence of all three phases of the dotted-quarter pulse across the three textural parts enhances the passage’s excitement, which builds in conjunction with the voice’s dramatic rise in register. This mounting energy causes the right hand to lose control of its motivic parallelism. Responding to the voice’s reversed contour at “not raise,” the right hand reverses its melodic contour (again, dotted brackets). The left hand answers by initiating imitative imbroglio in m. 7, similar to that of the introduction. Rather than deriving from phrase elision, this imbroglio results from rhythmic manipulation within the piano’s harmonic phrase (I–I6–ii9–V9).113 In the same measure, the voice collapses as it did in m. 5, keeping its text stress displaced from the metric accents of the piano. The reversed contour is here dramatized through a registrally climactic linear descent on “With joyful words,” which matches the right hand’s reversed motivic contour. The excitement spills over to the left hand, which reverses its motivic contour for the first time at m. 8. Just as the music is threatening to fall apart, the voice and right hand reprise the voice’s entrance (mm. 4–5) in support of the text’s rhyme “man”/“can,” and the left hand quickly follows suit. Before the harmonic phrase (I–III7–IV–V) can complete itself, the piano briefly but dramatically halts in the middle of m. 9. The pause rhetorically emphasizes the voice’s text, “Heaven’s High King,” the line to which the preceding text and music has been building. In its exclamation, the voice attempts to cadence in a metrically stable manner. The dotted rhythmic pattern, previously associated with the metric collapses of m. 5 and m. 7, now affirms the notated dotted-quarter pulse that has so far been the purview of the left hand. It does so at a moment in the reprise (m. 9) that corresponds with the voice’s first tumble (m. 5), showing that the speaker now takes control over his excitement. Channeled through newfound stability, the speaker’s praise of God bursts forth with sudden clarity. The stability is unique to the voice, however. The piano, rather than moving to the dominant as before (I–III7–IV–V), initiates a chromatic imitative imbroglio, subverting the voice’s attempt to stabilize meter and pushing the music toward the wrong dominant: V/vi. That wrong dominant is the same chromatic region touched upon in measures 4 and 8 in the form of III7–IV (V7/vi–VI/vi). Like m. 7, this imbroglio mixes ascending and descending contours. As the imitation extends into mm. 11–12, it relaxes back to the dotted-quarter pulses of close imitation, winding down the energy that built up over the course of the song’s opening section. At the same time, the reversal of contours in both hands and a recontextualization of the dotted rhythmic pattern in m. 12 signals that the subsiding energy will only be temporary. CONCLUSION: METRIC MANIPULATIONS AND METRIC IRREGULARITY Over the course of this article, I have made the case that composers of the twentieth and twenty-first centuries continued to use certain eighteenth-century motive-driven metric manipulations. I have shown that these manipulations are three paradigmatic ways in which melodic parallelism, in conjunction with perceptual streaming, manipulates meter, and I have offered extended analyses that demonstrate the form-functional and text-expressive roles that these manipulations can play in larger musical contexts. On a historical level, such sustained use of compositional techniques across several centuries and stylistic divides seems remarkable. On a perceptual level, it is perhaps not surprising at all. Meter, melodic parallelism, and streaming are all general properties of music perception, as is the paradigmatic manipulation of one by another. While the characterization of these paradigms may change over time, their fundamental cognitive nature probably does not. That said, composers of different times have explored these general cognitive capacities in different ways. In Example 22, textural density and density contour seem to be relatively novel aspects of motivic parallelism, ones which come to the perceptual fore precisely because more traditional pitch-based cues to meter are absent. Therefore, specific musical contexts may make use of our general capacity for metric manipulation by using a variety of motivic inputs. Composers have also explored the limits of meter in the context of metric manipulation. Most of the examples we have considered feature isochronous primary and false meters (Ex. 22 is a notable exception), and most of them also feature meters that are, for lack of a better word, locally stable, insofar as there is a single, clearly projected primary meter and a single, clearly projected false meter. While some degree of regularity is necessary scaffolding for metric manipulations to generate metrical dissonance, and while some degree of local stability is necessary for metric manipulations to be singularly identifiable, the full metric hierarchies need not be strictly regular, and the meters projected by motivic parallelism can fluctuate. Regarding irregularity, consider rehearsal 10 from Thomas Adès’s Piano Quintet, given in Example 27. Leading into this passage from rehearsal 9 (not shown), all five instruments unfold vast registral sweeps that descend through alternating minor thirds and major seconds. With the exception of some rhythmically even lines, the descending gestures consist entirely of parallel two-note, short-long rhythmic motives. Metric irregularity arises from the fact that: (1) the lines frequently change their internal short–long rhythmic relationship, (2) the short–long relationships between imitative lines differ, and (3) each line enters at a varying distance of imitation. The result is a passage that pits constantly fluctuating meters against one another, both simultaneously and successively. This metric flurry tumbles into the passage at Rehearsal 10, which fragments the previous short–long rhythmic motive in more stable imitation between piano and strings. Despite this relative stability, there is still internal irregularity, owing to the rhythmic relationships that result from the alternating notated 112 and 210 meters.114 Namely, the piano’s 112 + 210 profile is imitated by the strings’ 110+[110+112] profile. The ninth measure of the passage initiates a texturally rich metric free fall: a series of overlapping short–long motives are passed among the full ensemble in wildly varying instrumental combinations, creating imitative imbroglio. The motive is now strictly regular and establishes 210 as the basic metric unit. This regularity cuts against the prior close imitation’s two irregular metric configurations, and these two configurations themselves cut against the meters of the prior passage of close imitation. Thus, the music between rehearsal 9 and rehearsal 11 is all metric manipulation, and the meters therein feature varying degrees of regularity and irregularity. The passage has a thrilling effect, akin to Taruskin’s description of another Adès passage, in which “[f]ast ostinatos, often of a tricky, ear-beguiling complexity, coexist at varying speeds in contrasting colors and registers, evoking not linear distance but gyres and vortexes: sound in motion but not going anywhere.”115 EXAMPLE 27. Open in new tabDownload slide Close imitation and imitative imbroglio in Adès, Piano Quintet, rehearsal 10 EXAMPLE 27. Open in new tabDownload slide Close imitation and imitative imbroglio in Adès, Piano Quintet, rehearsal 10 Regarding local metric instability, consider as a final example the opening of the “Prelude” from Schoenberg’s Piano Suite, Op. 25, given in Example 28. The passage consists largely of close imitation. The first eight notes of the right hand (row form P4), which rhythmically support 38 meter, are answered by the left hand, which presents a rhythmically varied transposition of the melody (row form P10). The imitation is at the notated quarter note, which transforms the first two notes of the imitating line from an anacrusis figure into a downbeat figure, relative to the right hand’s dotted-quarter tactus. Additionally, the rhythmic profile of the left hand projects a duple (⁠ 616 ⁠) rather than triple (⁠ 318 ⁠) division of that tactus. The upper voice of the left hand continues with notes 5–8 of P10 but in the rhythm of the right hand in m. 1. Meanwhile, the lower voice of the left hand simultaneously unfolds notes 9–12 of P10 with a contour that is parallel to the previous two head motives. The rhythmic setting of this lower voice is parallel to that of the left hand’s head motive (four equal durations rather than short-short-long-short), while its metric setting is parallel to that of the right hand’s head motive (anacrusis rather than downbeat figure relative to the established dotted-quarter tactus). Exactly which of the two parallelisms, rhythmic or metric, comes to the perceptual fore, along with the corresponding 38 or 28 meter, can vary. In fact, these two parallelisms are perceptually competing. If a dotted-quarter pulse overrides the passage, then the left hand’s lower voice would not be perceived as parallel to the left hand’s head motive because the two would not be metrically parallel. If, on the other hand, the rhythmic parallelism overrides, then they would be perceived as metrically parallel, as downbeat gestures in 616 and 28 meter, respectively. To complicate matters further, the right hand continues with a melodically contrasting figure that is syncopated with respect to all of these metric possibilities. The local metric instability of this passage gives the performer room to influence the listener’s sense of meter and melodic parallelism in a substantial way. For instance, the performer might emphasize the notated meter throughout, drawing attention to the anacrusis parallelism between hands, or he or she might emphasize the fluctuating meters, drawing attention to the downbeat parallelism within the left hand. In both this and the Adès example, metric regularity and local metric stability are attenuated to a moderate degree. Nevertheless, the interplay between melodic parallelism and meter that defines metric manipulation gives both passages their rhythmic vitality. EXAMPLE 28. Open in new tabDownload slide Close imitation in Schoenberg , “Prelude,” Piano Suite, Op. 25, No. 1, mm. 1–3 EXAMPLE 28. Open in new tabDownload slide Close imitation in Schoenberg , “Prelude,” Piano Suite, Op. 25, No. 1, mm. 1–3 These final examples call into question the limitations of the concepts of imbroglio, close imitation, and imitative imbroglio. At what point are we still talking about techniques linked to the metric regularity of the eighteenth century, and at what point are we dealing with techniques that are characteristic of the twentieth and twenty-first centuries, like mixed meter and polymeter? After all, any example of mixed meter could in principle be regarded as imbroglio, so long as the meters coordinate with melodic parallelism. Similarly, a passage of polymeter could be composed in such a way that it resembles imbroglio, as may very well have been the case with Example 5. It seems better to deal with these problems on a case-by-case basis than to draw arbitrary boundaries. Surely we are dealing with a continuum, in which there are more and less archetypal examples of classic metric manipulations. Ultimately, a detailed, principled account of perception is of greatest interest. Since we have defined metric manipulations along perceptual lines, I see no harm in allowing overlap with other concepts where examples of those concepts also exhibit the definitive perceptual features of metric manipulations. At worst, the fact that certain features are common to overlapping concepts implies that such features are essential parameters by which we process music in general. I would like to thank David Temperley, John Roeder, and Henry Klumpenhouwer for their formative feedback during early stages of writing, as well as two anonymous readers for a number of incredibly helpful suggestions that were incorporated during the revision process. Footnotes 1 Horlacher (1995). 2 Ibid., 298. 3 Lewin (2006, Chapter 17); Temperley (2001, 299–303). For Lewin’s use of the term “motivic inertia,” see p. 352. 4 Van den Toorn (1987); Roeder (2004). Here I cite van den Toorn’s chapter, “Stravinsky Re-barred,” in Stravinsky and The Rite of Spring (1987) rather than the article in Music Analysis (1988). For a more recent discussion, and one which impressively synthesizes this earlier work with recent theories of meter, see van den Toorn and McGinness (2012). 5 See, for instance, his discussion of the role of “motive X” at the opening of “Syncopation” (Roeder 2004, 49–52). 6 Van den Toorn (1987, 85–86). See also the updated discussion of “Evocation” in Van den Toorn (2017), which, like van den Toorn and McGinness (2012), synthesizes his earlier analysis with more recent work on meter, particularly work that deals with the relationship between meter and melodic parallelism. Other examples that attenuate background periodicity include the opening Allegro from Renard and the “Royal March” from The Soldier’s Tale, both discussed in van den Toorn and McGinness (2012, Chapter 7). 7 Lerdahl and Jackendoff (1983, 75); Temperley (2001, 49–51); Temperley and Bartlette (2002). 8 Mirka (2009, 138). 9 Grave (1995); Mirka (2009, 133–51 and 189–98). Mirka (2009, 190) draws the term imitatio per thesin et arsin from Koch. For simplicity, I use Grave’s (1995, 193) term close imitation instead. Mirka (2009, 139) also borrows free fall from Grave (1995, 178 and 193). For reasons to be explained later, I call this technique imitative imbroglio. 10 Mirka (2009) identifies only two examples of imbroglio (136) and one example of free fall (141) that supposedly lack melodic parallelism. In fact, even these examples exhibit rhythmic and/or pitch-contour parallelisms. Since, by definition, close imitation also features melodic parallelism, I take parallelism to be a defining feature of the three techniques, which distinguishes them as special cases of more general categories of metrical dissonance. 11 On perceptual streaming, see Bregman (1990). The term refers to our ability to parse a musical stimulus (or, more generally, an auditory scene) into distinct but simultaneously unfolding musical lines (or sequential groups) on the basis of pitch distance/frequency separation, rate/speed, timbre, and other factors. See Bregman’s Chapter 6 for a discussion of streaming in music and Chapter 2 for streaming in a more general context. 12 On schemata, see Gjerdingen (2007). 13 Krebs (1999). See in particular the analyses of Berlioz’s Symphonie fantastique (187–92), some of Schumann’s songs (159–62), and some piano music by Schumann and Chopin (192–93 and 199). 14 Lerdahl and Jackendoff (1983, 18). See Caplin (2002) for a survey of how meter has been perceptually characterized over several centuries. 15 London (2012, 4). 16 Lerdahl and Jackendoff (1983, 19). 17 Ibid.; Benjamin (1984). 18 London (2012); also London (1995). 19 Berry (1976); Leong (2011). 20 Temperley (2013); Ohriner (2016). 21 Such meter-related percepts include not just a sensation of strong and weak beats but also sensations like syncopation (in association with rhythmic patterning), anacrusis (in association with grouping structure), and match/mismatch between text stress and text setting (in association with prosodic structure). 22 Yeston (1976, 66). 23 Jackendoff (1991); Hasty (1997); Mirka (2009). Others of note include Roeder (1994); Horlacher (1995 and 2001). 24 For pulse layer, see Krebs (1999, 23). For unit pulse, see Cohn (2001, 302). 25 Krebs (1999, 23). 26 Temperley (1995). 27 On modularity, see Temperley (1995); Fodor (1983). On conditions for melodic parallelism, see Temperley and Bartlette (2002, 128–30). 28 For a summary of the debate over modularity, see Barrett and Kurzban (2006). 29 On meter perception as modular, see Jackendoff (1991). On music perception as modular, see Jackendoff (1987). 30 Van den Toorn (1987, 83 and 86). 31 Imbrie (1973, 65). 32 Since my annotations seek to model a passage’s suggested meters, they will likely appear radical. While my own hearings do indeed skew radical, my annotations should not be read as prescriptions for conscious listening strategy or as complete descriptions of the total metrical experience of complex passages. Additionally, I sometimes resort to colloquial descriptions of the listener being drawn down a particular metric path, when a more precise account would be that the listener’s subconscious processing of meter is drawn down a particular metric path. At other times, I use the colloquialism in a more general sense, to describe the listener’s total hearing. Hopefully, my meaning is made clear by context. 33 DeBellis (2009); Temperley (2009). 34 An alternative to the mind-oriented approach that I develop here would be the body-oriented approach nicely summarized by Ohriner (2016). How the subconscious mental processing of meter interacts with bodily entrainment in passages of metric manipulation deserves further consideration. 35 In most cases, the notion of established meter and primary meter will be one and the same. However, in certain instances, particularly when one metric manipulation follows another, the most recently established meter may itself be a false meter and therefore different from the primary meter. In such cases, the identity of a manipulation is twofold and depends upon whichever meter, established or primary, is taken as the perceptual point of reference. Additionally, Mirka (2009, 138) uses the term false meter because her examples always give way again to a single, clearly delineated primary meter. Even though there are examples that make the primary/false dichotomy problematic, her terms are still helpful for singling out the meters involved in a given manipulation. 36 This definition of imbroglio is more general than Mirka’s (2009, 136), by which “imbroglio is a grouping dissonance that consists in regrouping Taktteile into new Takte,” the two principal levels of meter in eighteenth-century metric theory. 37 I use the term hemiola in the more general sense of Cohn (2001), rather than the historically contextualized sense of Mirka (2009, 159–64). I also treat it as a metric phenomenon that may or may not feature melodic parallelism. In contrast, I exclusively reserve imbroglio for passages that are generated from a repeating motivic fragment. In this way, all 3-against-2 imbroglios are hemiolas, but only some hemiolas are 3-against-2 imbroglios. 38 Mirka (2009, 135). 39 Temperley (1995, 145–46). 40 Ibid., 146. 41 Krebs (1999, Chapter 2). Throughout the discussion, I will make reference to Krebs’s taxonomy of metrical dissonances. Rather than repeat the citation each time, I refer the reader now to Chapter 2 of his book. 42 Krebs (1999, 244–48); Malin (2008, 75–85); Lewin (2006, 349–50); Dunsby (1992, 40–41). 43 Horlacher (1992). Thanks to an anonymous reader for pointing out this connection. 44 On continuous versus discontinuous superimpositions, see Horlacher (2011, Chapter 4). Unlike Stravinsky’s discontinuous superimpositions, which are generally accompanied by flexible motivic lengths in most or all of the strata, the superimposition in Example 6 features strict ostinati in both voices, even though the violin comes in and out of the texture. 45 For some additional examples of imbroglio, see Debussy’s twelfth piano etude “Pour les accords,” Bartók’s fourteenth bagatelle “Valse,” and the music that begins “Marie’s Lullaby” from Act I, Scene III of Berg’s Wozzeck. The latter example has the same form-functional role as the imitative imbroglio that will be discussed in Example 12. Both imbroglios are sentential continuations driven by motivic fragmentation. 46 Whether or not a listener can attend to two meters at once is an area of active investigation and debate. See, for instance, Temperley (2001, 219–20 and 228–29); Temperley (2008, 314); London (2012, 103–104); Poudrier and Repp (2013). Close imitation in particular brings the issue to the fore. For present purposes, I simply assume that the listener can consciously attend to either meter in alternation, making no claims about simultaneous perception. That said, the simultaneous presence of two suggested meters is bound to produce a sustained sense of metrical dissonance, whether one conservatively clings to a single metrical strand or radically switches between them. 47 The brackets in Example 7 indicating melodic parallelism are just one possibility. Often, there are fewer or even no internal parallelisms within each line. Close imitation’s most important melodic parallelism is between lines. 48 Mirka (2009, 190–95). 49 My metrical reading of this passage differs subtly from Mirka’s. She hears the movement’s theme implying strong beats at melodic peaks, such that violin I and viola I both begin Example 8 with a downbeat rather than an anacrusis. She argues that this “default meter,” which is only latent at the beginning of the movement, comes to the fore at m. 24 due to the absence of accompaniment in other parts of the texture. In contrast, I always hear the theme’s melodic peaks as anacruses, owing to the textural accent at the movement’s opening notated downbeat and the harmonic change (V7–I) at the onset of m. 24. In either reading, close imitation pits two phases of 34 meter against one another, one of which aligns with the notated downbeat. 50 Thus, this example distinguishes established meter from primary meter. With respect to the movement’s primary meter, Example 8 is 34 close imitation. With respect to the immediately preceding 24 imbroglio, Example 8 is 34 imitative imbroglio (to be defined momentarily). Because Example 8 marks a return to 34 meter rather than a further metric departure, it is principally heard as close imitation. 51 See, for instance, Cumming and Schubert’s (2015) survey of fuga ad minimam or stretto fuga. 52 On close imitation evoking chase, see Watkins’s (2010, 72) discussion of Josquin’s setting of “De tous biens plaine” and Allen’s (1999, 282) discussion of Britten’s “This Little Babe.” 53 For some additional examples of close imitation with interesting metrical implications, see “This Little Babe” from Britten’s Ceremony of Carols, Bartók’s “Song of the Harvest,” “Parodie” from Schoenberg’s Pierrot Lunaire, and Steve Reich’s Tehillim. 54 Grave (1995, 193); Mirka (2009, 139). 55 See Mirka’s (2009, 139) discussion of Türk’s example of imbroglio. 56 Grave (1995, 186–88). Grave does not identify this passage as free fall because it does not satisfy his narrower definition of the technique. However, it does satisfy my broader definition, in addition to capturing the perceptual effect common to other instances of imitative imbroglio. 57 Caplin (1998, 59–60). 58 This motivic relationship makes the contrasting status of measures 3 and 4 equivocal, which in turn makes the distinction between periodic antecedent and sentential presentation ambiguous. While I hear the melodic A♭ of m. 4 as unmistakably cadential in gesture, thus suggesting an antecedent-continuation hybrid, one could also hear mm. 1–4 as unfolding two statements of a single basic idea, thus suggesting a sentence. The ambiguity is enhanced by the absence of tonal cadences, which typically distinguish such borderline cases. See, for instance, Caplin’s (1998, 49–51) Example 4.4. See also Schoenberg’s (1967, 27) own discussion of antecedent phrases in which the “the coherence [between the basic and contrasting ideas] is more evident than the contrast.” 59 For some additional examples of imitative imbroglio, see Berg’s Four Songs, Op. 2, No. 2 (mm. 6–8) and Schoenberg’s String Trio, Op. 45 (mm. 96–98), discussed by Hyde (1984). For an example of imitative imbroglio flowing out of close imitation, see Schoenberg’s Three Piano Pieces, Op. 11, No. 2 (mm. 43–44). 60 Mirka (2009, 137–38). 61 On melodic parallelism and grouping, see Lerdahl and Jackendoff (1983, 51–53). On melodic parallelism and streaming, see Temperley (2001, 113). 62 For pertinent discussions of musical agency, see Monahan (2013) and Klorman (2016). 63 See not only Mirka (2009) but also Riemann’s (1903, 111–21) discussion of “Widerspruch zwischen Motivlänge und Takt” (“Contradiction between Motive Length and Measure”), Creston’s (1964) concept of overlapping, Cumming and Schubert’s (2015) historical survey of fuga ad minimam, and any discussion of imitatio per thesin et arsin, per arsin et thesin, in contrario tempore, in shifted rhythm, or with reversed accents, such as Mann (1965, 151); Koch (1802, col. 1039–1040); Goetschius (1902, 76–78); Prout (1969, 136). In all cases, melodic parallelism is implicitly, if not explicitly, recognized as a principal factor manipulating meter. 64 Mirka (2009, 147–51). 65 Temperley (2001, 210–11). 66 Ibid. 67 Opening imbroglio also produces subliminal dissonance between the false and notated meters. Mirka (2009, 205–208) questions and ultimately rejects Krebs’s notion of subliminal dissonance. I find myself skeptical as well, though I refrain from pursuing the issue here. Certainly, opening imbroglio brings the issue to the fore. 68 See, for instance, mm. 63–72 (not shown). 69 Other examples of opening imbroglio by Debussy include the first movement of his Violin Sonata, analyzed in great detail by Hasty (1999), and the eighth prelude (“La fille aux cheveux de lin”) from his Préludes, Book 1, which generates imbroglio by manipulating the rhythmic value of the first note. Both opening imbroglios impart a searching quality to their tonally ambiguous openings. Yet another adaptation of opening imbroglio that is especially characteristic of the twentieth and twenty-first centuries occurs when an opening motivic parallelism, at odds with the notated meter, repeats as an ostinato and extends past the entrance of another voice that projects the notated meter. Examples of this subtype include several songs by Charles Ives, such as “Those Evening Bells,” “The Light That Is Felt,” and “Two Little Flowers.” The latter song is analyzed by Krebs (1999, 234–36). An especially complex opening imbroglio that incorporates non-isochronous meter and syncopation begins the second main section of Ives’s “General William Booth” (m. 39). Other complex examples that begin internal sections include the second movement of Bartók’s String Quartet No. 1 (rehearsal 1, after a transitional, metrically unstable attacca beginning) and the third of Webern’s Five Pieces, Op. 5 (final section, after a substantial ritardando and a slow, meter-cancelling cadential gesture). 70 The reader will likely note that metrical dissonance in the two Barber examples is more pressing than in the Haydn example. The shorter distance of imitation, relative to tactus and tempo, produces conflict between levels of meter that are more central to the temporal envelope and which are therefore more salient. See London (2012, Chapter 2). Using an informal judgment of tempo, the hypermetric conflict in the Haydn example results from conflicting dotted-whole-note pulses that move at about 30 beats per minute. In contrast, the metric conflicts in “Despite and Still” and “The Praises of God” result from conflicting quarter and dotted-quarter pulses, respectively, which move at about 65 beats per minute. 71 For additional examples of opening close imitation that, like the Haydn example, feature imitation at the notated measure, see Barber’s “Sure on this Shining Night,” the “Trio” from Schoenberg’s Piano Suite Op. 25, and the “Dirge-Canons” from Stravinsky’s In Memoriam Dylan Thomas. For examples with varied distances of imitation, see Webern’s Five Canons, Op. 16. 72 See, for instance, Straus (2016, 31). 73 This perception is due to several factors: (1) the onset of the third statement is the first time two notes are struck together, which encourages perceptual streaming of a second contrapuntal voice at that moment; (2) the onset of the fifth statement brings with it a substantial change in timbre, which likewise encourages perceptual streaming of an additional voice at that moment; (3) factors (1) and (2) are also phenomenal accents that influence meter, which in turn influences the perception of motivic parallelism and streaming (Temperley 2001, 113); and (4) there is a general preference to avoid cases where a single note is included in more than one stream (Ibid., 101), which perceptually suppresses even-numbered statements. Furthermore, layering a motive that is only three notes long surely rubs up against some lower threshold of perceived motivic parallelism and grouping. 74 London (2012, Chapter 2). 75 That a consistently spaced series of imitations promotes the perception of a corresponding metric pulse has been discussed by Yeston (1976, 47–50) in the context of density as a type of accent and, more recently, by Klorman (2016, 228–33) in the context of “cycles of imitation” and “modules of patterned activity” as determinants of meter. As with the song’s opening, the slow tempo prevents the perception of a larger level of meter and any attending sense of hypermetric conflict that would have arisen from overlapping imitations. Comparison with the Haydn example of opening close imitation is instructive. Both examples feature imitation at the measure, but only the Haydn is fast enough to encourage a sense of hypermetric conflict. 76 Lewin (2006, Chapter 17) observes a similar conflict between vocal meter and notated or instrumental meter in other works by Schoenberg. My analysis is also indebted to Roeder (1994). 77 “Finstre, schwarze Riesenfalter / Töteten der Sonne Glanz.” 78 Krebs (1999, 57–61). 79 Ibid. 80 In instances of grouping dissonance, the number of conflicting pulses within pairs of conflicting metrical levels is also a measure of ratio complexity. In instances of displacement dissonance, it is a measure of what Krebs calls “tightness/looseness.” 81 Cohn (1992b). That article formalizes aspects of an earlier article (Cohn 1992a) while also serving as a point of departure for a later one (Cohn 2001). 82 London (2012, Chapter 2). 83 Frymoyer (2017). 84 Frymoyer (2017, 85) distinguishes essential features of a topic, those which occur in all instances of a topic and all of which must be present to identify a topic, from frequent features and stylistically particular features, which need not occur in every instance of a topic but which “contribute to the topic’s markedness and help nuance its expressive content.” Triple meter is an essential feature of the waltz. In part, I am using the presence of other essential, frequent, and stylistically particular features to deduce the presence of that essential feature. 85 Frymoyer (2017, 101–102) observes a similar textural spread of “ooms” and “pahs” in “Serenade” and also notes that the textural inversion of the pattern is idiomatic for Schoenberg. 86 Krebs (1999, 245) singles out some of the waltz rhythms as projecting the movement’s measure-level pulse. 87 Frymoyer (2017, 94–95). 88 For instance, phenomenal accents sometimes work with and sometimes work against the waltz meter. While some bass onsets align with the notated downbeat (mm. 9–11), others are syncopated away from it (mm. 1–2 and 5). Importantly, some of these bass syncopations result from Schoenberg’s idiomatic manipulation of the “oom-pah-pah” pattern (m. 2). Thus, a hearing that is informed by the waltz topic, and Schoenberg’s idiomatic treatment of it in particular, may give rise to a different perceived meter than a hearing that is not. Even so, unsyncopated phenomenal accents often counteract syncopated ones as when the piano’s melodic peak and the flute’s durational stress on the downbeat of m. 3 answer the syncopated bass of mm. 1–2. 89 Krebs (1999, 245). 90 Indeed, the only metric cues that Malin (2008, 77) identifies in mm. 12–13 are ones that support the waltz meter. He locates the half-note pulse as beginning at m. 14. 91 Dunsby (1992, 42). 92 See Mirka (2009, 147–51) for the standard formal functions of imbroglio. 93 This interpretation is consistent with Malin (2008) and Lewin (2006, Chapter 17). 94 The translation is the author’s own, with reference to Andrew Porter’s translation in Dunsby (1992, 40) and Stanley Appelbaum’s translation in the 1994 Dover edition of the score. 95 See Malin (2010, Chapter 1) for a discussion of normative settings of poetic meters in German lied. See in particular his common declamatory schemes for tetrameter lines set in triple-meter (his Table 1.2), all of which fit the description just given. 96 Krebs (1999, 245). 97 Dunsby (1992, 41); Malin (2008, 84–85). 98 Dunsby (1992, 41–42). 99 For row structure, see Bailey (1991, 191–92 and Appendices III and IV). Relative to Bailey’s system, I have relabeled rows so that C equals 0. For the present section, this change simply means that Bailey’s P8, R8, I8, and RI8 become P11, R11, I11, and RI11. 100 Precedent for the coordination of row structure and meter in the music of the Second Viennese School is given by Hyde’s (1984) analysis of primary and secondary harmonic dimensions in Schoenberg’s twelve-tone music. She shows that strata generated from these harmonic dimensions often correspond with the notated meter or create musically significant metrical dissonance. While many of her analyses convincingly describe middleground rhythmic structure, the extent to which secondary harmonies are perceptually viable cues to meter is debatable. I simply make the more neutral observation that metric manipulations in Op. 27, No. 1 coordinate with row pairs. I remain ambivalent as to whether this primary harmonic dimension has any influence on our perception of meter. 101 Textural or registral density is not among Lerdahl and Jackendoff’s (1983) list of phenomenal accents (17) or metrical preference rules (75–96), though one can reasonably assume that it counts as a form of stress as formalized by MPR 4 (78–79). Other authors do explicitly consider textural density as a form of accent, notably Roeder (2001), as well as Berry (1976, 341); Yeston (1976, 47–50); Hyde (1984, 22); Lester (1986, 29–30); Krebs (1999, 23). 102 Lerdahl and Jackendoff (1983, MPR 2). 103 An alternative metric reading of the third and fourth composite gestures maintains the 516 downbeat of the prior gestures and hears the internal organization as 3-plus-2. This hearing allows for a stable 516 meter throughout mm. 1–5 but is less sensitive to textural density parallelism. Either way, the status of these measures as opening imbroglio is unchanged. 104 Lester’s (1986, 29–30) emphasis on the role of context in determining relative textural accentuation serves as precedent for my textural density contour. 105 The fact that the three imitative phrases initially present two-attack gestures in separate registers is surely no coincidence. The perception of close imitation as close imitation and the perception of imitative imbroglio as imitative imbroglio hinge upon the separate streaming of component two-attack gestures. In the context of Example 22, the pitch material that begins each of these phrases uniquely affords such streaming. 106 See Wason (1987) for discussion. 107 Bailey (1991, 189–94). 108 Heyman (1992, 337). 109 Heyman (2012, 322–23). 110 Jackson (1971, orig. 1951). According to Heyman (1992, 337), Barber’s source for six of the translations was Seán O’Faoláin’s The Silver Branch (1968, orig. 1938). He used three of them directly but found the other three unsuitable. For this latter group, which includes “The Praises of God,” Barber commissioned new translations. Heyman’s account appears to be true for all six of the texts except “The Praises of God,” which in fact does not appear in The Silver Branch. It does, however, appear in Kenneth Jackson’s A Celtic Miscellany (1971, orig. 1951), from which Barber drew two other translations for the cycle. Therefore, it seems likely that Jackson’s translation was the one that Barber rejected in favor of Auden’s. 111 With respect to Monahan’s (2013) classification of agent types, these agents are individuated elements under the guise of a performative avatar. 112 Thanks to an anonymous reader for this text-painting observation. 113 The perception of this passage as imitative imbroglio hinges upon the preceding measure. Normally, inversionally related contours would not be perceived as parallel. However, m. 6’s rhythmic parallelisms perceptually associate the inversionally related contours of the right and left hands. If that were not the case, then we would simply perceive m. 7 as two lines moving in similar motion. 114 Time signatures in this movement express the total number of a particular division of the half note established at the beginning of the piece. Specifically, the top number counts the total number of a particular division that are present in each measure, while the bottom number expresses the division itself as a multiple of 2. Specifically, if one half note is expressed with the time signature 12 ⁠, then 24 divides that half note into two equal parts (two quarters), 36 divides it into three parts (three triplet quarters), 48 into four parts (four eighths), 510 into five parts (five quintuplet eighths), 612 into six parts (six triplet eighths), and so forth. 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TI - Metric Manipulations in Post-Tonal Music
JF - Music Theory Spectrum
DO - 10.1093/mts/mtaa020
DA - 2021-03-17
UR - https://www.deepdyve.com/lp/oxford-university-press/metric-manipulations-in-post-tonal-music-y0ftVGxAee
SP - 123
EP - 152
VL - 43
IS - 1
DP - DeepDyve
ER -