The Role of Segmentation and Expectation in the Perception of Closure Crystal Peebles

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2011 The Role of Segmentation and Expectation in the Perception of Closure Crystal Peebles

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COLLEGE OF MUSIC

THE ROLE OF SEGMENTATION AND EXPECTATION IN THE PERCEPTION OF

CLOSURE

CRYSTAL PEEBLES

A dissertation submitted to the College of Music in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Fall Semester, 2011

Crystal Peebles defended this Dissertation on October 31, 2011.

The members of the supervisory committee were:

Nancy Rogers Professor Directing Dissertation

Michael Kaschak University Representative

James Mathes Committee Member

Matthew Shaftel Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements.

For my parents, John and Lola Peebles

iii ACKNOWLEDGEMENTS

I first must thank my committee members for their unending support and guidance through the duration of this project. The unique perspectives contributed by Jim Mathes, Matt Shaftel, and Mike Kaschak positively shaped my initial inquiry and the subsequent outcome. I especially want to thank Mike for his assistance in designing the experiments, recruiting and testing participants, and analyzing the data. Finally, to the head of my committee, Nancy Rogers, I am immeasurably grateful for her constructive criticism, her keen attention to detail, and her encouragement, both during this project and throughout my graduate career. My experience as a graduate student in music theory program at The Florida State University has shaped me personally and professionally in more ways than I can count. I am indebted to the entire music theory faculty for providing opportunities for me to grow both as a teacher and as a scholar. I also value the meaningful friendships and professional relationships I have formed with my fellow graduate students at Florida State. I will always cherish the time we spent together in the T.A. office, in the library, and at the local pizza joint. Within the Tallahassee community, I would also like to thank my violin students and their parents for their untempered enthusiasm for music as well as the lovely people at St. Paul’s United Methodist Church. You have been my second family during my six years in Tallahassee, offering an unwavering community of love and support. Indeed, I thank God every time I remember you. I cannot begin to express my gratitude for my family’s love and encouragement. My parents, John and Lola Peebles, have consistently supported me in all I do, even when it takes me halfway across the country. A special note of thanks also goes to Rachel McCleery, whose loving companionship during my graduate studies has made an indelible mark on my life. I will always treasure our many meaningful conversations shared over a delicious dinner or a warm cup of coffee. Your critical commentary and insight certainly influenced this project and is reflected in these pages. Finally, I would like to acknowledge Boosey & Hawkes and European American Music Distributors for their permission to reproduce copyrighted excerpts of twentieth-century works by Bartók, Copland, and Webern.

TABLE OF CONTENTS

List of Tables ...... vii List of Figures...... ix List of Examples ...... x Abstract ...... xii CHAPTER 1: INTRODUCTION...... 1

CHAPTER 2: MUSICAL CHARACTISICS OF CLOSURE...... 6 Closure as the Completion of a Goal-Directed Process ...... 6 Closure as the Segmentation of Musical Experience...... 11 Hierarchy and Closure...... 15 Style and Closure...... 18 CHAPTER 3: MUSICAL EXPECTATION AND CLOSURE ...... 22 Formation of Expectations: Statistical Learning ...... 22 Expectation...... 26 Expectation in Music Theory ...... 26 Types of Expectation and Schema...... 29 Expectation and Memory: An Alternative View...... 38 An Expectation-based Model of Closure ...... 41 Three Analytical Vignettes...... 47 Schumann’s “Widmung” ...... 47 Webern’s “Der Tag ist vergangen”...... 57 Copland’s “The World Feels Dusty”...... 60 CHAPTER 4: EVENT SEGMENTATION THEORY...... 67 Event Segmentation ...... 67 Event Segmentation Theory ...... 73 Event Segmentation Theory and Musical Closure ...... 77 Experiment Overview ...... 81 Experiment 1 ...... 81 Experiment 2 ...... 81 Experiment 3 ...... 82 CHAPTER 5: EXPERIMENT 1...... 85 Method ...... 86 Participants...... 86 Stimuli ...... 86 Coding Procedure ...... 88 Participant Procedure...... 101 Results ...... 102 General Results...... 104

v Experiment 1a: Bartók Results...... 116 Experiment 1b: Mozart Results...... 124 Grouping Analysis...... 135 Discussion...... 149 CHAPTER 6: EXPERIMENT 2...... 153 Method ...... 154 Participants...... 154 Stimuli...... 154 Procedure...... 157 Results ...... 157 Discussion...... 162 CHAPTER 7: EXPERIMENT 3...... 165 Method ...... 166 Participants...... 166 Stimuli...... 166 Procedure...... 167 Results ...... 170 Discussion...... 179 CHAPTER 8: CLOSURE...... 181

APPENDIX A: SEGMENTATION RESPONSES IN EXPERIMENT 1...... 186

APPENDIX B: ANNOTATED SCORES FOR EXPERIMENT 3...... 201

APPENDIX C: COPYRIGHT PERMISSION LETTERS...... 208

APPENDIX D: IRB APPROVAL LETTER AND INFORMED CONSENT LETTER ...... 211

REFERENCES ...... 215

BIOGRAPHICAL SKETCH...... 222

LIST OF TABLES

2.1 Lerdahl and Jackendoff’s Grouping Preference Rules ...... 12 3.1 Text and Translation of “Widmung” ...... 49 4.1 Lerdahl and Jackendoff’s Grouping Well–Formedness Rules ...... 69 5.1 Musical Stimuli Characteristics for Experiments 1a and 1b ...... 88 5.2 Window Construction in Each Window...... 89 5.3 Arrival and Change Features in Bartók...... 90 5.4 Arrival and Change Features in Mozart...... 91 5.5 Total Number of Responses and Percentage Used in Data Analysis (Bartók)...... 105 5.6 Total Number of Responses and Percentage Used in Data Analysis (Mozart)...... 106 5.7 ANOVA Means for Interactions between Starting Task and the Nested Structure (Bartók)...... 110 5.8 Mixed Models Regression Analysis: Latency Time...... 110 5.9 Mixed Logit Regression Analysis: Number of Changes...... 111 5.10 Mixed Logit Regression Analysis: Ending Type...... 114 5.11 Mixed Logit Regression Analysis: Arrival Features, Third Movement ...... 117 5.12 Mixed Logit Regression Analysis: Arrival Features, Fifth Movement ...... 118 5.13 Mixed Logit Regression Analysis: Change Features, Third Movement...... 120 5.14 ANOVA Means for Interactions in Change Feature Analysis, Third Movement ...... 120 5.15 Percentage of Responses at Complete Silence in Coarse 2, Third Movement...... 122 5.16 Mixed Logit Regression Analysis: Change Features, Fifth Movement...... 123 5.17 ANOVA Means for Interactions in Change Feature Analysis, Fifth Movement ...... 124 5.18 Mixed Logit Regression Analysis: Arrival Features, No. 19...... 125 5.19 ANOVA Means for Interactions in the Arrival Feature Analysis, No. 19...... 127 5.20 Percentage of Responses at PACs in Fine 2, No. 19 ...... 128 5.21 Mixed Logit Regression Analysis: Arrival Features, No. 21...... 130 5.22 ANOVA Means for Interactions in the Arrival Feature Analysis, No. 21...... 131 5.23 Mixed Logit Regression Analysis: Change Features, No. 19 ...... 132 5.24 Mixed Logit Regression Analysis: Change Features, No. 21 ...... 132 5.25 Section Divisions in Bartók, String Quartet No. 5, Fifth Movement ...... 139 5.26 Mixed Logit Regression Analysis: Grouping Analysis ...... 147

vii 5.27 ANOVA Means for Interactions in the Grouping Analysis ...... 148 6.1 Exposure Excerpts ...... 155 6.2 Mixed Models Regression Analysis: Rating ...... 158 7.1 Mixed Logit Regression Analysis: Cadence and Hypermeter ...... 172 7.2 Mixed Logit Regression Analysis: Cadence Types...... 173 7.3 Mixed Models Regression Analysis: Response Time and Cadences ...... 177 7.4 Mixed Models Regression Analysis: Response Time and Cadence Types ...... 177 7.5 Mixed Models Regression Analysis: Ratings...... 178 7.6 Mixed Models Regression Analysis: Ratings and Response Time ...... 179

viii

LIST OF FIGURES

3.1 Continuum of Expectations ...... 33 3.2 Continuum of Expectations with Schemata ...... 34 3.3 Continuum of Expectation: Closural Expectations...... 44 4.1 Schematic Depiction of the Event Segmentation Theory ...... 74 4.2 Schematic Depiction of the Segmentation Process as Posited by EST...... 76 5.1 Interactions between Subject Group and Consistency (Mozart) ...... 109 5.2 Interaction between Starting Condition and Consistency (Mozart)...... 109 5.3 Interactions between Subject Group and Number of Changes (Bartók)...... 112 5.4 Interactions between Subject Group and Number of Changes (Mozart) ...... 113 5.5 Interactions between Subject Group and Ending Type (Bartók)...... 115 5.6 Interactions between Subject Group and Ending Type (Mozart) ...... 116 5.7 Possible Phrase Structure Analyses ...... 139 5.8 Mozart, String Quartet No. 19, mvmt. 4: Grouping Analysis of the Exposition...... 144 6.1 Two-way Interaction between Subject Group and the Exposure Composer...... 159 6.2 Three-way Interaction between Subject Group, the Exposure Composer, and the Rated Composer...... 160 6.3 Two-way Interaction between Participant Group and the Ratings for Composer (cadential excerpts) ...... 161 6.4 Two-way Interaction between Participant Group and the Ratings for Composer (all excerpts) ...... 162 7.1 Excerpt No. 6 from Mozart’s String Quartet in G Major (K. 156), third movement ...... 166 7.2 Interactions between Subject Group and the Presence of a Cadence ...... 172 7.3 Interactions between Subject Group and Cadence Type...... 175 A.1 Bartók, String Quartet No. 4, third movement ...... 187 A.2 Bartók, String Quartet No. 4, fifth movement...... 190 A.3 Mozart, String Quartet No. 19, fourth movement...... 195 A.4 Mozart, String Quartet No. 21, second movement ...... 199

LIST OF MUSICAL EXAMPLES

2.1 Beethoven, String Quartet, Op. 130, second movement, mm.1–8 (analysis after Meyer) ...15 3.1 Beethoven, God Save the King, WoO 78, mm. 1–6 ...... 40 3.2 Schumann, Myrthen, “Widmung” Op. 25, No. 1, mm. 1–13...... 50 3.3 Schumann, Myrthen, “Widmung” Op. 25, No. 1, mm. 14–29 ...... 54 3.4 Schumann, Myrthen, “Widmung” Op. 25, No. 1, mm. 37–44 ...... 56 3.5 Webern, Vier Lieder, “Der Tag ist vergangen,” Op. 12, No. 1, mm. 1–11...... 59 3.6 Webern, Vier Lieder, “Der Tag ist vergangen,” Op. 12, No. 1, mm. 18–21...... 60 3.7 Copland, Twelve Poems of Emily Dickinson, “The World Feels Dusty,” mm. 1–2...... 63 3.8 Copland, Twelve Poems of Emily Dickinson, “The World Feels Dusty,” m. 27...... 65 5.1 Mozart, String Quartet No. 19, fourth movement, mm. 89–93...... 92 5.2 Mozart, String Quartet No. 19, fourth movement, mm. 67–70...... 93 5.3 Mozart, String Quartet No. 19, fourth movement, mm. 76–78...... 93 5.4 Mozart, String Quartet No. 21, second movement, mm. 15–20 ...... 94 5.5 Bartók, String Quartet No. 4, third movement, mm. 20–23...... 95 5.6 Bartók, String Quartet No. 4, third movement, mm. 40–41...... 96 5.7 Bartók, String Quartet No. 4, fifth movement, mm. 235–239...... 96 5.8 Bartók, String Quartet No. 4, fifth movement, mm. 330–332...... 97 5.9 Bartók, String Quartet No. 4, fifth movement, mm. 74–76 ...... 97 5.10 Bartók, String Quartet No. 4, fifth movement, mm. 279–284...... 98 5.11 Bartók, String Quartet No. 4, third movement, mm. 6–35 (cello)...... 121 5.12 Mozart, String Quartet No. 21, second movement, mm. 1–8 (violin 1) ...... 131 5.13 Bartók, String Quartet No. 4, fifth movement, mm. 11–18 ...... 140 5.14 Bartók, String Quartet No. 4, fifth movement, mm. 102–108...... 140 5.15 Bartók, String Quartet No. 4, fifth movement, mm. 238–249...... 141 5.16 Mozart, String Quartet No. 19, fourth movement, mm. 1–34 (violin 1 and cello)...... 143 5.17 Mozart, String Quartet No. 19, fourth movement, mm. 118–135 (violin 1 and cello)...... 144 5.18 Mozart, String Quartet No. 21, second movement, mm. 40–44...... 146 6.1 Motive x from Bartók’s String Quartet, No. 4, first movement, m. 7...... 156 6.2 Motive y from Bartók’s String Quartet, No. 4, fifth movement, m. 16–18 ...... 156

x 7.1 Mozart String Quintet No. 4 in G Minor (K. 516), third movement, mm. 1–13...... 168 7.2 Mozart’s Sonata for Piano and Violin in B(+Major (K. 454), third movement, mm. 1–16...... 170 B.1 Mozart, Quartet No. 3 in G Major, K. 156, third movement...... 201 B.2 Mozart, String Quartet No. 8 in F Major, K. 168, third movement...... 203 B.3 Mozart, String Quartet No. 13 in D Minor, K. 173, third movement...... 205

ABSTRACT

In the musicological discourse, “closure” can refer to a variety of musical phenomena, but the language describing closure usually involves at least one of two common metaphors: closure is the completion of a musical process, or closure is the segmentation of musical experience. Along with these two descriptions of closure, musicians also recognize that closure’s markers vary between musical styles and that some moments of closure are stronger than others, articulating a composition’s hierarchical construction. These four characteristics of closure, gleaned from the musicological literature, inform my definition of closure: an anticipated end to a musical segment. This dissertation will empirically investigate the role of expectation in the perception of closure. I hypothesize that closure is not something intrinsic to a piece of music; rather, it relies on an individual’s previous musical encounters. This previous experience gives rise to musical expectations, and closure is experienced when a listener is accurately able to anticipate the end of a musical segment, on any hierarchical level. The degree of perceived closure correlates with a listener’s ability to predict an ending, coupled with relatively weak expectations for what will occur next. This perspective is informed by recent research in Event Segmentation Theory (EST), a theory from the field of cognitive psychology that investigates the segmentation of everyday non-musical events. Three experimental studies test this hypothesis. The first study determines whether listeners segment music according to the predictions made by EST. The results from this study corroborate previous research: listeners consistently use musical features to segment an ongoing composition, and the fine segmentation results are nested within the coarse segmentation results. The learning task in the second study ascertains whether exposure to an unfamiliar musical style will change a listener’s perception of closure in that style. While the data do not entirely confirm this hypothesis, results from this study suggest the importance of previous experience in the perception of closure. The third study finds a correlation between predicted endings in a familiar style and the rating of a listener’s perceived strength of closure. Results from all three studies support an expectation-based model of musical segmentation and the perception of closure.

xii CHAPTER 1

INTRODUCTION

Listeners and musicians have intense aesthetic opinions regarding the degree to which a particular musical ending sounds satisfying. “Closure” is the oft-used term to describe the listener’s feeling of satisfaction or completeness. Although the concept of musical closure is ubiquitous in the scholarly discourse, the exact meaning of closure can vary widely among authors. Despite these different meanings, similarities in closural metaphors speak to our shared experience of finality. This study examines that shared experience: exploring characteristics of closure, situating these characteristics in a listener’s musical expectations, and creating a cognitive model of musical closure that transcends stylistic boundaries. In the second half of this dissertation, I discuss a series of three experiments that test this model. I define closure as the feeling of finality that occurs at the anticipated end of a musical segment. This definition brings up three points that will be expanded throughout the course of this project. First, I am primarily concerned with the listener’s perception of closure, not with how a composer achieves closure in a composition or with pinpointing the moment at which closure occurs. By taking a listener’s perspective, I am free to explore how listeners experience closure in different repertoires without being bogged down by stylistic differences. Instead of specifically talking about musical signs of closure, I examine how these signs evoke the feeling of finality in a listener. Second, musical experience is segmented into discrete events that have a beginning and end. Being able to segment the continuous stream of acoustical input is a prerequisite to experiencing closure in the first place, for without endings there would be no closure. Finally, a listener must be able to anticipate the placement and content of an ending in order to experience finality. These expectations may not be conscious, and a listener will not always be able to anticipate the exact content of an ending, but expectation is an integral part of my model of closure. In this chapter, I illustrate various meanings of closure seen through a handful of recent contributions to the fields of music theory and musicology, where closure shapes the theoretic or analytic narrative. “Closure” is regularly used as a synonym for “resolution,” particularly a

1 cadence defining V-I progression in tonal music, but other times musical closure is highlighted because it advances the theoretical aims of the author, illustrates the stylistic tendencies of a composer, or supports the author’s overarching analytical narrative. Despite methodological differences, common metaphors of closure emerge. By far, the most common metaphor for closure is likening it to a goal at the end of a musical pathway, experienced as a point of finality or stasis, but closure can also be conceived as a boundary separating musical entities.1 These common metaphors speak to two “actions” of closure: (1) closure marks the achievement of a musical goal (usually coupled with a feeling of finality), and (2) closure segments a listener’s musical experience. While these metaphors are not necessarily explicit within the discourse, they do shape the concept of closure. James Hepokoski and Warren Darcy’s oft-cited Elements of Sonata Theory reconceptualizes sonata form as movements toward genre-defined goals (2006). These two main goals are the essential expositional closure (EEC)—the obligatory perfect authentic cadence (PAC) located near the end of the exposition—and the essential structural closure (ESC)—the PAC in the corresponding place in the recapitulation. This perspective shifts the focus of sonata form from a schematic script to a more dynamic process. According to Hepokoski and Darcy’s theory, the EEC is usually the first PAC following the initiation of the secondary theme: it is the moment towards which the preceding secondary theme has been “aiming” (120). The authors are careful to note that the EEC may not be the strongest cadence in the exposition; the EEC merely represents the goal of the exposition. One should not determine an EEC on the basis of what one imagines an EEC should “feel” like in terms of force or unassailably conclusive implication. Nor should one assume that we are making grand claims regarding either the completeness or the degree of the closure implied by the EEC. Its “closure” may not in fact be absolute or “fully satisfying” from the perspective of the larger proportions of or other telling factors within the exposition as a whole. The first PAC closing the essential exposition is primarily an attainment of an important generic requirement—nothing more and nothing less. (124)

Not only does the EEC mark the first confirmation of the new key (the goal of the exposition), it also separates the secondary theme from the closing theme, dividing the exposition into smaller

1 These two metaphors of closure are similar to two of Brower’s (2000) embodied image schemas: SOURCE-PATH-GOAL and CONTAINER. These yield the metaphoric concepts of musical motion and musical space. While a detailed study of an embodied basis of musical closure is outside the scope of this project, I speculate that our shared experience of closure is rooted in embodiment.

2 parts. “Closure” in this sense is not dependent on listener perception; rather, it is a compositional construct (according to Hepokoski and Darcy) that marks the end of a theoretically defined process. In some cases, a listener’s perception of closure contradicts the interpretation of closure from a theoretical perspective. Such is the case in Edward Pearsall’s (1999) article, which explores the analytical process through the lens of current cognitive theories. The second half of this article analyzes “Nun ich der Riesen Stärksten überwand” by Alban Berg (Op. 2, No. 3). Pearsall notes that the song ends on the dominant, an unexpected harmony that could signify a lack of closure. Yet, as he states, “when we listen to the song, we have the sense that the piece does end with finality” (246). In order to reconcile the perception of finality with the apparent open-ended conclusion, Pearsall reconstructs the analysis to make the ending “goal-directed” (253, footnote 20). By reinterpreting the last note of the penultimate melodic unit as an upper neighbor to the last pitch of the song, he is able to reinterpret previously unexplained pitches from earlier in the composition as semitone neighbors to the last pitch as well. In this example, the author constructs a goal-directed process toward the last note to account for his feeling of finality, and the analytical whole is shaped by this interpretation. This process of reconciling the perception of finality with the theoretical lack of closure (defined by not ending on a tonic harmony) illustrates Pearsall’s stance that music is not “a collection of immutable structures” but rather “a subject for intentional creative perception” (231). The achievement or denial of closure frequently supports a larger narrative, especially when closure is conceived as achieving a goal in the music, thus playing an integral role in conveying musical meaning. When closure is problematized in analysis, often it is because the expected goal of a musical process is postponed or even completely denied. Alternatively, as seen in Pearsall’s article, the experience of finality may contradict prevailing theories regarding closure. In other cases it is the very denial of closure that carries the expressive content of the composition. For instance, Ramon Satyendra (1997) examines four works by Lizst, each implying a key but lacking adequate tonic resolution; all four compositions prolong a dominant harmony that never resolves to a tonic chord on the same structural level. While Satyendra argues that these pieces are contextually closed (beginning and ending with the same harmony),

3 they remain open because the dominant harmony remains unresolved. This paradox (the “tension between contextual closure and tonal openness”) reflects the Romantic aesthetic (194). Other authors examine closure as a reflection of a particular composer’s stylistic tendencies. W. Dean Sutcliffe (2010) argues that Haydn’s slow movements written in the 1770s are marked by an “expressive ambivalence” that defines his style (98). One way Haydn creates this ambivalence, according to Sutcliffe, is by using the same passage to evoke two different affective attributes. In the Andante of Haydn’s Symphony No. 52, the same musical material both opens and closes the first phrase, creating “two different, apparently opposed, meanings” (102). Closure is somewhat obscured, compared with Mozart’s more “punctual” endings from the same period (110), but in Haydn’s slow movements this helps create the impression of ambivalence because the same gestures engender a feeling of initiation and finality. Closure in Mahler’s symphonies contributes expressively to the unfolding musical drama, according to Seth Monahan (2011). In his analyses, recapitulatory success or failure (as defined by Hepokoski and Darcy) correlates with the expressive outcome of the movement, but Mahler moves away from a “closure-oriented” tonal narrative in his later compositions (38). Thus, the expressive meaning of closure changes as Mahler’s style changes. Monahan states that Mahler’s earlier “sonata dramas are oriented specifically around the ability of the secondary theme (S) to attain tonic closure,” where “the S-theme acts like a musical agent bent on controlling its own modal/tonal fate, seeking to secure closure in the tonic major while avoiding a ‘tragic’ collapse into minor” (40). This goal-oriented perspective of closure supports Monahan’s dramatic narrative. At the annual meeting of the Society for Music Theory in 2010, John Roeder presented his analysis of Saariaho’s song for two sopranos, “The claw of the magnolia,” which is the third of five settings from Sylvia Plath’s poem “Paralytic.” As a part of his narrative, Roeder demonstrated how a gesture can become associated with closure as the piece unfolds and how surrounding pitch material may imbue this gesture with meaning. He noted that the tritone in m. 2 (between F4 and B4) sounds like an ending retrospectively because it precedes the first simultaneous attack of the song (F,4 and A,4). This reading elevates the tritone to a cadential gesture of sorts—a harmonic entity regularly segmenting phrases. Another analysis of this same passage suggests that two different diatonic sets are superimposed, one with a B tonic, the other

4 with a B( tonic. As Roeder noted, such a reading seems contradictory to hearing the tritone as an ending feature: “[T]he tonal focus modulates again to A,/B( and then to B. Such intuitions raise an interpretative problem: they do not attribute repose to a tritone, and so they run contrary to hearing stability at the {B, F}s that terminate the phrases.” To reconcile these readings, Roeder interpreted the {F,, A,} dyad as implying both tonalities simultaneously, combining the dominant of B with the tonic of B(, which allows the tritone to be interpreted as including both the dominant of B( and the tonic of B. By recasting this gesture in a larger analytic narrative, this same tritone, which concludes the entire song, “provides both convincing closure and an ingenious musical expression of the paralytic’s mentality.” Closure in this sense is not the realization of a musical goal, for as Roeder stated “the mezzo’s last F4 wants to fall again to A,3 tonic, but this goal … fails to be realized, leaving the listener musically, like the paralytic literally, in a state of suspended animation”; instead, closure here refers to a fitting ending considering the meaning of the text. This small sample of musicological discourse demonstrates how closure shapes the analytic and theoretic narrative. All of these examples serve to emphasize how important the feeling of closure is in our musical experience, and how the common metaphoric descriptions of closure speak to a shared experience of closure. By shifting the focus from how a composition or composer achieves closure to how a listener experiences closure, I create an expectation-based model for this shared experience. The satisfaction and feeling of finality associated with closure is tied to how a listener expects the piece to unfold and, more importantly, how and when a listener expects a composition (or a segment of a composition) to end. In the remainder of the first part of my dissertation, I explore four common characteristics of closure (Chapter 2) and describe how these characteristics are accounted for in an expectation-based model of closure (Chapter 3). This emphasis on expectation is supported by recent theories in event segmentation, which outline a possible cognitive process for the segmentation of music and the perception of closure (Chapter 4).

5 CHAPTER 2

MUSICAL CHARACTISICS OF CLOSURE

Leonard Meyer conveys an inclusive understanding of closure in his influential books Emotion and Meaning in Music (1956) and Explaining Music (1973). In these books, Meyer enumerates various musical parameters relating to closure, recognizes that closure occurs on different hierarchical levels, and considers closure in post-tonal music. He suggests four characteristics of closure, which will be fleshed out in more detail throughout this chapter: (1) closure is a completion of a goal-directed process resulting in an arrival of relative stability or rest; (2) closure segments a continuous musical stream into discrete events; (3) the strength of closure depends on many musical variables and plays an integral role in the hierarchic construction of a composition; and (4) closure is stylistically dependent.

The first two characteristics of closure were discussed as common metaphors of closure (closure is a directed goal and closure is a segmenting agent) in the previous chapter. The final two characteristics can also be inferred through a close reading of those same analyses; for instance, Hepokoski and Darcy (2006) recognize that PACs have varying degrees of finality, and even within the small sample of analyses in the previous chapter, authors highlight different signs of closure appropriate for the musical style. The extent to which an analyst emphasizes one of these concepts over another colors the resulting musical discourse, resulting both in different metaphorical descriptions of closure and in different evaluations of closure’s meaning within the analytic narrative. Closure as the Completion of a Goal-Directed Process

For both Robert Hopkins and Leonard Meyer, the completion of a musical process is the most important marker of closure; both state that without a process, the music will just stop and not close (Hopkins 1990, 4; Meyer 1956, 139). In other words, closure occurs upon completion of a commonly recognized musical process or event as defined through an analytical theory. For Meyer, the musical syntax of a particular style determines the processes that drive toward closure and is manifested through its primary musical parameters. In tonal music, these primary

6 parameters would include melody, rhythm, and harmony while timbre, dynamics, and register would be secondary parameters (1973, 88). Meyer values primary parameters over secondary parameters because these primary parameters point to a particular moment of cadential closure in tonal music, while secondary parameters merely contribute to the perceived strength of this closure.2 Closure defined through these goal-directed processes is understood as syntactical closure. For many theorists looking at tonal literature, the completion of the Schenkerian Ursatz defines syntactical closure, with the arrival of !+marking the attainment of a goal. This syntactic understanding of closure is pervasive in the musicological discourse. Mark Anson-Cartwright (2007) acknowledges that “one assumption about closure has abided in discourse about tonal music: the idea that it is synonymous with tonal (or structural or syntactic) closure—a state of rest articulated by a cadence, usually very close to, or even coinciding with, the ‘end’ of a piece or movement” (1). Even Patrick McCreless (1991), who addresses four types of closure, privileges syntactic closure over other varieties. In his analysis of Beethoven’s Piano Sonata in C minor (Op. 10, No. 1), McCreless reveals this preference by first “locating the point of syntactic closure,” because syntactic closure is “primary” (65). While Anson-Cartwright and McCreless are mainly concerned with closure of the entire piece or movement (or, using Agawu’s term (1987), “global closure”), tonal processes can create closure at the end of a phrase as well, with the goal being the last chord in a cadence. Although tonal processes at the local or intermediate level are less specifically prescribed, from a Schenkerian perspective, harmonic and contrapuntal structures of the Ursatz are projected onto lower structural levels (Cadwallader and Gagné 2006). Alternatively, the basic phrase model provides another source of smaller-scale musical processes: since the basic phrase model is a formulaic succession of sonic events (contextually defined by a particular musical style), the musical process consists of completing the step-by-step model. Even more simply, syntactic closure often serves as a synonym for the resolution of V to I on any structural level of a composition.

2 According to Meyer (1956), being able to predict when closure will occur is a prerequisite for being able to perceive closure.

7 While tonal closure from a Schenkerian perspective remains a theoretical construct, empirical research on the extent to which listeners perceive large-scale closure adhering to Schenkerian norms (e.g., a composition beginning and ending in the same key) is not clear.3 Nicholas Cook (1987) found that listeners indicated a sense of closure in recomposed works even when the music ended in a different key, suggesting that large-scale tonal closure is not necessarily the only marker of closure. These studies, however, did not ask whether a listener could detect these recomposed passages; Elizabeth West Marvin and Alexander Brinkman’s (1999) study demonstrated that expert musicians were able to detect whether musical passages began and ended in the same key. Michael Graubart (2003) recognizes the importance of tonal music’s goal-directed nature, noting “the sense of completion when, after setting-up of a charged dominant region and various ensuing tonal adventures and misadventures, the tonic key is firmly re-established” (34). This type of goal direction is missing in twelve-note music, so Graubert appeals to the completion of a twelve-note row, proposing that the twelfth note of the pattern would supply the needed “goal of the musical process” (34).4 Hence, this compositional method might substitute for tonal closure in non-tonal works, although Graubart admits that a listener may have trouble recognizing this pattern completion (specifically at the beginning of a row, given that a listener would not be able to anticipate the ending pitch-class until the row approached its end). Although Graubart perhaps carries his comparison between closure at the completion of a twelve-tone row and closure at a tonal cadence to an extreme, his proposal speaks to the pervasive use of a goal-directed syntactic concept of closure in musicological literature. Not all musicians, though, ascribe to this goal-oriented view of musical closure. Anne Hyland (2009) finds fault with syntactic closure as Hepokoski and Darcy’s (2006) main defining factor of sonata form. In her analysis of the first movement from Schubert’s C-Major String Quartet (D. 46), Hyland argues that the bias of goal-directed trajectories in Hepokoski and Darcy’s theory (e.g., the exposition moves towards the EEC) does not accurately describe this

3 I do not think that any analytic theory needs empirical validation. However, since the main crux of my study will focus on listener perception of closure, I will use empirical studies to support my model of the perception of musical closure. 4 As Graubart states, “twelve-note rows may give back to atonal music a goal-directed force and the possibility of closure” (36).

8 movement, which instead relies on rhetorical signs of closure. In contrast to syntactic closure, rhetorical closure consists of “those signals of a work’s finality or closure which are not tonal in nature” (113). While syntactical closure, defined through primary parameters, may be sufficient for teleologically-composed pieces in the tonal style, other musical features may contribute to a sense of goal-direction and the perception of closure. Like Hyland, Hopkins (1990) and Bryden (2001) turn to secondary parameters to explain a process of closure. In musical styles beyond common practice, secondary features may signify goal completion. In his study of Mahler’s music, Hopkins (1990) proposes the concept of “abatement” to explain closure for a composer who at times eschews traditional cadences. In order to depict abatement, Hopkins creates graphs that show the composite dynamics, registral pitch, durations, and concordance (i.e., consonance) of the entire texture along with the number of voices. For Hopkins, closure occurs when these parameters abate (or “descend”): for instance, durations increase, harmonies become more consonant, and dynamics soften. Hopkins, however, criticizes his own theoretic concept of “abatement” for not technically being a goal-directed process. He explicitly states that a goal-directed process is a requirement for closure because “for closure to occur, it is necessary — but not sufficient — for a discernible process or pattern in one or more musical parameters to imply a particular point of conclusion” (4; emphasis added). Hopkins recognizes that a listener cannot predict the moment closure will occur using his abatement principles, but there seems to be an eventual goal of “dying out” that the listener perceives. Even though Hopkins seems to be contradicting himself (i.e., abatement is the process of closure in Mahler, but because we cannot predict the moment at which the process is completed, closure can never occur), he suggests that a listener’s feeling of “finality” may depend on expectations other than predicting the exact moment of an ending. Kristy Bryden (2001) uses a similar model in her dissertation on closure in late twentieth- century chamber works. She begins with six characteristics of closural processes that transcend stylistic boundaries.

9 Closural processes are 1) temporal and may operate on both local and larger more global levels, 2) lines of increasing intensity followed by lines of decreasing intensity, 3) the creation and either the fulfillment or postponement of expectations, 4) a summary of past events, 5) the highlighting of concluding moments, and 6) transitional techniques leading into or foreshadowing the following event. (i)

The second of her six definitions outlines a theoretical process based on secondary parameters. Bryden’s intensity curves represent processes of musical growth and decline. She creates a graphical representation of her score analysis by mapping various musical elements: dynamics, registral height, textural space, frequency of attack, density, composite rhythm, and pulse. These are then averaged to create a composite curve.5 She posits that closure occurs when a rise in tension is followed by a decrease in tension, with a possible parallel in tonal music: the rise in harmonic tension followed by a decrease in tension at the end of a phrase. Bob Snyder (2000) echoes this description of the influence of secondary parameters on the perception of closure, stating “decreases in intensity can establish closure. If we look at changes in intensity of the elements in a melodic, temporal, or formal grouping, we find that all other things being equal, a grouping feels more closed the more the intensity of its various musical parameters decreases at the end.” (emphasis Snyder’s; 63)6

Snyder argues that conceptualizing the musical surface in terms of our own bodily experiences influences our perception of closure, comparing the feeling of repose in music to the way our bodies feel after we have completed an action. This embodied perspective of closure implies that we understand the metaphors of goal direction, completion, and finality through the way in which our bodies interact with the world. Many authors observe that the completion of a musical process results in a feeling of repose or finality (or, in Meyer’s words, an “arrival at relative stability” (1973, 81)). For

5 Bryden’s methodology. First, she awards equal weight to each parameter in the overall average when one parameter may exert more influence in projecting a close or continuation. Second, even though the data from these parameters are normalized to fit on a scale from 1–10, the units of measurement are so different that an increase of a single unit does not mean the same thing across parameters. Both of these render the composite curve almost meaningless because it attempts to capture too much different information. While the methodology may not achieve a “good” curve, Bryden’s idea of using secondary parameters to inform music analysis certainly has merit. 6 This emphasis on abatement and relaxation overlooks other instances of finality where there is more of a feeling of excitement.

10 instance, in his 2007 critical study of concepts of tonal closure, Anson-Cartwright posits that the feeling of rest is a result of tonal resolution. Bryden (2001, 1) also notes that the perception of decreasing intensity at the moment of closure results from a “dynamic temporal process” modeled by her intensity curves. This feeling of finality that accompanies the completion of a goal-directed process is further explored by David Huron (2006), who states that a listener perceives closure at the expected completion of some process, and—because the listener is less able to predict what will occur next—this completion is followed by a perceived loss of forward continuation. From Huron’s perspective, a feeling of repose is not created by musical parameters that diminish in intensity or the resolution of a “tense” harmony; rather, the decrease in predictability for subsequent events causes the perception of repose. Eugene Narmour (1990) agrees, defining closure as “syntactic events whereby the termination, blunting, inhibiting, or weakening of melodic implication occurs” (102). Although the completion of a goal-directed process and a feeling of finality are connected, it is important not to conflate these two characteristics of closure. A musical process need not be consciously perceptible, whereas the feeling of finality is a psychological experience. From a listener’s perspective, closure is the sense of finality that occurs at an anticipated ending. This perspective shifts the focus away from the music per se and toward an individual’s musical expectations. The completion of a goal-directed process does not itself elicit a feeling of finality; rather, this feeling stems from the combination of an anticipated ending with lessening of expectation for subsequent events. Closure as the Segmentation of Musical Experience

The point at which a listener experiences finality segments the musical experience. Closure marks the end of a musical event, resulting in a perceived boundary between two musical entities. Early in his book, Snyder (2000) defines closure as the establishment of a grouping boundary, allowing a listener to segment musical events (33). Meyer (1973) suggests that closure creates relatively stable musical entities (90), although many musicians might dispute the notion that all event boundaries necessarily correspond with a feeling of closure: for instance, analysts normally do not consider motives to have closure despite their local-level event boundaries. Not surprisingly, there is a close relationship between closure and segmentation, but it is not necessarily a causal relationship.

11 Meyer (1973) uses both primary and secondary parameters to establish musical grouping structure, focusing on the completion of harmonic units, changes in the musical surface, and repetition as a means to create event boundaries. Meyer freely uses the term “closure” when referring to segmentation at any level, including the identification of discrete motives. This sense of closure comes from what Meyer calls “patterning,” and he provides a list of various factors that delineate musical patterns: 1. the presence of similarity and difference between successive events within a particular parameter. Both complete uniformity and total heterogeneity preclude syntactic organization, and hence establish no stability-instability relationships; 2. the separation of one event from another in time, pitch, or both; or through clear differences in dynamics, timbre, or texture; 3. immediate repetition, whether varied or exact, of part or all of a pattern; 4. the completion of previously generated implications; 5. harmonic cadence and tonal stability. (83)

Many of these ideas regarding grouping are incorporated into Lerdahl and Jackendoff’s Grouping Preference Rules (GPRs), which reflect the principles of Gestalt psychology. While Lerdahl and Jackendoff (1983) do not specifically discuss closure, they do use secondary parameters such as attack points, register, dynamics, articulation, and duration to create grouping boundaries. A complete list of GPRs is provided in Table 2.1; notice that GPRs 2 and 3 use Meyer’s secondary parameters.

Table 2.1: Lerdahl and Jackendoff’s Grouping Preference Rules GPR 1: Avoid analyses with very small groups—the smaller, the less preferable. GPR 2: Group boundaries are heard at a slur or rest, as well as points where there is a greater attack-point time interval. GPR 3: A change in register, dynamics, articulation, and note lengths can distinguish group boundaries. GPR 4: Where the effects of GPR 2 and 3 are relatively more pronounced, a larger-level group boundary may be placed. GPR 5: Prefer grouping analyses that most closely approach the ideal subdivision of groups into two parts of equal length. GPR 6: Where two or more segments of the music can be construed as parallel, they preferably form parallel parts of groups. GPR 7: Prefer a grouping structure that results in more stable time-span and/or prolongational reductions.

12 Narmour (1990) exclusively focuses on the establishment of closure within a three-note grouping. In his Implication-Realization Model, Narmour suggests that the third note of a sequence creates closure when the interval formed between the second and third notes does not create any new implications (102). He also identifies six parametric conditions of closure, similar to Meyer’s list, which include: 1. a rest or repetition; 2. strong metric emphasis; 3. resolution of dissonance; 4. increase in duration; 5. smaller intervallic motion; 6. change of registral direction. (11–12)

Snyder (2000) builds on Narmour’s work, stating, “continuity is nonclosural and progressive, whereas reversal of implication is closural and segmentive” (148). This type of closure, Snyder argues, does not necessarily end anything, but it “helps articulate the contour of the phrase” (148). He differentiates this from closure at the end of the phrase with the designation “soft closure,” which refers to “having any kind of segmentation, however weak” (148). In his article on segmentation in post-tonal music, Christopher Hasty (1981) segments the musical surface using parameters such as timbre, dynamics, intervallic associations, register and contour. These parameters are described as musical domains, and Hasty suggests that groupings are formed by discontinuities in at least one domain. He also claims that music is typically segmented in such a way that the emerging groups are similar to one another; for instance, groups in a stronger segmentation may contain the same number of constituents and may share intervallic content. Hasty uses the term “closure” to describe a return to some musical quality from a prior segment within a phrase, like an overall aba form, and reserves this expression as a marker for higher-level formal divisions, such as a phrase or section. In a later article, he revisits closure’s role in creating phrase segments, stating that, “closure is itself the articulation of the unit since unrelated elements are thereby segregated” (1984, 172). “Closure” in this sense creates a phrase-like entity containing musical elements that are related to each other (e.g., notes segmented into the same set class, or notes in the same register). A phrase is “closed” off, becoming its own entity, not including unrelated elements. Dora Hanninen more carefully balances differentiation, similarity, and the role of music theory in her 2001 article, which explicates her general theory on music segmentation. Hanninen

13 posits three types of criteria for segmenting music: (1) sonic, which rely on disjunction between adjacent events or non-adjacent events, (2) contextual, which are based on associative relationships between two possible groups, and (3) structural, which reflect a theoretical orientation that remains purely conceptual until paired with sonic or contextual cues, resulting in a musical segment. Both Meyer (1973) and Hopkins (1990) also indicate that segmentation in music depends on a plethora of musical markers; however, they divide these markers into two types: primary parameters that allow a listener to project the moment of closure, and secondary parameters that can strengthen the presence of an ending or retrospectively mark a moment of closure. Changes in secondary parameters can create a sense of a new beginning, and hence a boundary, but retrospectively recognized closure and anticipated closure may be different psychological phenomena. The degree to which a listener is able to anticipate closure can vary as well, and it is important to recognize that the capacity to predict an ending is quite different from arriving at an ending and subsequently recognizing it as the end of a segment. Huron suggests an even closer connection between musical segmentation and closure: we perceive boundaries because we have experienced closure—a fulfillment of musical expectation. Thus, from the perspective of segmentation, anything that creates a separable unit is closed (2006). Meyer concurs, stating, A motive, a phrase, or a period is defined by some degree of closure. On the level of its closure—the level on which it is understood as a separable event—it is a relatively stable, formal entity. Though it contains and is defined by internal processes, once closed, it is not a process but a palpable ‘thing.’ (1973, 90)

This understanding allows for closure in motives, units that most musicians would not consider closed, as well as closure in segments that do not evoke any particular expectation for a specific ending point. These two characteristics of closure discussed thus far (i.e., closure as completing a musical process and closure as marking the segmentation of musical events) harkens back to the metaphors examined in the first chapter. This shared understanding of closure, especially from a listener’s perspective, will form the basis of my expectation-based model of closure. Before discussing segmentation and expectation from the perspective of cognitive psychology, I first describe two related characteristics of closure: (1) closure has varying strengths, creating

14 segments that group together on different hierarchical levels, and (2) goal-directed processes and specific closural expectations are defined by musical style. Hierarchy and Closure

Having enumerated the various parameters that affect closure (both primary and secondary), Meyer states, “the degree of closure … depends upon the shaping of the particular parameters at work, the degree of articulation contributed by each, and the number of parameters promoting or preventing closure” (1973, 88). To illustrate his point, Meyer presents an analysis of Beethoven’s String Quartet, Op. 103, second movement (reproduced here as Example 2.1), indicating that the sense of finality at the end of m. 4 is stronger than the sense of finality at the end of mm. 1 and 2 because m. 4 is articulated by rhythmic closure.7 Furthermore, the half cadence (HC) is weaker than the perfect authentic cadence (PAC) that follows in m. 8. The reason for this, according to Meyer, is that in a HC not all the musical elements are implying closure at the same time: the rhythm implies closure, but the harmony does not. As Meyer states, “a semicadence is a case of parametric noncongruence which has become archetypal in the stylistic syntax of tonal music” (85). Other authors further discuss how parametric congruence and noncongruence vary closure’s perceived strength, focusing especially on the role of secondary parameters in confirming or weakening a syntactical close (Hopkins 1990, Snyder 2000, Hyland 2009).

Example 2.1: Beethoven String Quartet, Op. 130, second movement, mm. 1–8 (analysis after Meyer [1973])

McCreless (1991) uses formal and rhetorical markers of closure to determine the location of structural (or syntactical) closure, implying that formal schema and rhetorical emphasis can

7 Meyer’s precise meaning is unclear, but I suspect Meyer may be referring to hypermetrical expectations.

15 modulate the strength of closure. If a composition has several possible points of syntactic closure, formal expectations can emphasize one of these PACs as the structural close. McCreless further states that rhetorical closure uses rhythmic and registral extremes to highlight the end of the melody, which can make one ending sound more conclusive than another ending. Kofi Agawu (1987) also discusses closure as occurring on various musical levels. While his definition of closure, “the tendency to close” (2), seems a bit circular, it emphasizes that closure is not synonymous with an ending, but rather is “dependent for its effect on the listener’s experience of the entire composition” (4). From Agawu’s perspective, an “ending” describes “local elements in the musical structure, whereas closure denotes a global mechanism” (4). This view of closure is similar to Anson-Cartwright’s third concept of closure, “that condition of immanent rest or finality which a piece or movement possesses as a temporal whole, by virtue of all the tendencies to close projected within that whole” (2007, 3). Global closure, according to Agawu, “secures closure for the entire piece” and fulfills these tendencies to close (6). There is only one global closure in a composition, and nested within this closure are subordinate closes on the local and intermediate levels. While global closure is the most decisive close, local closure “articulates the smallest meaningful units of the piece” and intermediate closure “nests one or more local closes” (6). In all of these cases, Agawu requires a syntactic V-I gesture at the end, but his idea of nested closes could be applied to music outside the tonal idiom. William Caplin (2004) discuses closure primarily at the phrase level, stating that the “cadence effects formal closure at middle-ground levels in the structural hierarchy of a work” (56). He goes on to explain that a “cadence creates musical closure, but not all closure in music is cadential,” reserving the term “cadence” for a limited number of hierarchic levels (56).8 For Caplin, cadences close specific musical processes (harmonic and melodic, in the case of a PAC); most importantly, cadences elicit a sense of formal closure. According to Caplin, a cadence follows the structural beginning of a group on the same hierarchic level, and any cadential harmonic paradigm must include a root-position dominant chord. While Caplin’s insistence that cadences must be on the same hierarchical level as the phrase beginnings is a bit

8 Caplin specifically states that the Ursatz does not end with a cadence because there is no true beginning to the Ursatz. Also, because he reserves the term “cadence” as the means to close a theme, the fact that the Ursatz’s structural close is on a higher hierarchical level precludes his use of this term. Caplin does indicate that a cadence can occur at the same time as the structural close.

16 idiosyncratic, it does emphasize that a combination of V followed by I will not achieve closure unless it concludes a formal unit. There is some interaction between musical hierarchy and the perceived strength of closure. While the strength of closure may depend on local musical cues, as previous research has indicated, it also depends on the boundary’s role in the overall musical hierarchy (Joichi 2006).9 Meyer further states, “every composition, then, exhibits a hierarchy of closures. The more decisive the closure at a particular point, the more important the structural articulation …. The way in which a particular parameter acts in articulating structure may be different on different hierarchic levels” (1973, 89). It seems that, according to Meyer, the strength of closure for a particular segment determines the hierarchical structure of the piece, and markers of closure at one level can vary from markers at another level. It follows that closure at the end of a phrase is weaker than closure at the end of a section, which in turn is weaker than closure at the end of a piece.10 I am not convinced that there is a simple correspondence between formal hierarchy and the perceived strength of closure at the end of any particular segment. Some research has shown that top-down knowledge of formal design can influence the perceived strength of a point of closure (Joichi 2006). Agawu (1987) also emphasizes listener knowledge of a how a composition should unfold: its “scheme.” Comparing poetry to music, he suggests, … the trained reader (or listener) approaches a lyric genre such as the Shakespearean sonnet with a set of expectation regarding its length, meter and rhyme scheme. The awareness of this scheme mediates the experience of the poem, and therefore of closure. The same is true of musical genres such as minuet and trio, nocturne, concerto, and prelude, genres in which various types of signs—some conventional, others arbitrary— are used to inform the listener of how and when a piece is going to end. (4)

The completion of a schematic formal unit thus elicits a feeling of finality based on expectations generated by previous experience, and this knowledge could lead to the various completions

9 Joichi also notices that the length of the preceding context influences decisions regarding the strength of closure (longer contexts are rated as having stronger closure), but longer segments ending with a higher hierarchical boundary are rated as more closed than are longer segments ending with a lower hierarchical boundary. 10 Caplin (2004) would qualify that statement, arguing that although the cadence located at the end of a piece may seem stronger than previous cadences, the cadence itself does not close the composition. “A cadence typically presumed to close an entire movement is often accorded a high degree of foreground rhetorical emphasis … [which] renders such cadential arrivals so prominent and forceful that they can give the impression that they must be concluding something more structurally significant than a thematic region alone” (64–65).

17 within a composition having varying strengths of finality. Meyer’s bottom-up view (the hierarchical arrangement of these closes depending solely on the “number of parameters promoting or preventing closure”) and this top-down view (underlying formal schemata influencing a listener’s perception) will be re-examined in Experiment 3, located in Chapter 7.

Style and Closure

Several authors have claimed that knowledge of style—even if only implicit—is a prerequisite for perceiving closure. According to Mary Louise Serafine (1988), closure is marked by stasis and rest compared to the surrounding material, and the factors that generate movement and stasis vary among styles. While markers of closure differ among styles, it may be possible to experience closure in unfamiliar styles by imposing knowledge gained by experience in some familiar style to the unfamiliar style. While markers of closure are highly conventionalized in tonal music (cadences, stepwise descent to !% etc.), they are more variable in recent music. This variability has led to two approaches to discussing closure in post-tonal music: (1) authors retain tonal models of closure even for music in a clearly non-tonal style (Kurth 2000, Pellegrino 2002) or (2) authors turn to alternative goal-directed processes, such as abatement and intensity curves (Hopkins 1990, Bryden 2001). Richard Kurth’s (2000) analysis of Schoenberg’s fourth string quartet is particularly revealing in regards to the first approach. He states that “memory is one of the general conditions for musical closure” (139), both within a work, where memory engages elements to create musical forms, and between works, where memory invokes materials from earlier pieces or compositional approaches. From this perspective, Kurth argues that latent tonal tendencies are present in Schoenberg’s fourth string quartet, suggesting that Schoenberg’s compositional background (and presumably a listener’s abundant experience with tonal music) allows tonal implications and realizations to serve as markers of closure in this work. Kurth states that closure occurs when “fluctuating tonal latencies can no longer be kept in a state of balanced suspension. The latency of one or several individual tonalities is then revealed … and itself becomes an attribute of closure, in moments that are characterized by vivid qualities of incipience and expectancy” (159). While other factors, such as duration and dynamic level, may also contribute to closure at those moments in the quartet, Kurth raises an important point: knowledge of structures within a work and between works can influence the way a listener perceives closure.

18 In her article on closure in John Adams’ music, Catherine Pellegrino (2002) specifically states that closure at the end of a work primarily depends upon tonal organization. Although she acknowledges that Adams’ music is not tonal, she suggests that discernible pitch patterns emerge, and the completion of these patterns contributes to closure. She states, [I]f the end of a work is to be experienced as closure and not simply as an arbitrary stopping point, the nature and placement of the point of closure must be anticipated. In other words, for closure to occur, the tonal organization of the music must either define its own endpoint or participate in a system in which a given endpoint is already defined. (150)

Pellegrino likens this experience of closure to achieving ! in the melody over the tonic harmony at the end of a tonal work. She also recognizes that other factors contribute to closure in this repertoire: the completion of a well-known formal structure and rhetorical, stereotypical ending gestures; she maintains, however, that these are subservient to tonal closure. In contrast to these approaches, Robert Clifford (2005) suggests that we abandon the notion of tonal closure in defining closure in atonal music, specifically addressing compositions by Webern. He suggests that we instead redefine our expectations for closure in this style of music based on compositional elements found in the piece. For isn’t tonal closure really about expectations set into motion by the composer? … Should we expect in atonal music, then, with its radically different melodic and harmonic landscape, the same type of musical experience, the same solid confirmation of musical expectations? I think not. (29)

The processes set in motion at the beginning of a work will differ from those in other compositions, and could include symmetrical arrangement of pitches around a center pitch or a series of gestures that balance each other (e.g., a rising gesture balanced by a descent). While Clifford questions whether these types of processes are perceptible, he emphasizes that there are alternative means of achieving closure besides those that are tonally motivated. Abatement (Hopkins 1990) and intensity curves (Bryden 2001) were addressed previously, but this approach to describing closure in non-tonal styles warrants further discussion. Returning to Meyer and Hopkins, the emphasis on goal direction as a marker of closure across styles leads to a disturbing conclusion: there can be no closure in music without a goal-directed process. Setting aside the obvious difficulties in defining what exactly constitutes a goal-directed process, I think most musicians would agree that the musical features determining

19 a goal-directed process depend on music style. The issue of style becomes increasingly problematic throughout the twentieth and twenty-first centuries, because works by different composers (and sometimes even works by the same composer) do not typically share the same musical syntax. If closure requires the completion of a goal-directed process, there must first be a goal-directed process to complete. Intensity curves, and the like, are similar to the phenomenon McCreless (1991) describes as rhetorical closure, “the importation of closural conventions or the use of harmonic, melodic, rhythmic, textural, orchestrational, dynamic, articulative, or registral extremes as a means of dramatizing the end of a piece” (51). Although some of these rhetorical conventions transcend styles (like Bryden’s closural processes), repertoires and composers can have their own idiosyncratic rhetorical ending gestures. For instance, Gretchen Wheelock (1991), George Edwards (1991), and Floyd Grave (2009) all focus on rhetorical indicators of closure in Haydn’s string quartets, while Wye Allanbrook (1994) looks at a “tune” (as defined in her article) as a closural sign in Mozart. In contrast to these composer-specific signs of closure, some theories of closure and segmentation attempt to define musical characteristics of closure that are not style specific (most notably, Lerdahl and Jackendoff 1983; Narmour 1990). One such example is durational closure (Joichi 2006), defined by rests, pauses, and longer durations at the end of a segment. While Narmour cites these characteristics as closural, Elizabeth Margulis (2007) found that the interpretation of silence (how much tension the silence carries) varies with context. This suggests that the interpretation of closure is based on more than changes in acoustic input—that the meaning of these supposedly cross-stylistic cues varies based on context and listener experience. Thus, stylistic competency is a direct manifestation of a listener’s experience, where expectations gathered through statistical learning (Huron 2006) influence the perception of closure. From the perspective of probabilistic learning, conventional signs of closure (such as cadential patterns) begin as recurring surface features that are gradually incorporated into a listener’s stylistic knowledge. As a listener experiences the same harmonic/melodic paradigms ending musical units, such paradigms begin to evoke the feeling of closure. Listeners are better able to anticipate endings in musical styles where they have sufficient experience.

20 Along with stylistic considerations in the perception of closure, the other three characteristics of closure explored in this chapter are dependent in some fashion on a listener’s previous musical experience. It is musical expectations engendered from these knowledge structures that contribute to the sense of goal-direction, the segmentation of musical experience, and the recognition of differing strengths of closure. The formation of expectations and their influence on a listener’s perception of finality will be further explored in the next chapter.

21 CHAPTER 3

MUSICAL EXPECTATION AND CLOSURE

As discussed in the previous chapter, there is a relationship between expectation and closure. To this effect, Eugene Narmour asserts that closure is a fulfillment of musical expectation followed by an absence of expectation for what will follow, or, in Narmour’s terms, closure is the realization of a melodic implication that does not create some new implication. Leonard Meyer (1956) even goes so far as to state that without any expectation of when and how a musical segment will end, the music will always sound incomplete; it will merely “stop” and will not “close.” David Huron, in his seminal study on musical expectation (2006), also acknowledges the role of expectation in the perception of closure. Building on the work of Huron and others, I propose a model of closure that explains how various characteristics of closure (completion of a goal-directed process, segmentation of musical experience, hierarchical construction, and stylistic dependence—see Chapter 2) are derived from expectation. This chapter concludes with my model of musical closure and illustrates its predictions in three short songs: Robert Schumann’s “Widmung,” Anton Webern’s “Der Tag ist vergangen,” and Aaron Copland’s “The World Feels Dusty.” Formation of Expectations: Statistical Learning

Previous research has shown that we are experts at extracting statistical regularities from auditory input, and this process of statistical learning leads to expectations for musical events (Krumhansl 1990; Huron 2006). An individual’s musical experience will therefore determine how closure is perceived; for example, the more often a person hears a certain harmonic or melodic unit at the conclusion of a musical segment, the more that the listener will associate that unit with closure. This is supported by a study (Eberlein and Frick 1992) that asked musicians to rate the strength of closure projected by cadential patterns from a variety of historical periods. The ratings correlated with an individual’s self-determined own stylistic competency, confirming that increased exposure to a musical style influences the perception of closure.

Since it is well documented that different musical styles have their own characteristic tokens of closure, these results are hardly surprising,11 but they leave an important question unanswered: how do listeners form an association between musical cues and a feeling of finality? A mere exposure effect (whereby listeners perceive closure because similar patterns have ended musical segments in the past) is an insufficient explanation: this simplistic view cannot account for how listeners segment music into meaningful units. A possible solution may be found in research on language acquisition, which has shown that an auditory stimulus is segmented based on sequential probabilities. As in language acquisition, these sequential probabilities may influence a listener’s segmentation of music and, thus, contribute to the perception of closure. Children acquiring a language are faced with a daunting task. Before they can even begin to learn semantic meaning and grammatical syntax, they must first learn to discern boundaries between words. This is a difficult task when based on acoustical cues alone, because word boundaries are not consistently marked in fluent speech (Saffran, Aslin, and Newport 1996). Saffran and her colleagues demonstrated that infants as young as eight months can extract transitional probabilities (the probability that one event will follow another) between spoken syllables. As an example, imagine that an infant hears the phrases “pretty baby” and “pretty flower.” The transitional probability between pre and ty is higher than the transitional probability between ty and ba simply because the former sounds have been heard in sequence more often.12 Saffran, Aslin, and Newport (1996) created a speech stream of three-syllable nonsense words where every syllable was spoken without accentual stress and at a steady tempo. The only cues to the location of word boundaries were the transitional probabilities between the sounds. In two separate experiments, infants were able to distinguish between “words” and “non-words,” as well as between “words” and “part-words,” after only a two-minute exposure period.

11 As Robert Gauldin (1988) wrote in his eighteenth-century counterpoint text, “Each period of music history has devised clichés associated with cadential formulas. These may include stereotyped soprano and bass melodic movements, harmonic progressions, rhythmic figuration, non-harmonic activity, and suspensions” (13). Following this statement, Gauldin presents cadential paradigms common to the late-Baroque period. Similar lists of stylistically appropriate cadential paradigms are included in his sixteenth-century counterpoint text as well (1985, 27 and 87). 12 The formula for calculating the transitional probability of x followed by y is y|x = Frequency of xy / Frequency of x. In the limited example above, the probability of pre being followed by ty is 2/2 = 1.0, while the probability of ty being followed by ba is 1/2 = 0.5.

Of course, there are other acoustical cues that assist in the perception of word boundaries (accentual patterns, intonational profiles, pauses, etc.), so it is especially remarkable that these infants showed significant learning despite such impoverished stimuli. This experiment has been replicated with adult participants (Saffran 2001), as well as with stimuli consisting of action sequences (Baldwin et al. 2008) and tones (Saffran et al. 1999). A more recent study replicated these results using chord sequences derived from an artificial harmonic syntax. Jonaitis and Saffran (2009) found that after a two-day exposure period listeners were able to generalize syntactical rules from the transitional probabilities governing chord succession, and subsequently to differentiate novel correct harmonic progressions from progressions that did not adhere to the artificial harmonic syntax. Compared to actual music, the stimuli were quite improvised (lacking, for instance, metrical regularities), yet listeners were able to extract transitional probabilities between chords after sufficient exposure. Although the experiment outlined above does not explicitly address the inference of musical segments based on transitional probabilities, it does suggest that a similar learning mechanism is used for both language and music. Comparable to word boundaries in language, musical boundaries are formed when two musical events have a relatively low transitional probability in a particular style. Such events are not limited to pitch and harmonic material (although these elements are the most explored in the literature), but can extend to timbre, rhythm, loudness, articulation, etc.13 The analytical preference to segment music at a point of change in the musical surface can be explained with the help of transitional probabilities. Recall from Chapter 2 Hanninen’s (2001) theory of segmentation, which posits that a change in a musical parameter (e.g., register, instrumental timbre, or articulation) creates a boundary in the sonic domain. Other authors (Lerdahl and Jackendoff 1983; Meyer 1973) have also used differentiation to segment musical experience. These authors imply that listeners expect continuity in all musical domains, an expectation that is formed through statistical learning. For instance, a large melodic leap could signify a boundary between two musical groups (similar to Lerdahl and Jackendoff’s GPR 3).

13 When using transitional probabilities, the grain at which probabilities are extracted must be specified. In music, this depends on the time window, or event type, in question when describing statistical regularities. Transitional probabilities can be calculated between motivic cells, chords, and individual notes, but one can also reduce the window size to calculate the transitional probabilities within a single sound. Such a fine grain of division, though, will not necessarily provide interesting results.

Folk songs from a variety of musical cultures reveal that smaller intervals occur more frequently (Huron 2006), increasing the transitional probability for pitches that are closer together in pitch space. Although I know of no database documenting the transitional probabilities of non-pitch domains, given that expectation is informed by statistical learning, it is likely that other musical domains have a transitional probability profile similar to that of intervallic succession, where no change or slight changes occur more frequently than do drastic sonic changes. That said, not every sonic disjunction will result in a meaningful musical boundary and a feeling of closure. The mind unconsciously uses statistical learning to extract transitional probabilities of musical events, which in turn guide segmentation.14 Along with extracting transitional probabilities, a listener also becomes sensitive to the likelihood that a particular sound will occur somewhere in a composition. Huron (2006) nicely summarizes this point by differentiating between inclusional probabilities and transitional probabilities.15 Inclusional probabilities convey the likelihood that a particular sound element will be present in the style, regardless of the preceding events, while transitional probabilities represent the likelihood that a sound element will occur based on the previous event. In tonal music, members of the tonic triad occur more frequently than do other scale degrees (inclusional probability), and the tonic chord usually follows a dominant harmony (transitional probability). Both sets of probabilities would give rise to musical expectations, but I posit that a segmentation resulting in the strongest feeling of finality, or closure, depends specifically on transitional probabilities. In addition to creating perceptual boundaries, information gleaned through statistical learning is generalized into a broad set of musical expectations called “schematic expectations.”

14 In an analytical narrative, transitional probabilities are not the only means of segmenting a musical stream. Take, for instance, Hanninen’s other criteria, contextual and structural. Forming associations between groups in a composition requires listeners to remember past material in order to form new groupings. This dynamic listening process is not based on a generalization of transitional probabilities. Structural criteria are based on a theoretical framework and are applied consciously to the sonic and contextual domains to create musical segments. Because statistical learning occurs unconsciously, using conscious theoretical knowledge to create groupings is a different phenomenon. 15 Huron labels inclusional probabilities as “zeroth-order probabilities” and transitional probabilities as “first-order probabilities.”

Expectation

Being able to anticipate upcoming musical events is an integral part of musical experience. This experience has not only been captured empirically through various experimental paradigms, but it is reflected in musical discourse. Empirical research indicates that not all of these expectations are explicit and that expectations can reflect different types of musical knowledge, such as generalized knowledge applicable to different works, or exact knowledge of a particular work. While I do not provide a comprehensive overview of musical expectation (see Huron 2006; Ockelford 2006), I first discuss how the concept of expectation informs discourse in the discipline of music theory, especially with regard to musical closure. After this summary, I turn to Huron’s four types of expectation (schematic, veridical, dynamic, and conscious), outlining concepts essential to an expectation-based model of musical closure.

Expectation in Music Theory

As Schmuckler (1989) states, “almost all contemporary music-theoretic analyses have adopted implicit or explicit ideas of expectation” (111). While “almost all” may seem like an overstatement, I believe that the aims of music theory, as a discipline, are indeed rooted in expectation. Some theorists strive to bring unconscious expectations to consciousness, while others create alternative sets of musical expectations, allowing listeners to experience music in new ways. This is readily evident in the language used in music theory pedagogy, analytical discourse, and theoretic systems. A common topic in which we invoke expectation in the music theory classroom is the deceptive cadence (or deceptive resolution, or deceptive motion). The term “deceptive” clearly indicates the use of an unexpected chord in place of the expected chord, and textbooks usually spell out clearly that listener expectations have been thwarted. Take, for instance, Clendinning and Marvin (2005): Bach’s solution at the end of the first phrase is to replace the expected tonic harmony with a tonic substitute, the submediant triad, to make a deceptive cadence: V7-vi. The name of this cadence is appropriate, since the drama of this harmonic “deception” can be striking. (300; emphasis added)

Other labels for musical phenomena reveal a foundation in expectation. Some musical vocabulary implicitly relies on expectation; consider “tendency tone” and “anticipation.”

Tendency tones require a particular resolution in common-practice tonality, expressing recurring patterns of dissonance resolution. Anticipations, a term that describes the early arrival of !+ (usually), anticipate the next harmony. In the realm of harmonic syntax, textbooks frequently organize the common pre-dominant chords into a hierarchy based on “strength” or how likely a given chord is to progress to dominant harmony. It is the higher transitional probability from 6 6 ii -V compared to IV-V that makes the ii chord a “stronger” pre-dominant than the IV chord. In 6 a similar vein, the transitional probability between V5/V-V is even higher, resulting in an even “stronger” pre-dominant harmony. In aural skills classrooms, some teachers advise students taking dictation to rely strategically on the conscious application of theoretical patterns to guide the listening experience. For instance, Rogers (1984) suggests that instructors train students to chunk the musical surface into memorable musical patterns to assist in melodic dictation, where the student learns to expect patterns taught in the written theory classroom. This “intelligent guessing” allows students to fill in missing pitches based on theoretical expectations. In their recent aural-skills textbook, Jones and Shaftel (2009) encourage students to fill in the harmonic content of cadences early in the listening process because “the harmonies in these measures will be very predictable” (3-10). In both written theory and aural skills classes, textbooks and instructors regularly appeal to student expectations—those formed through previous musical experiences and those formed within the classroom. Other writings about music regularly draw upon a hypothetical listener’s expectation, either explicitly or implicitly. As an example, Sarver (2010) explores how chromatic passages interact with prolongational processes in works by Richard Straus. Her analysis of the chromatic passage in mm. 34–40 of “Säusle, liebe Myrthe” makes explicit use of expectation. The digression leads to a cadential six-four in E( minor, which establishes the expectation for local closure in E( in the measures that follow. The illusory cadential six-four, however, is thwarted in m. 39 by an upward chromatic shift that leads to a surprising cadence in E major. (83; emphasis added)

For this short passage, Sarver draws on conventional tonal expectations to explain the “surprising cadence” that follows when expectations for closure are “thwarted.” Denial of closural expectations set up by a listener’s extensive familiarity with tonal syntax is integral to Sarver’s analytical methodology and ensuing narrative.

Forrest’s 2010 article “Prolongation in the Choral Music by Benjamin Britten” implies a slightly different view of expectation. Exploring the means by which a musical entity might be prolonged in a non-functional, yet triadic, musical style, Forrest makes the case for surface-level triads prolonging symmetrical middle-ground interval cycles, which in turn promote pitch centricity. Central to this discussion of musical expectation is his analysis of the fifth movement of Britten’s Ad majorem Dei gloriam, entitled “O Deus, Ego Amo Te.” In his analysis, Forrest shows how the first two sections of the movement establish the precedent for unbroken interval cycles, setting up the implicit expectation that the final two sections of the piece will also include complete interval cycles. When an ic3 cycle begins in the third phrase (starting with B major and moving to D major), he suggests that, “This incomplete cycle creates a strong expectation of F major, the next step in the cycle” (21; emphasis added). However, this projected expectation is not immediately satisfied: the ic3 cycle is temporarily suspended with a strong arrival on E( in the last section of the movement. The concluding phrase of the movement finally resumes the interval cycle, arriving on an F-major chord, which itself is prolonged by a complete ic3 cycle. To this effect, Forrest states, “Both voices then proceed through their familiar minor-third cycle to cadence ultimately on the pitch classes which began the piece, thereby completing the interrupted cycle…” (22). While the expectation for a complete ic3 cycle may not be shared by as many musicians as are expectations for syntactical tonal language, the expectation for continuity, especially continuity on deeper structural levels, is shared among music theorists. This expectation for continuity is built into many of our theoretic systems, especially theoretical narratives that rely on organicism or self-similarity. In Schenkerian analysis, we expect to find foreground musical structures in the middleground, and in transformational theory we expect transformations to relate sound objects to each other. Further, a Reti-style analysis would encourage listeners to find “homogeneity both between the movements and between the parts of one movement” within a multi-movement composition (Reti 1951 [reprinted 1978], 5). In short, any theoretical system creates expectations for how the structure of the music can be experienced or explained. The concept of expectation pervades the entire discipline of music theory—its pedagogy, analytical discourse, and theoretical systems. These expectations need not be empirically grounded: while empirical evidence is necessary for cognition studies, music analysis is

28 interpretative. An analyst draws upon explicit and implicit expectations (formed through previous musical engagements) and methodological choices to create an individual interpretation. However, as we saw with closure, the ubiquity of expectation in this discipline speaks to the general human experience of musical engagement. While listeners might not be able to verbalize their expectations, we have definite opinions regarding how music should go in a particular style.

Types of Expectation and Schema Different experiences of expectation emerge from this brief survey of music theory literature. Music theory pedagogy and Sarver’s thwarted expectation for phrase closure, for example, imply that listeners have generalized expectations regarding how harmonic syntax should proceed and how phrases should progress in common-practice tonality. In contrast, Forrest’s analytical expectation of ic3 cycle completion is based on prior events in that particular composition.16 This later experience could also be considered a conscious expectation, expectations dictated by a theoretical system or other musical knowledge, while expectations stemming from previous knowledge of a particular composition capture yet another type of expectation. These different experiences of expectation have led scholars, such as Bharucha, Huron, and Margulis, to categorize various types of expectation. Schematic expectations represent broadly enculturated patterns of events. According to Bharucha and Stoeckig (1987), these automatically formed expectations generalize musical patterns from a large musical corpus. Such patterns range from the consistent hypermeter and harmonic syntax of the Classical style to the timbre and riffs associated with punk music. I want to emphasize that these are generalized expectations: although a listener may have specific 4 expectations for ensuing events (for instance, a V2 chord in a Mozart piano sonata will lead a 6 listener specifically to expect a I chord), they are not based on knowledge of that particular work. Rather, these expectations are formed gradually by listening to many exemplars of a particular musical style and accumulating knowledge of their recurring patterns.

16 There is no clear boundary between piece-specific expectations and general expectations. Someone familiar with a large corpus of Britten’s works might form more general expectations for interval cycles, just as someone familiar with tonal music has general expectations for harmonic syntax.

In contrast, veridical expectations are formed by specific knowledge about the sequence of events in a single composition. Both Bharucha and Stoeckig (1987) and Huron (2006) use these two types of expectation to explain the musical surprise associated with a deceptive cadence (V-vi) in a well-known piece of music. Schematic expectations guide listeners to anticipate a tonic harmony following a V chord (the transitional probability for the progression V-I is higher than that of any other chordal succession), even if they veridically expect a vi chord based on previous experience with this particular composition. This violation of schematic expectations results in a feeling of “deception” even when a listener expects the surprising harmony. Put another way, general schematic expectations derive from learned categories of musical experience. Both psychologists and music theorists use the term schema to describe these learned categories. Like “closure,” “schema” is an often used but seldom defined term. Even among musicians, “schema” encompasses different shades of meaning, due in part to disciplinary differences (whether the focus of the study is psychological or musicological). Three of the most common uses of the word are exemplified in the writings of Meyer, Gjerdingen, and Huron. (For a comprehensive and more nuanced discussion of “schema,” see Byros 2009, especially chapter 5, part 1.) In Explaining Music (1973), Meyer posits that melodies in Western music derive from a limited set of melodic processes. Melodic processes represent basic archetypes, his term for “an innate or universally valid schemata” (Gjerdingen 1988, 7). Two archetypes that Meyer subsequently tested with Rosner are the gap-fill and changing-note archetypes. A gap-fill archetype consists of an initial upward melodic leap subsequently filled in by a stepwise descent, while the changing-note archetype is comprised of two melodic dyads, the first leading away from the tonic triad, the second leading back to the tonic triad (for instance, !-'-$-#). Rosner and Meyer (1982) found that listeners could abstract the archetype from musical exemplars of each category, then, in a forced-choice paradigm, they could identify the archetype present in novel musical clips. A later study (Rosner and Meyer 1986) expanded this work and found that these archetypes also influenced similarity judgments between musical excerpts.17

17 In a more recent article, Paul von Hippel (2000) questions the perceptual validity of these archetypes by re-examining the results from the 1982 and 1986 studies. Von Hippel concludes that gap-fill does not influence melodic shape, nor does it influence the classification of melodies to the extent that Rosner and Meyer suggest.

Gjerdingen’s (1988) work on schema builds upon the foundation laid by Meyer, especially Meyer’s changing-note archetype. Gjerdingen limits his study to schemata that generalize a musical event-sequence (notes and rhythms notated in the score). He differentiates scripts, which outline an event sequence, from plans, which contain information regarding intentionality rather than implying a particular series of events. Relating these two types of schemata to Meyer’s archetypes, a changing-note archetype is an example of a script, while a gap-fill archetype would be a plan. This distinction can account for style change; for instance, according to Gjerdingen, the eighteenth-century’s scripted phrase construction evolved into the nineteenth-century’s plan-like phrase. Although my own discussion of schematic expectations will not distinguish scripts from plans, it is important to recognize that schemata can vary in their specificity. Huron offers the most inclusive definition of schema, “a mental preconception of the habitual course of events” (2006, 419). Huron likens schemata to semantic categories, where “schemas are generalizations formed by encountering many exemplars. Our most established schemas reflect the most commonly experienced patterns” (225). Without schemata (which guide schematic expectations) it would be impossible to have any expectations for a novel work; listeners could only have expectations for a work after listening to it. Schemata also aid in encoding and remembering music; for instance, pitches presented in a tonal context are more easily remembered than those presented in a non-tonal context (see the discussion in Hérbert, Peretz, and Gagnon 1995, 194). Further support for the existence of schemata comes from instances in which these broad generalizations create an incorrect expectation or musical memory, as Huron discusses (2006, 210–16). For instance, a schema could be overly general (e.g., not providing specific enough expectations) or misapplied (e.g., approaching Non-Western music with Western expectations). Since schemata aid in remembering music, listeners tend to misremember an atypical musical pattern in a way that conforms to a more common schema. This brief overview shows that schemata can range in specificity, from less specific expectations (pitch proximity, stylistic timbres, and behavior of scale degrees in the major mode) to more specific expectations (a particular chord succession). The narrower understanding of “schema” posited by Meyer (universal archetypes) and Gjerdingen (style-specific harmonic/melodic progressions) are easily subsumed within Huron’s broad definition of

“schema.” Margulis (2005) addresses this range of schemata-types, positing that schematic expectation itself encompasses more than one type of expectation. Specifically, schematic expectations inhabit a continuum from relatively deep to relatively shallow, where depth relates to availability for direct access (from little to much availability), susceptibility to change through exposure (from little to much susceptibility), and scope of application (from more universal to more limited). Examples of increasingly shallow schematic expectations might be: expectations for closure; expectations for cadential closure in tonal music; expectations for common cadence types in music from the classical period; and expectations for common cadence figures in the music of Mozart, where these expectations are increasingly available for access, increasingly susceptible to change through exposure to new pieces within the relevant repertoire, and increasingly limited in scope. (666)

I agree that schematic expectations exist along a continuum, but, as noted by authors who specifically discuss deeply schematic expectations, there seems to be a question about the extent to which music alone informs the creation of these expectations. Expectations for pitch proximity and melodic regression transcend musical culture (for the most part), so there seems to be a perceptual preference for small melodic intervals and post-skip reversals. Indeed, many of these expectations do not apply just to musical stimuli, but adhere to the broad perceptual laws set forth by Gestalt theories of perception. Instead of teetering dangerously close to a chicken-or-egg question—which came first, a preference for small melodic intervals (evident in musical composition), or small melodic intervals in musical composition (informing a preference for these intervals)—I simply posit that these deeply schematic expectations are different from other types of schematic expectation because they are not distinctive to music and arise from general perceptual processes. Music-specific schematic expectations are then derived solely from musical experience.18 Both types of expectation are applicable to music, but only the latter is solely applicable to music. Figure 3.1 shows this continuum between deep schematic expectations (Margulis: “deeply schematic expectations”) and surface schematic expectations (Margulis: “shallowly schematic expectations”). The difference in shading indicates that the deepest of the deep expectations transcend musical culture and are cross-modal; however, there is no clear boundary between these expectations and ones that are unquestionably influenced by a particular musical

18 Musical experience here is understood in the broadest sense: listening to music, performing music, bodily engaging music, and understanding limits the body may place on performance can all contribute to these music- specific expectations.

32 culture. As Narmour explains (1990), these cross-modal expectations are formed through a bottom-up cognitive system (consisting of Gestalt principles), while the music-specific expectations are formed through a top-down cognitive system. Even so, these cross-modal expectations are evident as statistical regularities. Pearce and Wiggins (2006) present another perspective on the creation of these regularities, stating “patterns of expectation that do not vary between musical styles are accounted for in terms of simple regularities in music whose ubiquity may be related to the constraints of physical performance” (378). Whether these statistical regularities are determined by performance or perceptual limitations, and whether such expectations are formed through statistical learning or are innate, it remains that listeners expect continuity of sound (in terms of pitch proximity, location, timbre, etc.). Regardless of its origins, continuity is the cross-modal bedrock on which other expectations are constructed.

Figure 3.1: Continuum of Expectations

Figure 3.2 shows the continuum again with possible schemata located along the right side. The expectations on this continuum are implicit, evident in statistical regularities in the

33 music. Expectations for pitch proximity and melodic regression (Huron 2006) are considered deep expectations because they are the most widely applicable, providing generalized expectations. Style-specific schemata can range from general tonal and rhythmic expectations to more specific expectations for a particular harmonic progression. Within a composer’s oeuvre, his or her characteristic fingerprint may result in statistical regularities that differentiate these works from those of other composers writing within the same style. In general, a greater quantity of compositions informs the creation of deep schematic expectations while a smaller quantity of compositions informs the creation of surface schematic expectations.

Figure 3.2: Continuum of Expectations with Schemata

Empirical research addressing expectation has predominantly focused on schematic expectations. For instance, Schellenberg (1996, 1997) found empirical support for aspects of Narmour’s Implication-Realization theory, which makes relatively specific predictions for deep melodic expectation, particularly pitch proximity and pitch-reversal. Many authors have found resounding empirical support for expectations of pitch proximity (Shepard 1964; Deutsch 1991; Aarden 2003) using a variety of experimental methodologies and stimuli. Despite overwhelming evidence that pitch proximity is preferred, the expectation for pitch proximity can be influenced by other expectations, as Hérbert, Peretz, and Gagnon (1995) found in their probe-tone study, which examines listener preference for tones at the end of musical phrases, where scale degrees predicted the results better than did pitch proximity alone. So, while pitch proximity represents a deep schematic expectation, more accessible surface-level expectations (such as the tonal system) can exert greater influence on listener expectations. Surface schematic expectations, especially those pertaining to expectations within the tonal system, have been extensively explored. Along with Hérbert, Peretz, and Gagnon (1995), who focused on melodic phrase endings, other authors have examined more general melodic expectations (Carlsen 1981), harmonic expectations (Bharucha and Krumhansl 1983; Bharucha and Stoeckig 1986), and a combination of both (Schmuckler 1989). Other studies have examined types of musical expectation beyond a tonal context, and they still confirm the existence of expectations that are not work-specific, but applicable to a wider body of music (Cuddy and Lunney 1995). Finally, a series of cross-cultural expectation studies illustrates how these surface expectations are formed through previous exposure (Krumhansl et al. 1999; Krumhansl et al. 2000). Dynamic expectations, which Huron also discusses, exploit a listener’s short-term memory to form predictions of likely future events within a musical composition while it is being heard. Dynamic expectations are so named because they are relatively volatile compared to schematic and veridical expectations, and arise from brief exposures to a stimulus. Huron states, “as the events of a musical work unfold, the work itself engenders expectations that influence how the remainder of the work is experienced” (227). Adaptive expectations of this sort have been explored in empirical studies demonstrating that listeners unfamiliar with a particular style can pick out statistical probabilities after a short exposure period. Kessler, Hanse, and Shepard

(1984) performed a cross-cultural study using a probe-tone method to explore schemata based on tonal structure. Their Balinese and American participants listened to three melodies, one based on the Western scale and two based on Balinese scales (Pelog and Slendro), then rated the goodness of fit between the material they just heard and a probe tone. In general, the results found that pre-existing schemata based on first-order probabilities influenced ratings by enculturated listeners, while ratings by naïve listeners were based on pitch frequency (inclusional probabilities). Even listeners completely unfamiliar with the style were able to extrapolate statistical regularities from the given music to form a set of expectations. These three types of expectation (schematic, veridical, and dynamic) are very much related, as illustrated by Ockelford’s (2006) zygonic model of musical expectation. His model shows how implications (and hence expectations) can arise while listening to a musical composition. Ockelford differentiates between expectations within a musical segment and those between musical segments. Within a segment, there are implications of pitch proximity (we tend to expect small intervals), while expectations between segments are formed through four different experiences: 1) other material or materials occurring within the same hearing of the same performance of the same piece; 2) a different hearing or hearings of the same performance of the same piece (in the case of recorded music); 3) a hearing or hearings of a different performance or performances of the same piece; or 4) a hearing or hearings of a performance or performances of a different piece or pieces. (110)

The first expectation refers to dynamic expectations, which are molded by the ongoing composition. The second and third experiences result in piece-specific expectations, or veridical expectations, while the fourth results in generalized learning, influencing schematic expectations. Ockelford relates the interaction of structures within a segment (which he calls within- group structures) and the interaction of structures between two different segments (called between-group structures). “Previous structures,” which inform schematic and veridical expectations, are stored in long-term memory while “current structures” are encoded in short- term memory. Previous structures form between-groups expectations and can also be a general or specific indication of future events. Dynamic expectations guide between-group expectations,

36 while pitch proximity forms within-group expectations.19 As a listener hears a composition multiple times, more specific expectations are formed, but these expectations are always contextualized by schematic expectations. Although these expectations seem categorically discrete, all three operate concurrently, allowing a listener to experience musical expectations in unfamiliar music as well as thwarted expectations in well-known music. According to Huron and Ockelford, the differences between schematic and veridical expectations arise from the way in which the information is encoded in long-term memory; however, the difference between schematic and dynamic expectations is less clear. First, both types of expectation are formed through a common learning mechanism: statistical learning. Second, assumptions behind what is valued in dynamic expectations seem to be rooted in schematic expectations. Expectations for continuity and repetition are deep schematic expectations, but the specific musical elements to be repeated or continued are piece-specific. As discussed earlier, Forrest’s analytical narrative implies that the expectation for interval cycle completion is formed as Britten’s composition progresses. Given that dynamic expectations are considered implicit, and this particular pattern could be captured by transitional probabilities, a listener could indeed form an unconscious expectation for interval-cycle completion. However, the foundation for this expectation would be the listener’s schematic expectation for repetition in a work, blurring the line between these two types of expectation. Furthermore, since Britten uses interval cycles regularly in his works, a listener could unconsciously form a general schema for this compositional characteristic after exposure to many exemplars.20 Even though dynamic expectations may sometimes be difficult to distinguish from schematic expectations, the term remains useful because the concepts behind dynamic expectations strongly influence music analytical discourse. Ockleford emphasizes that the expectations in his model are not explicit and are formed unconsciously; however, there are times when expectations rise to the surface of consciousness. A knowledgeable listener hearing the first movement of a Mozart piano sonata will have specific

19 Ockelford distinguishes pitch proximity from other forms of schematic expectations, very similar to my own representation of the continuum between various types schematic expectation. Ultimately, I still maintain (along with Margulis [2005] and Huron [2006]) that pitch proximity is a deeply schematic expectation. 20 Whether the completion of an interval cycle can be an implicit expectation is debatable. It is more likely that conscious knowledge of Britten’s compositional preference for interval cycles shapes a listener’s hearing of a work. In any case, Forrest uses the language of dynamic expectation to shape his narrative.

37 formal and structural expectations that, assuming some training and technical vocabulary, could be explicitly articulated (e.g., the second theme will probably have a lyrical character, and the recapitulation will probably be preceded by a prolonged dominant harmony). Conscious expectations “arise from conscious reflection and conscious prediction” (Huron 2006, 235), bringing us full circle back to the role of expectation in music theory. Theoretic systems ask us to carry another set of expectations into our musical experiences, which can enhance our musical experience. Many music-theoretical systems invoke the language of expectation, but we should be careful not to confuse conscious expectations reflecting implicit expectations with those that arise solely from abstract theories. I do not presume that abstract theoretical expectations are invalid, but it is important—given the pervasive references to expectation in our scholarship and teaching—to recognize the distinctive varieties of expectation.

Expectation and Memory: An Alternative View

While these different types of expectation seem to capture our experience with music, the underlying assumption that they reside in different memory structures is problematic. Huron (2006) posits two different types of memory guiding schematic and veridical expectations. Knowledge of individual pieces is stored in episodic memory (also known as autobiographical memory), while auditory generalizations are stored in semantic memory. Huron notes that this distinction is problematic for two reasons (225). First, familiar works may leave out biographical episodic content (although we can remember a composition along with the context in which it was heard, we are also capable of remembering a composition without explicitly recalling the context). Also, all auditory generalizations began as a single exemplar of a recurring pattern, suggesting that all semantic memories began as a large collection of episodic information. Rather than two distinct systems, Hintzman posits a multiple-trace memory model that can account both for schemata abstraction and for veridical expectations. In Hintzman’s multiple-trace memory model (1986, 1988, 2010), each experience is recorded in long-term memory as a separate memory trace—in contrast with models where subsequent exposures to a given stimulus strengthen an existing memory trace for that stimulus. Hintzman suggests that schema abstraction of everyday concepts (like “chair” or “table”) is determined by a person’s exposures to many exemplars of a category, each exposure laying down a memory trace. The memory traces encode various features of each exemplar, such as the context in which the

38 exemplar was experienced, along with other sensory characteristics. Abstract concepts are then derived from this pool of episodic traces. When a retrieval cue interacts with all of these traces simultaneously, it activates traces according to their similarity with the cue. Traces that are more similar to the cue are more strongly activated than other traces, and the summed content of these activations represents the information retrieved from memory (Hintzman 1986). This concept of memory can also reflect the results of statistical learning: the number of activated traces informs inclusional probabilities, while the number of activated traces involving a particular event succession informs transitional probabilities. This memory model can also be applied to music cognition. Although Hintzman has not explored the creation and content of memory traces for temporal experiences, if each musical experience results in a separate memory trace, then this model can account for both veridical and schematic expectations without relying on two separate memory systems.21 When a person listens to music, each musical trace is activated in parallel. Traces that are most similar to the current auditory input are activated more strongly and will have the greatest impact on listener expectations; less similar traces, while present, will influence expectations to a lesser degree. In this model, generalized schematic expectations are based on the activation of memory traces from many different pieces of music. The range of specificity for expectation depends on the degree to which these traces share the same subsequent events. A large number of memory traces lead us to expect pitch proximity, but these traces do not imply the same pitch or scale degree because the context of each trace is so different. In contrast, harmonic progressions conforming to tonal syntax may activate fewer memory traces, but these traces will overwhelmingly involve a tonic chord following a dominant harmony, creating a more specific expectation. Memory traces for a particular composition provide even more specific expectations, of course. Because all these traces respond in parallel, a listener can have several different expectations for a single piece of music. Once again, consider a deceptive cadence, which, as previously discussed, can be surprising even in a well-known composition. When a listener hears a dominant chord, all

21 The creation of memory traces would probably be influenced by the way in which a listener interacts with music. A listener’s ability to use language to label musical events, the extent to which a listener is paying attention to the music, and how the listener is parsing the musical surface would probably influence the creation and content of the memory traces. Also, the way in which a memory trace is activated would differ from Hintzman’s original conception because listening to music is a temporal experience.

39 memory traces containing an experience of this harmony are activated, including the memory trace(s) for the work itself. In the vast majority of these traces, the dominant chord is followed by a tonic harmony, eliciting a strong and relatively specific expectation for tonic. This expectation is in direct conflict with the even more specific expectation for the submediant chord that stems from the listener’s experience with this particular piece. Increased exposure to a particular composition can lessen the effect of a surprising musical feature, like the deceptive cadence, and Hintzman’s model can account for this type of experience. Consider, for example, the opening phrase of “America” (“My Country ’tis of Thee”; Beethoven’s arrangement of the identical “God Save the King” is shown in Example 3.1). This six-measure phrase contains a deceptive resolution in the fourth measure. The abnormal length of the phrase (six measures instead of the more typical four) and the deceptive motion violate schematic expectations and should therefore elicit surprise. However, “America” is so familiar in our culture that listeners have multiple memory traces for this song. The sheer number of traces correctly predicting the features of the phrase and the greater activation of these traces based on their similarity to the incoming input lessens the influence of the generalized expectations based on a listener’s cumulative musical experience. Because this model relies on specificity of expectation as well as a listener’s cumulative musical experience, it can account for the simultaneous occurrence of different expectations as well as a listener’s changing expectations with increased exposure.

Example 3.1: Beethoven, “God Save the King,” WoO 78, mm. 1–6

Hintzman’s conception of memory allows us to consider two distinct factors influencing our expectations: the specificity of an expectation and the number of times a listener has been exposed to a particular pattern. Figure 3.2 depicted both generalized expectations and specific expectations for particular pieces (that is, both schematic and veridical expectations). The specificity and quantity of memory traces determines the strength of an expectation, where

40 higher specificity and greater trace quantity result in stronger expectations. For instance, tonal syntax makes highly specific predictions about the harmonic and melodic content of a composition, and the considerable exposure to music conforming to these norms creates strong expectations in Western listeners.

An Expectation-based Model of Closure

The concept of expectation can also provide insight into the listener’s experience of musical closure. This idea is nothing new; recall Meyer’s (1956) statement about closure: “A stimulus series which develops no process, awakens no tendencies, will . . . always appear to be incomplete” (139). Whether expectations are implicit or explicit, Meyer is quite adamant that a listener must anticipate the point at which a musical segment will terminate in order to experience a feeling of finality. Observing the definition of closure from Chapter 1 (the expected end to a musical segment, resulting in a feeling of finality), closure necessarily depends upon expectation. The characteristics of closure—completion of a goal-directed process, segmentation of musical experience, hierarchical construction, and stylistic dependence—describe the listener’s experience. To capture the various experiences of closure proposed by this model, I suggest three types of closure: anticipatory closure, arrival closure, and retrospective closure. These describe a listener’s phenomenological perception of closure, where each of these types of closure draws upon a different set of expectations, resulting in a different feeling of closure. Segmentation is a prerequisite to experiencing musical closure. After unconsciously learning the transitional probabilities of various musical domains, a listener is able to segment the musical surface into meaningful musical units. Some of these segmentations reflect deep schematic expectations (e.g., expectations for continuity and proximity), while other segmentations depend on stylistic knowledge. If a style consistently uses a formulaic pattern at boundary locations, then this pattern itself becomes associated with endings. Consider for a moment the classical cadence, V-I. Nothing inherently links this harmonic succession with closure; only through a learned schematic expectation has the authentic cadence—especially the perfect authentic cadence (PAC)—become synonymous with closure. Because musical boundaries are formed at points with a lower transitional probability (and hence a higher prediction error), the uncertainty of subsequent events leads to the closing off of the musical segment, resulting in a feeling of finality.

According to Huron, this feeling of finality is “a direct consequence of learned first-order probabilities” (2006, 167). He associates “closure” or a feeling of “home” with the positive emotions resulting from a correct prediction based on these transitional probabilities. A listener misattributes this positive feeling to the sound itself (in the case of a PAC, to the tonic triad). This understanding of the relationship between expectation and closure works well for tonal music, but more recent music does not have so many first-order probabilities that transcend an individual composition. Expectations for twentieth- and twenty-first-century works typically result from fewer episodic traces (surface schematic expectations) or tend to be overly general (deep schematic expectation). Specific expectations supported by many memory traces (from the middle of the continuum) are not present in this repertoire, unlike in tonal music. Without a strong prediction effect, listeners do not have as strong of a sense of finality. Huron notes that the uncertainty following a cadence also contributes to the sense of finality. In my model, more specific expectations for the end of a segment lead to a greater change in the listener’s ability to predict subsequent events. Once again, consider the PAC in the Classical style. A knowledgeable listener will have strong expectations for the tonic arrival, but not necessarily for subsequent events, resulting in a large increase in prediction error. Compare this to a listener who is not fluent in the Classical style and therefore did not strongly expect this same tonic arrival. Both listeners may have similar uncertainty for events following the cadence, but the knowledgeable listener will experience a greater decrease in the ability to predict subsequent events, resulting in a greater feeling of finality for the same passage of music. Considering that the feeling of finality is the product of a successful prediction (and its resulting positive valence) followed by a rise in uncertainty for subsequent events, and that memory traces for music are activated in parallel, the experience of musical closure is directly related to a listener’s prior experience and the implicit expectations derived from this experience.22 The multiple-trace memory model can account for a comparative rise in uncertainty even in well-known pieces, given that general schematic expectations are an amalgamation of all active memory traces for the musical context. While not all traces are

22 Listeners also experience closure when an ending conforms to conscious expectations. For instance, a listener might expect a segment-concluding Figure that occurs early in a composition to return in a significant way, closing another segment later in the work. Also, conscious knowledge of musical structure could lead a listener to anticipate when an ending is likely to occur.

42 activated to the same degree (the ones that share the most features with the incoming sonic input are more strongly activated), the sheer variety of musical content following a typical ending gesture results in a higher prediction error for the next event.23 As discussed in Chapter 2, many aspects of closure are style dependent, but broader schematic expectations allow the experience of closure not only in unfamiliar pieces but in unfamiliar styles as well. As Huron notes, however, the crossover that occurs with schematic expectations between styles does not always provide contextually sensitive expectations. More general expectations, like the expectation that phrases normally relax at the end, can transcend styles (Hopkins 1990), but whether this expectation is a product of understanding music through embodied motion (Snyder 2000) or acquired through statistical learning is a question that warrants more research. I would argue that the strongest sensation of closure is typically associated with music- specific schematic expectations (as opposed to cross-domain schematic expectations), which may account for the common description among music theorists that closure occurs at the end of a goal-directed process. This feeling of goal direction is often misattributed to the music (or, more specifically, to an actively unfolding musical process), when in fact the feeling is an artifact of the listener’s ability to predict with increasing certainty subsequent events within a musical segment. Consider, for instance, a schema that provides a general outline of successive events (such as Gjerdingin’s do-ti-re-do schema or Byros’ le-sol-fi-sol schema). As each event in such a schema occurs, the transitional probability for subsequent elements increases in that context. More specific listener expectations have a higher transitional probability between successive elements, resulting in a greater feeling of goal direction and, ultimately, closure. The continuum of expectation specificity also applies to closure, as depicted in Figure 3.3. On the deepest level, we expect some sort of musical closure—a feeling of finality at

23 To explore how traces can be activated to different degree (as opposed to a binary activation), consider a categorization task. Suppose you see a chair, and for this illustration this chair has five features: “sitability,” four legs, no arms, a back, and a location close to the ground. The memory trace for a different chair that shares all of these features will be more strongly activated than the memory trace for a three-legged barstool, which would only share the “sitability” and no arms features with the perceived stimulus. While these features are binary in nature, they may be weighted differing amounts in determining the degree of activation of a particular memory trace (in this example “sitability” is more of a requirement for something to be a chair than whether the chair has arms). In actuality, the mind probably keeps track of many more features than this simple example, including context. In music, the process may be more complicated due to the temporal nature of music and listener limitations in remembering the preceding musical context.

43 the end of a music segment or piece. Margulis (2005) agrees that closure is a deep schematic expectation; it is also a cross-modal expectation (in general, we expect sounds to end eventually, and, from a Gestalt perspective, we see broken objects as completed wholes), not a music- specific expectation. This deeply schematic expectation is extremely general, applicable to all music.

Figure 3.3: Continuum of Expectation: Closural Expectations

Appearing just above these expectations are general expectations for phrase length, ending gestures, and performative signs of closure, all of which contribute to a basic phrase shape—usually corresponding to an increase in tension and a subsequent relaxation. These

44 general expectations are applicable across styles, but musical patterns found in a smaller collection of musical works (style-specific, genre-specific, or composer-specific patterns) also shape expectations. Endings that conform to the surface end of the schematic expectation continuum result in a greater feeling of finality because of the relatively high specificity of the expectations they engender. With the frequent use of a formulaic cadence in certain styles, a listener has more exact expectations for the end, resulting in a better ability to predict when phrases will end and consequently an increased feeling of goal-direction. The number of memory traces supporting a particular progression would also influence the feeling of goal-direction, where an increased number of traces would increase the anticipation of the ending. The more specific an expectation is, the less applicable it will be to a variety of pieces: for instance, there are forms of closure specific to a particular period, genre, or even composer. At the top of the diagram are expectations for closure based on previous encounters with a particular composition. Even though these work-specific expectations allow a listener to anticipate the end of a musical segment accurately, the quantity of these specific episodic traces is dwarfed by a listener’s more general cumulative musical experiences; the feeling of finality would be less intense than the feeling of finality following signs of closure from the middle of the continuum. Because the feeling of finality results from a change in the listener’s ability to predict subsequent events, especially specific expectations leading to the end of a segment will produce a greater subsequent decrease in predictability. For instance, the feeling of closure following the end of a harmonic schema is stronger than an ending indicated by a long note because the expectations are more specific (in regards to content and timing), resulting in a larger difference in a listener’s ability to predict subsequent events. Deeper schematic expectations are too general to elicit specific expectations for the end of a segment, resulting in a smaller change in prediction error. At the same time these expectations are unfolding, listeners still carry surface schematic expectations and perhaps veridical expectations for closure. Similar to the experience of a deceptive cadence, an ending that conforms to a listener’s veridical expectations for a particular piece, but that overall denies schematic expectations, could lead to a less intense feeling of finality because some expectations imply continuation while other imply an ending. The

45 proportion of continuation and ending implications results in various degrees of closure, creating a sense of hierarchical closes within a piece. I posit three different types of closure, based on the type of expectations governing the feeling of finality and the amount of change in the prediction error, which results in closes with different strengths. Anticipatory closure occurs when a listener can predict when the musical segment will be completed. Anticipatory closure can be experienced through all the types of expectation, but, as mentioned earlier, schematic expectations on the surface end of the spectrum seem to create the greatest feeling of finality. Anticipatory closure is the strongest type of closure because the expectations leading into the final event are so strong, resulting in a large rise in prediction error. Veridical and dynamic expectations can also lead a listener to experience anticipatory closure, even if a composer eschews conventions set forth by schematic expectations; however, without the combined weight of many exemplars, the experience of closure may not be as strong.24 Arrival closure occurs when a listener experiences finality before the beginning of the next segment. This is best understood in Narmour’s definition of closure: a musical event that creates no further implications. Like anticipatory closure, arrival closure depends upon a listener’s schematic expectations and requires a decrease in the ability to predict subsequent events, but in arrival closure the listener does not know when a musical segment is going to end until it actually ends. Sonic features (learned through statistical learning) such as an extended note or silence signify the ending’s arrival, but the transient increase in prediction error is not as high as in anticipatory closure because the expectations approaching a particular ending are not as strong. Retrospective closure can only barely be classified as closure, since it refers to experiencing an ending solely because a new beginning has occurred. Meyer would not classify this as closure at all, although he does suggest that closure occurs prior to a recognized beginning, such as the beginning of a parallel consequent phrase (Meyer 1973, 86). In my view, rather than experiencing finality because the next event is more difficult to predict than previous

24 An evaded (or deceptive) cadence would be an example of denied anticipatory closure. A listener is primed to expect an ending following the dominant harmony, but the chord that follows implies continuation instead. While a listener may experience some finality with this harmony, like the closing off of a subphrase, the feeling is not nearly as strong as it would have been had the expected harmony occurred instead.

46 events, we instead experience an ending because the current event defied expectations for continuation implied by the previous event. Retrospective closure can be characterized as a failure to recognize an ending precisely when it occurs. Deeply schematic expectations are at work here, based mainly on sonic disjunction. While multiple listenings may change a once retrospective close to an arrival or anticipated close, these veridical expectations will not elicit the same effect as shallow-end schematic expectations.

Three Analytical Vignettes

This section will briefly examine closure in three songs that represent different musical styles and carry different sets of schematic expectations: Robert Schumann’s “Widmung” from Myrthen, Op. 25, No. 1; Anton Webern’s “Der Tag ist vergangen” from Vier Lieder für Singstimme und Klavier, Op. 12, No. 1; and Aaron Copland’s “The World Feels Dusty” from Twelve Poems of Emily Dickinson. My analyses, representing the perspective of an experienced listener, will focus on schematic, dynamic, and conscious expectations; obviously, multiple repetitions of a single work would also create more specific veridical expectations. I will highlight goal-directed processes and surface features that most compellingly project closure in each song, briefly exploring how schematic and dynamic expectations influence closure. Because the text can contribute to closure through repetition, rhyme scheme, and semantic meaning, I chose these three texted works to illustrate the role of expectation in the perception of closure.

Schumann’s “Widmung”

Many authors portray the completion of a tonal process as the main marker of closure; however, these tonal markers of closure, such as cadences and the completion of the Ursatz, combine with several musical elements to create a sense of closure. Other markers of ending, such as increased duration and strong metrical articulation, interact with pitch-based signs of closure to create a hierarchy of segmentation, ranging from subphrase to phrase to section to the entire song. While subphrases are not typically considered “closed,” they are usually marked by musical characteristics that also accompany phrase endings. These elements (such as change of texture, increase in rhythmic duration, and silence) create perceptual boundaries in the musical surface because of the discontinuity in the sound. Other surface characteristics (such as a

47 decrease in tempo, softer dynamics, and falling pitch contour) also signify endings, usually coinciding with the end of a subphrase or a phrase. All of these features, which reflect common ending gestures, contribute to the perception of closure. From a tonal standpoint, “Widmung” is relatively straightforward. It begins in A( major, and the first part of its simple ternary form contains a single phrase. The B section of the ternary form begins with a common-tone modulation to E major ((VI). Over the course of this section, the music slips back to A( by reinterpreting the A-major chord in m. 25 as a B(( chord ((II in A( major). The B section sets up the return of the A section with a prolonged dominant, which could be read from a Schenkerian perspective as the arrival of " in an interrupted structure. The A' section begins in m. 30, exactly repeating the music and text from the beginning until m. 35. Here Schumann tonicizes ii instead of IV, and the lyrics return to the text from the end of the B section. The tempo broadens and the vocal line rhetorically leaps up to F5–E(5 (covering the structural "* before falling conclusively to ! on the strong beat of m. 39, achieving tonal closure (from a Schenkerian perspective, completing the Ursatz). The text (provided along with an English translation in Table 3.1) is a setting of F. Rückert’s poem. In the first half of the poem, set in the A section of Schumann’s song, the author acknowledges that his love is his entire life. The anaphora preceding each characteristic of his lover (du meine) is contrasted with the anaphora “du bist” in the second half of the poem (set in Schumann’s B section). In this second half, the author describes the transformative power of his lover’s affection. The twelve-line poem consists of rhymed couplets, where both lines within each couplet have the same number of syllables. The poem alternates between couplets of eight and couplets of nine syllables until the last couplet, which breaks the pattern and substitutes an eight-syllable couplet in place of the expected nine-syllable couplet. Rückert’s consistent syllabic structure and rhyme scheme within each couplet provide a listener with very specific expectations for the ending of each couplet. The A section has only one true ending, as dictated by tonal schemata: the perfect authentic cadence in m. 13 (see Example 3.2) completes the goal-directed harmonic process initiated at the beginning of the song. Other musical markers, such as the middleground descending step progression and the relatively long vocal note followed by a rest (coupled with the diminuendo and ritardando in the piano) strengthen the feeling of closure at this point. These

48 musical features represent deep schematic expectations, which apply to a larger variety of works than do the more surface schema for tonal syntax. Other points in the A section (such as in mm. 5 and 10) also include a descending pitch contour, a longer rhythmic duration, and diminuendos to mark endings, but these points do not evoke the same feeling of finality as does the cadence in m. 13. The more surface schemata of tonal process allow a listener to predict a more specific type of ending (a tonic chord on a strong beat) than do more general schematic signs of ending (or, to use Meyer’s term, “secondary parameters”).

Table 3.1: Text and Translation of “Widmung” Poem by F. Rückert [trans. by Reinhard 1989, 128-9] The number of syllables in each line is noted to the left of the text 8 Du meine Seele, du mein Herz, You my soul, you my heart, 8 Du meine Wonn', o du mein Schmerz, You my bliss, oh you my grief, 9 Du meine Welt, in der ich lebe, You my world in which I live, 9 Mein Himmel du, darin ich schwebe, My heaven, you, therein I soar, 8 O du mein Grab, in das hinab Oh you my grave down into 8 Ich ewig meinen Kummer gab! I eternally gave my sorrow!

9 Du bist die Ruh, du bist der Frieden, You are repose, you are peace, 9 Du bist von Himmel, mir beschieden. You are bestowed to me by heaven. 8 Daß du mich liebst, macht mich mir wert, Your love for me makes me worthy to myself, 8 Dein Blick hat mich vor mir verklärt, Your gaze has transfigured me within my own eyes, 8 Du hebst mich liebend über mich, You lift me above myself with your love, 8 Mein guter Geist, mein beßres Ich! My good spirit, my better self!

A listener could segment the first phrase into smaller units; as Meyer (1973) explains, a hierarchy of closure emerges based on the proportion of musical parameters projecting an ending to the parameters projecting continuation. A listener’s previous musical encounters will determine whether the features of Schumann’s first phrase project closure or continuation. Because harmony is one of the best predictors of endings in this style, an experienced listener will presumably first sense closure in m. 13. The subphrase-concluding harmonies prior to this point imply continuation because an experienced listener will have specific expectations for subsequent harmonies. A subphrase in this analysis consists of a grouping on a lower hierarchic level than the harmonically-driven phrase.25

25 While in this analysis, subphrases are marked by an initiating and concluding gesture occurring on the same hierarchical level, subphrases in other pieces could be formed on the basis of discontinuity within the phrase. Further, in this analysis, there are different levels of subphrases: larger subphrases can be divided into smaller subphrases.

The first two subphrases (mm. 1–3 and mm. 4–5; refer to Example 3.2) are similarly delineated by rests and end with a relatively long note on a strong beat. The first subphrase ascends to C5 over a prolonged tonic harmony, and a change of harmony initiates the second subphrase, which reaches beyond the registral boundary established by the first subphrase before ø6 stepping down to " (harmonized with the borrowed ii 5 chord) in m. 5. Both the first and second subphrases clearly set up the expectation that more music will follow, but in the local context they group together to form a higher hierarchical unit. Although musical elements at the end of the second subphrase also imply continuation (setting up sentential expectations and arriving on an unstable scale degree and harmony), the descending gesture in mm. 4–5 balance the rising gesture in mm. 2–3, creating a stronger boundary at m. 5. The text influences my interpretation as well: the last word’s rhyme confirms the grouping of these subphrases. In other words, I am able to predict the conclusion of the second subphrase better than the first because of the rhyme scheme and repeated syllabic pattern.

Prefix to the opening subphrase

Example 3.2: Schumann, Myrthen, “Widmung” Op. 25, No. 1, mm. 1–13 The annotations under the score represent the two levels of subphrase analysis discussed in the text.

Example 3.2 (continued): Schumann, Myrthen, “Widmung” Op. 25, No. 1, mm. 1–13

4 Both the subphrase that begins with the V2 chord in the second half of m. 5 and the 4 subphrase that begins with the V2/IV chord in the second half of m. 7 use the same harmonic progression, first in the home key, then tonicizing IV. Even without a rest separating the two events, the repetition of the harmonic progression and basic melodic outline ("-!-$-#), the 4–3

51 suspension on the strong beat, and the dynamic expectation of subphrase length (established by 4 the first two subphrases) suggest that the V2/IV chord in the second half of m. 7 begins a new event. Again, these subphrases group together because of their musical similarity; a listener would have strong expectations for the location of the end of this second subphrase because of the harmonic and melodic repetition. A dynamic expectation of subphrase length coupled with the number of syllables present in each line of text also provides fairly specific expectations for this point of conclusion. The arrival on the pre-dominant harmony with the rhyming final word of the couplet in m. 9 does initially sound like the conclusion of the subphrase, fulfilling a listener’s expectation for an ending. However, the material that immediately follows (end of m. 9–beginning of m. 10) does not sound like a complete subphrase: it sounds like a stronger ending than the resolution of the 4–3 suspension in m. 9. Despite confounding dynamic expectations for subphrase length, hearing the arrival on " in m. 10 as an ending confirms other dynamic expectations. “O du mein Grab” begins with the same words and melodic material as the end of the second subphrase (mm. 4–5), producing specific expectations for an ending. One possible reading of the grouping structure is that this short segment groups with the previous subphrase to prolong the pre-dominant area, creating a longer subphrase in mm. 8–10, which, when combined with the previous subphrase in mm. 6–7, essentially replicates the harmonic motion in mm. 2–5. Even though both measures conclude with a descent down to ", m. 10 sounds more implicative than does m. 5. Perhaps the premature stop in the middle of a line and the absence of a complete rhyming couplet project continuation at the surface level, while the expanded pre-dominant chord increases anticipation for an upcoming cadence at the middleground level. This anticipated completion of a harmonic schema and the unexpected subphrase length overshadows other signs of ending. This section’s last subphrase is longer than the previous ones, concluding in m. 13 with a PAC. Interestingly, Schumann disguises the end of the fifth line, which occurs on the downbeat of m. 11 (the expected place for the line to end, as implied by the previous subphrase lengths). The rising melodic contour and short note values make “in das hinab” sound more like a musical beginning than an ending. The cadential arrival coincides with the conclusion of a rhymed couplet, and, although the end of the couplet’s first line was not musically articulated, Schumann takes advantage of the internal rhyme in line five. In this first section, Schumann’s compositional

52 decisions and the text of the poem influence the perceived grouping structure of the subphrases, the conclusiveness of the endings, and the sense of closure at the end of the A section. Even though Schumann concludes the first phrase with a #-"-! melodic motion coupled with a strong harmonic cadential gesture, an experienced listener is unlikely to hear this as the final close of the piece. There has not been enough music; a listener familiar with Romantic Lieder would know that a contrasting section, or at least another stanza, usually follows. Furthermore, the poem itself remains open; the speaker has only listed the characteristics of his love. Musicians who take an organicist analytical position may further state that the full implication of the borrowed (& has not been fully realized, necessitating more music. The common-tone modulation to (VI (enharmonically respelled as E major) begins the song’s next section (see Example 3.3). This section is differentiated from the first not only by this key change but also by a change in the accompaniment pattern and the longer durations in the melodic line. After the half cadence (HC) in m. 21, harmonic and melodic patterns from the first section recur followed by another common-tone modulation back to the home key. Despite a ritardando and a return of the original accompaniment figure, the return to the original key does not sound like the third part of a ternary form. Part of the reason is that elements from the A section gradually emerge from the B section, blurring the boundary from the perspective of tonal and thematic content. It is not until the HC in m. 29, which concludes the phrase begun in m. 22, that there is a strong enough anticipated ending to close the B section of this Lied. The rhymed couplet, the dominant prolongation preceding this point, and the ritardando that occurs in the previous measure all contribute to the close of this section. However, the very nature of a HC and, to a lesser extent, the ascending melodic line implies continuation. In his paper at the 2010 meeting of the Society for Music Theory, Poundie Burstein explored this very issue of continuation at a half cadence, noting that the implicative nature of the V chord sometime blurs the distinction between a half-cadential ending and an elided authentic cadence.

Example 3.3: Schumann, “Widmung” from Myrthen, Op. 25, No. 1, mm. 14–29

From a theoretical perspective, a HC can end a phrase, but the phrase is not considered “closed.” If closure is seen as the completion of a goal-directed process, the most common harmonic process in tonal music is the motion away from tonic and then motion back towards

54 tonic. For instance, in his textbook Harmonic Practice in Tonal Music, Gauldin describes half cadences as open cadences compared to closed authentic cadences (2004, 132). However, listeners do experience a sense of some finality at a HC because of the role of expectation in the perception of closure. While a HC does not conclude on a “restful” tonic chord, it does signify the end of a common harmonic paradigm. As previously discussed, listeners misattribute the feeling of a goal-directed process to the increased prediction success when successive elements in a script-like schema are confirmed. Since the ending on V can be anticipated, there is a degree of finality at the arrival of a HC, and yet a HC does not sound as closed as an authentic cadence because the dominant harmony itself implies continuation. Despite the prevalence of half- cadential harmonic patterns, there are still many more traces in long-term memory where the V chord does, in fact, proceed to a tonic harmony.26 Because Schumann’s A' section replicates many elements from the beginning, I will not provide a thorough analysis of this section, but a few words about the structural close and the codetta are warranted. To heighten the expectation of closure in m. 39, Schumann uses rhetorical and formal markers of closure. Returning to the last two lines of the poem, Schumann concludes the song’s narrative by reiterating the transformative power of the poet’s love. The dramatic leap up to &+before the leap down to the final tonic covers the structural descending step progression. This rhetorical flourish points towards the approaching cadence, whose finality is further emphasized by a ritardando. An experienced listener would know that the song is unlikely to end with this structural 4 close, because most Lieder conclude with a piano codetta. The passing 2 chord following the cadence implies a continuation, which is realized by the return of the accompaniment Figure from the beginning. This codetta divides into two segments (see Example 3.4), each one concluding with a V-I harmonic motion. Adopting Caplin’s (2005) perspective on phrase and cadence, these two-bar units do not constitute a phrase: they are merely an external phrase extension, repeating the cadential gesture from the previous phrase.27 The last one sounds more

26 There are instances where the half cadence can sound more conclusive. Most notably, the Phrygian half cadence (typically iv6-V) is a common harmonic formula in Baroque music that may conclude non-final movements in multi-movement works. 27 According to Caplin, a cadence must end a formal unit. These two-bar units do not end anything; rather, they are extra endings tacked onto the end of the phrase.

4 final because it lacks the passing 2 chord on the third beat of m. 43 and the tonic harmony is sustained as the tempo slows down and the music fades out.28

Example 3.4: Schumann, “Widmung” from Myrthen, Op. 25, No. 1, mm. 37–44

In this analysis, the completion of harmonic schemata projected the strongest feeling of closure. Harmonic schemata, by their very nature, are broad generalizations formed by many exemplars and tend to elicit rather specific expectations, allowing a listener to experience anticipatory closure at cadential points. Signs of closure such as silence and increased duration contribute to a work’s grouping structure, but perhaps not its sense of closure (especially at the level of the subphrase) because the arrival of these features aren’t as strongly anticipated.29

28 One can point to the final sonority of this song, an A(-major triad in second inversion as evidence that this song does not have a satisfying ending; however, I hear the low A(2 at the beginning of the measure as the functional bass note for the entire measure. Further when viewed as a part of the entire song cycle, this opening song contains implicative elements in terms of the overall narrative of the cycle, but in this analysis, I only examined closure within the context of this single song. My analysis of Copland’s song “The World Feels Dusty,” will consider closure within the context of the entire song cycle. 29 A listener with less experience in this musical style might have quite a different impression of endings. I imagine that sonic disjunctions might exert much more influence in the song’s segmentation and in the listener’s perception of closure.

Returning to Meyer’s (1973) suggestion that the strength of a particular ending can influence the perception of form, it follows that the strongest closes conclude the larger sections of the ternary form, while less strong endings delineate and group the subphrases. Furthermore, sophisticated listeners may use genre-specific knowledge—the relationship between the piano and voice, stylistic knowledge about typical Romantic era harmonic language, and conscious knowledge about prototypical formal construction—to shape expectations, affecting their perception of closure for this work.30

Webern’s “Der Tag ist vergangen”

In my analysis of closure in “Widmung,” I relied primarily on tonal paradigms. Although segmentation in post-tonal styles may seem more reliant than tonal music on differences in the musical surface, I believe that schematic knowledge structures still provide a top-down guide to segmentation. One such structure is an increase in tension followed by a decrease in tension, marking a complete unit (this is also discussed by Bryden [2001] and Hopkins [1990]). This deep schematic expectation does not imply a specific type of ending or point of ending, but refers to a general phrase “shape” based on exposure to many different types of music.31 Both Meyer’s primary and secondary musical parameters can influence our learned association between “falling” or “decreased intensity” and our perception of closure. Even in tonal music, musicians maintain that we experience an increase in harmonic intensity followed by a relaxation at cadences. According to Huron (2006), this feeling of intensity and relaxation is misattributed: it is our strong first-order expectations at the dominant chord followed by the reward for a correct prediction at the tonic chord. Some other musical elements (discussed in the previous analysis), such as falling pitch contour and a decrease in tempo and dynamics, can also contribute to a sense of lessening intensity. Violations of the even deeper expectation for continuity in sound also play a role in the segmentation of music. Abrupt changes in pitch and articulation can segment a work into motivic units, usually occurring within a phrase, while other changes, such as the intrusion of silence and

30 This interaction between a “bottom-up” construction of form and pre-existing “top-down” knowledge of formal structure will be explored further in Chapter 7. 31 Some authors derive this structure from our embodied experience (Snyder 2000), while others attribute it to the perception of movement by musical forces (Bryden 2001). In either case, statistical generalizations of how musical segments should end are accumulated in long-term memory.

57 the lengthening of durations, usually occur at the end of a phrase. It is the degree to which these elements are anticipated, if they are at all, that gives rise to feelings of closure. Schematic knowledge of phrase shape and discontinuity in the sound influence a listener’s sense of closure (and therefore formal structure) in Webern’s “Der Tag ist vergangen.” Dynamic expectations also play a role in establishing which musical parameters will contribute to the sense of closure. Consider, for instance, the song’s opening measures (reproduced in Example 3.5), which illustrate the parameters that contribute to the shape of phrases in this work: dynamics and pitch register, where an increase in the dynamic level and pitch height build musical tension, followed by relaxation as the dynamic level drops and the pitches descend. This basic shape is expanded in the first vocal phrase, where the vocal line has two distinct peaks, one in each line of the poem, with the second peak reaching a step higher than the first. The piano line has a similar shape in mm. 5–6, but it does not align with the vocal shape. The vocal line is foregrounded in this phrase, due, in part, to the higher register, making the vocal rest at the end of the phrase more salient than the silence separating gestures in the piano part. A listener who did not recognize a phrase ending with the arrival of the G) in m. 6 (arrival closure) would almost certainly realize the phrase had concluded with the first instance of silence in the vocal line (retrospective closure).32 If this silence is insufficient, the piano punctuates the end of the phrase with a two-chord gesture that collapses in pitch space (a span of 56 semitones contracting to 34 semitones). The first phrase creates a dynamic expectation for phrase length and basic phrase shape. The second phrase traverses more pitch space, reaching past the registral boundaries of the first phrase, but still descends in pitch space at the end of the phrase. The end of the second phrase sounds more conclusive because its length exactly matches that of the first phrase, confirming a listener’s expectations for when the phrase should end. Coupled with the rhyme scheme, a listener can experience arrival closure on “mir”—or even anticipatory closure, if the listener is paying attention to phrase length.

32 There are elements present in this first phrase that could elicit anticipatory closure: the foreshortening of the contour segments and the syntax of the text.

Webern VIER LIEDER, OP. 12 © 1925 by Universal Edition A.G., Wien; © Renewed; All rights reserved Used by permission of the European American Music Distributors LLC, U.S. and Canadian agent for Universal Edition A.G., Wien Example 3.5: Webern, Vier Lieder, “Der Tag ist vergangen,” Op. 12, No. 1, mm. 1–11

In the first stanza, an increase in the dynamic level and pitch height correlates with an increase in tension, which is relaxed as the dynamic level and pitch drop, but this pattern does not hold true at the end. While the dynamics decrease in intensity towards the end (Example 3.6), the vocal line leaps a diminished octave up to F5. One could argue that the pitch is displaced an octave and it essentially moves only a half step from the preceding F,, but even aside from this explanation there are other elements that clearly contribute to the sense of closure here. First, the dynamic expectations established by the first stanza suggest that the length of the second stanza will be similar, which it is, and also that it will probably end with a word conforming to the

59 poem’s rhyme scheme, which it does. The descending perfect fifth interval between the last pitch of phrase one (G4) and that of phrase two (C4) is inversionally related (in pitch space) to the last pitches of phrases three and four (B(4 and F5). This intervallic balance may also contribute to closure.33

Webern VIER LIEDER, OP. 12 © 1925 by Universal Edition A.G., Wien; © Renewed; All rights reserved Used by permission of the European American Music Distributors LLC, U.S. and Canadian agent for Universal Edition A.G., Wien Example 3.6: Webern, Vier Lieder, “Der Tag ist vergangen,” Op. 12, No. 1, mm. 18–21

Incidentally, ending a song with an upward leap is not uncommon within Webern’s own oeuvre; for example, the well-known songs “Wie bin ich froh” and “Vorfrühling” end with rising vocal leaps. While this otherwise unusual interval may be a composer-specific sign of closure, the small number of examples of this gesture ending a musical segment compared with the vast number of more “typical” endings may still imply “openness” or “continuation” for even the most expert of Webern listeners.34

Copland’s “The World Feels Dusty”

In his setting of Emily Dickinson’s poem “The world feels dusty,” Copland manipulates a listener’s expectation for closure. His consistent use of two-bar groupings and stereotypical tonal patterns at the beginning of the song creates a set of dynamic expectations that are left unfulfilled

33 An analysis could also imply “latent tonal tendencies” (Kurth 2000) by pointing to allusions of a tonal relationship between these two intervals (suggesting that the first and third phrase end with a kind of HC that is answered by a PAC). While this is a possible hearing, I think other factors discussed in my analysis play a larger role in projecting closure. 34 One could argue that regarding a large ascending leap as strong closure would constitute an attempt to normalize music that is intended to be unusual. The very idea of the text—“Give to the deceased eternal rest”— suggests eternal stasis, not closure at all, so Webern may be manipulating closural expectations in order to explore meaning within the text.

60 as the song progresses. These unfulfilled expectations for closure might lead the listener to an understanding of the poem that differs from reading Dickinson’s words without music, and presumably Copland’s compositional choices reflect his own interpretation of the poetry. Of course, we might also understand this song differently in the context of the entire song cycle. The text for this song is taken from the 1929 Bianchi edition of Dickinson’s poems, which include quite a few changes from Dickinson’s original poem. For instance, the last two lines were changed from “And Hybla Balms—Dews of Thessaly, to fetch—” to “Dews of thyself to fetch and Holy balms.” According to Cherlin (1991), the 1929 edition also removes the possibility of enjambment by inserting periods at the end of each stanza, thereby limiting the number of possible readings of this poem. The dashes at the ends of stanzas equivocate, no less than those internal to quatrains. At the ends of stanzas dashes avoid the strong sense of closure that the unfortunate editorial choice of 1929, periods, bring. Hence, “Honors—taste dry—Flags—vex” are separated by versification, yet connected by belonging to the same short catalogue of things dry, vexing, things not needed that can crowd out those most needed. (58)

Still, multiple readings of the text are possible. Looking just at the text, this poem can be understood as leaving behind the dusty “honors” and “flags” of this world and longing for close companionship while death is embraced. Another interpretation places the poem within the context of Copland’s song cycle.35 “The world feels dusty” immediately follows the poem “Why do they shut me out of heaven?” Taken in this context, Baker (2003) argues that the speaker longs for the “dews” of this world, since she will not receive the “honors” of the next. At the moment of death, when the good Christian is said to weary of the world and seek heavenly waters for spiritual relief, Dickinson argues that one thirsts for the dew of this world, not the next. “We want the dew then Honors taste dry.” The honors that come with the “privilege” and “victory” of death in anticipation of salvation—to invoke the metaphors of the nineteenth-century Calvinist—“taste dry” on the tongue of one who has just learned in song three that she will be denied happiness in the afterlife. Dickinson looks to the soothing waters of worldly friendship as a “holy balm” that might restore one to life on earth. (11)

35 Soll and Dorr’s (1992) research indicates that Copland intended for the song cycle to be heard as a whole (100). Their subsequent analysis reveals features supporting their cyclic reading, where “the intricate musical and textual materials combine to create a highly organized and unique overall structure” (101).

In either case, Copland’s manipulation of a listener’s expectation for closure can color the meaning of the text. This analysis will focus on musical expectations Copland creates in the beginning of the song and what the confirmation or denial of these expectations might mean. Although diatonic, this song does not project a clear tonal center in the manner of Schumann’s “Widmung,” but the diatonic (or perhaps very weakly tonal) nature of this piece creates tonal implications, unlike Webern’s highly chromatic song “Der Tag ist vergangen.” F, minor seems to be prevalent in the piano part, but the voice emphasizes D major in the first few measures. This conflict is also present at the end of the first stanza, where the voice clearly implies B minor (with a skip down a fifth in the vocal part at the end of the first stanza to emphasize pitch-class B), but the piano part does not corroborate this tonal center. Fleeting tonal implications would activate traces of previous experiences with tonal music, eliciting tonal expectations. The piano introduction establishes an expectation for two-measure subphrases with an emphasis on the second beat of each measure (see Example 3.7). The vocal line continues this two-measure division in the first two lines of the poem, and both of these subphrases create a dynamic expectation that registral extremes in the vocal line will correlate with segmentation. The established subphrase length from the piano introduction projects a boundary after “dusty” in m. 4, even though the contour ascends to this pitch and the rhythmic syncopation emphasizes the weak syllable of this word. The stronger boundary in m. 6 concludes a higher-level subphrase unit. The features contributing to the close in m. 6 include the completion of a thought in the text, the slightly longer note on the word “die,” and a longer break in the vocal line. The pitch in m. 6 is higher than in m. 4, confirming a dynamic expectation that a range extreme correlates with the end of musical segments. Copland changes the subphrase grouping in the reminder of the first stanza. In m. 7, the vocal line articulates a one-measure group, with the durational accent beginning on the second beat of the measure, echoing the sighing piano gesture from the beginning. The piano part supports this reading: the recurring gesture is transposed up a third for just this measure before slipping back down to the original pitch level in m. 8. The increased pace is surprising, differentiating this subphrase from the previous material.

The World Feels Dusty by Aaron Copland, text by Emily Dickenson © Copyright 1951 by The Aaron Copland Fund for Music, Inc. Copyright Renewed. Boosey & Hawkes, Inc., Sole Licensee. Reprinted by Permission. Example 3.7: Copland, Twelve Poems of Emily Dickinson, “The World Feels Dusty,” mm. 1–2

The last line of text appregiates a B-minor triad, using the same syncopated rhythm from m. 4, and concludes on the lowest vocal pitch sounded thus far (B3). While this creates an arch- shaped phrase (the register gradually ascends through B4 in m. 4 to the E5 in m. 7 before falling quickly in the last line), other musical parameters do not follow the pattern of abatement suggested by Hopkins (1990). The accompaniment at this cadential point subtly changes from a sighing gesture to a rising step gesture in an inner voice, but perhaps the most obvious continuational parameters are the increased tempo and dynamics.36 In summary, the first stanza sets up these expectations: 1) Text: four lines in a stanza, abcb rhyme scheme, 5+5+5+4 syllabic pattern 2) Two-measure subphrases (except for the last three measures in the vocal line) creating balanced larger groups (2+2) 3) Diatonic, but not strongly tonal, melodic line 4) Generally, registral extremes mark endings 5) More specifically, phrases end with a+%-! gesture, concluding with the pitch B3

However, in the second stanza, many of these dynamic expectations are altered to match the changes in the text. The rhyme scheme changes to abbc and the syllabic pattern slightly shifts to 6+4+5+4. These changes, along with the descending contour in mm. 12–13 and the similar melodic gestures in mm. 14 and 15, lead me to group the subphrases a bit differently from the first phrase. I hear a 1+2+1 grouping instead of the balanced 2+2 structure I heard earlier. The last note of this section overshoots the anticipated B3 from the first section, arriving on A,3. Cherlin (2003) recognizes that

36 The use of secondary parameters to imply continuation at cadential points is not atypical for Copland’s settings; see “There Came a Wind Like a Bugle” and “Heart, We Will Forget Him.”

the low A, on ‘rain’ is clearly a substitute for the B of ‘dry,’ which is the ‘expected’ note—the fresh note for refreshing ‘rain.’ This touch is quite effective, and it works in conjunction with a modulation (extending the term slightly so that it can fit this not-quite- tonal context) projected by a shift in the piano's ostinato. (73)

These changes in the second stanza, along with the piano’s registral change (now reaching down to G2), the louder dynamics, and the faster tempo, set this section apart from the first. Copland’s B section creates an expectation for ternary form, confirmed by the return of the original tempo in m. 17 and the opening sonority (minus pitch-class B) in m. 19. However, any expectation for a clear return to the A section is thwarted by the lingering A, in the piano part and the new vocal line. A literal repetition of the A section would not capture the poet’s transformed perspective: that friendship provides needed comfort at the time of death. The material in mm. 23–24 imitates the pitch and rhythmic content of mm. 7–8 (where the pace increased in the first phrase), both setting similar texts—“we want the dew then” (mm. 7–8) and “Dews of thyself to fetch” (mm. 23–24). The listener may consequently develop strong expectations for the phrase in this final section to close on B3, similar to ending in m. 9; however, the phrase instead arrives on A,3. Along with this surprising pitch, the abrupt change of pitch collection (G Aeolian) and the final rising gesture in the piano (m. 27; see Example 3.8) suggest that this song is not closed at all, it is just one in a cycle. While elements at the end of this song imply finality, and multiple hearings of the song can allow a listener to experience a sense of closure, the first encounter might leave a listener unsatisfied. Copland may have chosen to undermine strong closure at the end of this song in order to underscore the text. The poem ends trapped in the time between life and death; strong closure would imply death. Here the poet wants to hold onto life in this world as long as possible. This lack of satisfactory closure leads me to consider further how this poem functions in the larger context of the song cycle. Baker (2003) argues that its placement after “Why do they shut me out of heaven?” shows that the poet chooses a worldly life, ministering to friends, over the afterlife. This reading is supported in Copland’s last song of the cycle, “The Chariot,” where the protagonist will not “stop for Death.” Although this reading creates a single trajectory from the beginning of the cycle until the end, I tend to favor the interpretation of the song offered in the previous paragraph. For me, this song cycle explores various aspects of the human experience: our relationships with nature, with each other, and, ultimately, with death. Copland’s

64 blatant thwarting of rather specific expectations created in the first stanza captures the timelessness Dickenson drafted, denying death as long as possible in order to enjoy earthly friendship.

The World Feels Dusty by Aaron Copland, text by Emily Dickenson © Copyright 1951 by The Aaron Copland Fund for Music, Inc. Copyright Renewed. Boosey & Hawkes, Inc., Sole Licensee. Reprinted by Permission. Example 3.8: Copland, Twelve Poems of Emily Dickinson, “The World Feels Dusty,” m. 27

In the three preceding examples, we have seen that expectation informs a listener’s sense of closure, segmenting musical experience. The perception of goal direction is an artifact of transitional probabilities formed through a listener’s familiarity with a musical style. The positive valence resulting from a confirmation of a listener’s expectation for the end of a segment followed by a weakening of expectations for subsequent events (i.e., an increase in prediction error) causes a feeling of finality (or momentary repose). The perceived strength of closure will correlate with the specificity of expectation and number of traces in long-term memory, which together will influence the difference between the transitional probabilities for sonic entities approaching and leaving an ending. From here, I hypothesize that there are two main factors that influence our perception of closure: 1) Knowledge structures will guide our expectations for when and how musical segments will conclude. These knowledge structures give rise to schematic, veridical, and conscious expectations, promoting anticipatory and arrival closure. 2) At the same time, sonic disjunctions in the musical surface features will segment musical experience. We expect musical surface features to continue in a similar manner (deep schematic expectation); when they don’t, we retrospectively perceive closure.

Musical surface features can either support or contradict the expectations formed through knowledge structures, and the weight of elements projecting closure compared to those

65 projecting continuation creates a hierarchical grouping structure. I predict that sophisticated listeners with more experience in a particular style will tend to rely more on knowledge structures than on sonic features. Expectations from both of these types of features are incorporated in the Event Segmentation Theory (EST), which is a cognitive model of segmentation. The next chapter explores this cognitive model and applies it to the perception of musical structure and closure.

CHAPTER 4

EVENT SEGMENTATION THEORY

Chapters 2 and 3 illustrated that segmentation is closely related to closure, comprising an integral part of my definition of closure—the anticipated end of a musical segment. Segmentation in music depends both on the bottom-up processing of sensory features and on the top-down processing of knowledge structures. Deep schematic expectations for sound continuity are reflected through the bottom-up sensory features that segment musical experience (for instance, the musical features listed in Lerdahl and Jackendoff’s GPRs 2 and 3). Knowledge structures inform surface schematic expectations, allowing a listener to anticipate endings and providing a framework for musical segmentation. Event Segmentation Theory (EST), as proposed by Christopher Kurby and Jeffrey Zacks (2007), incorporates segmentation based on learned knowledge structures and changes in sensory features into a single cognitive model. Kurby and Zacks’ proposed process by which we segment everyday events is grounded in expectation, which, when applied to music, can account for the perception of musical closure. Event Segmentation

An “event,” as defined by Kurby and Zacks (2007), is “a segment of time at a given location that is conceived by an observer to have a beginning and an end” (72). This definition is extremely similar to how musicians define a phrase, which can be considered a discrete event in music. For instance, Lerdahl and Jackendoff (1977) define a phrase as “the lowest level of grouping which has a structural beginning, a middle, and a structural ending (a cadence)” (123). If we carry this line of thinking to its logical conclusion, then any musical “object” is an “event” since it exists as a temporal experience; for instance, a single tone has a beginning and end, so by the definition posited by Kurby and Zacks, it is an event. But this conclusion goes too far because musical tones are not usually heard in isolation; instead, tones are usually grouped together to create larger units. Because I am examining the perception of musical closure, I examine grains of segmentation resulting from the creation of formal units, starting with subphrases through entire pieces.

Event segmentation is “the process by which people parse a continuous stream of activity into meaningful events” (Zacks and Swallow 2007). Research has shown that event segmentation is an automatic, hierarchical process, and is essential for guiding memory and learning. In many event segmentation experiments, participants designate perceived boundaries through an explicit task. Although this does not directly support the idea that event segmentation is automatic, widespread agreement among individuals on the location of event boundaries suggest that individuals may be tapping into ongoing event processing (Kurby and Zacks 2007; Zacks, Speer, and Reynolds 2009). Even music segmentation studies reveal a high level of agreement among participants on the location of boundaries (Joichi 2006). Listeners broadly agree on the location of musical segments across a variety of literature (Deliège 1987; Deliège et al. 1996; Krumhansl 1996). Even when confronted with ambiguous stimuli, participants using the same segmentation strategy still generally agree (Pearce, Müllensiefen, and Wiggins 2010), implying a shared underlying cognitive process. However, an explicit task may “change the nature of the perceptual processing” (Zacks and Swallow 2007, 80); Zacks, Tversky, and Iyer (2001) found that participants’ segmentation behavior varies depending on whether the participants verbally described the event and, to a lesser extent, their familiarity with the stimulus. Brain-imaging data provide much stronger evidence for an automatic process. In one such study, participants passively watched movies of actors portraying everyday events while their brains were scanned. The fMRI showed increased brain activity at points later designated by the same subjects as event boundaries (Zacks et al. 2001). A related music study found similar results. Musically untrained participants listened to excerpts from a multi-movement orchestral work by William Boyce while their brain activity was recorded with fMRI (Sridharan et al. 2007). There was increased brain activity in two distinct regions of the brain coinciding with movement boundaries: first there was an increase in activity in the ventral network, corresponding to violations of musical expectancy, followed by an increase in activity in dorsal network, corresponding to the processing of new musical information. Despite not directly attending to the event structure of the stimuli, participants in both studies were still sensitive to event boundaries. Event segmentation is hierarchical and occurs simultaneously on multiple time scales (Kurby and Zacks 2007). When asked to mark the smallest meaningful units and the largest

68 meaningful units, participants’ fine-grained divisions are nested within their coarse-grained divisions (Zacks, Speer, and Reynolds 2009). Music is also understood to be hierarchical: notes form motives, which form subphrases, which form phrases, etc. Lerdahl and Jackendoff (1983) have laid out grouping well-formedness rules (GWFRs) as well as grouping preference rules (GPRs, discussed previously) to explain how a listener creates groups as well as how these groups are hierarchically related.37 These rules are listed in Table 4.1.

Table 4.1: Lerdahl and Jackendoff’s Grouping Well-Formedness Rules GWFR 1: Any contiguous sequence of pitch-events, drum beats, or the like can constitute a group, and only contiguous sequences can constitute a group. GWFR 2: A piece constitutes a group. GWFR 3: A group may contain smaller groups. GWFR 4: If a group G1 contains part of a group G2, it must contain all of G2. GWFR 5: If a group G1 contains a smaller group G2, then G1 must be exhaustively partitioned into smaller groups. (37–39)

Being able to segment an activity into events can also guide learning and understanding. Zacks et al. (2006) demonstrate that subjects tend to parse events in a similar manner, usually creating segments falling into nameable events, and the better a person can form large meaningful groups, the better he or she will remember the activity. Here, elderly adults segmented movies of everyday events; some adults did the task “well,” meaning their segmentation followed the patterns of the group, while other adults were not as successful. In a subsequent identification task, participants were shown still pictures, some of which were drawn from the movies and others of which were not. Participants who segmented the movies successfully also better identified the visual images from the movies. This research is directly applicable to music. As discussed in Chapter 3, some ear-training curricula teach undergraduates to listen for larger patterns in order to remember the passage for dictation, since creating discrete, namable units aids in remembering the music.38

37 In their chapter on grouping structure, Lerdahl and Jackendoff liken the grouping of the musical surface to “partitioning the visual field into objects, parts of objects, and parts of parts of objects” (36). This perspective is quite different from my more phenomenological approach, comparing the grouping of the musical surface to the segmentation of experience. 38 Ease of segmentation might also relate to individual aesthetic preferences: musical processing would be facilitated for a person who could easily segment a composition into meaningful events. A similar correlation 69

Both top-down knowledge structures and bottom-up sensory characteristics influence segmentation (Zacks 2004). Knowledge structures, as defined by Zacks, are “representations that capture recurring patterns of covariation” (2004, 980), referring to transitional probabilities gleaned through statistical learning. Other authors refer to knowledge structures using different terms such as event schemata (Hard, Tversky, and Lang 2006) and situation models (Zwaan and Radvansky 1998). Knowledge structures guide the top-down processing of events, especially for perceived goals and intentions. Research has shown that top-down knowledge of goals assists in segmentation, and event boundaries coincide with changes in perceived intention (Baldwin and Baird, 2001; Baldwin et al., 2008; Hard, Tversky, and Lang 2006; Zacks 2004). When the actor’s goals are unpredictable, viewers tend to segment an activity into smaller units, suggesting that knowledge structures particularly assist in creating larger groups. In music, stylistic competency might also assist in creating larger groups. For instance, the first section of Schumann’s “Widmung” (discussed earlier) contains a single phrase, although surface discontinuities suggest several subphrases. A listener less familiar with Schumann’s style may not be able to perceive harmonic intention towards the tonic goal over these breaks in the sound. This is readily apparent in the undergraduate classroom, where instructors have to teach music students not to be “tricked” by surface discontinuities and to focus on the longer, harmonically driven phrase. In music, knowledge structures are revealed through musical expectations, both implicit and explicit. In light of the discussion from the previous chapter, knowledge structures can take the form of generalized schemata (e.g., tonality), learned knowledge (e.g., formal archetypes), and piece-specific knowledge. While an expectation for continuity can be a knowledge structure, especially when used consciously or when it creates dynamic expectations within a composition, the deepest expectations for continuity merely rely on sonic disjunctions and correspond with the bottom-up changes in sensory characteristics.39 Segmentation created by bottom-up processing relies on changes in movement features or spatial location to produce event boundaries (Magliano, Miller, and Zwann 2001). In the visual

between processing fluency and aesthetic preference in visual art has been demonstrated (Reber, Winkielaman, and Schwarz 1998). 39 Refer to Figure 3.1 for an illustration of the different types of schematic expectations.

70 realm, when a person or object changes direction or speed, a boundary is perceived, and these changes correlate with increased activity in brain regions involved with motion processing (Zacks, Braver, et al. 2001). Even segmentation based on surface features alone can create a nested hierarchical structure, where event boundaries with a large number of feature changes are perceived as more important than those with fewer changes (Newtson, Engquist, and Bois 1977). Changes in the musical surface equate to these visual discontinuities; for instance, Lerdahl and Jackendoff’s (1983) GPRs 2, 3, and 4 (see Table 2.1) are based on sensory characteristics, indicating that a change in attack-point, register, dynamics, articulation, and duration distinguish group boundaries, while more marked changes result in higher-level boundaries. Deliège (1987) has shown that when musicians are asked to segment a short excerpt, most of their divisions correspond to these GPRs. When listening to recorded music, one cannot see physical motion, unlike the visual stimuli used in studies examining event segmentation. However, many descriptions of music employ motion words (for instance: a stepwise ascent, a downward leap), suggesting that, even when motion is not literally present, it is still conceptually understood.40 Research in discourse processing suggests that conceptual changes in sensory characteristics have the same effect on event segmentation as do physical changes (Zacks, Speer, and Reynolds 2009). Of course, the influence of musical “motion” on segmentation becomes much more complex when combined with a visual stimulus such as a performer, conductor, score, or dancer. While this is outside the scope of my study, it would be interesting to see the extent to which visual input influences auditory segmentation.41 Comparable to the expectation continuum discussed in Chapter 3, in which there was no clear boundary between cross-modal expectations and musically-derived expectations, segmentation prompted by knowledge structures and segmentation prompted by sensory characteristics cannot be sharply distinguished. Zacks and Swallow (2007) also characterize elements essential to segmentation in terms of a continuum: Further, we believe that a number of little-studied features, from purely sensory to purely conceptual, must be important for event segmentation. Toward the sensory end are

40 Gjerdingen (1994) likens our experience of motion in music to apparent motion in visual studies: a sequence of flashing lights can create the impression that light is moving from one place to another. Others (Clarke 2001) explain our perception of motion in music from an embodied perspective. 41 For instance, observers can acquire both structural and expressive information from musicians’ motions (Nusseck and Wanderley 2009).

features such as sound, lighting, and contact between actors and objects. Toward the conceptual end are features such as goals and social conventions. In the middle are features such as sequential statistical structure—that is, the order in which events tend to occur. (83)

Other research indicates an interaction between knowledge structures and movement features (characteristics of the object’s movement), supporting four postulates (Zacks 2004, 983): 1. Movement features contribute to the identification of fine event segments. 2. Grouping these fine segments into larger units can be based on aspects of the activity other than movement features. Observers rely less on movement features as the grain of encoding becomes larger. 3. Inferences about actors’ intentions can affect how and to what extent movement features drive the identification of event segments. 4. Inferences about actors’ intentions can be influenced by both intrinsic features of the stimulus and by top-down information.

Sensory characteristics (e.g., movement features) contribute more to the segmentation of small units than to larger units. The extent to which an observer can infer an actors’ intention determines the influence of sensory characteristics on segmentation, and intention itself is inferred both by top-down information and by sensory input. Usually fine-level events are described with the actor’s motion path, while coarse-level events are described with the actor’s intention. As previously mentioned, intention isn’t the only determiner of course-level events: hierarchical event segmentation can result even without an overarching event schema. More change in motion results in a higher-level segment, which could then be stored as a new knowledge structure (Deliège 2006; Hard, Tversky, and Lang 2006). Even in music, knowledge structures can influence the perception of sensory characteristics and vice versa. Returning once again to music theory pedagogy, one of the main goals of an aural skills curriculum is to teach students strategies for determining the structure of a composition. Students who learn to label musical events are more likely to parse the musical surface in a way that highlights those events. According to the tenets of statistical learning, repetitions of musical patterns, even atypical patterns, guide the creation of new knowledge structures. For instance, as a listener is exposed to more instances of a particular melodic paradigm occurring at the end of a segment (as determined by movement features), the listener will began to expect the end of a segment when the melodic paradigm is heard (Eberlein and Frick 1992; Huron 2006). Segmentation therefore facilitates both learning and memory. Event

Segmentation Theory, outlined in the next section, incorporates these characteristics of event segmentation into a single cognitive model. Event Segmentation Theory

According to Kurby and Zacks (2007), “the Event Segmentation Theory (EST) proposes that perceptual systems spontaneously segment activity into events as a side effect of trying to anticipate upcoming information” (72). Predictions in this model are formed both by knowledge structures and by sensory characteristics, as discussed earlier. Because “segmentation results from the continual anticipation of future events” (77), a person can adaptively encode event structure from a continuous stream, understand the intention of an actor (hence anticipate the actor’s future actions), and select future actions in response to the ongoing event. “Correct” segmentation has distinct evolutionary advantages: being able to chunk an interval of time together as a single event saves on cognitive resources and, as seen earlier, improves comprehension. Also, being able to group events together hierarchically assists in learning and problem solving. The way we segment experience reflects the environment in which the human perceptual system developed, as stated by Kirby and Zacks (2007): None of this would be true if the structure of the world were not congenial to segmentation. If sequential dependencies were not predictable, if activity were not hierarchically organized, there would be no advantage to imposing chunking and grouping on the stream of behavior. In this regard, as in many others, human perceptual systems seem to be specialized information-processing devices that are tuned to the structure of their environment. (78)

EST posits that perceivers form a representation of the event—an event model—in working memory. These event models capture “what is happening now” and guide predictions about upcoming actions. As long as predictions are accurate, the event model is maintained, integrating the new information, but when prediction errors rise, a boundary is perceived as the event model is updated. At this moment, the system becomes more sensitive to incoming information. As a new event model is established, prediction errors fall and the system stabilizes once again. Periods of stability in this system are then perceived as single events, while periods of change create perceptual boundaries (Kurby and Zacks 2007; Zacks et al. 2007; Zacks et al. 2009).

Figure 4.1 (reproduced from Zacks et al. 2007, 274, Figure 1) is a schematic depiction of this theory. Sensory inputs include information collected by the peripheral nervous system, such as visual, auditory, and tactile information. These inputs are transformed by perceptual processing, which produces “rich multimodal representations with rich semantic content” (274). Here objects are identified, motion trajectories are determined, and intentions and goals are inferred. The ultimate goal of the processing is to make predictions about the future state of events. Event models bias processing since they “provide a stable representation of the current event” (275), and they are only open to new sensory input when they are updated at event boundaries (discussed in more detail below). While event models are “active and accessible representations” of current events, the amount of information held in these models exceeds the amount of information held in working memory. Zacks and colleagues (2007) suggest that the mental capacity of the event model is extended by efficiently using previously stored knowledge structures (275).

Figure 4.1: Schematic Depiction of the Event Segmentation Theory (Zacks et al. 2007, 274, Figure 1). The grey arrows show the flow of information while the dashed arrow represents the signal that initiates an updating of event models. Sensory input only feeds into the event models when the model is updated.

Event schemata represent the knowledge structures in this model. While they can be understood as “semantic memory representations that capture shared features of previously encountered events” (Zacks et al. 2007, 275), Hintzman’s view of schematic abstraction as

74 deriving from the summed activation of episodic traces can also be applied here (refer back to Chapter 3). No matter the perspective, these event schemata “contain previously learned information about the sequential structure of activities” (Zacks et al. 2007, 275). These knowledge structures, which represent learned statistical regularities, interact with the current representation of the event, influencing its shape. In turn, the content in the event model shapes long-term memory through a learning process. So, in terms of expectations derived from knowledge structures, when the actor achieves the perceived goal, there is a momentary rise in prediction error, since the observer cannot predict the actor’s future intentions. A similar effect was noted in the last chapter, where the event following an authentic cadence is less predictable than the goal tonic chord. The event model is updated as the perceiver discerns the actor’s next goal. These knowledge structures correspond with longer events, whereas fine segmentation is usually influenced by changes in motion. Being able to predict the movement of objects and people around us is essential to being able to interact with the world, so when an actor changes direction and speed, the perceiver has to form new predictions about where the actor will be next in order to interact effectively. There are deep-seated expectations for continuity (e.g., in music, pitches in a certain register are usually followed by notes in that same register), so when there is an unexpected disruption, the event model is updated, incorporating new sensory input in order to form a new set of expectations. Figure 4.2 (from Kurby and Zacks 2007, 73, Figure 1) illustrates a schematic depiction of segmentation process, portraying event models as relatively robust representations of the current event. This perceptual constancy allows the ongoing event to be a “single entity despite potential disruptions in sensory input such as occlusion or distraction” (Zacks et al. 2007, 274). The first panel shows that the event model accurately guides perceptual processing and predictions, therefore it is not open to new sensory input. Only when the prediction error rises does the current model become insufficient, at which point it resets and integrates new perceptual information (Kurby and Zacks 2007). Several studies have corroborated this facet of the model: observers had superior long-term memory at event boundaries, suggesting greater sensitivity to sensory information at event boundaries (Baird and Baldwin 2001; Zacks et al. 2006; Swallow, Zacks, and Abrams 2009).

The model suggested by EST may be easily assimilated into a theory of event segmentation in music, but with one important difference. As originally conceived, EST considers perceptional changes of motion and intentionality, not conceptual changes; however, the predictions made by EST can account for event segmentation in narratives, which rely on conceptual changes. In discourse comprehension, readers are able to track multiple dimensions at once. Despite changes in character, location, character goals, causal relationships, and time, readers are able to follow and understand what is going on in the text. Several researchers, including Zwaan and Radvansky (1998), have suggested that we use situation models to comprehend the action in the discourse. When there is a discontinuity in any of these dimensions (such as a change in location), the reader updates the situation model. According to Zwaan’s (1995) event-indexing model, readers monitor five independent dimensions of the situation model: time, space, protagonist, causality, and intentionality. A change in any one of these dimensions prompts an update to the corresponding index in the situation model. Because updating the model takes time, reading time increases as the number discontinuous elements increases in a narrative (Zwaan, Langston, and Graesser 1995).

Figure 4.2: Schematic Depiction of the Segmentation Process as Posited by EST (Kurby and Zacks 2007, 73, Figure 1)

Further recent research by Zacks, Speer, and Reynolds (2009) suggests that EST both supports and extends discourse comprehension theories (basically equating the event model and

76 the situation model). Because the event-indexing model addresses conceptual events, while EST focuses on live-action events, Zacks and his colleagues designed experiments to discern whether the predictions made by EST are applicable to conceptual events and whether the predictions made by the event-indexing model are applicable to live-action events. In their first two experiments, the authors presented either a set of narratives or a set of short films to two different groups of participants, who were asked to divide the stimuli into smaller events. For both groups, the event-indexing model predicted the location of participants’ boundaries, and a later study confirmed that boundaries in narratives corresponded with story elements rated by readers as less predictable. These findings indicate that both physical cues and conceptual changes enable event segmentation. Using a combination of empirical research and computational modeling, Pearce, Müllensiefen, and Wiggins (2010) illustrate that expectation, based on probabilistic learning, can also inform the segmentation of musical melodies, further speculating that it can be extended to all auditory stimuli. They hypothesize that, similar to the mechanisms of segmentation described by EST, “boundaries are perceived before events for which the unexpectedness of the outcome and the uncertainty of the prediction are high” (1375). The first principle of segmentation, “the unexpectedness of the outcome,” refers to discontinuities in the sound, roughly corresponding with Lerdahl and Jackendoff’s GPRs 2 and 3 (unexpected disruptions in the musical surface). Their results indicate that a computer model, using only probabilistic learning, can segment a melody according to their first principle in a way that mirrors the results from expert listeners. From a phenomenological perspective, this results in a retrospective marking of a boundary. The second principle, “the uncertainty of a predication,” refers to the way preexisting knowledge structures guide segmentation. Both principles are derived from statistical learning and inform listener expectation. EST provides a cognitive mechanism that describes how we segment not only visual or conceptual experience, but musical experience as well. Event Segmentation Theory and Musical Closure

Because EST is applicable both to live-action events as well as to conceptual events, EST interacts with an expectation-based model of musical closure. Considering only the auditory experience of music (setting aside visual input from the score or a performer), according to EST, boundaries are formed when the event model is updated because of an increased prediction error

77 in the music. Both sensory input from the musical surface and pre-existing knowledge structures influence the creation of the event model and the ensuing predictions. This theory has several implications for music cognition in general and for the perception of closure in particular. First, EST represents an automatic and unconscious model for segmentation; it does not require conscious attention. While listeners can focus their attention on segmenting music, it occurs spontaneously as well, as seen in brain imagining studies. For instance, Knösche et al. (2005) asked musicians to determine whether a melody they heard contained any note outside of the key while their brain waves were measured with an EEG. The authors found that between 500 and 600 ms following the end of a phrase, there was a positive wave spike (called a closure positive shift) in the electrical output of the brain structures that guide memory and attention processes.42 The location of this closure positive shift suggests increased attention following the end of a phrase, not merely resulting from the identification of phrase boundaries.43 An extension of this study examined the difference between musicians and non-musicians. Although both groups experienced a closure positive shift following the end of a tonal phrase, Neuhaus, Knösche, and Friderici (2006) note differences between the musical features that elicited this effect. This study manipulated the last chord implied by the melody (either I or V), the length of the last note, and the length of the silence between phrases. Both groups responded to all three markers, but musicians were more sensitive than non-musicians to the implied harmony. The authors speculate that musicians, who had more stylistic knowledge of closure, used top-down knowledge, while non-musicians relied more on sensory features. Event segmentation occurs on multiple time scales simultaneously, creating a hierarchical construction of the musical grouping structure. Hierarchical grouping structures are explored in detail by Lerdahl and Jackendoff (1983), and empirical work by Krumhansl (1996) supports the perceptual validity of hierarchically construed musical segments. In Krumhansl’s study, participants designated section endings on three different time scales. First, they segmented the entire first movement of Mozart’s Piano Sonata in E( Major, K. 282, followed by the first fifteen measures of the movement, and finally just the first eight measures. As the musical excerpt’s

42 This closure positive shift is similar to the positive shift found at the end of spoken phrases in language studies. 43 This might reflect the gating mechanism in EST. This cognitive control mechanism delegates more processing resources (thereby increasing sensitivity to new input) at boundaries when the event model is updated.

78 length decreased, participants were told to decrease the grain size of the segmentation, and the results indicated a high correlation between the responses for the large and small sections. Boundaries at different segmentation grains imply varying degrees of continuation and closure. EST posits that we can simultaneously hold event models on multiple time scales, which can account for the feeling of closure at the level of a phrase even while the listener expects a continuation of the piece: although a hypothetical event model is updated on the phrase level, a separate event model could continue on the level of the entire composition. Other studies specifically addressing the question of musical closure, rather than segmentation in general, usually explore the knowledge structures guiding a listener’s experience of closure. For instance, Rosner and Narmour (1992) played two pairs of chords and asked participants to rate which pair seemed more closed.44 Unsurprisingly, they found that V-I was rated as more closed than III-I, IV-I, or VI-I. Most likely due to the brief context, there was no effect for soprano scale degree and only a weak effect for inversion. Tonic is usually described as the goal of V; recall from Chapter 3 that this feeling of goal directedness is an artifact of first- order probabilities. Because a tonic chord can go just about anywhere, a listener has no strong expectations for the next event, creating a perceptional boundary. While the findings from probe-tone studies are intended to measure melodic expectancy and are usually used to support a hierarchical model of tonality, Aarden (2003) suggests that these studies really examine the perception of closure. Aarden posits that due to the nature of the design (a retrospective rating of a tone following a musical context) these studies really ask how well a particular tone would complete that musical unit, reflecting learned schema of the distribution of tones as the final note in a melody (ii-iii). From this perspective, probe-tone studies support the model of closure based on expectations formed through statistical learning. For instance, because !+is statistically more likely to conclude musical units, listeners rated !+as a better fit to end the musical context compared to the other scale degrees.

44 Rosner and Narmour described closure to their participants as the degree of conclusiveness or satisfaction of a musical ending. They also described the varying strength of closure by likening it to punctuation, “The most strongly closed progressions says that a piece has finished. This is like the words, ‘THE END,’ at the conclusion of a story. Less closed chord progressions in music act like a full stop (a period) at the end of a sentence, signaling that one thought is complete and a new one will follow. Still less closed progressions behave like semicolons and tell you that one complete thought will be followed by a closely related one. Just as a writer must use punctuation marks correctly, a composer must get his or her signs of closure right” (390).

Hierarchical knowledge structures can also influence the perception of closure. Joichi (2006) examines two related issues: (1) the perception of closure in small musical units in relation to the larger hierarchical structure and (2) the variation of a particular cue’s influence on the perception of closure among different hierarchical levels. In one study, Joichi divided binary- form excerpts into four shorter units (usually evenly dividing the binary into fourths), which were played either individually or grouped into longer contexts. The most robust finding was a positive correlation between the listener’s rating of completeness and the length of the excerpt. With a longer context, participants had more opportunity to anticipate the point at which the excerpt would conclude, especially if the longer context had a cadential arrival occurring halfway through. This cadence at the midpoint provided a fairly specific expectation for the location of the eventual ending. EST predicts that expectations for schematic knowledge structures, like the ones explored above, will influence the perception of higher hierarchic levels, while changes in surface events will dictate boundaries at lower levels. At the moment the schematic structure is completed, there is a rise in uncertainty for subsequent events, initiating an update of the event model. As discussed in the previous chapter, the more specific an expectation is for a particular ending, the greater the change in expectancy levels after that ending occurs, and this amount of change correlates with the strength of closure. Fulfillment of expectations for endings derived from knowledge structures results in the feeling of anticipatory and arrival closure. Changes in the musical surface can lead to an increase in prediction error. However, the expectation for continuity (and other similarly deep schematic expectations) is very general in nature and does not regularly lead to a feeling of finality at the end of a segment dictated solely by changes in the musical surface. In EST, a musical boundary forms when the expectation for continuity is violated; changes in sensory input initiate an updating of the event model. Inexperienced listeners rely on these surface discontinuities more than seasoned musicians do because they have not formed the knowledge structures necessary to segment their experience. Nevertheless, for all listeners, a greater change in the musical surface will result in the creation of a higher-level boundary. Retrospective closure is associated with changes in the continuity of sound.

Experiment Overview

To explore the association between segmentation and expectation in the perception of musical closure, I conducted a series of studies designed to test three main hypotheses of EST: (1) musical experience is segmented unconsciously, hierarchically, and consistently among subjects; (2) stylistic knowledge in the form of learned musical schemata influences a listener’s perception of closure; and (3) boundaries are formed at moments of transient increases in prediction error.

Experiment 1

Earlier empirical research has shown that listeners segment music consistently and hierarchically (Deliège 1989; Krumhansl 1996). The purpose of this experiment is to replicate these findings using the same methodology outlined in Zacks, Speer, and Reynolds (2009). Listeners will be asked to indicate the end of both fine- and coarse-grained segments while listening to string quartet movements by either Mozart or Bartók. In accordance with past research, I hypothesize that listeners will segment the musical stream consistently and hierarchically. This study will also examine correlations between a set of musical features and perceived boundaries. Along with correlations between the musical surface and event boundaries, I will also see whether factors such as musical expertise or the order in which tasks are completed apparently influence listeners’ perception of event boundaries. For instance, perhaps it is easier to make decisions about larger boundaries after hearing the movement in its entirety, or musicians might indicate boundaries at larger formal units more consistently than do non- musicians. Participants more familiar with Bartók’s music, and with twentieth-century music in general, might mark boundaries more consistently. While this study does not directly ask about closure, it does establish where listeners perceive boundaries, and it may lend support for applying EST to music.

Experiment 2

The perception of closure is contingent on a listener’s musical expectations, especially those that anticipate the completion of a musical schema. As explored in previous chapters, these expectations are formed through musical experiences. Event Segmentation Theory supports a

81 developmental story for the formation of these knowledge structures and how they can influence an individual’s perception of closure. When confronted with a new style, a listener relies on changes in the musical surface to segment the composition into smaller events, with bigger changes resulting in a higher hierarchical boundary. With repeated exposure to the style, statistical regularities allow the listener to develop expectations for how various hierarchical levels of the piece should unfold in this style. When events include stylized signs of endings, a listener becomes able to predict that an ending is about to occur. This study will test the hypothesis that learned stylistic cues influence our perception of closure. This study is in two parts. First, participants will listen to string quartet music during a twelve-minute exposure period and will mark endings within each excerpt by pressing a key- combination on the computer. Participants will be randomly assigned to one of two conditions: one group will listen to excerpts by Bartók and the other group will listen to excerpts by Mozart. In the second part of the study, participants will rate the degree of closure for two blocks of short excerpts, one drawn from the Bartók quartet and the other from the Mozart quartet. I expect that ratings for cadential paradigms in the Mozart excerpts will be higher than those for the Bartók excerpts, based on a presumed greater listener familiarity with Mozart’s style. While I do not expect a strong effect, I hope to see that participants exposed to as little as twelve minutes of Bartók’s music will interpret closure in these works differently from the group of participants who initially listened to Mozart. Even though studies have shown that participants pick up on statistical regularities in auditory stimuli rather quickly, this study may not produce robust differences between the conditions because it asks a slightly different question. Other statistical learning studies ask whether a series of sounds form a grammatical entity based on an exposure period. However, all of the testing excerpts in this task are grammatical entities in the style they represent, and participants instead must make an interpretive judgment regarding the suitability of an excerpt to end a musical unit in that style.

Experiment 3

The first two experiments examine two facets of EST: the segmentation of music and the influence of learned musical schemata on the perception of closure. This experiment seeks to support the theoretical claim that the perception of closure stems from being able to predict the moment of the completion for a schematic unit, followed by a transient increase in prediction

82 error. In their examination of the segmentation of narratives, Zacks, Speer, and Reynolds (2009) found that boundaries tended to occur when the activity in the narrative was rated as less predictable. However, subjective ratings predictably did not account for all of the event boundaries, especially those formed through a change in character, so the authors suggested the need for a more objective measure of prediction performance (323–324). In this study, instead of asking participants retrospectively to rate the predictability of a musical segment, I will ask participants to predict the moment at which a musical unit will conclude. I will then correlate these results with the listener’s perceived degree of closure. Participants in this study will include both musicians and non-musicians, and all musical excerpts will come from minuet movements of three Mozart string quartets (K. 156, K. 168, and K. 173). After the prediction task, participants will hear excerpts from the same minuets in one of two conditions: either in the order in which they occur in the movement or in a random order. Participants will rate each excerpt’s strength of closure on a seven-point scale. Participants in the ordered condition will see a schematic representation of the movement to help locate each excerpt within the movement. In the prediction task, I expect that musicians, who probably are more familiar with Mozart’s compositional style, will be more successful than non-musicians at predicting phrase endings. Since the minuets used for this study are all in binary form, participants will hear each section of the movement at least twice, so I anticipate that all participants will make more accurate predictions the second time through each section. Further, the predictability of a musical unit’s conclusion may vary with the type of musical ending; for instance, a PAC may be more predictable than a HC. According to EST, endings that are better predicted should correlate with a higher rating of closure. Also with the data from the rating task, I will look for a main effect for condition (ordered vs. unordered excerpts), which might reveal that formal hierarchy can influence the perception of closure. If ratings for the same excerpt vary widely between participants in different conditions, my results might indicate that a schematic understanding of form contributes to the sense of musical closure. As previously discussed, the strength of closure informs the hierarchy of a composition; however, this study may instead demonstrate that

83 schematic knowledge of formal structures affects the listener’s perception of the strength of closure.

CHAPTER 5

EXPERIMENT 1

This first study does not explicitly examine a listener’s perception of closure; rather, it addresses what I consider a prerequisite to this larger issue by looking only at segmentation. Event Segmentation Theory (EST), as discussed in Chapter 4, provides a model for the perception of closure that is compatible with previous research in musical expectation and segmentation. Experiments 1a and 1b only consider segmentation, to see whether listeners segment music in a manner consistent with this theory. To test this, I adopted an experimental paradigm previously used in studies to support EST. The design for Experiment 1 is based on the segmentation task used in Zacks, Speer, and Reynolds (2009), in which participants either read or listened to several narratives detailing the everyday activities of a seven-year-old boy and were asked to divide the continuous narrative, identifying points at which “one meaningful unit of activity ended and another began” (309). Each participant read or heard every narrative twice, once to indicate the largest unit of meaningful activity (coarse segmentation) and once to indicate the smallest unit of meaningful activity (fine segmentation).45 The results indicated that participants segment narratives hierarchically—with smaller units nested within larger units—and that conceptual changes in the narratives can predict the presence of a boundary. In the terms of EST, the event model updates at a conceptual change (like a change in temporal or spatial location), since change is less predictable than continuity, and at the end of an event defined by pre-existing event models. In my study, participants segmented two complete string quartet movements using a similar segmentation task. In Experiment 1a, participants segmented two movements by Béla Bartók, and in Experiment 1b, participants segmented two movements by Wolfgang Amadeus Mozart. Consistent with Zacks, Speer, and Reynolds, I hypothesize that listeners will segment the music hierarchically and that their segmentation will consistently correlate with various musical features falling into two broad categories: arrival features, marking the end of a musical segment; and change features, epitomized by Lerdahl and Jackendoff’s Grouping Preference

45 The order of tasks was counterbalanced between subjects.

Rules (GPRs) 2 and 3. Further, based on the literature examined in Chapter 4, I predict an increased response time for the coarse-grained segmentation task compared to the fine-grained task and that these higher-level boundaries will correlate with an increased number of change features. Method

Participants

In both studies, participants were divided into three groups based on their musical expertise: non-musicians, first-year undergraduate music majors, and graduate/professional musicians. There were 32 participants in Experiment 1a (14 non-musicians, 9 undergraduate musicians, 9 graduate musicians) and 33 participants in Experiment 1b (14 non-musicians, 10 undergraduate musicians, 9 graduate musicians).

Stimuli

Two sets of stimuli were used in this study, one from twentieth-century non-tonal practice and the other from the common-practice tonal idiom. In Experiment 1a, participants listened to the third and fifth movements from Béla Bartók’s String Quartet No. 4; in Experiment 1b, participants listened to the fourth movement from Wolfgang Amadeus Mozart’s String Quartet No. 19 in C major (K. 465) and the second movement from Mozart’s String Quartet No. 21 in D major (K. 575). Mozart’s music unquestionably exemplifies the common-practice style, whereas Bartók’s music represents just one of many twentieth-century styles. Bartók’s style tends to be relatively accessible to listeners unfamiliar or uncomfortable with non-tonal music because he incorporates phrase lengths and formal divisions familiar from the common-practice repertoire, and he usually provides a metrical framework. His String Quartet No. 4 particularly epitomizes these stylistic characteristics. One inherent difficulty in using pre-composed pieces of music in an experiment is that many elements of the stimuli cannot be controlled. For instance, given the experiment’s reliance on existing recordings, the exact length of the movement and tempo could not easily be manipulated. To compensate, I used strict selection criteria. First, I wanted to use a genre and instrumental group that is well established in both the common-practice and twentieth-century repertoires, a criterion met by the string quartet. I only considered short string quartet movements

(lasting under five minutes) that included both a clearly distinguishable melody and also a strongly articulated formal structure that could be divided into smaller phrases. Finally, I wanted to include one fast movement and one slow movement in each study, so I specifically sought fast and slow movements for both composers. Bartók has the smaller repertoire (six string quartets compared with Mozart’s twenty- three), so I began by selecting two movements by Bartók that fit my criteria before turning to Mozart’s repertoire to find suitable pairs. Bartók’s slow third movement from his fourth string quartet has characteristics of a theme and variation movement, which is then organized into a larger ternary form. This movement significantly features the cello, which plays the opening theme and subsequent variations, accompanied by sustained chords in the upper strings for the first 34 measures. The matching Mozart movement (String Quartet 21, second movement) also has a clear ternary construction and extensively features the cello (especially in mm. 38–50). To match the sonata-like thematic construction of the fifth movement from Bartók’s fourth quartet, I used the last movement of Mozart’s Quartet No. 19 (the “Dissonance” Quartet), which is in sonata form.46 Although the two movements have vastly different characters, both conclude longer works, suggesting that their respective composers considered their degree of finality appropriately strong for the conclusion of a significant work. Presumably to enhance its degree of closure, the last movement of Bartók’s string quartet harkens back to the first movement, repeating its ending gesture at a much slower tempo. The last movement of Mozart’s “Dissonance” Quartet features an extensive coda, ending with a recurring motive from the secondary tonal area (STA). Even though the Mozart movements are not from the same quartet, the two movements chosen are still suitable companions because both were written later in Mozart’s life (No. 19 was composed in 1785 and No. 21 in 1789). Table 5.1 outlines the basic characteristics of each movement. Along with these four movements, I selected two shorter excerpts for practice before data collection. Participants in Experiment 1a listened to another excerpt from Bartók’s fourth string quartet, the first 49 measures of the first movement (lasting 1:43) as performed by the Emerson String Quartet; participants in Experiment 1b listened to the third movement of Mozart’s String Quartet No. 2 (K. 155) as performed by the Amadeus String Quartet. Both excerpts introduced

46 In order not to exceed the five-minute time limit, I chose a recording that did not repeat the exposition.

87 participants to the style of music used in the study and exemplified the grouping of phrases into clearly differentiated sections.

Table 5.1: Musical Stimuli Characteristics for Experiments 1a and 1b Bartók, No. 4, Bartók, No. 4, Mozart, No. 19, Mozart, No. 21, mvmt 3 mvmt 5 mvmt 4 mvmt 2 Experiment 1a 1a 1b 1b Tempo marking Non troppo lento Allegro molto Allegro Andante Time (in m:ss) 5:12 5:05 5:22 4:01 Performers47 Emerson String Emerson String Emerson String Amadeus String Quartet Quartet Quartet Quartet Number of Measures 71 392 419 73 Meter 4/4 2/4 2/4 3/4

Coding Procedure

The most practical way to accommodate variations in subject response time was to examine only responses made in predetermined time “windows” in each movement.48 I analyzed each movement and created two types of windows: Type 1 Windows, coinciding with a meaningful arrival feature, and Type 2 Windows, determined by changes in the musical surface. Listeners were free to indicate endings at any point, and I do not mean to suggest that these windows are the only correct places to respond. The windows occur in locations that I thought were likely dividing points because of their musical features, allowing me to explore how a set of chosen features predicts listener responses resulting in a simplification of the data analysis. Type 1 Windows begin with the onset of the beat containing the last note of a segment and continue on until the beginning of the next musical segment, whether it is a section, phrase, or subphrase. It would have been interesting to see if participants responded immediately to the end of a formal unit or if they instead waited until the beginning of the next formal unit to make a decision, but because I was unable to determine the length of time between the listener’s

47 The Bartók recordings are performed by the Emerson String Quartet on the CD Bartók: The String Quartet (1988). Mozart’s String Quartet No. 19 is also performed by the Emerson String Quartet in their 2005 album Mozart String Quartets K. 465 “Dissonance”, 458 “The Hunt” & 421. Unfortunately, the Emerson Quartet did not record the slow movement from Mozart’s String Quartet No. 21, so the recording used here was performed by the Amadeus String Quartet in their 1988 recording Mozart: The String Quartets. 48 Alternatively, I could have followed Krumhansl (1996), who smoothed out responses over a two-beat window in her data analysis of a similar data set. Because I am examining more features than Krumhansl and I am not working from a MIDI source, using predetermined windows is a better option.

88 perception of an ending and his/her subsequent response, I included both the ending and subsequent beginning in a single window. Type 2 Windows do not correspond with an ending, but instead occur at some sort of change in the musical surface as defined by the “change features” described below. I created these windows to begin with the onset of the beat before the change occurs and to continue on for one to five beats, depending on the tempo (some windows are shorter to avoid overlapping with another window). Window beginnings always coincide with the beginning of the beat, even when the last melodic note of the phrase begins off the beat (for instance, when Mozart includes a suspension). Because listeners might conceivably respond to the harmonic arrival as opposed to the melodic resolution, Type 1 Windows begin at the initiation of the goal harmony. When the melody is presented in canon, listeners might respond to the melodic ending in the leading voice, so in these cases the window begins with the last note of the leading voice. In all such cases, the imitation was temporally close, and the ending of the following voice fell within the same window. Windows exist in various sizes, both within a movement and between movements. Table 5.2 presents the number of windows found in each piece as well as the average duration of these windows (measured both in seconds and in beats). This variation in window length will not affect the data analysis. While the windows are useful for identifying which features are present, they are also useful for determining the extent to which the data is hierarchically constructed, as well as for measuring the consistency of the responses between listenings.

Table 5.2: Window Construction in Each Movement Average number of beats Average duration of Movement Number of windows in each window* windows (high/low) (high/low) Bartók 3 43 3.53 s (13.7 s / 1.39 s) 2.77 beats (10 / 2) Bartók 5 94 1.87 s (5.2 s / .69 s) 4.76 beats (12 / 2) Mozart 19 77 1.61 s (3.11 s / .60 s) 4.01 beats (7 / 2) Mozart 21 40 2.73 s (5.14 s / .92 s) 2.65 beats (5 / 1) *not including the last window in each movement, which lasted until all the sound faded out

From these movements, I chose a set of musical features that could influence listener segmentation and catalogued the presence of these features in each window. There are two categories of features: features that define musical endings (arrival features) and features 89 corresponding to a change in the musical surface (change features). Each composer has a different set of features, defined in Tables 5.3 and 5.4.49 Once defined, most of the musical features can simply be catalogued from the music, but some rely on analytic interpretation.

Table 5.3: Arrival and Change Features in Bartók Arrival Intervallic Direction Descent; Ascent: Melodic line has at least a two-note descending or Features ascending figure Intervallic Approach -1/-2; -3/-4; -5/-7; +1/+2: The distance in semitones to the final melodic pitch of a segment measured from the previous melodic pitch Duration Change Compared to the preceding melodic sound, the last note of the segment is longer or shorter Cadences Falling fourth (4th); Falling third (3rd); Low-high Chord (LH); Single Chord (1); Double Chord (2): Defined by common ending gestures in these two movements50 Change Silence Complete Silence; Melodic Silence; Non-Melodic Silence: Silence Features in the entire texture, just the melody, or in at least one non-melodic instrument Orchestration New Instrument; New Melodic Instrument: A new instrument Changes joins the texture or a new instrument performs the melody Other Changes Register Change: The melodic line leaps up or down an octave Dynamic Change: The melody is performed louder or softer Ostinato Change: The underlying ostinato changes in pitch content or rhythmic figuration

Most of the arrival features are pitch-centered structural features: the approach to the last melodic note, the scale-degree of the last melodic note and its harmonic support (Mozart only), and the presence of a cadential paradigm (defined by the repertoire). Duration change is included in this category (as opposed to the change features) because a change in duration can punctuate the end of a segment (so called “durational closure”).51 As stated in Chapter 3, listeners have learned though previous experience with music which specific features define the end of a musical unit, and when an expectation for an ending gesture is fulfilled, the listener experiences anticipatory or arrival closure. While this study does not explicitly ask about closure, an expectation-based view of closure would suggest that listeners more familiar with a particular

49 These lists do not represent an exhaustive list of features that could influence the responses to a musical segmentation task. 50 The labels in the parenthesis are the labels used throughout this chapter to designate specific cadential gestures in the Bartók. See the discussion regarding Examples 5.4–5.10 for more detail about these cadences. 51 See Narmour (1990) and Joichi (2006).

90 repertoire, or even the typical cadential gestures of a style, will consistently respond to these features. These end-defining features roughly correspond with a “goal,” such as !, the tonic triad, or the conclusion of a cadential gesture. EST predicts that our understanding of goals and intentions helps us segment life experience on a coarser grain. Musical “goals,” which are merely a metaphor resulting from a misattribution of the positive emotions experienced when a listener makes a correct prediction, still have perceptual salience.52 Since determining the “goal” of a musical unit is highly subjective, especially in the Bartók movements, which do not conform to a widely shared syntax, these end-defining features as a group do not necessarily signify goals, but a listener could interpret some of them as goals.

Table 5.4: Arrival and Change Features in Mozart Arrival Scale-Degree !;+#;+%; and+"+or+': scale-degree of the last melodic note of the Features musical segment as defined by the local tonal context Harmony/Harmonic I; V; V7: Last harmony of a musical segment as defined by the local Progression tonal context V-I; x-V: Motion into the last harmony of a musical segment as defined by the local tonal context Intervallic Direction Descent; Ascent: Melodic line has at least a two-note descending or ascending Figure into the final note of a segment Leading Tone Ascent to Tonic Steps/Embellished Step Descent; Step Ascent: Melodic line has three or more notes Steps descending or ascending by diatonic step Embellished Step Descent; Embellished Step Ascent: Melodic line has three or more notes descending or ascending by diatonic step with surface embellishment Duration Change Compared to the preceding melodic sound, the last note of the segment is longer or shorter Cadences PAC; IAC; HC; Evaded Cadence: Defined by tonal cadential paradigms. Change Silence Complete Silence; Melodic Silence; Non- Melodic Silence: Silence Features in the entire texture, just the melody, or in at least one non-melodic instrument Orchestration New Instrument; New Melodic Instrument: A new instrument Changes joins the texture or a new instrument performs the melody Other Changes Register Change: The melodic line leaps up or down an octave Dynamic Change: The melody is performed louder or softer

52 As explored in Chapter 3, Huron (2006) suggests that the feeling of finality or repose associated with closure is an artifact of correctly anticipated endings. These expectations result from learned transitional (first-order) probabilities.

In both Mozart movements, the local tonal area (not the overall key of the movement) determines scale-degree designations and harmonic and cadential labels. For instance, in the exposition from the C-major “Dissonance” Quartet, the STA turns from G Major (V) to tonicize E(+Major ((VI in the context of G major)—see Example 5.1. Even though there is no cadence in E(, the I-V-I progression in that key clearly implies E( as a local tonic in this short passage. Therefore, the melodic G4 that ends the opening subphrase of the longer phrase is interpreted as #.

Example 5.1: Mozart, String Quartet No. 19, fourth movement, mm. 89–93 The Type 1 Window is annotated on the score with a solid box

In both the Mozart and the Bartók analysis, the directional approach into the last melodic note of a musical unit is easily catalogued from the musical surface—either a descent or ascent. In the case of Example 5.1, there is a melodic descent into # from the preceding B(. Specific ordered pitch intervals in the Bartók movements are also determined from the musical surface. These particular intervals were chosen because of their prevalence at endings in both movements and roughly correspond to a downward leap, a smaller downward skip, and a stepwise ascent or descent. Step progressions in the Mozart analysis only consider a surface stepwise ascent or descent, but often a mid-range step progression is decorated with embellishing tones. After removing these tones, if the resulting melodic line moves three diatonic steps up or down in its approach to the last note of a musical segment, then it is classified as an embellished step progression. The two annotated examples below show cadential arrivals from the fourth movement of Mozart’s String Quartet No. 19. Example 5.2 (mm. 67–70) shows an approach to a

PAC in G major, which arrives on the downbeat of m. 69. The annotations highlight members of the underlying step-progression (which is embellished by a series of escape tones) by circling notes involved in the stepwise descent. The final note of the phrase is approached from above, but does not appear to include three diatonic steps leading to the cadence until a layer of embellishment is removed, so this phrase ending only has a melodic descent and an embellished step descent. In addition to both of those features, Example 5.3 (mm. 76–78) also has a stepwise descent as the sixteenth notes cascade down to the cadential G4 in the first beat in m. 77. In this case, the embellished descent connects the B4 and A4 in m. 76 with the final G4 of the phrase.

Example 5.2: Mozart, String Quartet No. 19, fourth movement, mm. 67–70 The Type 1 Window is annotated on the score with a solid box.

Example 5.3: Mozart, String Quartet No. 19, fourth movement, mm. 76–78 The Type 1 Window is annotated on the score with a solid box.

Cadential gestures vary between repertoires. In the Mozart movements, cadences are defined by standard harmonic and melodic paradigms. A perfect authentic cadence (PAC) is narrowly defined as a root-position V-I progression ending with ! in the melody, which is 93 contrasted with the more broadly defined imperfect authentic cadence (IAC)—a cadential V-I progression in which either chord (or both chords) may not be in root position or, more likely, the melody does not conclude on !. A half cadence (HC) ends a formal unit with a V chord. An evaded cadence is not technically a cadence; rather, it is the denial of cadential expectation. Here this term encompasses both the deceptive cadence (typically a V-vi progression) and a weakened authentic cadence. An evaded PAC is illustrated in Example 5.4, where Mozart denies a perfect authentic arrival in m.16. Instead of landing conclusively on a root-position tonic harmony, the bass voice slips to a I6 chord, the cello revisits the melody from mm. 13–14, and the top voice takes up an accompanimental texture. The cadential expectation set up by the dominant chord in m. 15 is finally resolved in m. 19.

15 19

Example 5.4: Mozart, String Quartet No. 21, second movement, mm. 15–20 The Type 1 Windows are annotated on the score with a solid box. The Type 2 Windows are annotated on the score with a dashed box.

To clarify, the presence of these harmonic and melodic paradigms does not necessarily signify a cadence. I agree with Caplin’s 2004 definition of cadence in the Classical style, which describes cadence as a syntactic ending to mid-level formal units. In Caplin’s words, “a cadence must end something” (56), and that something is usually a phrase. However, the moment of cadential articulation may or may not coincide with the conclusion of a phrase, an issue explored in more detail below. The cadential gestures in the Bartók movements are not representative of a wider twentieth-century style or even of cadences in Bartók’s own oeuvre. So, in this context, a cadence is a movement-specific gesture that concludes a mid-level formal unit. In the third

94 movement, a descending fourth gesture concludes many of the variations. This melodic Figure is usually presented with a long-short durational pattern; see m. 21 in Example 5.5 (the phrase ends on the third beat of m. 21). A lesser-used cadence in this movement is a descending minor third (illustrated in Example 5.6), which is used extensively in the fifth movement (Example 5.7). Also in the fifth movement, Bartók uses a multi-voiced chord in all the instruments as a concluding gesture, and this assumes several guises throughout the movement. At times it is presented as a single chord, as in the cadential arrival in m. 332 (Example 5.8). More often, a held lower note precedes the single chord. This lower note is usually presented in unison, for instance in mm. 280–281 (not serving a cadential function in this passage), but it also takes other forms like in m. 75 (see Examples 5.9 and 5.10). Another variation of this cadential type is articulating the chord twice following a long held note (mm. 283–284, also in Example 5.10).

String Quartet No. 4 by Béla Bartók © Copyright 1929 by Boosey & Hawkes, Inc. Copyright Renewed. Reprinted by Permission. Example 5.5: Bartók, String Quartet No. 4, third movement, mm. 20–23 (Falling fourth — 4th) The Type 1 Window is annotated on the score with a solid box. The Type 2 Windows are annotated on the score with a dashed box.

String Quartet No. 4 by Béla Bartók © Copyright 1929 by Boosey & Hawkes, Inc. Copyright Renewed. Reprinted by Permission Example 5.6: Bartók, String Quartet No. 4, third movement, mm. 40–41 (Falling third — 3rd) The Type 1 Window is annotated on the score with a solid box. The Type 2 Windows are annotated on the score with a dashed box.

235 237

String Quartet No. 4 by Béla Bartók © Copyright 1929 by Boosey & Hawkes, Inc. Copyright Renewed. Reprinted by Permission Example 5.7: Bartók, String Quartet No. 4, fifth movement, mm. 235–239 (Falling third — 3rd) The Type 1 Window is annotated on the score with a solid box.

330

String Quartet No. 4 by Béla Bartók © Copyright 1929 by Boosey & Hawkes, Inc. Copyright Renewed. Reprinted by Permission Example 5.8: Bartók, String Quartet No. 4, fifth movement, mm. 330–332 (Single chord — 1) The Type 1 Window is annotated on the score with a solid box.

String Quartet No. 4 by Béla Bartók © Copyright 1929 by Boosey & Hawkes, Inc. Copyright Renewed. Reprinted by Permission Example 5.9: Bartók, String Quartet No. 4, fifth movement, mm. 74–76 Single chord preceded by lower dyad — LH-1 The Type 1 Window is annotated on the score with a solid box.

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String Quartet No. 4 by Béla Bartók © Copyright 1929 by Boosey & Hawkes, Inc. Copyright Renewed. Reprinted by Permission Example 5.10: Bartók, String Quartet No. 4, fifth movement, mm. 279–284 Single chord preceded by single pitch class — LH-1 (not a cadence here); Double chord preceded by single pitch class — LH-2 The Type 1 Window is annotated on the score with a solid box. The Type 2 Window is annotated on the score with a dashed box.

For duration changes, the notated rhythmic value of the last note of a segment had to be longer or shorter than the note immediately preceding it. A similar procedure was used to determine a change in register or dynamics, where the feature is present if there is a notated octave leap or change in dynamics. For practical reasons I did not interpret either feature, determining both through a score-based analysis. Although the leap to the F* following the cadence in Example 5.3 lands on an embellishing tone that resolves upward to the G, it is not interpreted as a register change because on the surface of the music it is a major seventh leap, not an octave leap. Dynamic change was determined through a score-based analysis, only relying on the composer’s written directions for dynamics, which the performers conveyed faithfully. While there are varying degrees of change for all three features, I decided to treat them as binary features, indicating only whether such a change was present. The last two features, register and dynamic change, usually don’t correspond to a musical ending; instead, they belong to the second category of features—ones that contribute to an acoustic change. Along with register and dynamic change, the other features (silence, texture change, and orchestration change) indicate some change in the musical surface and can possibly elicit 98 retrospective closure by indicating a new beginning or the space between an ending and a subsequent new beginning. Even though listeners were instructed in this study to indicate musical endings, they might not realize an ending had occurred prior to the onset of a new beginning. EST, and more specifically the segmentation study by Zacks, Speer, and Reynolds (2009), suggests than an increased number of changes in a stimulus will correlate with an increased likelihood of segmentation, especially on a coarser grain of segmentation. The absence of sound is one of these acoustic changes that could influence the segmentation task. I distinguish complete silence from melodic silence and from non-melodic silence, although certainly these categories are interrelated. Both melodic and non-melodic silence occur in moments of complete silence, so I reserve these terms for instances in which not all instruments are silent. Referring back to Examples 5.2 and 5.5, complete silence occurs immediately following the cadence (the black line in the Bartók example indicates a caesura), while only melodic silence occurs after the PAC in Example 5.4. Melodic silence can occur simultaneously with non-melodic silence, though. Following the PACs in Examples 5.3 and 5.4, at least one non-melodic instrument temporarily drops out, thinning the texture. In contrast to silence, the addition of an instrument thickens the texture. This change can coincide with a change in orchestration, where the new instrument becomes a melodic force (as in Example 5.4, m. 16). For each window, I recorded whether a particular feature was present. Arrival features always occur at the beginning of a window coinciding with the last note of a musical segment (Type 1 Window) or the last note before a change (Type 2 Window). Change features occur later in the window; in a Type 1 Window they follow the ending and coincide with the new beginning, while they occur before the second beat is completed in a Type 2 Window. The presence of a musical ending was determined through my own analysis, which reflects a more complex interaction between the various arrival features (going beyond merely cataloguing their presence), and my analysis also represents a possible well-formed hierarchal grouping structure for each movement. I analyzed each movement for the location of subphrase, phrase, and section endings, which determined the placement of Type 1 Windows.53 Since I am admittedly bringing my own musical experience and bias into this study, I will briefly outline

53 The presence of these formal endings was also coded with the other features.

99 how I created a three-level grouping structure, by determining the end of subphrases, phrases, and sections for each movement. Because I decided that all grouping structures must be well-formed, as defined by Lerdahl and Jackendoff (1983), and I was working with a limited vocabulary for data analysis purposes, some of my analytic designations use these terms—especially “subphrase”—in non- traditional ways.54 While the hierarchical relationships between sections, phrases, and subphrases remain constant between composers, some of the defining features of these units vary. Also, determining the type of hierarchical ending represents my own analytic interpretations (even more so than evaluating the features already mentioned), and does not represent an objective measure of the phrase structure. For the Mozart compositions, my definition of a “phrase” conforms to current analytic understanding of this term: a formal musical unit consisting of a beginning, middle, and end, most of the time concluding with a cadential gesture. Following Caplin (2004), who disentangles phrases and cadences (allowing for phrases to exist without cadential punctuation), a phrase is not necessarily completed immediately following a cadential gesture, for a phrase also encompasses any phrase extensions that follow the cadence. I use “subphrase” to describe formal units smaller than a phrase, and in order to have a well-formed hierarchical analysis, a phrase must be divided into subphrases either completely or not at all. I use this designation for both parts of the presentation as well as for the continuation of a sentential formal structure, for legs in a sequence, for the material between the cadential arrival and the end of a phrase (i.e., an external phrase extension), and for introductory material preceding the beginning of a phrase (i.e., a prefix), although the “subphrase” label might not be completely apt in every case. While I could have expanded my analytic vocabulary, acknowledging each feature individually, grouping these features together under “subphrase” simplifies the data analysis. A “section” describes formal units larger than a phrase. Not every unit larger than a phrase received the designation of a section; instead, sections unite areas of the movement that share the same formal function, the same key, and related melodic ideas. Formal designations in Bartók are more open to interpretation since there is not a widely agreed upon definition of “phrase” in this repertoire. Given that cadential arrival, as narrowly

54 A list of Lerdahl and Jackendoff’s well-formedness rules can be found in Chapter 4, Table 4.1.

100 understood from common-practice style, is absent, I decided to analyze these works using a top- down approach, starting with large sections. I first divided each movement into large sections, grouping together music that is thematically related, shares the same pitch-collection, and implies the same formal function. I then divided the sections into phrases, units that seemed to have a beginning, middle, and end. In many cases these units ended with a shared musical gesture that could arguably be described as “cadential” because of its prevalence at endings. Finally, if there seemed to be any internal divisions in the phrase, I then further divided the phrases into subphrases. Like in the Mozart analysis, “subphrase” was also used to describe music that functions as a prefix or suffix.

Participant Procedure

After giving informed consent, participants were assigned to one of two conditions, which determined the starting task. In order to differentiate between the coarse and fine segmentation tasks while avoiding unfamiliar technical vocabulary, I described the tasks to all participants using a linguistic analogy. The directions stated: In language, sentences group together to form paragraphs. The same is true in music, where smaller sentence-like phrases are combined to form larger paragraph-like sections. In this task, you will hear the same piece of music four times. The first time, you will press the SPACEBAR every time you hear the end of a PARAGRAPH-LIKE SECTION. Because you may change your mind about the location of the boundaries, you will repeat this activity in the second listening. In the third and fourth listenings, you will indicate the end of sentence-like phrases.55

After the participants read the instructions and were given the opportunity to ask questions, they began with a practice task on a short excerpt before segmenting the actual stimuli. Participants in Experiment 1a listened to the first 49 measures of the first movement of Bartók’s String Quartet No. 4, and participants in Experiment 1b listened to the third movement of Mozart’s String Quartet No. 2 (K. 155). The first time through, they performed the segmentation task as dictated by their condition. If participants performed the task in a manner that demonstrated understanding of the instructions (designating between 8 and 15 fine divisions or between 3 and 7 coarse divisions) they continued on to segment the practice excerpt again using the other grain of division. Subjects who did not achieve the needed number of responses

55 This order was changed in the other condition.

101 received feedback and additional instruction before performing the same segmentation task again. After the minimum requirements were met in both tasks, subjects were given the opportunity to ask any additional questions before moving on to the actual test. While listening to the entire movement, participants in the coarse segmentation condition first indicated event boundaries delineating groups of phrases and formal sections, while participants in the fine segmentation group first indicated boundaries for shorter events, such as a phrase or subphrase. Because segmenting music in real time could be a difficult task, the participants immediately repeated the task before switching conditions and performing the other task on the same movement. Thus, all participants listened to each movement four times, performing both the coarse and fine segmentation tasks twice on each movement. Everyone listened to both movements through headphones and indicated event boundaries by pressing the space bar on a computer, which recorded the times for these key presses. Participants in Experiment 1a listened to the third and fifth movements of Bartók’s String Quartet No. 4, while participants in Experiment 1b listened to the fourth movement of Mozart’s String Quartet No. 19 (K. 465) and the second movement of Mozart’s String Quartet No. 21 (K. 575).56 Following this task, participants completed a questionnaire documenting musical experience and familiarity with the compositions. Results

Each subject had four trials with each movement, which I will identify as Fine 1, Fine 2, Coarse 1, and Coarse 2 (the number indicates whether it was the first or second time the participant performed that particular segmentation task on the given movement). Since there is no limit to the number of responses an individual could make, nor can I reliably determine listener response time (i.e., the time between a given feature and the key press), the data analysis only examines presses that occurred within the predetermined windows. The dependent variable is a binary variable indicating whether the participant responded within a particular window (scored as 1) or not (scored as 0). I used two different types of mixed models regressions in this analysis section. Both regression types take into account the fact that individual participants may respond differently

56 The order in which the movements were heard was counterbalanced between participants.

102 during the task and allow for the assessment of variables such as whether the participant was a musician or a graduate student, along with the start tempo (fast or slow) and start segmentation (fine or coarse) for each participant. Most analyses used a mixed logit model (i.e., a mixed- models logistic regression) to analyze the binary response variable. This regression is used to predict the odds of a participant responding to a feature of the stimulus (or any other independent variable), and this information is conveyed by the odds ratio (OR) value. Odds ratios of 1.0 indicate that the odds of a response are as likely when a specific feature or variable is present as when it is not. Odds ratios greater than 1.0 indicate that the odds of a response increase when the feature is present, while odds ratios less than 1.0 indicate that the odds of a response decrease when the feature is present. While odds ratios can’t be less than zero, there is no upper bound for these ratios. The other type of mixed models regression was used to analyze continuous dependent variables, such as response time. This regression does not produce an odds ratio, but rather a series of coefficients showing the weight of each variable on the outcome as predicted by the regression equation. For this study, only results significant at p < 0.05 could be included in the results; indeed, most of the discussion will highlight results significant at p < 0.02 to avoid over-interpreting spurious results. Analysis of interactions will focus on the apparent influence of musical training (specifically, whether the subjects were non-music majors, music majors, or post-graduate musicians). For interactions significant at p < 0.02, I ran an ANOVA to determine the direction of the interaction. In these interactions, I usually compare two groups of participants, one with a higher level of musical training to one with a lower level of training. When I compare musicians to non-musicians, the “musicians” group includes both graduate and undergraduate musicians, but when I compare graduates to undergraduates, the undergraduate group includes both the undergraduate musicians and the non-musicians (all of whom were undergraduates). I labeled the ANOVA tables throughout the chapter with the headings “Less Musical Training” and “More Musical Training” to distinguish between these types of groups. I interpreted the direction of the interaction by comparing the change between the means for instances when a particular feature is present and instances when it is not for each subject group. For each composer, I examine how well the Fine 1 and Coarse 1 conditions predict the Fine 2 and Coarse 2 responses respectively (i.e., within-subject consistency) and how well the

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Coarse 1 and Coarse 2 responses predict the Fine 1 and Fine 2 responses (i.e., nested lower levels). For each composer, I also observe the influence of tempo and segmentation task on latency (i.e., the delay between the beginning of a window and the subject’s response). Then, for each individual movement, I use a series of mixed logit regressions to explore how well the coded arrival features, change features, and formal endings outlined earlier in this chapter predict the responses. These data cannot conclusively indicate whether subjects are responding to these musical features; rather, they represent the probability of a response given the presence of a set of features.

General Results

To get an overall picture of the responses in these movements, Figures A.1 through A.4 in Appendix A tally the total number of responses associated with each beat. The red line indicates responses in the Fine 2 trial, while the dashed purple line shows the Coarse 2 trial. The distinct peaks and valleys in all four movements imply that listeners were responding to musical features consistently, rather than just pressing the spacebar in a random manner. For clarity, I have labeled the peaks with the measure number and beat in the measure where it is located. Notice that the dashed-purple line peaks (coarse segmentation) tend to match up with the red peaks, suggesting a nested hierarchical structure. For participants segmenting the Mozart movements (A.3 and A.4), the peaks and valleys are more sharply articulated than they are for the Bartók movements, suggesting more consensus among these participants. All participants tend to take more time to indicate coarse boundaries; generally these boundaries occur slightly later than do the boundaries in the fine condition. Overall, as expected, there are far fewer coarse segmentation responses than fine segmentation responses.

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Table 5.5: Total Number of Responses and Percentage Used in Data Analysis (Bartók) Percentage of Total number of Average number of Movement Trial Subject Group responses in a responses responses window Bartók, Fine 1 Non-musicians 420 30.00 64.76% No. 4 Undergraduates 186 20.67 78.49% Mvmt. 3 Graduates 109 12.11 95.41% Total 715 22.34 73.01% Fine 2 Non-musicians 369 26.36 65.58% Undergraduates 192 21.33 71.35% Graduates 104 11.56 93.27% Total 665 20.78 71.28% Coarse 1 Non-musicians 111 7.93 88.29% Undergraduates 62 6.89 96.77% Graduates 48 5.33 93.75% Total 221 6.91 91.86% Coarse 2 Non-musicians 96 6.86 93.75% Undergraduates 50 5.56 96.00% Graduates 44 4.89 100.00% Total 190 5.94 95.79% Total 1791 55.97 77.22% Bartók, Fine 1 Non-musicians 453 32.36 83.00% No. 4 Undergraduates 256 28.44 83.98% Mvmt. 5 Graduates 252 28.00 88.49% Total 961 30.03 84.70% Fine 2 Non-musicians 502 35.86 79.48% Undergraduates 337 37.44 81.90% Graduates 278 30.89 88.13% Total 1117 34.91 82.36% Coarse 1 Non-musicians 146 10.43 82.88% Undergraduates 92 10.22 84.78% Graduates 92 10.22 89.13% Total 330 10.31 85.15% Coarse 2 Non-musicians 121 8.64 85.95% Undergraduates 71 7.89 85.92% Graduates 76 8.44 80.26% Total 268 8.38 84.33% Total 2676 83.63 83.74%

While the figures in Appendix A show every response made in the Fine 2 and Coarse 2 trials, I am only considering responses that fell inside one of the predetermined windows for data analysis, discarding responses not meeting this requirement. Tables 5.5 and 5.6 show the total number of responses in each trial, divided by subject group, and the percentage of those responses that fell into a window. A high number of responses was retained in all four movements. These responses indicate a general trend: as musical expertise increases, participants

105 make fewer responses during the segmentation task, and, a majority of the time, greater musical expertise also correlates with a higher percentage of the responses falling in the predetermined windows.

Table 5.6: Total Number of Responses and Percentage Used in Data Analysis (Mozart) Percentage of Total number of Average number of Movement Trial Subject Group responses in a responses responses window Mozart, Fine 1 Non-musicians 713 50.93 65.08% No. 19 Undergraduates 496 49.60 76.01% Mvmt. 4 Graduates 270 30.00 85.19% Total 1479 44.82 72.41% Fine 2 Non-musicians 665 47.50 64.06% Undergraduates 500 50.00 74.80% Graduates 315 35.00 88.25% Total 1480 44.85 72.84% Coarse 1 Non-musicians 218 15.57 82.11% Undergraduates 184 18.40 80.43% Graduates 113 12.56 69.91% Total 515 15.61 78.83% Coarse 2 Non-musicians 121 8.64 85.95% Undergraduates 197 19.70 78.17% Graduates 125 13.89 82.40% Total 443 13.42 81.49% Total 3917 118.70 74.44% Mozart, Fine 1 Non-musicians 163 11.64 76.07% No. 21 Undergraduates 230 23.00 88.26% Mvmt. 2 Graduates 136 15.11 88.97% Total 529 16.03 84.69% Fine 2 Non-musicians 316 22.57 78.80% Undergraduates 230 23.00 86.96% Graduates 130 14.44 94.62% Total 676 20.48 84.62% Coarse 1 Non-musicians 128 9.14 79.69% Undergraduates 82 8.20 84.15% Graduates 37 4.11 78.38% Total 247 7.48 80.97% Coarse 2 Non-musicians 126 9.00 77.78% Undergraduates 73 7.30 86.30% Graduates 39 4.33 79.49% Total 238 7.21 80.67% Total 1690 51.21 83.55%

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Using these data, the first set of mixed logit regressions demonstrates how well one set of subject responses predicts another set of responses.57 Results indicate that participants are consistent in their responses between trials in the same condition. Across both Bartók movements, Fine 1 and Coarse 1 responses predict Fine 2 and Coarse 2 responses, respectively (t(4251) = 6.19, p < 0.001, OR = 3.24 and t(4251) = 8.25, p < 0.001, OR = 20.4). The same trend occurs across both Mozart movements (Fine: t(3757) = 5.76, p < 0.001, OR = 5.57; Coarse: t(3757) = 12.73, p < 0.001, OR = 25.16). In both of these cases, the odds ratios suggest that participants who respond in a particular window the first time through the piece are more likely to respond in that window the second time through the piece. In both the Bartók and Mozart conditions, the difference in odds ratios between the fine task and coarse task is significant, indicating more consistency in the coarse condition, but the Bartók responses are not significantly different from the Mozart responses.58 Only in the Mozart condition, are there two significant interactions. First, musicians in the fine condition are more likely to respond in a window within which they had responded previously. This effect is even stronger for graduates, suggesting that an increase in musical training correlates with increased consistency (see Figure 5.1). This effect is only in the fine condition; there is no interaction in the coarse condition. Second, the starting segmentation task influenced consistency in the coarse condition: participants who began with the fine task tended to be more consistent in the coarse condition (Figure 5.2). This could reflect a learning effect since the coarse condition was the third and fourth listenings for these participants, but a similar interaction was not found in the Bartók condition. Instead, the use of consistent cadential paradigms at the end of fine divisions in the Mozart stimuli might facilitate the formation of larger sections, suggesting a bottom-up approach to determining formal sections.

57 In all of these mixed logit analyses, the odds ratio shows the probability of a response when a given variable is present. In other words, the presence of a variable can predict the occurrence of a response. In this particular case, I am treating the presence of a response in another trial as a variable to see if one response can predict another. Used this way, “predict” is not time sensitive: the data from a later response can predict the presence of a response in an earlier trial. 58 Odds ratios are said to be significantly different if one odds ratio does not fall within the confidence interval of the other odds ratio. In short, I am saying that I am 95% confident that these ratios are different from one another. In the Bartók analysis the confidence interval for the fine odds ratio is (2.232, 4.698) and the confidence interval for the coarse odds ratio is (9.969, 41.763), while in the Mozart analysis the confidence interval for the fine odds ratio is (3.11, 10.00) and the confidence interval for the coarse odds ratio is (15.31, 41.33).

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In order for the resulting subject analysis to be hierarchically constructed, every coarse response should correspond with a fine response, but obviously not vice versa. In both composer conditions, Coarse 1 is a significant predictor for Fine 1, while Coarse 2 is a significant predictor of Fine 2.59 In the Bartók analysis, Coarse 1 and 2 responses are strong predictors of Fine 1 and 2 responses (t(4251) = 7.25, p < 0.001, OR = 4.52 and t(4251) = 3.00, p = 0.003, OR = 2.54), indicating that the fine responses are nested within the coarse responses. The odds ratio for the first trial in each condition is slightly higher than that of the second trial, but this difference is not significant. The Mozart analysis shows the same trend: Coarse 1 responses significantly predict Fine 1 responses (t(28) = 4.248, p < 0.001, OR = 3.69), and Coarse 2 responses significantly predict Fine 2 responses (t(28) = 3.04, p = 0.005, OR = 4.44). As with the Bartók analysis, the difference between odds ratios is not significant. For the participants in the Bartók condition, the starting segmentation task significantly interacted with the coarse responses, where the ability of the coarse responses to predict the fine responses varies based on the starting segmentation task. The direction of the difference is represented by the estimated means shown in Table 5.7. In both cases, the difference between the estimated means for subjects beginning with the coarse segmentation task is significantly higher than for the subjects who began with the fine segmentation task, so the coarse responses are better predictors of the fine responses when participants start with the coarse segmentation task. These participants are therefore more likely to have their fine segmentation responses nested within the coarse responses. Unlike in the Mozart condition where starting with the fine segmentation task produces more consistent results, participants had an advantage in the Bartók condition when they began with the coarse segmentation task. The segmentation task and tempo of the movement affected participant response time across the board. Response latency was measured from the beginning of each window to the time at which the subject responded, and it varies significantly between different tempos and segmentation tasks (Table 5.8). Segmentation task and tempo were coded as binary variables where 0 represents the fine segmentation task and a fast tempo and 1 represents the coarse segmentation task and a slow tempo. Both coefficients are positive, indicating that subjects were

59 I did not examine whether Coarse 2 predicts Fine 1 or whether Coarse 1 predicts Fine 2 because this would compare the first trial in one condition with the second trial in the other condition.

108 slower to respond in the coarse segmentation task or while listening to the movement with the slower tempo. The first result confirms the observation made previously that coarse responses tend to occur later than fine responses (refer to Appendix A, Figures A.1-A.4). The latter result is also unsurprising because the response windows are almost twice as long in the slow movements, providing the opportunity for a longer response time.

Figure 5.1: Interactions between Subject Group and Consistency (Mozart) Each line connects the mean number of responses in the Fine 2 trial that do not occur in the same window in both trials to the mean number of responses that do occur in the same window in both trials.

Figure 5.2: Interaction between Starting Condition and Consistency (Mozart) Each line connects the mean number of responses in the Coarse 2 trial that do not occur in the same window in both trials to the mean number of responses that do occur in the same window in both trials.

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Table 5.7: ANOVA Means for Interactions between Starting Task and the Nested Structure (Bartók)60

Start with Fine Start with Coarse Outcome Feature62 p-value63 variable61 Feature Feature Feature Feature

Absent Present Absent Present Fine 1 Coarse 1 0.268 0.621 0.241 0.705 0.019 Fine 2 Coarse 2 0.324 0.687 0.232 0.745 0.008

Table 5.8: Mixed Models Regression Analysis: Latency Time

Standard Approx. Composer Fixed Effect Coefficient t-ratio p-value error d.f. Bartók Intercept64 976.716640 39.947454 24.450 27 <0.001 Segmentation 1011.440535 170.049966 5.948 3582 <0.001 Tempo 1447.353184 155.966148 9.280 3582 <0.001 Mozart Intercept 1002.587521 64.547880 15.532 28 <0.001 Segmentation 338.847945 53.545578 6.328 4500 <0.001 Tempo 711.824574 101.598533 7.006 4500 <0.001

The next set of analyses examines whether the probability of a segmentation response increases as the number of changes in the music increases. For this analysis, I counted the number of changes occurring in each window. The features included in this count are: complete silence, melodic silence, non-melodic silence, entrance of a new instrument, and a change of register, dynamics, or ostinato.65 In the Bartók movements, the number of changes in a given window ranges from 0–7, but windows with more than four changes are grouped together because there are relatively fewer windows with more than four changes, resulting in a scale

60 These means are not the same estimated means produced by the regression, but they still indicate the direction of the interaction. 61 Also known as the dependent variable; it is the variable that the regression predicts. 62 In this case, the means represent the number of windows in which there is a fine response, but not a coarse response (feature absent) and the number of windows in which there is a fine response and a coarse response (feature present). 63 In all of the ANOVA tables in this chapter, the p-values come from the mixed models regression, not the actual ANOVA. 64 The intercept is needed for the regression equation and it does not represent anything meaningful (it is the point where the line crosses the y-axis when the other variables are not included in the equation). 65 Change of ostinato only occurred in the Bartók stimuli.

110 from 0–4. The Mozart windows have fewer changes (only ranging from 0–4), so windows with three or more changes are grouped together, forming a scale from 0–3. The results from a mixed logit regression predicting the presence of a listener-perceived boundary from the number of changes in a window are shown in Table 5.9. A positive coefficient indicates a higher probability of a boundary, and the p-value indicates whether an increase in the number of changes is a statistically significant predictor of the observed behavior.

Table 5.9: Mixed Logit Regression Analysis: Number of Changes

Composer Outcome Standard Approx. Odds Confidence Coefficient t-ratio p-value variable error d.f. Ratio Interval Bartók Fine 1 0.280069 0.049584 5.648 4251 <0.001 1.323221 (1.201,1.458) Fine 2 0.093373 0.089227 1.046 4251 0.295 1.097871 (0.922,1.308) Coarse 1 0.300257 0.081595 3.680 4251 <0.001 1.350206 (1.151,1.584) Coarse 2 0.624884 0.062921 9.931 4251 <0.001 1.868029 (1.651,2.113) Mozart Fine 1 0.276388 0.053886 5.129 3757 <0.001 1.318359 (1.186,1.465) Fine 2 0.180791 0.109938 1.644 3757 0.100 1.198165 (0.966,1.486) Coarse 1 0.440043 0.103856 4.237 3757 <0.001 1.552774 (1.267,1.903) Coarse 2 0.631480 0.076264 8.280 3757 <0.001 1.880391 (1.619,2.184)

In the Bartók responses, in three of the four trials, the amount of change significantly predicts the subject responses. For Fine 1, Coarse 1, and Coarse 2, an increase in the number of changes increases the chance of responding—especially for Coarse 2, whose odds ratio is significantly greater than those of the other three trials. There is also an interaction effect for the first three outcome variables and graduate students, illustrated in Figure 5.3, where the lines connect the estimated means determined by an ANOVA analysis. The slopes of lines representing graduates are steeper than those representing undergraduates, indicating that graduates are more likely to respond as the number of changes increases. The two lower graphs show that coarse responses are best predicted by four or more changes in the musical surface, indicated by the large jump from 3 to 4 instead of the incremental rise seen in the fine responses. The difference between the two subject groups in Coarse 2 is not significant.

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Figure 5.3: Interactions between Subject Group and Number of Changes (Bartók) There is not a significant interaction between the subject groups in Coarse 2.

Now referring to the Mozart analysis, there is also a main effect for an increase in the number of changes in three of the four trials (Fine 1, Coarse 1, and Coarse 2). The odds ratios in both coarse trials are significantly larger than the odds ratios in the fine trials, indicating that more musical changes are needed before a listener will respond in the coarse condition, as compared with the fine condition. There was only one interaction between the fixed effect (number of changes) and a subject group (graduates) occurring in the Fine 1 trial, where graduates are less likely to respond overall. Despite the lack of this interaction effect in the other trials, I have showed all with estimated means for all four trials for easier comparison with the Bartók results. In the fine condition, there is an inconsistent upward slope as the number of changes increase, while participants in the coarse condition are increasingly likely to respond as number of changes increase. This might suggest that phrase ending analyses are less dependent

112 upon changes in the musical surface, and perhaps participants are paying attention to other musical features in Mozart, while subjects are much more sensitive to changes as a demarcation of boundaries in Bartók.

Figure 5.4: Interactions between Subject Group and Number of Changes (Mozart) The only significant difference between subject groups occurs in Fine 1.

My own grouping analysis might provide a more nuanced measure of boundary strength, since it reflects an interaction between arrival features which I deemed meaningful for a particular piece and change features taken from the surface of the music. To determine how well my three-level grouping hierarchy predicts responses, I coded the windows according to the type of ending each contained. A window containing at least a section ending was coded as 3; a window containing a phrase ending was coded as 2; a window containing a subphrase ending was coded as 1. This creates a rating that corresponds to the hierarchical level of the ending.

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These designations are my own analytical interpretations, of course, but there is a main effect for an increase in hierarchical ending level on responses in all four outcome variables in both composer conditions (see Table 5.10). Overall, the odds ratios for the ending ratings in the coarse condition are significantly higher, indicating a much higher probability of responding as the hierarchical level changes from a lower level to a higher level. In the Bartók condition, there is an interaction between graduates and the ending ratings in the first three conditions (Figure 5.5), where graduates tend not to respond as often as undergraduates within a window containing no ending or just a subphrase ending; conversely, graduates are more likely to respond within a window that concludes a section. The Mozart condition also exhibits this same interaction between the ending type and level of expertise.66 As Figure 5.6 illustrates, graduate responses are less likely to occur without some sort of ending, especially in the coarse condition, where graduates wait for at least a phrase ending before responding.

Table 5.10: Mixed Logit Regression Analysis: Ending Type

Composer Outcome Standard Approx. Odds Confidence Coefficient t-ratio p-value variable error d.f. Ratio Interval Bartók Fine 1 0.583101 0.070496 8.271 4251 <0.001 1.791586 (1.560,2.057) Fine 2 0.365162 0.122154 2.989 4251 0.003 1.440748 (1.134,1.830) Coarse 1 0.936090 0.155891 6.005 4251 <0.001 2.549992 (1.879,3.461) Coarse 2 1.160561 0.144327 8.041 4251 <0.001 3.191725 (2.405,4.235) Mozart Fine 1 0.576789 0.141974 4.063 3757 <0.001 1.780312 (1.348,2.352) Fine 2 0.615687 0.167034 3.686 3757 <0.001 1.850927 (1.334,2.568) Coarse 1 1.050279 0.074346 14.127 3757 <0.001 2.858447 (2.471,3.307) Coarse 2 1.220777 0.223261 5.468 3757 <0.001 3.389822 (2.188,5.251)

Neither a simple count of changes nor the presence of an ending determined by a grouping analysis can examine how particular musical features predict listener responses in each movement. Movements were separated for these subsequent analyses because different features may predict endings in each movement. For similar reasons, a separate analysis was run for each of the four trials. The first set of regressions looks at the arrival features, which vary between

66 This interaction is between musicians and non-musicians in the Fine 1, Fine 2, and Coarse 1 conditions; and between graduates and undergraduates in the Fine 2, Coarse 1, and Coarse 2 conditions.

114 composers (refer back to Tables 5.3 and 5.4). Because some of these arrival features strongly correlate with one another (e.g., a PAC will always occur with !) they were not combined into one large regression; instead, I ran several smaller regression analyses. The change features were also divided into separate regressions according to their location in a window; for instance, silence is more likely to occur following the end of a segment and before a new beginning, while the other change features usually signify a new beginning. The final regression examines the extent to which analytic endings (subphrase, phrase, and section) predict a perceived boundary. In all of these analyses, the presence of a feature was coded as 1, so a positive coefficient indicates that a musical feature predicts the segmentation responses, while a negative coefficient means the listener is less likely to respond within a window containing the given feature.

Figure 5.5: Interactions between Subject Group and Ending Type (Bartók) There is not a significant difference between the subject groups in Coarse 2.

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Figure 5.6: Interactions between Subject Group and Ending Type (Mozart) There is not a significant difference between the subject groups in Fine 1.

Experiment 1a: Bartók Results

Arrival Features: In both movements, arrival features were grouped into four separate analyses: the interval into last note of a segment (Type 1 Window) or first note of a window (Type 2 Window) and whether it was approached from below or above; change of duration; and cadential type (which varied between movements). Tables 5.11 and 5.12 summarize the significant results from this set of regressions. Overall, no single feature or set of features predicts responses across both Bartók movements; instead, the features that correspond with listener responses are movement-specific.

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Table 5.11: Mixed Logit Regression Analysis: Arrival Features, Third Movement

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Coarse 1 0.965358 0.200947 4.804 1398 <0.001 2.625727 (1.770,3.895) Descent Coarse 2 0.897002 0.130830 6.856 1398 <0.001 2.452240 (1.897,3.170) Intervallic Direction Fine 1 1.228127 0.206982 5.933 1398 <0.001 3.414828 (2.275,5.125) Ascent Coarse 1 1.136407 0.217230 5.231 1398 <0.001 3.115554 (2.034,4.771)

Coarse 2 1.242533 0.216170 5.748 1398 <0.001 3.464376 (2.267,5.294)

-5 Coarse 1 1.768610 0.243063 7.276 1392 <0.001 5.862696 (3.639,9.445) -7 Coarse 2 2.218797 0.210323 10.549 1392 <0.001 9.196257 (6.087,13.894)

Intervallic Fine 1 1.921392 0.429727 4.471 1388 <0.001 6.830462 (2.940,15.871) Approach +1 Fine 2 0.723158 0.297351 2.432 1388 0.015 2.060932 (1.150,3.693) +2 Coarse 1 1.363304 0.287454 4.743 1392 <0.001 3.909086 (2.224,6.871) Coarse 2 2.108026 0.343805 6.131 1392 <0.001 8.231973 (4.193,16.161)

Duration Coarse 1 1.049846 0.199121 5.272 1403 <0.001 2.857210 (1.933,4.223)

Change Coarse 2 0.875178 0.231805 3.775 1403 <0.001 2.399303 (1.523,3.781)

Coarse 1 1.277560 0.174930 7.303 1372 <0.001 3.587874 (2.546,5.057) Cadence Falling 4th Coarse 2 1.333816 0.161271 8.271 1372 <0.001 3.795498 (2.766,5.208)

For the third movement, most of the main effects point toward the influence of the falling fourth cadence on listener segmentation in the coarse condition (an example of this cadence is found back in Example 5.5). Along with a descent of five semitones, this cadential gesture also features a duration change, where the arrival note is shorter than the preceding note. While the main effect for an intervallic ascent, specifically by one or two semitones, is not associated with the falling fourth cadential gesture, the melodic note in the last window of the movement is approached by an ascending step. Almost everyone in each trial identified this window as boundary point. Even though this does not constitute a predefined cadential gesture, it does illustrate how the results can by swayed by particular compositional features. The arrival features in the fifth movement do not indicate a systematic preference for any particular cadential gesture. There is a positive main effect for a melodic descent in two trials, while participants are less likely to respond to a melodic ascent (note the negative coefficient). Musicians, however, exhibit less reaction to a melodic descent; an interaction suggests that the contour leading to the final note of a segment is not a strong indicator of course endings for

117 musicians.67 The more specific intervallic approaches illustrate a similar trend: regardless of the interval size, a descending contour better predicts responses. Again, an interaction in the coarse condition for the descending step suggests that this preference for downward intervals may not hold across subject groups. While undergraduates are more likely to respond when this feature is present, this feature does not influence graduates, supporting that motion into the final note of a segment is not a strong indicator for boundaries as musical training and segmentation grain increases.68

Table 5.12: Mixed Logit Regression Analysis: Arrival Features, Fifth Movement

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Fine 1 0.521713 0.150503 3.466 2806 <0.001 1.684911 (1.254,2.263) Intervallic Descent Direction Coarse 2 0.437531 0.151715 2.884 2806 0.004 1.548878 (1.150,2.085) Ascent Coarse 2 -0.887467 0.229938 -3.860 2806 <0.001 0.411697 (0.262,0.646) -1, -2 Coarse 2 0.551656 0.151708 3.636 2796 <0.001 1.736125 (1.290,2.337) Fine 1 0.587790 0.205178 2.865 2796 0.004 1.800005 (1.204,2.691) Intervallic -3, -4 Approach Coarse 1 0.760485 0.228989 3.321 2796 <0.001 2.139314 (1.366,3.351) -5, -7 Fine 1 1.779049 0.720338 2.470 2796 0.014 5.924219 (1.444,24.311) +1, +2 Coarse 2 -1.440268 0.610440 -2.359 2796 0.018 0.236864 (0.072,0.784)

Duration Fine 1 0.568032 0.154410 3.679 2811 <0.001 1.764791 (1.304,2.389)

Change Fine 2 0.622929 0.175157 3.556 2811 <0.001 1.864380 (1.323,2.628)

1 Coarse 2 -2.097373 0.804417 -2.607 2800 0.009 0.122779 (0.025,0.594) Cadences 2 Fine 2 0.755961 0.255543 2.958 2796 0.003 2.129657 (1.291,3.514) L-H Coarse 1 1.052860 0.307220 3.427 2796 <0.001 2.865836 (1.569,5.233)

In both fine trials, there is a main effect for duration change; this is unlike the third movement, where duration better predicted the coarse responses. Perhaps this difference reflects the association between the long-short rhythmic Figure and the falling fourth cadential gesture in the third movement, while the fifth movement has no consistent relationship between a particular durational pattern and phrase endings. This is further reflected in the lack of main effects for

67 For non-musicians, the ANOVA means increased from 0.062 to 0.126 when the melody descended, compared with the smaller percent increase from 0.054 to 0.120 for musicians. 68 For undergraduates, in Coarse 1 the ANOVA means increased from 0.095 to 0.140 when the melody descended, compared with the smaller percent increase from 0.100 to 0.111 for graduates, and in Coarse 2 the ANOVA means increased from 0.067 to 0.133 when the melody descended, compared with the smaller percent increase from 0.072 to 0.093 for graduates.

118 cadential gestures, where the only positive main effects include the double chord gesture (Fine 2) and the low-high succession (Coarse 2). There was an interesting interaction in the first fine trial involving the double chord cadential gesture and musical expertise: the ANOVA means indicate that all subjects are more likely to respond at a double chord cadence, but musicians demonstrate a higher percent increase with the presence of this feature, and graduates show an even higher percent increase.69 Change Features: Another set of mixed logit regressions calculated the odds ratios for the change features in each movement. Tables 5.13 and 5.16 summarize the main effects for these features. In both movements, participants tend to respond to silence fairly consistently, especially in the coarse trials, but other change features vary between movements. For instance, register, dynamic, and ostinato changes tend to influence the results more in the third movement than in the fifth movement. Complete silence and a thinning of the texture tends to predict responses in the third movement, and there is an interaction between subject groups and non-melodic silence, where a thinning of the texture influences graduates (who are overall less likely to respond) more than undergraduates. (All interactions for this set of features are located in Table 5.14.) Another feature that usually follows endings, melodic silence, significantly predicts an absence of a response in the coarse condition. This feature usually occurs at subphrase divisions and in the middle of musical segments in this movement, which is reflected in these results. For instance, consider the cello melody from mm. 6–35 (Example 5.11). In this example all the windows are marked in mm. 19–29 and these windows are annotated with the percentage of participants who responded in each window (Coarse 1 trial only). These low-performing silences may be too short to evoke a boundary, or another feature, like phrase length or melodic content, may be influencing the participants’ performance at this grain of segmentation.

69 For non-musicians, the ANOVA means increased from 0.288 to 0.379 at a double chord cadence, compared with the larger percent increase from 0.054 to 0.120 for musicians; for undergraduates, the ANOVA means increased from 0.271 to 0.400, compared with the larger percent increase from 0.017 to 0.047 for graduates.

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Table 5.13: Mixed Logit Regression Analysis: Change Features, Third Movement

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Complete Coarse 1 1.551360 0.371348 4.178 1393 <0.001 4.717880 (2.277,9.776) Silence Coarse 2 2.194610 0.280773 7.816 1393 <0.001 8.976497 (5.174,15.572) Melodic Coarse 1 -0.797169 0.227236 -3.508 1393 <0.001 0.450603 (0.289,0.704) Silence Fine 1 2.180737 0.311925 6.991 1393 <0.001 8.852828 (4.801,16.326)

Non-melodic Fine 2 1.485596 0.228470 6.502 1393 <0.001 4.417596 (2.822,6.916) Silence Coarse 1 1.477900 0.425064 3.477 1393 <0.001 4.383729 (1.904,10.093) Coarse 2 2.521323 0.451601 5.583 1393 <0.001 12.445049 (5.131,30.186)

New Coarse 1 1.113262 0.339207 3.282 1398 0.001 3.044271 (1.565,5.923) Instrument Coarse 2 1.818096 0.128201 14.182 1398 <0.001 6.160116 (4.790,7.922)

New Mel. Fine 1 0.998206 0.302832 3.296 1398 0.001 2.713410 (1.498,4.915) Instrument Coarse 1 0.874641 0.366009 2.390 1398 0.017 2.398015 (1.169,4.917)

Fine 2 0.362799 0.154054 2.355 1393 0.019 1.437347 (1.062,1.945) Register Coarse 1 0.868092 0.304006 2.856 1393 0.004 2.382360 (1.312,4.326) Coarse 2 0.775337 0.297488 2.606 1393 0.009 2.171325 (1.211,3.892) Fine 1 0.973550 0.206354 4.718 1393 <0.001 2.647326 (1.766,3.969) Dynamics Coarse 1 1.336720 0.204935 6.523 1393 <0.001 3.806536 (2.546,5.691) Coarse 2 2.513043 0.484093 5.191 1393 <0.001 12.342428 (4.774,31.907) Ostinato Coarse 2 0.664673 0.227824 2.917 1393 0.004 1.943855 (1.243,3.039)

Table 5.14: ANOVA Means for Interactions in Change Feature Analysis, Third Movement

Outcome Feature Level of Musical Less Musical Training More Musical Training variable Experience for p-value Those with More Feature Absent Feature Present Feature Absent Feature Present Training Fine 1 Lose Instr. Graduate 0.298 0.632 0.150 0.556 0.004 Fine 2 Lose Instr. Graduate 0.280 0.545 0.147 0.525 0.003 Coarse 1 Lose Instr. Graduate 0.075 0.439 0.007 0.434 <0.001 Coarse 2 Silence Graduate 0.086 0.598 0.089 0.278 0.001 Fine 1 New Instr. Graduate 0.356 0.446 0.158 0.500 0.001 Fine 2 New Instr. Graduate 0.327 0.395 0.152 0.481 0.013 Coarse 2 New Melody Graduate 0.112 0.326 0.070 0.472 0.013 Fine 1 Register Graduate 0.355 0.478 0.185 0.506 0.01 Fine 2 Register Graduate 0.316 0.459 0.164 0.543 <0.001

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9% 2% 6% 69%

3% 0% 3%

String Quartet No. 4 by Béla Bartók © Copyright 1929 by Boosey & Hawkes, Inc. Copyright Renewed. Reprinted by Permission Example 5.11: Bartók, String Quartet No. 4, third movement, mm. 6–35 (cello) The Type 1 Windows are annotated on the score with a solid box. The Type 2 Windows are annotated on the score with a dashed box.

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On the other hand, all participants strongly respond in the coarse condition to the presence of complete silence, which usually is reserved for the ends of phrases and sections. In Coarse 2, however, the effect is tempered for graduates, indicating that not every complete silence indicates a boundary in this condition. Returning to the cello melody in Example 5.11, complete silence is marked in the texture by a short, black vertical line. Table 5.15 lists all the points of silence in this short passage followed by the percentage of undergraduate and graduate responses in the Coarse 2 trial. Only after m. 34, which doesn’t have complete silence, does the texture change and a new melody enters, initiating what I consider a new section.70 On their second time performing the coarse segmentation task, graduates may have learned enough not to be “tricked” by the complete silence before the end of this section.

Table 5.15: Percentage of Responses at Complete Silence in Coarse 2, Third Movement Window Location Undergraduates Graduates m. 13 78% 22% m. 21 74% 11% m. 34 39% 89%

The last two sets of regressions examine how changes usually associated with new beginnings affected listener responses. All of the changes have a main effect in at least one of the coarse conditions, but the two strongest predictors in this condition are the introduction of a new instrument and a change in dynamics. There is no main effect for the entrance of a new instrument in fine segmentation task, but there is an interaction between this feature and graduates, who tend to respond more to this cue than undergraduates. In contrast, the entrance of a new melodic instrument significantly predicts responses in the fine condition, but the interaction remains the same: in Coarse 2, graduates are more likely to respond to this cue.71 In sum, both features, which sometimes roughly coincide, significantly predict listener responses, especially in the coarse conditions. Among the other change features, dynamic change is especially predictive of coarse segmentation (producing a significantly higher odds ratio in

70 Even though complete silence is not indicated in the score, the performers insert a little space between beats 2 and 3 in m. 34. 71 There is also an effect for this feature in Fine 2 (which is not included in the chart): t(1398) = 2.01, p = 0.044, OR = 2.83.

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Coarse 2), and there is both a main effect and interaction for a change in register, especially for graduates, for whom this feature has a pronounced effect in the fine condition. For the features present between musical segments in the fifth movement, complete silence consistently predicts listener responses, especially in the coarse condition (notice the significantly higher odds ratios), while non-melodic silence only predicts responses in the coarse condition (see Table 5.16). Although there is no main effect for melodic silence, this feature is involved in a couple of interactions (Table 5.17). In Fine 1, musicians are more likely to respond to melodic silence, whereas non-musicians show no reaction. The interaction in the Coarse 1 trial reveals a different trend: participants are less likely to respond to melodic silence, undergraduates more so than graduates. This suggests that, for trained musicians, melodic silence is sufficient for a fine boundary, but not necessarily for a coarse boundary.

Table 5.16: Mixed Logit Regression Analysis: Change Features, Fifth Movement

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Fine 1 0.976257 0.265263 3.680 2801 <0.001 2.654503 (1.578,4.465) Complete Silence Coarse 1 1.910363 0.319696 5.976 2801 <0.001 6.755540 (3.610,12.641) Coarse 2 2.114830 0.305034 6.933 2801 <0.001 8.288176 (4.558,15.070) Non-melodic Coarse 1 0.610535 0.170981 3.571 2801 <0.001 1.841417 (1.317,2.575) Silence Coarse 2 1.190035 0.146008 8.151 2801 <0.001 3.287195 (2.469,4.376)

Fine 1 -0.502388 0.187898 -2.674 2806 0.008 0.605084 (0.419,0.874) New Instrument Coarse 1 -1.102216 0.214054 -5.149 2806 <0.001 0.332134 (0.218,0.505) Coarse 2 -0.665164 0.157920 -4.212 2806 <0.001 0.514189 (0.377,0.701) Dynamics Coarse 2 1.024097 0.277650 3.688 2801 <0.001 2.784581 (1.616,4.798)

During the third movement, the introduction of a new instrument predicts a listener response, but during the fifth movement we observe the opposite effect. This could be an effect of the more complex contrapuntal texture of the fifth movement compared with the texture of the third movement. This more complex texture could also explain the lack of main effects for the change features that mark the beginning of a new musical segment. Dynamic change in the Coarse 2 trial produced the only main effect; however, an interaction reveals that this is almost entirely attributable to graduates.

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Since Bartók’s music did not necessarily conform to an established syntax, the arrival features that listeners used to decide upon boundaries vary between pieces. Surprisingly, though, silence is the only change feature that is consistently used as a boundary marker for both movements. More specific feature interactions might have been concealed by this broad overview: for instance, listeners may only respond when a certain combination of change and arrival features are present. My future research will pursue this avenue, but my own grouping analysis can function as a simplification of these interactions, since these features influenced my decisions. I will return to this point after examining the influence of arrival and change features in Mozart.

Table 5.17: ANOVA Means for Interactions in Change Feature Analysis, Fifth Movement

Outcome Feature Level of Musical Less Musical Training More Musical Training variable Experience for p-value Those with More Feature Absent Feature Present Feature Absent Feature Present Training Fine 1 Mel. Silence Musician 0.296 0.302 0.258 0.301 0.007 Coarse 1 Mel. Silence Graduate 0.112 0.084 0.109 0.085 0.008 Fine 2 Dynamic Graduate 0.314 0.334 0.259 0.368 0.007 Coarse 1 Dynamic Graduate 0.072 0.146 0.044 0.181 0.021

Experiment 1b: Mozart Results

Arrival Features: While the features that best predicted responses in the Bartók excerpts were fairly evenly divided between arrival features and change features (especially in the third movement), arrival features, such as melodic scale degrees and cadential figures, become highly predictive of responses in the Mozart stimuli. Tables 5.18 and 5.21 list the main effects for the arrival features, which were grouped into six different regressions comparing similar features: scale-degrees, harmony/harmonic progression, intervallic direction, step progressions, duration, and cadences. While some of these features are also explored in the Bartók analysis, a majority of these features are only associated with endings in the tonal style. For Mozart’s String Quartet No. 19, melodic !, #, and % are all highly predictive of listener responses, especially in the coarse condition (notice the high odds ratios). While it may seem strange to have such high odds ratio for %, in this movement, the three largest sections— exposition, development, and recapitulation—all end with %+in the soprano. There is not a

124 consistent main effect for !+in the fine condition because non-musicians tend not to respond to this feature while musicians are likely to respond (see the interaction table: Table 5.19). There are additional interactions between the other scale degrees and subject group in the fine condition: all participants—especially musicians—are less likely to respond to #+in the melody, whereas all participants—especially non-musicians—are more likely to respond to %.+These results suggest that musicians are more sensitive to scale degrees, reserving most of their responses for cadences with ! in the melody.

Table 5.18: Mixed Logit Regression Analysis: Arrival Features, No. 19

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Fine 1 1.018028 0.409848 2.484 2492 0.013 2.767730 (1.239,6.183) !+ Coarse 1 3.680713 0.647215 5.687 2496 <0.001 39.674674 (11.151,141.161) Coarse 2 2.834016 0.612873 4.624 2496 <0.001 17.013647 (5.115,56.592)

Scale Coarse 1 2.762380 0.611132 4.520 2496 <0.001 15.837484 (4.778,52.500) #+ Degrees Coarse 2 1.755356 0.528397 3.322 2496 <0.001 5.785508 (2.053,16.306) Fine 1 1.344350 0.422937 3.179 2492 0.001 3.835691 (1.674,8.791) %+ Coarse 1 4.561242 0.738300 6.178 2496 <0.001 95.702250 (22.498,407.095) Coarse 2 3.738453 0.577161 6.477 2496 <0.001 42.032921 (13.553,130.356)

I Coarse 2 1.563465 0.638883 2.447 2496 0.014 4.775340 (1.364,16.715) Harmony/ V7 Coarse 2 1.848644 0.617211 2.995 2496 0.003 6.351204 (1.893,21.306) Harmonic Progression V-I Coarse 2 1.561891 0.638213 2.447 2500 0.014 4.767829 (1.364,16.667) x-V Coarse 2 1.464869 0.597402 2.452 2500 0.014 4.326977 (1.341,13.962)

Descent Fine 2 0.967142 0.308031 3.140 2493 0.002 2.630415 (1.438,4.812) Fine 1 1.770332 0.473346 3.740 2493 <0.001 5.872802 (2.321,14.858) Intervallic Direction Ascent Fine 2 1.732640 0.432869 4.003 2493 <0.001 5.655566 (2.420,13.217) Coarse 1 1.678095 0.396861 4.228 2493 <0.001 5.355344 (2.459,11.662) LT-Tonic Fine 1 -1.576431 0.407705 -3.867 2493 <0.001 0.206711 (0.093,0.460)

Fine 1 0.641761 0.204140 3.144 2488 0.002 1.899823 (1.273,2.835) Descent Fine 2 0.663260 0.209690 3.163 2488 0.002 1.941109 (1.287,2.928) Steps/ Emb. Steps Coarse 2 -0.663897 0.240564 -2.760 2492 0.006 0.514841 (0.321,0.825) Emb. Fine 1 0.771459 0.287521 2.683 2488 0.007 2.162920 (1.231,3.801) Ascent Fine 2 0.811606 0.264175 3.072 2488 0.002 2.251521 (1.341,3.780)

Duration Coarse 1 0.980611 0.106508 9.207 2503 <0.001 2.666084 (2.164,3.285) Change Coarse 2 1.083713 0.220590 4.913 2503 <0.001 2.955633 (1.918,4.554)

Cadences Evaded Coarse 2 -1.733752 0.646037 -2.684 29 0.012 0.176621 (0.047,0.662)

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Harmonic progression only had a significant effect in Coarse 2, suggesting that harmonic goals only influence segmentation on a coarse grain. The increased likelihood of responding following a dominant harmony is a bit surprising, but an interaction effect shows that musicians are less likely than non-musicians to respond when that feature is present. Structural features of the movement, like the standard " over V at the end of the development, may also account for this result. The approach to the last note of a segment is also significant, but not consistent between trials. A descending stepwise melodic line into the last note predicts responses in both fine trials, but a more general descending melodic contour only predicts responses in Fine 2. The opposite effect occurs in the coarse condition, where participants are less likely to respond to a descending stepwise line—a feature that in this particular movement is associated more with cadential articulations within the exposition and recapitulation than with the ends of these sections. A significant interaction shows that non-musicians are mostly responsible for this effect in the coarse condition; musicians exhibit no change based on the presence or the absence of this feature. Particular compositional characteristics of this movement might account for this result: the approach to %+at the end of the exposition, development, and recapitulation (before the coda) is not a stepwise descent, and the entire movement concludes with an ascending gesture, ' ! in the melody. There is a strong main effect for an ascending motion into the last note of a segment, and an interaction shows that graduates are slightly more likely than undergraduates to respond to this feature in the fine condition. On the other hand, while an embellished ascending line also predicts the fine responses, graduates are much less likely to respond than undergraduates when this feature is present. This might reflect the tendency for the less-experienced musicians to perceive a boundary in mm. 29–30 (see Example 5.16) and other similar passages, in contrast to more experienced musicians.72 This moment of silence interrupts the ongoing phrase and is preceded by an embellished stepwise ascent that concludes on % (supported by a dominant harmony). Participants who are listening for the arrival of harmonic and melodic “goals” probably would not perceive a boundary at this point, but participants who are responding to

72 For instance, within this particular window in Fine 1, 11% of graduates responded, 70% of undergraduate musicians responded, and 93% of non-musicians responded.

126 changes in the surface might. This trend is verified by the negative main effect for the leading tone. While listeners do not indicate endings in Fine 1 for the motion from '-!, an interaction reveals that graduates are much more likely to respond to this feature.73 In general, increased expertise seems to elevate arrival features that project a harmonic or melodic goal.

Table 5.19: ANOVA Means for Interactions in the Arrival Feature Analysis, No. 19

Outcome Feature Level of Musical Less Musical Training More Musical Training variable Experience for p-value Those with More Feature Absent Feature Present Feature Absent Feature Present Training Fine 1 ! Musician 0.452 0.467 0.346 0.524 <0.001 Fine 2 ! Musician 0.364 0.446 0.381 0.549 0.019 Fine 1 # Musician 0.461 0.440 0.438 0.275 0.004 Fine 1 % Musician 0.430 0.582 0.390 0.504 0.001 Coarse 2 V Musician 0.179 0.116 0.202 0.088 0.007 Coarse 2 x-V Musician 0.165 0.157 0.199 0.137 0.018 Coarse 2 Step Descent Musician 0.185 0.106 0.173 0.165 0.009 Fine 1 Ascent Graduate 0.441 0.573 0.306 0.424 0.001 Fine 2 Ascent Graduate 0.408 0.518 0.364 0.528 0.004 Fine 1 Emb. Ascent Graduate 0.449 0.596 0.342 0.256 0.002 Fine 2 Emb. Ascent Graduate 0.419 0.508 0.410 0.322 0.003 Fine 1 LT-Tonic Graduate 0.469 0.458 0.307 0.506 <0.001 Fine 2 LT-Tonic Graduate 0.430 0.440 0.371 0.605 0.002 Fine 1 Duration Musician 0.434 0.503 0.344 0.532 0.007 Fine 1 PAC Graduate 0.460 0.491 0.358 0.246 <0.001 Fine 2 PAC Graduate 0.431 0.430 0.416 0.345 0.01 Coarse 1 PAC Graduate 0.169 0.200 0.128 0.044 0.001

Surprisingly though, none of the cadences were predictive at the p < 0.02 level,74 but there are interactions involving cadences and graduates in almost every trial. While undergraduate responses show little (Fine 2) or no (Fine 1 and Coarse 1) influence from a PAC, graduates consistently are less likely than undergraduates to respond in a window with a PAC (note the decreasing means at the bottom of Table 5.19 for graduates).75 This seems

73 This particular arrival feature might account for graduates responding more to an ascending motion. 74 There is a main effect for the PAC in Coarse 1: t(2465) = 2.24, p = 0.025, OR = 1.54. 75 This trend continues in the Coarse 2 trial, but the interaction is only significant at p = 0.046, meaning the difference between the two groups has a greater likelihood of occurring by chance.

127 counterintuitive given the previous results that indicated that tonal structural features predict endings. As will be discussed in more detail below, this movement had a large number of external phrase extensions (i.e., extra material following the cadence but occurring before the end of the phrase). Graduates, who are presumably more familiar with Mozart’s style, would be more likely to wait until the end of the phrase extension (which extends the cadence) before indicating a response.76 Furthermore, some of the PACs in this movement aren’t as strong as other PACs. Perhaps musicians are more choosy than non-musicians about which PACs indicate a boundary, as indicated in Table 5.20. This table displays the percentage of responses for three windows in the passage from mm. 70–87. Graduates do not respond at all to the weaker PAC in m. 73, while everyone responds in greater numbers to the cadential arrival in m. 77. Following this arrival is a ten-measure phrase extension prolonging the tonic harmony. At the conclusion of this passage, everyone is much more likely to indicate a boundary.

Table: 5.20 Percentage of Responses at PACs in Fine 2, No. 19 Window Location Undergraduates Graduates m. 73 29% 0% m. 77 50% 56% m. 87 67% 89%

Table 5.21 reveals no main effects for scale degree at p < 0.02 in String Quartet No. 21, however ! does significantly predict the fine endings.77 Since there was no subject group interaction present with this feature (see Table 5.22), there might be a feature interaction, where subjects respond to !+only when another feature is present. The significant main effect in the fine condition for the presence of a tonic chord also suggests that this may be the case. There is also a main effect for the presence of a dominant chord in this condition, but the odds ratio for the tonic chord is twice that of the dominant.78 Harmonic motion into a tonic harmony is only significant in Coarse 1, but the presence of a V-I progression correlates with a much higher response rate for

76 I only noted the cadential arrivals in my coding even though the phrase extensions carry the cadential function until the end of the phrase. 77 In Fine 1, t(1201) = 2.00, p = 0.046, OR = 4.46 and in Fine 2, t(1201) = 2.06, p = 0.039, OR = 8.01. Despite a high odds ratio for this feature, the large standard error reveals the high variability in the data, increasing the p value. 78 Due to the large standard error, these ratios aren’t significantly different.

128 the graduate subject group in the fine condition; this is due mostly to a higher baseline for the undergraduates, implying that undergraduates are less discriminate in their responses (the same pattern occurs in Coarse 2, but with the musicians subject group—see Table 5.22). While musicians are more likely to respond to a V-I progression, they are less likely than non- musicians to respond to a progression that terminates on the dominant in the fine condition. However, in Coarse 2 the opposite is true: both groups again tend to not respond to an ending on the dominant, but this effect is lessened for musicians, meaning that they are more likely than non-musicians to respond. This may relate to main effect of the HC in the coarse condition, suggesting that cadential goals influenced segmentation more in the coarse condition than in the fine condition. Unlike the previous movement, where there were no main effects for the presence of the cadence, participants more consistently responded to cadential articulation in Mozart’s String Quartet No. 21. Across the board, PACs are significant, and in both coarse conditions there was also a main effect for the IAC and HC, although the odds ratio for the HC is significantly lower than for the PAC. This movement has considerably fewer phrase extensions, so a majority of the time the cadence coincides with the end of the phrase. This is the only movement that exhibits a consistent main effect for a stepwise descent. Although a general downward approach to an ending is not significant, a stepwise descent, even when embellished, predicts increased responses across all four trials.79 This may reflect the melodic construction of this piece, where clearly defined subphrases end with a stepwise descent (m. 2) or an embellished stepwise descent (m. 4) (see Example 5.12). Like in the previous movement, a general upward contour, including the motion from the leading tone to the tonic, significantly predicts the absence of a response in two of the trials. Again, musicians are less likely than non-musicians to perceive an ending when the line ascends, but they are more likely than non-musicians to perceive an ending when the leading tone ascends to tonic. A stepwise ascent is predictive in three trials, while an embellished stepwise ascent is only significant in Fine 2 (an example of an embellished stepwise ascent appears in mm. 5 and 6 of Example 5.12).

79 An interaction reveals that this effect for a descending stepwise line, however, is absent for graduates in the Coarse 2 trial, where this feature does not influence their responses compared with those of the undergraduates.

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Table 5.21: Mixed Logit Regression Analysis: Arrival Features, No. 21

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Fine 1 2.783041 0.849425 3.276 1215 0.001 16.168114 (3.054,85.594) I Harmony/ Fine 2 2.793356 1.131480 2.469 1217 0.014 16.335743 (1.774,150.403) Harmonic Motion V Fine 1 2.123094 0.794719 2.672 1215 0.008 8.356952 (1.757,39.739) V-I Coarse 1 1.257265 0.407899 3.082 1213 0.002 3.515791 (1.579,7.827)

Ascent Coarse 1 -1.720381 0.545702 -3.153 1209 0.002 0.178998 (0.061,0.522) Direction Fine 2 -2.448702 0.816184 -3.000 1206 0.003 0.086406 (0.017,0.429) LT-Tonic Coarse 2 -2.937525 0.957314 -3.069 1209 0.002 0.052997 (0.008,0.347) Fine 2 1.507373 0.284820 5.292 1201 <0.001 4.514854 (2.582,7.895) Descent Coarse 1 1.058496 0.309171 3.424 1203 <0.001 2.882034 (1.571,5.286) Coarse 2 1.463821 0.323258 4.528 1203 <0.001 4.322443 (2.292,8.150) Fine 1 1.418066 0.567440 2.499 1201 0.013 4.129126 (1.356,12.571) Ascent Fine 2 1.218496 0.394620 3.088 1201 0.002 3.382096 (1.559,7.336) Steps/ Emb. Coarse 1 1.616638 0.553836 2.919 1203 0.004 5.036132 (1.699,14.928) Steps Fine 1 1.184301 0.331546 3.572 1201 <0.001 3.268403 (1.705,6.264)

Embellished Fine 2 2.014063 0.294312 6.843 1201 <0.001 7.493704 (4.206,13.350) Descent Coarse 1 1.228347 0.453447 2.709 1203 0.007 3.415580 (1.403,8.315) Coarse 2 0.712774 0.298505 2.388 1203 0.017 2.039641 (1.136,3.664) Emb. Ascent Fine 2 1.240258 0.399695 3.103 1201 0.002 3.456504 (1.578,7.572)

Fine 1 1.592021 0.484712 3.284 1201 0.001 4.913670 (1.898,12.718) Fine 2 2.365207 0.487669 4.850 1201 <0.001 10.646245 (4.089,27.716) PAC Coarse 1 2.058855 0.255570 8.056 1203 <0.001 7.836993 (4.747,12.939) Coarse 2 1.955235 0.270974 7.216 1204 <0.001 7.065582 (4.152,12.024) Fine 2 2.449530 0.991296 2.471 1201 0.014 11.582905 (1.656,81.000) Cadence IAC Coarse 1 1.848909 0.699153 2.644 1203 0.008 6.352888 (1.612,25.044) Coarse 2 1.854143 0.767237 2.417 1204 0.016 6.386224 (1.417,28.774) Coarse 1 1.314523 0.414939 3.168 1203 0.002 3.722974 (1.649,8.403) HC Coarse 2 1.419039 0.484763 2.927 1204 0.003 4.133147 (1.597,10.699) Evaded Fine 2 -1.82185 0.699290 -2.605 1201 0.009 0.161726 (0.041,0.638) Cadence

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Table 5.22: ANOVA Means for Interactions in the Arrival Feature Analysis, No. 21

Example 5.12: Mozart, String Quartet No. 21, second movement, mm. 1-8 (violin 1) The Type 1 Windows are annotated on the score with a solid box. The Type 2 Windows are annotated on the score with a dashed box.

Change Features: There is an overall lack of main effects for change features in the Mozart movements, indicating that change alone is insufficient to create a sense of ending. The amount of surface change in both movements is much less than in the Bartók movements, and thus presumably plays a smaller role in the segmentation task. The change features were analyzed in the same groups as in the Bartók analysis: silences, orchestration changes, and other changes. The significant results from these analyses are shown in Tables 5.23 and 5.24. There are fewer change features positively influencing the results compared with the Bartók analyses: in fact, String Quartet No. 19 has positive coefficients only for complete silence and a change in dynamic level. Surprisingly, String Quartet No. 21 does not have an effect for complete silence, but other changes influence participants’ responses.

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Table 5.23: Mixed Logit Regression Analysis: Change Features, No. 19

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Fine 1 1.299193 0.232535 5.587 2493 <0.001 3.666337 (2.324,5.785) Fine 2 1.110595 0.282217 3.935 2493 <0.001 3.036164 (1.746,5.281) Silence Coarse 1 1.803089 0.274909 6.559 2493 <0.001 6.068363 (3.540,10.404) Coarse 2 2.011653 0.312752 6.432 2493 <0.001 7.475663 (4.048,13.804)

Melodic Fine 1 -0.691147 0.289167 -2.390 2493 0.017 0.501001 (0.284,0.883) Silence Coarse 1 -1.830045 0.532366 -3.438 2493 <0.001 0.160406 (0.056,0.456) Fine 1 -1.103671 0.177798 -6.207 2493 <0.001 0.331651 (0.234,0.470) Other Instrument Fine 2 -0.980578 0.191200 -5.129 2493 <0.001 0.375094 (0.258,0.546) Silence Coarse 1 -0.907200 0.219563 -4.132 2493 <0.001 0.403653 (0.262,0.621)

New Fine 1 -0.975525 0.354085 -2.755 2493 0.006 0.376995 (0.188,0.755) Instrument Fine 2 -1.638651 0.426600 -3.841 2493 <0.001 0.194242 (0.084,0.448) Coarse 1 -0.756947 0.259056 -2.922 2498 0.004 0.469096 (0.282,0.780) Register Coarse 2 -0.674887 0.270200 -2.498 2498 0.013 0.509214 (0.300,0.865) Fine 1 0.770116 0.179109 4.300 2493 <0.001 2.160017 (1.520,3.069) Dynamics Coarse 1 1.664430 0.293689 5.667 2498 <0.001 5.282661 (2.970,9.397) Coarse 2 2.220171 0.317209 6.999 2498 <0.001 9.208909 (4.944,17.154)

Table 5.24: Mixed Logit Regression Analysis: Change Features, No. 21

Outcome Coefficient Standard t-ratio Approx. p-value Odds Confidence variable error d.f. Ratio Interval

Non-mel Sil Coarse 1 0.861873 0.187515 4.596 1206 <0.001 2.367591 (1.639,3.420) New Instr Fine 2 -0.903296 0.293516 -3.078 1211 0.002 0.405232 (0.228,0.721) New Mel Fine 2 0.610553 0.255521 2.389 1211 0.017 1.841450 (1.115,3.040) Register Fine 1 0.756718 0.239491 3.160 1211 0.002 2.131269 (1.332,3.410) Coarse 1 0.971746 0.257615 3.772 1211 <0.001 2.642554 (1.594,4.381) Dynamics Coarse 2 1.016433 0.248980 4.082 1211 <0.001 2.763320 (1.695,4.504)

The negative coefficients in Mozart’s String Quartet No. 19 may reflect that participants were using cues other than surface changes in the segmentation task, and these changes tend to distinguish larger units. Consider, for instance, the changes of register in mm. 16 and 17 (refer to Example 5.16): while the first follows the end of a phrase, the second does not. Accordingly, participants are much more likely to respond in m. 16 than in m.17 (in the Coarse 1 trial, 45% of the participants respond in m. 16 compared with only 9% in m. 17). However, a pair of subject

132 group interactions show that participants with formal musical training are more likely than non- musicians to indicate endings when the register changes.80 This probably reflects the tendency for musicians to be more consistent than non-musicians in their responses, but does not change the overarching trend that register change by itself probably does not influence segmentation, especially in the coarse condition. Also, as seen in the third movement of Bartók’s quartet, a thinning of the texture is not sufficient to perceive a boundary. An analysis examining feature interactions would probably reveal that when these change features are combined with a cadential gesture, participants are more likely to respond to them. Complete silence, on the other hand, is highly predictive in both conditions—especially in the coarse condition, where the odds ratio is significantly higher. Besides silence, only dynamic change elicits a positive main effect, and this occurs only in the coarse condition. This reflects a feature interaction between cadential arrival followed by the introduction of a new theme and a change in dynamics: Mozart is much more likely to change the dynamics than to change the register at these points. Further, in Fine 2, despite not having a main effect for dynamics, musicians are much more likely to respond to a change in dynamics than non- musicians, while the opposite is true in Coarse 1, when musicians are less likely to respond.81 This suggests that musicians may be more influenced by these sorts of change features at a finer grain of segmentation, while arrival features project coarse boundaries. The second movement of String Quartet No. 21 is the first movement examined here where complete silence does not predict a response. This may be a result of the compositional design of this movement. Complete silence never occurs at cadential points; instead, it only articulates subphrase divisions in mm. 2 and 10 as well as in the corresponding points in the return of the opening section: mm. 44 and 52. As in the previous movements, melodic silence is still not a strong predictor of the results, but a thinning of the texture with a non-melodic silence is significant in the Coarse 1 trial (Table 5.24). An interaction shows that graduates are more

80 For non-musicians, in Fine 2 the ANOVA means increased from 0.383 to 0.433 when the register changed, compared with the larger percent increase from 0.428 to 0.492 for musicians, and in Coarse 1 the ANOVA means increased from 0.168 to 0.206 when the register changed, compared with the larger percent increase from 0.089 to 0.170 for musicians. 81 For non-musicians, in Fine 2 the ANOVA means increased from 0.367 to 0.433 when the dynamics changed, compared with the larger percent increase from 0.346 to 0.577 for musicians, and in Coarse 1 the ANOVA means increased from 0.080 to 0.433 when the dynamics changed, compared with the smaller percent increase from 0.062 to 0.170 for graduates.

133 likely to respond to this same feature in the fine condition than are undergraduates, who are less likely to change their behavior when the feature is present.82 This is opposite from the effect found in the previous Mozart movement, perhaps reflecting a different compositional structure where a thinning of the texture co-varies with new sections. The other change features that predict a segmentation response include a new melodic instrument and changes of register or dynamics, but none of these features is consistently significant across trials. Generally, just the introduction of a new instrument predicts the absence of a response for all participants in the Fine 2 trial (like in the previous movement), but when the orchestration of the melodic line changes in this same trial, participants respond more often. This suggests that just the entrance of a new instrument isn’t important for segmentation, unlike a change of timbre in the melodic line. In this movement, like the third movement of Bartók’s Fourth String Quartet, the violin and cello exchange the melodic role several times (usually at the beginning of a new phrase), perhaps accounting for this result. A registral change increases responses in the fine condition, while a dynamic change only increases responses in the coarse condition. An interaction reveals that graduates in Fine 2 and musicians in Coarse 2 are more likely than other subjects to respond to dynamic changes.83 As before, Mozart tends to shift dynamics at important structural points. In this movement, the second phrase begins much louder than the sotto voce first phrase; the contrasting B section suddenly begins softer following the loud cadential gesture; and so forth. In both movements, arrival features best predicted listener responses, especially for participants with increased musical experience. As expected, many of the features associated with tonal closure influenced segmentation. The change features, on the other hand, do not consistently predict responses, suggesting one of two things: (1) because listeners have a familiar musical syntax on which to base their segmentation, they are less swayed by surface changes; or (2) listeners are influenced by surface changes, but only when these changes are combined with

82 For undergraduates, the ANOVA means increased from 0.497 to 0.504 in Fine 1 and from 0.483 to 0.496 in Fine 2 when the textured thinned, compared with the larger percent increase from 0.325 to 0.475 in Fine 1 and 0.333 to 0.465 in Fine 2 for graduates. 83 For undergraduates, in Fine 2 the ANOVA means increased from 0.478 to 0.524 when the dynamics changed, compared with the larger percent increase from 0.319 to 0.603 for graduates. For non-musicians, in Coarse 2 the ANOVA means increased from 0.175 to 0.296 when the dynamics changed, compared with the larger percent increase from 0.080 to 0.346 for musicians.

134 another feature. These feature interactions are not captured by the current data analysis. My own grouping analysis can represent how these features may interact in a segmentation task. As already noted, the data corroborate the hierarchical levels identified by my grouping analysis, but this next set of analyses explores how well one of these “ending types” (subphrase, phrase, and section) predicts responses. Before looking at the data, I will briefly describe which musical features contributed to my own grouping analysis.

Grouping Analysis

Bartók, String Quartet No. 4, Third Movement: As discussed previously, because the notion of “phrase” and “subphrase” are less objective in twentieth-century repertoire than in common-practice repertoire, I first divided the movement into sections, defined mainly by changes in texture, melodic content, and melodic instrument. Formally, I hear this movement as a series of varied repetitions of a theme that are organized into a larger ternary structure: the opening A section (mm. 1–34), a contrasting B section (mm. 34–55), a return to the A material (mm. 55–63), plus a coda that incorporates elements from both previous sections.84 The analysis of phrases, and especially subphrases, in this style is quite open to interpretation. After dividing the movement into sections, I further divided it into eight phrase- like units, mostly informed by changes in the sustained chord and silence in the entire texture. At the beginning of this movement, a diatonic chord leads into the cello’s first melodic entrance in m. 6. I interpret the first five measures as a prefix to the beginning of the phrase, and in order to create a well-formed hierarchical structure, I coded it as a subphrase within the larger phrase. This analysis does not capture the introductory character of the opening five measures, nor does it convey the feeling of a beginning at m. 6. Alternatively, I could have separated the first five measures from the material starting in m. 6 by creating two phrases; however, the first five measures do not contain a sense of a beginning, middle, and end. This analytical choice of interpreting the opening five measures as part of a larger phrase is consistent with my subsequent choices to designate phrase beginnings at the chord changes throughout this movement.

84 Other formal designations are also possible, such as sonata form and strophic construction (Bayley, 2000, 363–4). While a decision about the formal designation is not essential to this study, it is important to note the movement’s range of possible interpretations.

135

The body of this eight-measure phrase (mm. 6–13) further divides into 4+4 subphrases. Measure 10 introduces a new melodic gesture following an inversion of the falling fourth cadential Figure used throughout this movement to mark endings in both A sections. Other analytic writings support this sense that m. 10 marks a division within a larger unit. Bayley notes a division here, and recognizes that “the background continuity of a sustained harmony” is retained “in order that the melody is perceived as an eight-bar entity” (2000, 375).85 Refer to Example 5.11, which shows the cello melody from mm. 6–35. The beginning of the second phrase (mm. 14–20) poses new questions regarding the interpretation of the sustained harmony, which changes on the fourth beat of m. 13, preceding the cello entrance on the third beat of m. 14. I could interpret this music between the presentation of the chord and the cello melody as a prefix to the ensuing melodic entrance of the cello, comparable to mm. 1–5. However, unlike the beginning, these three beats seem too short to constitute a subphrase. Another alternative is to consider these three beats as belonging to neither phrase (i.e., merely existing between phrases), but the resulting phrase analysis will not be well- formed unless this unit is a phrase itself, which would be inconsistent with the analysis of the opening five measures. The remaining alternative is not to divide the subphrase (mm. 13–17) into smaller units, recognizing that the beginning of the phrase may not exactly coincide with the melodic beginning. In this case, and for similar instances in this movement, I chose this third alternative, which does not explicitly mark the melodic entrance. Similar questions regarding beginnings and endings arise in the analysis of the fifth movement of this quartet. The division of the second phrase into subphrases creates a structure similar to the first phrase, where an inversion of the material from m. 10 motivates a subphrase division in m. 17, beat 3. Dividing the last phrase of this section (mm. 21–35) is more difficult than dividing the first two phrases. Bayley (2000) places her only subphrase division at m. 31, drawing a connection between the cadential material found in m. 19, beat 4 through m. 21, beat 3 and the material in mm. 29–30. I agree that mm. 29–30 is cadential, so I also placed a new subphrase at 31. However, I interpreted the material in 31–34 as a cadential extension, not as a consequent response to the material in mm. 21–31. The unsettled character of mm. 31–34 transitions to the B

85 Bayley uses different terminology at this point. From her perspective, each of the phrases I note is in fact a period containing its own antecedent and consequent phrases (which I describe as subphrases). We agree about the boundaries of these entities, but we interpret the music on slightly different hierarchical levels.

136 section, which begins in m. 35. I also heard another subphrase division at the end of m. 25, occurring around the same point in the phrase as the subphrase divisions in the first two phrases. Even though m. 26 does not pick up the same melodic content as the subphrases that began in mm. 10 and 17, it does repeat the opening gesture from m. 22, beat 3, clearly articulating a new beginning. I did not further divide the phrase, despite the melodic silence in m. 27 (which, in my opinion, just articulates the motivic repetitions as the melody becomes more fragmented). The B section begins on the third beat of m. 34 and features less homogeneity between the phrases than did the preceding A section. This section also has three phrases: mm. 34–41, mm. 42–47, and mm. 47–55. The first phrase has a subphrase division on the second beat of m. 37, when the rhythmic kernel introduced in m. 35 morphs into a more melodic rendition. Also at this point, the texture of the harmonic accompaniment changes to a tremolo figure, further setting this material apart. Following a strong falling third cadence, the second violin takes up the melody in the short second phrase, with a subphrase division coinciding with the first melodic rests in this phrase, at m. 44. The last phrase of this section (mm. 47–55) presents two contrasting ideas, organizing the phrase into three subphrases with a loose aba construction. The canonic presentation of a new rambunctious melodic idea interrupts the “circling around C” melody in m. 50, thus initiating a new subphrase. This subphrase is short-lived; the phrase returns to its previous melodic content on the third beat of m. 51. The third section (A' section) is a single phrase in sentential structure. A variation of the opening melody is played in inverted canon between the cello and the first violin. Each subphrase ending is marked by the descending fourth cadential gesture in the cello. Measure 64 begins the last section of the piece, a coda that incorporates ideas from the previous sections. I did not divide this coda into subphrases: although a listener could segment this section at one of the abundant rests, I believe there is insufficient contrast to divide this phrase. Instead, the rhythmic kernel from the B section spins out over the A diatonic harmony from the A section. Most of my interpretation of the grouping structure was based on differentiation of melodic material, a variable not included in my data analysis. These points are usually articulated by some sort of change in the musical surface or by an arrival feature, which I included in my data analysis. A similar interaction between change and arrival features influenced my analysis of the grouping structure in the fifth movement.

137

Bartók, String Quartet No. 4, Fifth Movement: I divided this movement into eight large sections, outlined in Table 5.25. The thematic content of this driving movement has some similarities to sonata form, where the material in Sections 2 and 3 returns in Sections 6 and 7 as a quasi-recapitulation after a developmental Section 5. Sections are demarcated by the introduction of a new melodic idea, new texture, or new ostinato figure. Much of the movement, in fact, employs some ostinato, which changes throughout the course of the piece. This ostinato, which continues past the end of melodic gestures, sounds like a backdrop upon which the melodic phrases are presented. Although the continuous ostinato sounding between phrase presentations doesn’t clearly belong to the phrases on either side, I had to interpret the music between melodic gestures either as a prefix or as a suffix in order to use only well-formed hierarchical structures (as discussed in the context of the third movement). A pictorial representation of these possibilities is presented in Figure 5.7. Usually my analytic decisions interpreted the earliest element (whether the ostinato or the melody) as the beginning of the phrase. For instance, the first phrase in the second section (mm. 11–18, reproduced in Example 5.13) began with an ostinato figure, so the ostinato is a prefix, like the hypothetical phrase diagram in Figure 5.2b. The first phrase in the third section (Example 5.14) begins with the melody, so the accompanimental material is a suffix, like Figure 5.2a. Even though Section 6 recapitulates melodic material from Section 2, my interpretation of the phrase structure shifts with the introduction of the strong descending third cadence in the fifth section. In Section 2, phrases concluded with the end of the movement’s primary melodic theme (Example 5.13); however, in Section 6 repeated chords from the beginning concluding with a descending third cadence follows the melodic theme (Example 5.7). This cadence sounds like a stronger ending than did the conclusion of melodic theme (Example 5.15); my phrase analysis of this section therefore looks quite different from the expositional presentation in Section 2. Because the development marked the unison descending third as a strong cadential gesture, its presence elevates the repeated chords to a subphrase within the phrase proper rather than a suffix (although the limited vocabulary I used for the sake of data analysis does not preserve the distinction between an internal subphrase and a suffix).

138

Table 5.25: Section divisions in Bartók, String Quartet No. 5, fifth movement Section Formal Function Measures 1 Introduction 1–11 2 Exposition: First Theme 11–101 3 Exposition: Second Theme 102–121 4 Closing material 121–151 5 Development 152–238 6 Recapitulation: First Theme 238–343 7 Recapitulation: Second Theme 344–374 8 Coda 374–392

Figure 5.7: Possible Phrase Structure Analyses A complete arc in the phrase diagram represents the main content of the phrase, while the incomplete arc leaning on it represents either a prefix (if it comes before) or a suffix (if it comes after). In order to create a well-formed grouping analysis, connected arcs collectively form a single phrase.

139

My analysis of this movement was based on differentiation (as in the third movement), but context influenced my categorizing of the prevailing ostinato as a beginning or ending. The ways in which various musical features shaped my interpretation of the context is difficult to capture using only the arrival and change features from the data analysis, but features that particularly influenced my segmentation included cadential gestures, changes of ostinato, and melodic content and repetition.

140

Mozart, String Quartet No. 19 in C Major (“Dissonance”), K. 465, Fourth Movement: In my analysis of both Mozart movements, arrival features, especially those associated with tonal paradigms, principally shaped my analysis, while formal schema and phrase length also contributed to my interpretation. The primary tonal area (PTA) of this sonata- form movement resembles a rounded sectional binary form (without the repeats), where the first sixteen measures present a periodic structure followed by an eight-measure phrase group leading into a return of the main theme (see Example 5.16). Each phrase in the opening period, an antecedent phrase ending on the dominant and the parallel consequent concluding on tonic, can be divided into a pair of clearly articulated subphrases, where the first three subphrases conclude on a dominant harmony. Following the PAC in m. 16, the next eight measures form a parallel phrase group, where each phrase begins on the tonic but quickly moves to prolong the dominant for the remainder of the phrase. These phrases lack true cadential articulation, but the melodic repetition suggests two phrase-like units grouped together under a higher hierarchical umbrella. This emphasis on the dominant and the shorter phrase lengths rhetorically signifies the beginning of the binary form’s second reprise. In m. 24, the opening melody returns, but instead of immediately concluding with a PAC, the phrase is expanded by repeating the rising fourth gesture up a step in the first subphrase (mm. 28–29) followed by two beats of complete silence before initiating the cadential formula.

141

Following the PTA, a typical independent transition begins, with a cadential arrival on the dominant of V (a D-major chord) in m. 49, followed by a six-measure phrase extension prolonging the cadential harmony. While the goal of this harmonic motion is achieved in m. 49, I could not consider m. 49 to be the end of the phrase because it would have left an unacceptable gap in the hierarchical analysis: mm. 49–54 do not constitute a phrase (there is no harmonic motion) and the next phrase does not begin until after the medial caesura with the initiation of the STA. Because mm. 49–54 follow the structural ending, they are not technically a subphrase, but in order to form a nested hierarchical analysis that acknowledges the cadential arrival in m. 49 and the formal phrase ending in m. 54, it seemed reasonable to designate both mm. 34–49 and mm. 49–54 as subphrases. Both subphrases are nested within a single larger phrase, forming the entire transition section. I divided the STA in three sections. The first, mm. 54–88, remains in G major (dominant of the original key). The second, mm. 88–103, tonicizes E( major ((VI of G) before returning to G for the cadence in m. 103, and this section elides into the third, which continues until the end of the exposition (refer to Figure 5.8, illustrating the division of the entire exposition into sections, phrases, and subphrases). In this well-formed analysis, all music must be included in a phrase and in a section, but it need not belong to a subphrase because not every phrase is divided into subphrases. For instance, the phrase that begins the STA (mm. 35–61) does not easily divide into smaller units, and so the subphrase level is absent from my analysis at this point. To this point, I have used subphrases to account for external phrase extensions, but the subphrase level is also used to account for internal phrase expansions, including those caused by an evaded cadence. Measures 118–135 present one such use of subphrases (see Example 5.17). The cadential arrival occurring in m. 125 follows a deceptive motion in m. 122. This evaded cadence initiates an internal expansion, dividing the phrase into two shorter subphrases. Three subphrases follow the PAC in m. 125: the first two (mm. 125–129 and 129–131) extend the phrase by repeating the cadential formula, and the third detonicizes G major with the introduction of F)+in preparation for the repeat of the exposition (which is not taken in the recording I used for this study) or for the C-minor beginning of the development section. Along with illustrating the division of the exposition into smaller groups, Figure 5.8 also shows the

142 location of cadential arrivals in relation to phrase endings.86 My analysis of the recapitulation followed the model established in the exposition since the recapitulation essentially replicates the formal construction of the exposition (except that STA2 is expanded with a deceptive motion leading to a tonicization of (II in m. 306). Both remaining parts of the movement, the short development and coda, consist of a single larger section divided into three phrases.

Example 5.16: Mozart, String Quartet No. 19, fourth movement, mm. 1–34 (violin 1 and cello)

86 I could have included additional grouping levels between the phrase level and section level since not all phrase endings are equivalent. One such example occurs in mm. 70-77, where the PAC in m. 73 is weaker than the PAC in m. 77, creating a longer eight-measure unit (not counting the phrase extension that follows). While such an addition would better reflect the grouping structure of the movement, it was omitted in order to simplify the data analysis.

143

PTA TR STA1 STA2 K

1 4 8 12 16 20 24 29 34 49 54 61 69 73 77 87 91 95 103 117 121 125 129 131 135 HC PAC PAC HC HC PAC (PAC) PAC PAC PAC PAC

Figure 5.8: Mozart, String Quartet No. 19, Fourth Movement: Grouping Analysis of the Exposition The top line shows phrase boundaries; the bottom line shows subphrase boundaries.

Example 5.17: Mozart, String Quartet No. 19, fourth movement, mm. 118–135 (violin 1 and cello)

144

Formal schema (including typical phrase length) and arrival features (such as cadential articulation and harmonic goals) influenced my segmentation in this movement. In my analysis, endings were marked by typical cadential paradigms and beginnings were marked by new melodic material or by a repetition of previous melodic material. While surface changes in dynamics, articulations, and register may coincide with a beginning, they did not play a major role in my grouping analysis. Given that the second movement of the String Quartet No. 21 shares the same tonal syntax and is written in the same style, I used a similar procedure for my analysis of this movement. Mozart, String Quartet No. 21 in D Major, K. 575, Second Movement: I divided this andante movement into five large sections: the primary theme (mm. 1–19), transition (mm. 20– 33), secondary theme and retransition (mm. 34–42), return of the primary theme (mm. 43–61), and closing material with a codetta (mm. 62–73). The A-major primary theme is a two-phrase parallel period where both phrases exemplify sentential structure and the second phrase evades an expected cadence in m. 16 before arriving on the tonic in m. 19 (refer back to Example 5.2). As in the previous movement, I analyzed the evaded cadence as completing a subphrase (from mm. 12–16) and initiating a new subphrase (from mm. 16–19). Each part of the sentential structure—both parts of the presentation and the entire continuation—is also analyzed as a subphrase. The transition begins with a sequence that passes the melodic material between the instruments, eventually making its way to the dominant (E Major). Despite the complete I-V-I progression in mm. 20–23 (A major) and in mm. 24–27 (F" minor), I interpret every two measures as a subphrase, synchronized with the sequential repetition of the melodic line. The cadential arrival occurs in m. 31 on a HC in E major, but it is immediately extended by two external phrase expansions (analyzed as subphrases) until the end of the formal phrase in m. 33. The secondary theme in E major, which is only two phrases long, follows this transition. The first violin plays the melody in the first phrase, ending with an IAC, and the cello picks up the melody in m. 38, reaching a PAC in m. 41. E major is then detonicized with the introduction of a D!, setting up the return of the primary theme (see Example 5.18). Because this retransition is so brief, I heard it as an extension of the phrase begun in m. 38, yet another example of the cadence occurring before the end of the phrase. The return of the primary theme mirrors the formal

145 structure from the beginning, complete with an evaded cadence, and m. 62 initiates the closing section of the piece. The second of the two phrases in this section is extended past the cadential arrival in m. 69. The two subphrases that follow repeat the cadential pattern, rhetorically serving as a codetta to this movement.

Example 5.18: Mozart, String Quartet No. 21, second movement, mm. 40–44

Data Analysis: While my decisions were based on many listenings and conscious reflection, participants in this study had limited experience with these compositions and did not have the opportunity to reflect on their segmentation decisions. Despite these differences, the participants’ segmentation decisions significantly mirrored my own, especially as musical expertise increased. This set of analyses investigates the extent to which analytical ending types, defined by my grouping analysis, predict subject responses. The results from these regressions are in Table 5.26. Among all participants, phrase endings consistently predict responses. Sometimes this effect is particularly strong; for instance, the coarse trials in Bartók’s third movement have exceedingly high odds ratios. Subject group interactions reveal that the group with more musical training is more likely to respond at phrase endings (with the exception of Bartók’s fifth movement).43 Most of these results are driven by the less experienced musicians having a relatively higher baseline mean for when a phrase ending is absent. This suggests that non-

43 This result is inexplicable, especially since all section endings corresponded with a phrase ending and the main effect for section ending in this movement indicates that participants respond consistently to that feature.

146 musicians are in less agreement with my analysis, and looking at the results as a whole, they tend to be less discriminating overall.

Table 5.26: Mixed Logit Regression Analysis: Grouping Analysis

Outcome Coefficient Standard t-ratio Approx p-value Odds Confidence variable error d.f. Ratio Interval

Section Fine 1 2.834667 0.957010 2.962 1393 0.003 17.024731 (2.604,111.310) Fine 1 1.701294 0.502734 3.384 1393 <0.001 5.481033 (2.044,14.697) Fine 2 1.917259 0.547971 3.499 1393 <0.001 6.802289 (2.321,19.933) Phrase Bartók Coarse 1 4.000502 0.690529 5.793 1393 <0.001 54.625563 (14.093,211.732) Mvmt. 3 Endings Coarse 2 6.247745 1.037728 6.021 1393 <0.001 516.845955 (67.473,3959.08) Fine 2 -0.545557 0.214859 -2.539 1393 0.011 0.579519 (0.380,0.883) Subphrase Coarse 1 -1.310557 0.464784 -2.820 1393 0.005 0.269670 (0.108,0.671) Coarse 2 -2.955109 0.911855 -3.241 1393 0.001 0.052073 (0.009,0.312) Coarse 1 2.190514 0.265271 8.258 2801 <0.001 8.939810 (5.315,15.036) Section Coarse 2 1.588419 0.248499 6.392 2801 <0.001 4.896003 (3.008,7.968) Fine 1 0.939456 0.161433 5.819 2801 <0.001 2.558589 (1.865,3.511) Bartók Fine 2 0.684197 0.187449 3.650 2801 <0.001 1.982180 (1.373,2.862) Mvmt. 5 Phrase Endings Coarse 1 0.870921 0.214951 4.052 2801 <0.001 2.389110 (1.568,3.641) Coarse 2 1.310339 0.201581 6.500 2801 <0.001 3.707429 (2.497,5.504) Fine 2 0.315503 0.095895 3.290 2801 0.001 1.370949 (1.136,1.654) Subphrase Coarse 2 -0.604209 0.207700 -2.909 2801 0.004 0.546507 (0.364,0.821)

Coarse 1 0.642937 0.256859 2.503 2493 0.012 1.902059 (1.149,3.148) Section Coarse 2 1.202767 0.405722 2.965 2493 0.003 3.329315 (1.503,7.377) Fine 1 1.209364 0.254545 4.751 2493 <0.001 3.351351 (2.034,5.521) Mozart No. 19 Fine 2 0.907300 0.356961 2.542 2493 0.011 2.477624 (1.230,4.989) Endings Phrase Coarse 1 1.545690 0.152140 10.160 2493 <0.001 4.691206 (3.481,6.322) Coarse 2 1.722955 0.248001 6.947 2493 <0.001 5.601058 (3.444,9.109) Subphrase Coarse 1 0.624000 0.200877 3.106 2493 0.002 1.866379 (1.259,2.767)

Fine 1 1.647495 0.615075 2.679 1206 0.007 5.193953 (1.554,17.362)

Fine 2 2.249056 0.595786 3.775 1206 <0.001 9.478788 (2.945,30.508) Phrase Coarse 1 2.410880 0.425501 5.666 1206 <0.001 11.143764 (4.836,25.680) Mozart No. 21 Coarse 2 2.840864 0.509186 5.579 1209 <0.001 17.130561 (6.308,46.520) Endings Fine 1 0.920706 0.317333 2.901 1206 0.004 2.511062 (1.347,4.680)

Subphrase Coarse 1 1.997244 0.378694 5.274 1206 <0.001 7.368718 (3.505,15.491)

Coarse 2 1.284160 0.476020 2.698 1209 0.007 3.611634 (1.419,9.190)

147

The results for section endings depend somewhat on the tempo of the movement and the grain of segmentation. There are not as many main effects for the end of a section in the slower movements because these movements have fewer sectional divisions that are spread out over a longer period of time. Participants with less musical training tend to indicate boundaries more often (seen in the total counts of all responses in Tables 5.5 and 5.6) and this would lessen the effect of section on the results, especially in the slow movements. The end section feature is notably absent from the main effects for the slow Mozart movement, but there is an interaction with this feature in the Coarse 1 trial. As seen in Table 5.27, both graduates and undergraduates respond to this feature, but graduates have a higher percent change (notice the high baseline again for the undergraduates). This interaction is replicated in the other three movements.

Table 5.27: ANOVA Means for Interactions in the Grouping Analysis

Movement Outcome Feature Level of Musical Less Musical Training More Musical Training variable Experience for p-value Those with More Feature Feature Feature Feature Training Absent Present Absent Present Fine 1 Section Musician 0.350 0.893 0.247 0.847 0.01 Fine 1 Section Graduate 0.336 0.826 0.179 0.972 0.011

Bartók Coarse 2 Phrase Graduate 0.076 0.696 0.027 0.917 <0.001 Mvmt. 3 Coarse 1 Section Graduate 0.107 0.750 0.030 0.944 <0.001 Fine 1 Subphrase Musician 0.354 0.464 0.191 0.463 <0.001 Fine 2 Subphrase Graduate 0.288 0.430 0.115 0.426 0.005

Bartók Coarse 1 Section Graduate 0.072 0.429 0.056 0.569 0.003 Mvmt. 5 Coarse 2 Phrase Graduate 0.020 0.146 0.340 0.121 <0.001

Coarse 1 Section Musician 0.122 0.411 0.089 0.482 0.013 Fine 1 Phrase Musician 0.370 0.580 0.233 0.660 <0.001 Mozart No. 19 Fine 1 Phrase Graduate 0.351 0.633 0.131 0.609 <0.001 Fine 2 Phrase Musician 0.306 0.518 0.266 0.690 <0.001 Fine 2 Subphrase Musician 0.393 0.395 0.421 0.449 0.001

Coarse 1 Section Graduate 0.138 0.558 0.024 0.511 0.02 Mozart No. 21 Coarse 2 Phrase Musician 0.126 0.429 0.027 0.456 0.02 Fine 1 Subphrase Musician 0.363 0.536 0.184 0.573 0.003

The effect of subphrase is less clear over all four movements. Looking first at the Bartók responses, participants rarely respond within the windows containing a subphrase division (observe the negative coefficient), especially in the coarse condition. This suggests that listeners

148 tend to reject lower-level endings when asked to note higher-level endings. In the third movement, despite the negative coefficient for the main effect of subphrase in Fine 2, musicians are more likely than non-musicians to indicate a boundary at a subphrase division in the fine condition. Table 5.27 illustrates that when a subphrase ending is present in the third movement of the Bartók quartet, there is little difference between the means of the two subjects groups. In the fine condition, when a subphrase ending is not present, the group with more musical experience has a much lower mean, resulting in a higher percent change for when the feature is present. This indicates that the effect of subphrase is less pronounced on non-musicians than it is on musicians, reflecting once again that non-musicians may be less discriminating in their responses and don’t agree with my analysis to the same extent as do the musicians. While in the fast Mozart movement, subphrases are only significant predictors in Coarse 1, there is an increased number of main effects for subphrase in the slow Mozart movement. For both movements, there is an interaction for this feature: although the presence of a subphrase ending does not change the non-musician’s responses much, musicians have a higher percent change when a subphrase ending is present. Again, this reflects a more consistent segmentation strategy for participants with more formal training.

Discussion

The results from this experiment support the hypotheses posited by EST: 1) participants will segment a given stimulus consistently between trials; 2) different participants will segment a given stimulus consistently; (3) the resulting segmentation will form a nested hierarchical structure; and (4) pre-existing knowledge structures will influence segmentation. The expectations both for continuity and for goal-directed musical successions derive from these knowledge structures. Differences between the subject groups further support this last hypothesis. Non-musicians tend to perceive more boundaries that aren’t paired consistently with musical features, but as musical expertise increased participants are more likely to respond consistently to particular features. More musical experience—both listening and performing— would create knowledge structures that could assist in this segmentation task.44

44 For future data analysis, it might be helpful to divide subjects according to how often they indicated a boundary, given that participants may have been segmenting on different hierarchical levels (meaning that one listener’s phrase might be another listener’s section).

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Overall, participants segmented the compositions consistently between trials, forming a nested hierarchical structure, and participants somewhat agreed about the location of these boundaries. There is no significant difference between the odds ratios in the Bartók and Mozart conditions for these main effects, pointing to a shared cognitive process that is not style-specific, although the musical features that mark boundaries differ between the styles represented by these composers. These different features may have resulted in different segmentation strategies, reflected in the interactions between the starting segmentation task and consistency for the Mozart subjects and between the starting segmentation task and hierarchy for the Bartók subjects. In the Mozart condition, participants who began with the fine segmentation task tended to be more consistent in their coarse responses. The opposite is true for participants who segmented the Bartók movements: these participants produced a better nested analysis when they began with the coarse segmentation task. The aural analysis of the Mozart movements improved when participants were instructed to listen first for fine-grained boundaries, which usually coincide with a cadential paradigm. This type of musical syntax is missing in Bartók’s style, so change in the musical surface apparently informed the participants’ segmentation decisions. Participants in the Bartók condition who first divided the movements into large sections seem to have formed a more stable representation of the movement into which their fine responses were nested. Since Mozart’s style does not have as many surface changes differentiating larger sections, it may have been easier for participants to group together already determined shorter musical segments into longer sections, as opposed to dividing a longer section into shorter phrases. Both of these experiences of the musical structure are supported by the theoretic cognitive mechanism that guides event segmentation as posited by EST. First, coarse segments are usually marked with the culmination of some sort of “goal” or a more drastic change in the musical surface compared to the surrounding input. The Bartók analysis was influenced more than the Mozart analysis by the number of changes in the musical surface, especially the perception of coarse divisions. Returning to Figure 5.5 (the estimated mean response in a given trial for the number of changes), the coarse condition shows a large increase in response rate when there are between three and four musical changes, suggesting that the change features highlighted in this analysis strongly influenced segmentation when present in sufficiently large

150 quantities. The creation of a nested structure is facilitated by first identifying these points in a style where standard cadential gestures are not the norm. Further research suggests that memory tends to be better at perceptual boundaries because these are the moments at which event models update, incorporating new input from the ongoing perceptual stream (Swallow, Zacks, and Abrams 2009). Perhaps participants in my study remembered these points better than other moments in the music, and this assisted in the fine segmentation task. The feature analysis reveals that when a movement has goal-directed features (such as consistent cadential progressions), participants tend to rely on them more than on surface changes, especially when segmenting on a coarse grain. When goal-directed features are absent, however, an increased number of changes creates a hierarchical structure. In the Mozart results, participants relied mainly on arrival features to mark both fine and coarse boundaries. Most of the arrival features reflect transitional probabilities (it is highly likely that an end would follow #, but not necessarily $), which would allow participants to anticipate an ending in this repertoire more so than in the Bartók movements. Since sections weren’t delineated by drastic changes in the musical surface, participants had to group together shorter segments to build longer sections. Even though these arrival features, which resemble a musical goal, predict responses in both conditions, they are far more likely to predict responses in the coarse condition. This effect increases with musical training, suggesting that musicians use these arrival cues consistently to segment musical experience. Even though the absence of standard cadential paradigms in the Bartók examples makes goal achievement difficult to quantify, features associated with movement-specific cadential paradigms tend to predict coarse boundaries in the third movement. In this movement, the falling fourth cadence and other arrival features associated with this cadence (a specific duration pattern and intervallic succession) consistently predict coarse responses.45 This can be contrasted with Bartók’s fifth movement, where a change in duration predicts fine responses because it is not consistently paired with a cadential goal. Although, for both composers, not every feature that predicts a coarse response is coupled with a cadential paradigm and cadential paradigms can also

45 It is difficult to distinguish whether listeners where responding to these cadential gestures or to the large amount of surface change that usually followed these gestures. A follow-up study that controls for these variables in the segmented stimuli might be able to distinguish the extent to which a listener depends on arrival and change features.

151 predict fine segmentation, a general trend that associates goal-directed motion with coarse divisions emerges from this data. EST also predicts that fine divisions occur at a change in motion, which in music would presumably involve a change in the acoustical stream. Although a durational change predicts fine responses in Bartók’s fifth movement, as just mentioned, no consistent effects otherwise support this hypothesis. Because these analytical features are very general, some of the fine division predictors may have been lost in an over-generalized picture, explaining this lack of effect. Coding more specific feature interactions (for instance, adding features that acknowledge a particular change in duration or register) or coding in the degree of change might yield different results. For all four movements, the formal divisions I previously identified tended to be the best predictor of listeners’ responses. Of course, my own analysis did not solely rely on the presence of a change in the musical surface; I also considered motivic and melodic repetition, conformity to formal schema, and phrase length, among other things. This evaluation was analytically complex rather than simplistic, and it depended more on my prior musical experience than on individual surface features. Despite disparities in musical training and experience, listeners evidently agreed to a remarkable extent with my formal analysis. In the fast movements, subjects tended to corroborate my higher-level endings, while in slow movements they were more likely to confirm my lower-level endings, perhaps revealing a general feeling of phrase length. Participants with more musical training were even more likely to respond at my formal divisions, presumably reflecting similarities in our musical experience and training. This experiment demonstrates that pre-existing knowledge structures can influence segmentation. Both expectations for continuity and arrival features derive from learned transitional probabilities, but, as discussed in Chapter 3, the degree of finality would correlate with the degree to which the arrival of the ending was anticipated and with the subsequent rise in prediction error. The next study uses a learning task to explore how arrival features may influence the perception of closure.

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CHAPTER 6

EXPERIMENT 2

Experiment 1 found that listeners, despite varying familiarity with the musical style, could segment a musical stream consistently based on features in the music; as previously discussed, determining meaningful musical segments is a necessary precursor to the actual perception of closure. Previous research has suggested that the ability to segment a given stimulus, as well as the associated perception of closure at the end of a segmented unit, derives from unconsciously learning the statistical structure of music. Probabilistic learning, which creates expectations that guide listener segmentation, falls into one of two categories: inclusional probabilities and transitional probabilities. Transitional probabilities are the most associated with closure, because listeners who are able to anticipate endings will experience a stronger feeling of finality at the end of a unit. In the previous study, transitional probabilities were associated both with goal completion and with a change in the acoustic landscape, the latter revealing an expectation for continuity. Broadly speaking, coarse segmentation responses correspond with arrival features (equivalent to achieving a musical goal), while fine segmentation responses reflect a change in musical motion; however, this correspondence is not consistent and varies according to musical training. Presumably, the boundaries marked by coarse segmentation elicited a stronger feeling of finality in the participants than did the boundaries marked by fine segmentation alone. While the specific feeling of finality (anticipatory, arrival, or retrospective) wasn’t explored, participants consistently use cues to make decisions about segmentation and their ability to make these decisions consistently depends upon musical experience. Transitional probabilities broadly stemming from a listener’s previous musical experiences as well as transitional probabilities learned as a particular composition unfolds guide a listener’s segmentation of an unfamiliar style. If a consistent feature concludes segments, listeners can pick up on these first-order probabilities, resulting in a greater feeling of finality when this feature occurs. Experiment 2 examines the process by which listeners learn the musical markers of endings in two styles: a more familiar common-practice style exemplified by the composer Wolfgang Amadeus Mozart and a twentieth-century style represented by the

153 composer Béla Bartók. As discussed in the previous chapter, Bartók tends to provide a metrical framework and to employ phrase lengths and formal divisions familiar from common-practice style. More important for my purposes, consistent gestures conclude phrases in the representative composition by Bartók used in this experiment. While the first-order probabilities for Bartók’s cadential gestures may not be as high as for Mozart’s cadential gestures, the goal of this study is to see whether listeners can extract these cadential cues. While many statistical learning tasks have shown that listeners are sensitive to both inclusional and transitional probabilities, this study determines whether exposure to an unfamiliar style can change the way a listener interprets a “satisfactory ending.” Any effects from this study would not be robust, for several reasons. First, the statistical learning task outlined in this chapter has an additional layer of interpretation: rather than asking participants whether a test item is a grammatical entity within a style, this study asks participants to determine whether an ending sounds “complete” or “satisfying.” Also, this task uses music from the existing repertoire, which could not be controlled for all the transitional probabilities between sound elements. Finally, while Bartók is more consistent than many other twentieth-century composers in his ending gestures, learning any first-order probabilities from a twelve-minute exposure could be a difficult task. Method Participants The participants were divided into three subject groups determined by their levels of formal musical training. Data from 21 undergraduate non-musicians (who received psychology credit for participating in this study), 22 undergraduate music majors (who received extra credit in their freshman Music Theory class), and 10 graduate music majors (who received a $10 gift card for their participation) were included in this study. Data from 10 additional participants were discarded due to technology problems. Stimuli Stimuli consisted of clips from Mozart’s String Quartet No. 19 in C Major (“Dissonance”), movements 1, 2, and 4; and Bartók’s String Quartet No. 4, movements 1, 3, and

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5.87 To create the exposure period, I selected excerpts from each movement that conclude with a cadential gesture. Table 6.1 lists the excerpts used in the exposure period, all of which were created in Audacity by segmenting the original digital file. All excerpts for each composer were then combined into a single audio file in the order in which they occur in the composition. Each clip was heard twice in succession with successive clips separated by three seconds of silence. The resulting Mozart and Bartók sound files were each slightly over twelve minutes long.

Table 6.1: Exposure Excerpts

Composer Movement Measure Numbers Time (s)

Bartók 1 1–49 (beat 1) 104.34 Bartók 1 148 (beat 4)–161 26.66 Bartók 3 1–5 22.93 Bartók 3 13 (beat 4)–21 34.00 Bartók 3 47–55 (beat 1) 37.28 Bartók 5 15–57 45.00 Bartók 5 121–148 22.86 Bartók 5 238–284 (beat 2) 35.88 Mozart 1 23–44 (beat 2) 38.55 Mozart 1 176–211 62.54 Mozart 2 1–13 (beat 2) 46.56 Mozart 2 26–39 (beat 1) 52.74 Mozart 2 101–109 (beat 2) 33.02 Mozart 4 1–34 26.85 Mozart 4 258–291 26.92 Mozart 4 326–348 18.87 Mozart 4 371-419 40.21

From these same movements, I selected 115 test clips representing each composer (a total of 230 clips). These clips were catalogued either as cadential (target stimuli) or as non-cadential fillers. For the Bartók stimuli, the average time for the 55 cadential excerpts is 3.06 seconds

87 The Emerson String Quartet performed both of the recordings used in this study from the albums Bartók: The String Quartets (1988) and Mozart String Quartets K. 465 “Dissonance,” 458 “The Hunt” & 421 (2005).

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(SD = 1.28), while the average time for the 51 cadential Mozart stimuli is 3.59 seconds (SD = 1.36). Some of the same cadential points were heard more than once, each one having a different length context preceding the cadential point. For the Mozart stimuli, the sound clips began at the initiation of the pre-dominant area (long context) or the dominant area (short context). For the Bartók stimuli, the sound clips began between 2 and 10 beats prior to cadential arrival. Sixty percent of the cadential excerpts were present in the exposure; participants heard these clips in a semi-random order. While the clips were randomized within each movement, the movements were heard in the order in which they occurred in the composition. Cadential gestures in Mozart’s string quartet include authentic cadences (both the PAC and the IAC) and half cadences, as defined in Chapter 5. Cadential gestures in Bartók’s string quartet include those defined in Chapter 5: the descending fourth and the descending third gestures as well as the multi-voiced chord, which can be presented by itself, immediately repeated, or following a lower note. To supplement this list of cadences, the ends of motives x and y and the diatonic chord that concludes the third movement were also treated as cadential. Motive x is a chromatic gesture that occurs both in its prime form (Example 6.1) and inverted in pitch-space. This motive is introduced in the first movement in m. 7 and reappears about halfway through the fifth movement. Motive y first occurs in the fifth movement in m. 16. Like motive x, the rhythmic gesture is the primary identifier for this motive (see Example 6.2).

Example 6.1: Motive x from Bartók’s String Quartet, No. 4, first movement, m. 7

Example 6.2: Motive y from Bartók’s String Quartet, No. 4, fifth movement, m. 16–18

The target clips were constructed to include as much of the final cadential event as possible, cutting the clip right before the beginning of the next event. Unlike the first experiment where I could not differentiate between the feelings of anticipatory, arrival, or retrospective

156 closure, the construction of the stimuli in this experiment allowed me to examine specifically the feeling of closure based solely on arrival features rather than discontinuities in the musical surface. In some cases, the construction of the music resulted in a “clipped” ending in the sound file, especially for cadences that weren’t followed by a rest. Because participants might be sensitive to this sound, I cataloged the presence of silence in the music, along with other features such as the type of cadential gesture and the length of the excerpt for data analysis.

Procedure

After giving informed consent, participants were assigned to one of two listening conditions that determined the exposure content: participants heard the excerpts either by Mozart or by Bartók. While listening to the exposure track, participants were asked to indicate on the computer every time they heard an ending to ensure they were paying attention. Following the exposure, they listened to the test clips from both composers (order of presentation was counterbalanced between participants) and rated how complete each ending sounded on a seven- point scale.88 All of their responses were recorded on a computer. Upon completion of the rating task, participants filled out a brief questionnaire documenting their familiarity with the compositions and their musical experience.

Results

The results only examine data from the target stimuli: ratings from the clips that conclude with a cadential gesture. Using a mixed-model regression, I examine the influence of several independent variables on the dependent rating variable: within-subject variables, which record characteristics of the stimuli (the composer of the excerpt, whether a rest followed the cadential arrival, the length of the excerpt, and the order in which the clips were presented) and between- subject variables (exposure composer, composer first rated, and subject group, as determined by musical experience). Composer and silence are binary variables (Bartók = 0 and Mozart = 1; no silence = 0 and silence = 1), while group is a three-level variable (Non-musicians = 0, Undergraduate Musicians = 1, and Graduate Musicians = 2). The question order is a number

88 The instructions read to the participants were: “In this part of the study you will use a seven-point scale to rate how well the short musical clip would end a musical idea. In music, some endings sound more conclusive than others. If the musical clip does not sound at all like an ending, then press 1. Use higher numbers to indicate stronger endings, with 7 representing the strongest possible ending. Since this is a matter of opinion, don’t worry that there is a right or wrong answer. Feel free to use the entire range of the scale.”

157 from 1–115, corresponding with the order of the excerpts within each block (determined by composer), and time is the length of each excerpt measured in seconds.

Table 6.2: Mixed Models Regression Analysis: Rating

Row Standard Approx. Fixed Effect89 Coefficient t-ratio p-value Number error d.f. 1 Intercept 3.072478 0.164794 18.644 51 <0.001 2 Exposure -0.561667 0.217472 -2.583 51 0.013 3 First Rated 0.065684 0.218071 0.301 51 0.764 4 Group 0.593148 0.125842 4.713 51 <0.001 5 Rated Composer 0.790687 0.126829 6.234 5159 <0.001 6 Exposure 0.069363 0.197554 0.351 5159 0.726 7 First Rated 0.141623 0.195685 0.724 5159 0.469 8 Group 0.307577 0.111427 2.760 5159 0.006 9 Silence 1.845760 0.139089 13.270 5159 <0.001 10 Exposure 0.013615 0.177474 0.077 5159 0.939 11 First Rated -0.157893 0.177682 -0.889 5159 0.374 12 Group 0.040004 0.116624 0.343 5159 0.732 13 Excerpt Length 0.274982 0.039850 6.900 5159 <0.001 14 Exposure 0.079446 0.051066 1.556 5159 0.120 15 First Rated -0.065781 0.051092 -1.287 5159 0.198 16 Group -0.066598 0.029681 -2.244 5159 0.025 17 Question Order -0.007765 0.000878 -8.847 5159 <0.001 18 Exposure 0.002446 0.001237 1.976 5159 0.048 19 First Rated 0.001444 0.001246 1.159 5159 0.247 20 Group -0.001042 0.000807 -1.291 5159 0.197

An interaction between the variables that document the composer of a rated excerpt and the composer a participant heard during the exposure period would indicate that the exposure period influenced the listener’s perception of closure. As seen in row 6 of Table 6.2, the interaction between exposure and composer is not significant. Despite the lack of direct support

89 A few notes on this table: the first row is the coefficient needed for the regression equation. The between- subject variables underneath it show the influence of being in any one of these groups on the rating variable. The between-subject variables underneath a given within-subject variable show the interaction between these subject groups and a given independent variable.

158 for the main hypothesis of this experiment, other variables significantly influenced the rating data. For instance, rows 2 and 4 show a main effect for two of the between-subject variables— exposure and group. The negative coefficient for exposure indicates that the ratings made by participants who listened to Bartók during the exposure period are generally higher than the ratings made by participants who listened to Mozart, while the positive coefficient for group indicates that participants with more musical experience also tend to rate all the excerpts higher. A separate ANOVA reveals an interaction between exposure and subject group on the mean rating of the excerpts. This interaction reveals that the graduate musicians who were exposed to Bartók drive the main effect of higher ratings for the Bartók excerpts (see Figure 6.1). In fact, a significant three-way interaction shows that the ratings for cadential gestures in Bartók made by graduate students who listened to Bartók during the exposure period are much higher than the ratings made by any of the other subject groups for the same cadential gestures (Figure 6.2).

Figure 6.1: Two-way Interaction between Subject Group and the Exposure Composer

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Figure 6.2: Three-way Interaction between Subject Group, the Exposure Composer, and the Rated Composer The first Figure shows the mean ratings for the Bartók stimuli, and the second Figure shows the mean ratings for the Mozart stimuli.

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The main effect for rated composer shows that all participants tended to rate the excerpts composed by Mozart higher than those composed by Bartók (row 5), and the significant interaction for group (row 8) suggests that the three subject groups evaluated the composers differently. While all three groups exhibit the general trend of rating Mozart excerpts higher then Bartók excerpts, graduate musicians rate both composers higher, suggesting more familiarity with both composers (see Figure 6.3). Undergraduates seem to be more familiar with the Mozart stimuli than with the Bartók stimuli; their estimated mean rating for the Bartók stimuli is closer to that of the non-musicians, whereas their estimated mean rating for the Mozart stimuli is closer to that of the graduate musicians. This effect is accentuated in the data set that includes the non- cadential filler ratings (see Figure 6.4).

Figure 6.3: Two-way Interaction between Participant Group and the Ratings for Composer Only the cadential excerpts are included in this data set.

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Figure 6.4: Two-way Interaction between Participant Group and the Ratings for Composer All the excerpts (both cadential and non-cadential) are included in this data set.

The remaining within-subject variables are all significant. The presence of silence has the greatest effect on the ratings, suggesting that participants were paying more attention to the acoustical properties of the final note of the excerpt rather than the approach to the last note of the excerpt. The positive coefficient for the length indicates that as the length of the excerpt increases, the rating increases, but the negative coefficient in the interaction suggests that participants with more musical training aren’t as influenced by the length of the stimulus. The final variable, question order, shows that as the experiment progressed all participants tend to rate the excerpts lower. While this could suggest that participants became slightly more discerning between degrees of cadential articulation as the experiment progressed, a significant, but weak negative correlation between all the ratings (including the ratings for non-cadential fillers) and the question order reveals that all the ratings gradually decreased as the experiment progressed (r = -0.055, p = 0.01). Discussion

While there isn’t a significant effect for the interaction between the exposure composer and the rated composer (exposure match), these data suggest other trends that are supportive of

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EST. Increased familiarity with musical style increases the ratings for closure. Musicians, who are presumably more familiar with common-practice repertoire, rate Mozart’s excerpts higher than the non-musicians do; graduates, who are presumably more familiar with twentieth-century repertoire, rate Bartók’s excerpts higher than the other two groups do. Further, graduate musicians seem to be more affected by the exposure period. While both groups of graduates rate the Mozart excerpts higher than the Bartók excerpts, graduates who were exposed to Bartók rate the Bartók excerpts higher than did the participants who were exposed to Mozart. Given their more extensive musical experience, graduates could assimilate new stylistic markers of closure better than participants with less musical experience could. Exposure match does not have a significant main effect on the rating of the target stimuli, which may be a product of the design of this experiment. The twelve-minute exposure period was probably too short for participants to acquire stylistic cues for endings. In their statistical learning study, Jonaitis and Saffran (2009) found that participants only learned a novel harmonic syntax after a two-day exposure period. Further, the present study did not ask whether the stimuli formed a grammatical entity, as most statistical learning tasks do; rather, it asked for an aesthetic judgment of completeness. Such opinions may require even more experience with a style, consistent with the increased ratings by the more experienced musicians. Second, the strong main effect for silence suggests that acoustical properties of the last pitch influenced ratings more than the feeling of finality experienced at the arrival of the last pitch. An alternatively designed study could control for this variable by prematurely clipping the last note of every cadence, which would shift attention towards the predictability of the last pitch. Both Experiments 1 and 2 show the importance of pre-existing knowledge structures in musical segmentation and the perception of closure. While the exposure period in this study failed to create new knowledge structures, the main effect for musical expertise (measured by formal training) suggests that previous knowledge did, in fact, influence the results. Research reviewed in Chapters 3 and 4 suggests that both segmentation and the perception of closure depend upon a listener’s expectations. Increased experience with a particular style would presumably create more accurate expectations, which could be reflected by increased ratings for more familiar music because the feeling of finality results from accurate expectations followed by a rise in uncertainty for subsequent events. While Experiment 2 does not specifically examine

163 the influence of expectation on closure, Experiment 3 explicitly asks participants to predict when musical phrases will end. Endings that are more predictable should correlate with an increased feeling of finality.

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CHAPTER 7

EXPERIMENT 3

This last experiment tests the third hypothesis of EST: anticipated endings followed by a rise in uncertainty for subsequent events correspond with a feeling of finality. Zacks, Speer, and Reynolds (2009) tested this hypothesis by asking participants to rate retrospectively the predictability of clauses from a longer narrative. The authors found that the perceived predictability decreased as the number of changes in the narrative increased. Participants also tended to read less predictable clauses more slowly than predictable clauses, suggesting an update of the event model during unpredictable clauses. While there was a correlation between reading speed and predictability, Zacks, Speer, and Reynolds note that a retrospective rating of predictability may not be the most reliable measure, and they suggest that a real time measure of predictability might provide more support for EST. In Experiment 3, I measure predictability by asking participants to anticipate the endings of musical phrases while listening to three complete movements by W.A. Mozart. Following this prediction task, participants rated the degree of completeness for short clips from these movements. In this rating task, one group of participants heard the clips in order of the movement, while the other group of participants heard a random-order presentation of the clips, allowing an examination of the relationship between the perception of closure and the formal structure of a composition. Meyer (1973) suggests that the formal structure of a composition is articulated through a hierarchy of closes. His bottom-up construction of structure suggests that stronger endings result from more parameters projecting closure; however, a listener’s previous experience with typical formal structures could also influence an ending’s perceived strength. This top-down view suggests that knowledge structures represent yet another parameter that can then “project” closure, hence influencing the perceived strength of closure.

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Method

Participants

The participants were divided into three subject groups determined by their levels of formal musical training. Data from 24 undergraduate non-musicians (who received psychology credit for participating in this study), 27 undergraduate musicians (who received extra credit in their freshman Music Theory class), and 23 graduate student musicians (who received a $10 gift card for their participation) were included in this study. Each subject group was divided into two conditions that determined the nature of the rating task. In the random condition, participants heard the clips in random blocks by movement, while in the visual condition participants not only heard the clips in the order they occurred in the movement but also saw a visual representation of the movement, an example of which is replicated as Figure 7.1.

Figure 7.1: Excerpt No. 6 from Mozart’s String Quartet in G Major (K. 156), third movement. Participants were instructed that the blue box represents the relative length and location of the clip.

Stimuli

Stimuli in this study used the minuet and trio movements from three string quartets by W.A. Mozart: String Quartet No. 3 in G major (K. 156), third movement; String Quartet No. 8 in F major (K. 168), third movement; and String Quartet No. 13 in D minor (K. 173), third movement. Participants listened to all three movements as performed by the Amadeus String Quartet. (The scores of these movements are located in Appendix B.) I chose these particular movements because Mozart controls two musical features that may influence the predictability of phrase endings: consistent four-bar hypermeter and clear cadential arrivals. First, while K. 168

166 maintains a consistent four-bar hypermeter throughout, the other two movements contain phrase expansions and extensions that disrupt the established four-measure groupings. This variability in the length of phrases forces the listeners not to rely exclusively on predictable metrical cycles to anticipate endings. Second, the three movements contain a variety of cadential paradigms, including all three significant cadence types: PAC, HC, and IAC).90 For experimental purposes, there is also a practical advantage that the majority of cadences in these movements do not involve a melodic suspension (i.e., the harmonic and melodic arrivals coincide). For the prediction task, I combined all three movements into a single audio file, inserting fifteen seconds of silence between successive movements (the order of the movements was counterbalanced between participants). Participants listened to this file through the digital audio software Audacity, recording their predictions for endings on a separate track by pressing a key on the computer keyboard. I then converted this label track into a text file that listed every participant response according to how much time had progressed from the beginning of the file for subsequent data analysis. I followed the model used in Experiment 2 to create the excerpts for the rating task. In each movement, I selected excerpts that concluded different formal units in each composition, representing subphrase, phrase, and section endings. As in Experiment 2, I created these clips by splicing the original audio file using Audacity. The clips varied in length from two to six measures, where each clip began with the onset of a formal unit (subphrase or phrase) and concluded with the release of the last sound of that formal unit. These clips were drawn from the first iteration of a passage on the recording, with the exception of clips from the return of the Minuet section. The clips were paired with a visual representation of the movement and were heard either in the order in which they occur in the movement (visual condition) or in random blocks (random condition).

Procedure

After the participants gave informed consent, they read and listened to instructions for the first part of the study before completing two practice excerpts: In the first part of the study you will listen to several pieces. While listening, try to predict the moment at which a musical phrase ends. Your goal is to press the control-m at

90 My hypermetrical interpretations and cadence analyses are annotated on the scores in Appendix B.

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the exact moment the phrase is completed. The composer could surprise you, so it’s okay if you press prematurely. Just keep on listening and try to anticipate the next ending. You will hear two practice excerpts—complete the practice and compare your answers with the ones provided. The two practice excerpts were chosen because they illustrated the nature of the task and trained the participants to predict endings actively rather than react retrospectively to a phrase ending. The first example, the first reprise from Mozart’s String Quintet No. 4 in G minor, third movement (K. 516), is a modulating contrasting period with phrases of different lengths. The second phrase is longer due in part to an internal expansion caused by a deceptive cadence in m. 10. Most listeners who did the task correctly were initially tricked by this deceptive cadence, although only some were also tricked the second time. Listeners heard this excerpt through Audacity (the actual sound wave was hidden from view) and indicated their predictions on a separate label track. After completing this first practice excerpt, participants compared their label tracks to ones that indicated the cadences. Participants who did poorly or did not understand the task repeated the task on this excerpt.

Example 7.1: Mozart String Quintet No. 4 in G Minor (K. 516), third movement, mm. 1–13

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The quick tempo and the possibility for multiple interpretations made the second excerpt, Mozart’s Sonata for Piano and Violin in B #major, third movement, mm. 1–16 (K. 454), a bit more difficult than the previous practice excerpt. While I hear a parallel period with a HC in m. 8 and a PAC in m. 16, it is also possible to interpret HCs in both mm. 4 and 12, creating a double period. For this reason, this excerpt was chosen to demonstrate to the participant that there could be multiple “right” predictions in this task, and also that their interpretation of phrase endings might change over time.91 Because this excerpt also has a suspension, subjects were instructed to predict when the goal harmony would arrive, not when the dissonant melodic tone(s) would resolve. As before, after completing the practice task, participants compared their results with my responses; if they did poorly, they repeated the task. Any remaining questions were addressed before the participants began the prediction task with the test stimuli. Following a successful completion of the practice tasks, participants began the prediction task on the three minuet and trio movements. Afterwards, participants rated clips from these movements on a seven-point scale to indicate how complete the end of the clip sounded.92 The presentation mode of this task, random or visual, varied according to the subject’s assigned condition. Following this rating task, participants filled out a questionnaire documenting their familiarity with the compositions and their musical training.

91 As a side note, many participants only predicted endings at mm. 8, 12, and 16, pointing towards this change. The first half of the second phrase (mm. 9–12) is the same as the previously heard first phrase, except for a change in orchestration. If more predictable cadences correspond to stronger closes, this suggests that the V chords in mm. 4 and 12 are less closed than the one in m. 8, which was only predictable in the second listening. 92 This task used the same directions as Experiment 2.

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Example 7.2: Mozart’s Sonata for Piano and Violin in B #Major (K. 454), third movement, mm. 1–16

Results

This results section is divided into two parts. The first examines the results only from the prediction task, specifically assessing the musical features that led listeners to predict the end of a phrase successfully. As in Experiment 1, I created windows around the endings for this part of the analysis. Some of these endings coincided with a cadential arrival, while others merely demarcated subphrases (all windows are marked on the scores in Appendix B). These windows began 500 ms before the arrival of the ending and lasted for 1500 ms after this point.93 None of the windows overlapped. I measured response time from the onset of the last note, so responses occurring before the last note received a negative response time while responses occurring after

93 In the case of suspensions, the window began 500 ms before the beginning of the goal harmony.

170 the last note received a positive response time. The results show that listeners are more sensitive to cadential cues than they are to hypermetric regularities: in general, listeners best predict the tonic arrival in a PAC. The second section examines correlations between the participants’ ratings for closure and their responses from the prediction task, along with the correlation between a listener’s response time in the prediction task and his/her rating of closure. While the data indicate that both predictability and response time influence the ratings, so do other independent variables such as cadential closure within the clip and the overall length of the clip. The first regression, which analyzes the data from the prediction task, examines whether formal units that conclude either with a cadence or at a temporal distance of four or eight measures from the end of the previous phrase are associated with an increased probability that a participant will predict the end of a formal unit (see Table 7.1). The significant value for group (in the second row) indicates that as musical expertise increases, so does the participant’s ability to predict the ends of phrases. Of the two independent feature variables, only the presence of a cadence significantly predicts participant responses (participants are 1.8 times more likely to respond when a cadence occurs). There is a significant interaction between musical expertise and the presence of a cadence, where participants with more musical expertise are more likely to respond at a cadential gesture (see Figure 7.2). The hypermeter variable examined whether phrases that exhibit a regular 4-bar hypermeter are more predictable than phrases that have some sort of phrase expansion. As seen in the bottom third of Table 7.1, there is no main effect for ending points occurring 4 or 8 measures after the end of the previous formal unit. Evidently these participants were able to predict endings based on the presence of a cadence and were not necessarily influenced by hypermeterical regularities or irregularities. Looking more closely at the main effect for cadence, I separated this variable into three categories based on the type of cadence (PAC, HC and IAC) and ran an additional analysis with these variables (the results from the mixed logit regression analysis are located in Table 7.2). While there is not a significant main effect for the HC, there are significant main effects for both the PAC and the IAC. Listeners are more than twice as likely to predict an ending when a tonic chord concludes the phrase. The tonic arrival in both the PAC and IAC always follows a dominant harmony, so listeners’ expectations for the ending are presumably influenced by the high transitional probability between V and I. In contrast, because the dominant harmony of the

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HC is not always preceded by the same harmony, a listener may not be able to accurately predict its arrival.

Table 7.1: Mixed Logit Regression Analysis: Cadence and Hypermeter

Standard Approx. Odds Confidence Fixed Effect94 Coefficient t-ratio p-value error d.f. Ratio Interval Intercept -1.176341 0.274569 -4.284 9023 <0.001 0.308405 (0.180,0.528) Group 0.462805 0.114176 4.053 72 <0.001 1.588524 (1.265,1.995) Cadence 0.607246 0.168288 3.608 9023 <0.001 1.835371 (1.320,2.553) Group 0.801740 0.081178 9.876 9023 <0.001 2.229417 (1.901,2.614) Hypermeter -0.114407 0.161683 -0.708 9023 0.479 0.891895 (0.650,1.224) Group -0.094700 0.077748 -1.218 9023 0.223 0.909646 (0.781,1.059)

Figure 7.2: Interactions between Subject Group and the Presence of a Cadence

94 As in the analyses in Chapter 5, the odds ratio in each row for every within-subject variable shows the odds of a participant’s response if the feature is present (with the exception of the first row, which is only needed for the regression equation). The “Group” row for each within-subject variable shows the interaction between musical expertise and the independent variable.

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Table 7.2: Mixed Logit Regression Analysis: Cadence Types

Standard Approx. Odds Confidence Fixed Effect Coefficient t-ratio p-value error d.f. Ratio Interval Intercept -1.298018 0.323561 -4.012 9022 <0.001 0.273072 (0.145,0.515) Group 0.551098 0.127846 4.311 72 <0.001 1.735157 (1.345,2.239) PAC 0.784639 0.197140 3.980 9022 <0.001 2.191616 (1.489,3.225) Group 1.260553 0.103436 12.187 9022 <0.001 3.527371 (2.880,4.320) HC 0.109291 0.182932 0.597 9022 0.550 1.115487 (0.779,1.597) Group 0.708266 0.085718 8.263 9022 <0.001 2.030468 (1.716,2.402) IAC 0.913797 0.221879 4.118 9022 <0.001 2.493774 (1.614,3.852) Group 0.420757 0.104090 4.042 9022 <0.001 1.523114 (1.242,1.868)

I am defining these cadences by their traditional harmonic paradigms, as explained in Chapter 5; however, these movements challenge some of these traditional markers of “cadence” and “phrase.” Phrases are traditionally defined as having some sort of harmonic motion, with the cadence representing the culmination of this motion. Several times in these movements, there is no harmonic motion leading into the point of ending. One such example occurs in m. 16 in the F-major. String Quartet (K. 168). Here, the B section ends on a V chord that arrives in m. 15; however, the end of the phrase is not until m. 16, so I coded the HC as occurring at that point (refer to the annotated scores in Appendix B). Also in this movement, a HC that arrives in m. 36 is followed by a post-cadential extension that repeats the cadential gesture. In this case, the I-V gesture in m. 40 is not coded as a HC, despite the hypermetric four-measure groupings, because it merely extends the ending that arrived in m. 36. Four measures later, in m. 44, the trio concludes with the same type of cadential gesture from m. 15, but this one extends the tonic for two measures. Even though the “goal-directed motion” concludes in m. 43, hypermetrical expectations project an ending at m. 44, which is where the trio concludes. Most of the cadential types are clear in these movements, but there are a few moments of possible cadential ambiguity. In his 2010 talk at the Annual Meeting of the Society for Music Theory, Burstein effectively demonstrated that distinguishing between a HC and an elided PAC could be difficult, especially when there is continuous motion from the dominant chord of the HC to the tonic beginning of the next phrase. Measures 54–55 of the G-major Quartet represent one such case of this type of cadential ambiguity: despite the convincing arrival on the dominant

173 in m. 54, listeners could interpret the cello’s downward motion into the tonic pitch on the downbeat of m. 55 as the ending instead. A similar situation occurs in mm. 24–25 of the same quartet. Here an arrival on the dominant in m. 24 marks the end of the B section, but at this point the second violin initiates a gesture that leads into the return of the A section. It could be possible that without a break in the sound, listeners would not experience arrival closure in m. 24, but rather retrospective closure when the opening theme recurs. This ambiguity surrounding the HC may further explain the lack of a main effect for this cadence type. Along with the main effect for the PAC and the IAC, musical expertise also affects the results of the prediction task. Overall, as musical expertise increases, participants are more likely to make their predictions within the two-second windows around the cadence points. Specifically, for all three cadence types there is an interaction between the cadence type and musical expertise (see Figure 7.3, which graphs the ANOVA estimated means for each participant group). Compared to the non-musicians, the musician groups have a larger change in their responses when there is a PAC. For the HC, only the graduate musicians are more likely to respond; all participants respond to the IAC, but to different extents. Response time data for the points at which listeners predicted an ending were also analyzed. Response time data less than zero signifies that the participant responded prior to the onset of the last note of the formal unit, while a response time greater than zero signifies that the participant pressed after the onset of the last note. Most of the data is greater than zero, which could reflect the time it takes for a participant physically to respond to a prediction. It could also reflect the difficulty of the prediction task, where participants may be responding retrospectively to an ending point despite instructions to predict endings. Even so, response times can still measure the fulfillment of expectations, given that faster response times should correlate with expected musical events.

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Figure 7.3: Interactions between Subject Group and Cadence Type

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Figure 7.3 (continued): Interactions between Subject Group and Cadence Type

Since there is no main effect for hypermetric regularity, these analyses will only consider the influence of cadences on the timing of the prediction. As seen in Table 7.3, as musical expertise increases, the response time decreases (note the negative coefficient for group in the third row). This result suggests that more experienced musicians better predict the approach of an ending. The positive coefficient for the presence of a cadence is surprising, because cadences represent highly predictable patterns in music. The more predictable a pattern, the faster listeners should respond to it. The interaction reveals that more experienced musicians respond faster to cadential patterns.

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Table 7.3: Mixed Models Regression Analysis: Response Time and Cadences Standard Approx. Fixed Effect95 Coefficient t-ratio p-value error d.f. Intercept 0.821911 0.072698 11.306 3988 <0.001 Group -0.126699 0.031078 -4.077 72 <0.001 Cadence 0.114577 0.038407 2.983 3988 0.003 Group -0.048349 0.017685 -2.734 3988 0.006

Looking at specific cadence types (Table 7.4), there is a main effect for all three cadence types on the response time. A smaller coefficient corresponds with a smaller increase in the response time for that cadence. Participants respond faster to a PAC than to either a HC or an IAC. For windows in which participants responded to a HC, their response time was faster than for an IAC. However, it is important to remember that this analysis uses a slightly different data set, only using the points where subjects responded. This may have removed then more ambiguous cadences, leaving those that were especially predictable. For both the PAC and the IAC, there is a subject group interaction indicating that participants with more musical experience responded more quickly.

Table 7.4: Mixed Models Regression Analysis: Response Time and Cadence Types Standard Approx. Fixed Effect Coefficient t-ratio p-value error d.f. Intercept 0.821587 0.072173 11.384 3986 <0.001 Group -0.125998 0.031354 -4.019 72 <0.001 PAC 0.104156 0.043245 2.408 3986 0.016 Group -0.071626 0.019831 -3.612 3986 <0.001 HC 0.135055 0.046483 2.905 3986 0.004 Group -0.035412 0.021012 -1.685 3986 0.092 IAC 0.264896 0.052113 5.083 3986 <0.001 Group -0.095702 0.023666 -4.044 3986 <0.001

95 This table (and Table 7.4) is similar to the corresponding one found in Chapter 6 (Table 6.2). In Table 7.3, there is a significant main effect for cadence: when a participant is predicting a cadential arrival, the coefficient for that variable is factored into the regression equation. The first group variable (a three-level variable where 1 = non-musicians, 2 = undergraduate musicians, and 3 = graduate musicians) is always present in the equation whether or not a cadence is present, but the group variable under cadence is only factored into the equation when a cadence occurs.

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Data from the second half of the study reveals no main effect for the rating condition, whether visual or random on the ratings of closure, nor did the condition factor into in any interaction. There are several possible interpretations: 1) participants in the visual condition may have disregarded the visual information; 2) participants in the random condition may have been able to place the clip correctly within the formal hierarchy, given that they heard each movement in its entirety prior to the rating task (which seems improbable due to memory constraints); or 3) the visual information may have corroborated the rating that would have occurred even without it. Both the first and last possibilities support Meyer’s statement that the form of a piece emerges from its hierarchy of closes (1973). Because condition did not influence the rating results, it was not included in the data analysis. The remaining independent variables (whether the participant anticipated a particular end in the prediction task, the length of the excerpt, and the presence of a cadence) all significantly influence the rating task. Both the “predicted” and the cadence variables are binary variables (1 = participant predicted that particular ending in the previous task and 1 = presence of a cadence), while the length variable is coded in seconds. For each of these three variables, an increase corresponds to a significant increase in the rating of closure, with the presence of a cadence having the largest effect. Before taking into account any of the independent variables, there is no significant difference between the ratings made by subjects with different levels of expertise, but there are interactions between subject group and predicted ends as well as subject group and the presence of a cadence. Participants with more musical experience consistently rate the clips higher when these variables are present.

Table 7.5: Mixed Models Regression Analysis: Ratings Standard Approx. Fixed Effect Coefficient t-ratio p-value error d.f. Intercept 1.851092 0.310883 5.954 3643 <0.001 Group 0.054959 0.142029 0.387 72 0.700 Predicted 0.418119 0.157657 2.652 3643 0.008 Group 0.270692 0.076986 3.516 3643 <0.001 Length 0.288156 0.031036 9.285 3643 <0.001 Group -0.022383 0.014364 -1.558 3643 0.119 Cadence 1.296993 0.162001 8.006 3643 <0.001 Group 0.191809 0.078961 2.429 3643 0.015

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The final analysis uses only the rating data from clips in which the participant successfully predicted the ending to see if there is a correlation between ratings and response time. A negative coefficient for the response time variable in Table 7.6 indicates that as response times increase the ratings of closure decrease. While there is no main effect for response time, there is an interaction: as musical expertise increases, subjects are more likely to give the clips with a faster response time in the prediction task a higher rating.

Table 7.6: Mixed Models Regression Analysis: Ratings and Response Time Standard Approx. Fixed Effect Coefficient t-ratio p-value error d.f. Intercept 5.044658 0.297488 16.958 1875 <0.001 Group 0.186685 0.128796 1.449 72 0.152 Response Time -0.282416 0.311667 -0.906 1875 0.365 Group -0.405425 0.152425 -2.660 1875 0.008

Discussion

Overall, the data support the hypothesis that anticipated musical endings evoke a feeling of closure. The data illustrate a correlation between a listener’s ability to predict an ending as the composition unfolds and that listener’s subsequent rating of closure for that particular ending. Further, cadences that are traditionally considered more closed were better predicted in the first task and had faster response times (in other words, participants responded more consistently and quickly to an anticipated PAC than to the other cadences). As seen in the previous studies, musical experience influenced the participants’ results. Here, the main effects were magnified for the participants with more musical experience: participants with more experience successfully predicted more endings, and for these endings experienced participants predicted all the cadences types better than participants with less experience did. Their ability to anticipate endings more quickly and accurately in the prediction task suggests that the participants with increased musical experience drew from knowledge structures supported by many more exemplars of common ending paradigms in this style. These experienced participants showed a stronger correlation between their ratings and their data from the prediction task: both the endings they predicted and their faster response times correlate with higher ratings for closure.

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Surprisingly, the rating condition had no influence on the rating task: participants in both the visual and random rating conditions showed no difference in their clip ratings. These data support Meyer’s assertion that form emerges from a hierarchy of closes more than top-down knowledge of formal structure influences the perception of closure. Appendix B shows windows for each movement, the percentage of participants who indicated an ending in that window, and the mean rating in each window. While there is not always an exact match between the formal structure and the data, many times the endings that demarcate the conclusion of a formal section were better predicted, and subsequently were given a higher rating. Event Segmentation Theory posits that an increase in the transient prediction error creates a perceptual boundary. While I was unable to measure directly any increase in this transient prediction error following a cadence, it is safe to assume that the ability of a listener to predict upcoming musical material following a cadence is lower than their ability to predict the cadential arrival. The correlation between the prediction and rating tasks further suggests that larger increases in prediction error results in a hierarchically significant musical boundary, eliciting a stronger feeling of closure.

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CHAPTER 8

CLOSURE

Four characteristics of closure inferred from the musicological literature form the foundation for my definition of closure and my cognitive model for the perception of closure outlined in this dissertation: 1) closure segments a continuous musical stream into discrete events 2) closure is stylistically dependent 3) closure is a completion of a goal-directed process resulting in an arrival of relative stability or rest 4) the strength of closure depends on many musical variables and plays an integral role in the hierarchic construction of a composition While my own definition of closure, the anticipated end to a musical segment, responds to the concept of “closure” as used in musical analysis, my methodology is removed from the music itself as an object of study, alternatively focusing on the perception of closure. In other words, instead of examining closural processes in a particular musical style or a specific composer’s corpus, the cognitive model for the perception of closure (developed in Chapters 3 and 4 and supported by the three experiments in Chapters 5, 6, and 7) uses recent research in event segmentation and musical expectation to explore how and why a listener perceives closure. Corroborating previous studies examining event segmentation, Experiment 1 established the possibility of a shared cognitive process in musical segmentation. Specifically, the results from this study showed that subjects were highly consistent in their segmentation responses, both within an individual subject and between subjects, and that subjects perceived event structure hierarchically, where smaller musical segments combine to form larger segments. This study also revealed that specific musical features can predict a listener’s perception of an ending, and this correlation grows stronger with musical training. Many times, a perceptual boundary occurred at the end of a schematic unit or following a discontinuity in the musical surface, corresponding with the arrival and change features in Experiment 1. Segments that terminate with an arrival feature would presumably sound more closed (resulting in anticipatory or arrival closure) than would segments ending with a change feature (resulting in retrospective closure).

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Results for segmentation consistency and nested lower levels did not significantly vary for the participants who segmented Mozart and the participants who segmented Bartók, but there was a difference in the types of features that signaled an end in these two styles. This suggests that the cognitive mechanism of segmentation remains constant between styles, while the specific features that signal closure may change. Subjects who segmented Mozart tended to rely on arrival features, while subjects who segmented Bartók tended to rely on change features. The arrival features in Mozart represent well-learned endings from the common-practice style, while the arrival features that predicted endings in Bartók tended to be peculiar to these particular compositions. Because participants who segmented Bartók could not rely on previously learned endings representing a wide variety of compositions, they tended to rely more on surface changes during their task. Learning ending gestures for a style, or even for a specific piece, is an unconscious process dependent on listener experience. According to Hintzman’s multiple trace theory (1986), every encounter with a stimulus creates a trace in long-term memory. Of course, the quality of the information stored in the trace is contingent on listener attention to the stimulus and the type of encounter with the stimulus. The number of traces in LTM that anticipate the conclusion of a particular ending gesture determines whether a listener experiences closure. For instance, while a listener may have veridical expectations for an ending in a particular composition, a listener may also have many more traces in LTM for continuation at that point, lessening the sense of closure. Experiment 2 used a learning task to explore whether a listener can associate the arrival features of a particular compositional style with the feeling of closure. The aim was to see whether a brief period of listening to excerpts by either Mozart or Bartók would influence subsequent ratings of closure of similar endings. While there wasn’t an interaction between the composer heard during the exposure period and a listener’s rating of that composer (maybe due to the exposure period being too brief, or to my inability to control the transitional probabilities between sound elements), participants with more musical training rated all cadential excerpts higher than did those participants with less training. Given that more experienced musicians presumably have had more exposure to cadential gestures in both styles, these higher ratings support the learned association between closure and a particular musical gesture. Further, graduate music students who were exposed to Bartók tended to be more sensitive than other

182 subject groups to the learning task, suggesting that their increased training allowed them to assimilate cadential cues more quickly from a less-familiar style. The perception of goal direction towards an ending also supports our ability to pick out transitional probabilities. The feeling of moving towards a musical goal is an artifact of being able to predict with increasing certainty subsequent events in a phrase. Studies have revealed expectations for acoustic continuity as well as expectations for learned musical patterns. Event segmentation theory is an expectation-based model of event segmentation where an unexpected event (e.g., a discontinuity in the musical surface) or the expected completion of an event causes a perceptual boundary. According to my definition of closure, not every end of every segment produces a feeling of finality. Anticipatory and arrival closure capture the experience of an anticipated ending, while retrospective closure represents a failure to predict the moment of closure. In retrospective closure, a discontinuity signals a beginning, but the preceding ending wasn’t accurately predicted or recognized at the moment it occurred. Experiment 3 asked listeners to predict endings in three Mozart minuet movements. Most of their responses coincided with cadences—especially authentic cadences, which represent highly predictable endings in the common-practice style. Data from a subsequent rating task showed that listeners rated the endings they predicted in the previous task as more closed than other endings from the same composition. These data suggest that the strength of closure is directly related to the predictability of an ending; larger structural boundaries were generally more predictable and received higher ratings, supporting Meyer’s argument that form emerges from a hierarchy of closes. The degree to which closure permeates the musicological discourse is a testament to its analytical and aesthetic importance and speaks to an essential characteristic of the music listening experience. Despite stylistically varied markers of closure, I posit that an innate cognitive mechanism engenders the perception of closure. EST provides a model for musical segmentation and closure that transcends stylistic boundaries and captures some of our musical intuitions about closure: that closure is contingent upon musical expectation and prompts a hierarchical understanding of a composition. The perception of closure is thus a product of an ongoing cognitive process that segments our continuous life experiences into discrete events.

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Two different agents of closure can be inferred from the language used in musicological discourse: the music (referring to a compositional process) or the mind (referring to a psychological experience). While these perspectives may seem irreconcilable, the four characteristics of closure can serve as a point of intersection, and only the language differences remain. Because the perception of closure (or at least the evocation of closure) shapes musical analyses of all kinds, we should look past the differences in language and recognize the underlying role of expectation (whether musical or disciplinary) in musical analysis. By considering closure as a result of musical expectation, we can better reevaluate how we use the concept of closure to shape our analysis of music. While this project builds a strong case for the role of expectation in both the creation of musical segments and the perception of closure, work on this topic remains to be done. My own studies were large in scope, deriving their stimuli from actual musical compositions, and there was no limit on the number of segmentation/prediction responses a subject could make. I plan to reanalyze some of the data collected because there are additional ways to examine it that I didn’t pursue in this dissertation. For instance, participants in Experiment 1 could be divided into subject groups based on how often they indicated a boundary during the segmentation task. From a pragmatic perspective, this would ensure that subjects segmenting on the same hierarchical level would be grouped together, and preferred segment length might distinguish musically experienced listeners better than did degree programs. In Experiment 2, I did not discuss the data collected during the exposure period (while listeners listened to music in the exposure period, they indicated endings using a computer keyboard). While there wasn’t an interaction effect for exposure composer and rated composer, there might be a correlation between the endings identified by a participant in the exposure period and that participant’s ratings of closure in subsequent task. In all of the studies, additional musical features could be examined for their effect on participants’ segmentation/prediction responses. Additionally, I plan to perform more focused and controlled studies that I hope will produce more robust results in support of these theories. For instance, to replicate the failed learning task in Experiment 2, I could create a statistical learning task where I compose the material in the exposure period, controlling for the transitional probabilities between pitches (using a non-tonal style). Every pitch could be presented at a steady rate, but cadential figures

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(which would be a composed pitch pattern particular to this task) would be followed by rests. I would then compare the listener’s ratings of these cadential pitch-patterns to the listener’s ratings of pitch-patterns from the beginning and middle of segments. Two avenues for future research include examining the influence of previous knowledge structures on the formation of new closural expectations and the influence of non-compositional features on the perception of closure. This expectation-based theory of closure posits that through statistical learning listeners associate ending gestures with closure even in an unfamiliar style, but the extent to which already learned closural gestures may influence this process is unknown. While a learning task similar to Experiment 2 could explore this issue, such an experiment could also be expanded into a cross-cultural study that could specifically examine the influence that learned closural gestures in one style may have on the perception of closure in a different style. In regards to non-compositional features influencing the perception of closure, the data from Experiment 2 showed that the acoustic properties of the final pitch of a segment might influence the perception of closure. A study that specifically manipulated the final sound of a segment could reveal how performance aspects may shape the perceived structure of a composition. Another avenue for further research is the influence of bodily gestures, including those that necessarily accompany a live performance, on the perception of formal structure and closure. This project differs from previous theoretical and cognitive studies regarding closure by casting both the creation of discrete segments from an ongoing musical stream and the perception of closure at the end of some of these segments as contingent upon a listener’s musical expectations. While much work remains to be done, the theoretical literature, previous cognitive studies in both music and event segmentation, and the three experiments presented in this dissertation support the connection between segmentation and expectation and their influence on the perception of closure.

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APPENDIX A

SEGMENTATION RESPONSES IN EXPERIMENT 1

The figures in this appendix plot all of the responses made over the course of each movement in the Fine 2 and the Coarse 2 trials. Points on the solid red line illustrate the total number of segmentation responses made during each beat in the Fine 2 trial; points on the dashed purple line represent the total number of segmentation responses made during each beat in the Coarse 2 trial. These counts represent the responses made by all three subject groups: non- musicians, undergraduate musicians, and graduate musicians. Relatively high numbers of responses are labeled on the Figure with the measure and beat number of their occurrence (where the first number in the label is the measure number and the second number is the beat within that measure). Figures do not illustrate the same number of measures because they are divided by formal sections within each movement. Figures A.1 and A.2 represent the responses made by the participants in Experiment 1a (n = 32), and Figures A.3 and A.4 represent the responses made by participants in Experiment 1b (n = 33).

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Figure A.1: Bartók, String Quartet No. 4, third movement

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Figure A.1 (continued): Bartók, String Quartet No. 4, third movement

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Figure A.1 (continued): Bartók, String Quartet No. 4, third movement

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Figure A.2: Bartók, String Quartet No. 4, fifth movement

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Figure A.2 (continued): Bartók, String Quartet No. 4, fifth movement

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Figure A.2 (continued): Bartók, String Quartet No. 4, fifth movement

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Figure A.2 (continued): Bartók, String Quartet No. 4, fifth movement

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Figure A.2 (continued): Bartók, String Quartet No. 4, fifth movement

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Figure A.3: Mozart, String Quartet No. 19, fourth movement

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Figure A.3 (continued): Mozart, String Quartet No. 19, fourth movement

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Figure A.3 (continued): Mozart, String Quartet No. 19, fourth movement

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Figure A.3 (continued): Mozart, String Quartet No. 19, fourth movement

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Figure A.4: Mozart, String Quartet No. 21, second movement

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Figure A.4 (continued): Mozart, String Quartet No. 21, second movement

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APPENDIX B

ANNOTATED SCORES FOR EXPERIMENT 3

This appendix includes all three movements used in Experiment 3, including some annotations: cadences are marked above each system, the hypermeter is notated between the violin 2 and viola parts, and vertical lines through the score signify the points I used in data analysis for the prediction task. Under each system, I included the percentage of participants who predicted an ending at various points (on the first listening) as well as the mean rating. Not every point from the prediction task was included in the rating task due to time constraints.

1 PAC HC

1 2 3 4 1 2 3 4 3

20.5% 6.8% 63.0% 2.6 5.0

10 PAC

4 1 2 3 4 1 2 3 4

9.6% 79.9% 1.4 5.2

Example B.1: Mozart, Quartet No. 3 in G Major, K. 156, third movement

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19 IAC HC

3 4 1 2 3 4 1 2 3

42.3% 32.4% 19.2% 15.1% 3.5 2.0 2.1

28 IAC PAC HC

4 1 2 3 4 1 2 3 4

27.0% 2.5% 66.2% 66.2% 1.4 6.4

1 2 3 4 1 2 2 2

4.1% 1.6

Example B.1 (continued): Mozart, Quartet No. 3 in G Major, K. 156, third movement

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45 PAC

3 4 1 2 3 4 1 2 3

67.1% 5.6% 4.9 1.9

54 HC PAC

4 1 2 3 4 1 2 3 4

56.9% 11.0% 75.7% 69.4% 2.5 1.7 3.8 5.7

Example B.1 (continued): Mozart, Quartet No. 3 in G Major, K. 156, third movement

HC PAC

1 2 3 4 1 2 3 4 1

5.4% 53.3% 82.9% 1.6 3.1 5.6

Example B.2: Mozart, String Quartet No. 8 in F Major, K. 168, third movement

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10 “HC” HC

2 3 4 1 2 3 4 1 2 3 4 1

20.5% 80.0% 51.3% 2.1 4.4

22 PAC PAC

2 3 4 1 2 3 4 1 2 3 4

85.3% 12.2% 83.6% 1.9 5.6 6.2

33 HC “PAC”

1 2 3 4 1 2 3 4 1 2 3 4

29.7% 28.4% 57.3% 3.2 4.4

Example B.2 (continued): Mozart, String Quartet No. 8 in F Major, K. 168, third movement

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IAC IAC

1 2 3 4 1 2 3 4 3 4

60.6% 63.5% 3.1 2.5

11 PAC HC

1 2 3 4 1 2 3 4 3 4

81.9% 24.3% 60.3% 5.75 2.4 4.3

21 IAC

1 2 3 4 1 2 3 4 1 2

51.4% 4.2% 2.0

Example B.3: Mozart, String Quartet No. 13 in D Minor, K. 173, third movement96

96 There is an incorrect note in m. 8: the cello performs a B!" instead of the notated C3.

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31 HC PAC

3 4 3 4 1 2 3 4 1 2 3 4

62.0% 41.7% 84.9% 3.1 2.6 6.5

43 HC

1 2 3 4 1 2

38.4% 3.0

49 PAC

1 2 3 4 1 2 3

31.5% 78.1% 3.0 5.9

Example B.3 (continued): Mozart, String Quartet No. 13 in D Minor, K. 173, third movement

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56 HC

4 1 2 3 4 1 2

69.0% 3.6

63 HC PAC

3 4 1 2 1 2 3 4

41.9% 76.4% 6.0

Example B.3 (continued): Mozart, String Quartet No. 13 in D Minor, K. 173, third movement

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APPENDIX C

208

209

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APPENDIX D

IRB APPROVAL LETTER AND INFORMED CONSENT LETTER

Office of the Vice President For Research Human Subjects Committee Tallahassee, Florida 32306-2742 (850) 644-8673 · FAX (850) 644-4392

APPROVAL MEMORANDUM

Date: 6/23/2010

To: Crystal Peebles

Address: Dept.: MUSIC SCHOOL

From: Thomas L. Jacobson, Chair

Re: Use of Human Subjects in Research Listener perception of segmentation and closure in music

The application that you submitted to this office in regard to the use of human subjects in the proposal referenced above have been reviewed by the Secretary, the Chair, and two members of the Human Subjects Committee. Your project is determined to be Expedited per 45 CFR § 46.110(7) and has been approved by an expedited review process.

The Human Subjects Committee has not evaluated your proposal for scientific merit, except to weigh the risk to the human participants and the aspects of the proposal related to potential risk and benefit. This approval does not replace any departmental or other approvals, which may be required.

If you submitted a proposed consent form with your application, the approved stamped consent form is attached to this approval notice. Only the stamped version of the consent form may be used in recruiting research subjects.

If the project has not been completed by 6/22/2011 you must request a renewal of approval for continuation of the project. As a courtesy, a renewal notice will be sent to you prior to your expiration date; however, it is your responsibility as the Principal Investigator to timely request renewal of your approval from the Committee.

You are advised that any change in protocol for this project must be reviewed and approved by

211 the Committee prior to implementation of the proposed change in the protocol. A protocol change/amendment form is required to be submitted for approval by the Committee. In addition, federal regulations require that the Principal Investigator promptly report, in writing any unanticipated problems or adverse events involving risks to research subjects or others.

By copy of this memorandum, the Chair of your department and/or your major professor is reminded that he/she is responsible for being informed concerning research projects involving human subjects in the department, and should review protocols as often as needed to insure that the project is being conducted in compliance with our institution and with DHHS regulations.

This institution has an Assurance on file with the Office for Human Research Protection. The Assurance Number is IRB00000446.

Cc: Nancy Rogers, Advisor HSC No. 2010.4328

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Office of the Vice President For Research Human Subjects Committee Tallahassee, Florida 32306-2742 (850) 644-8673 · FAX (850) 644-4392

RE-APPROVAL MEMORANDUM

Date: 5/4/2011

To: Crystal Peebles

Address: Dept.: MUSIC SCHOOL

From: Thomas L. Jacobson, Chair

Re: Re-approval of Use of Human subjects in Research Listener perception of segmentation and closure in music

Your request to continue the research project listed above involving human subjects has been approved by the Human Subjects Committee. If your project has not been completed by 5/1/2012, you must request a renewal of approval for continuation of the project. As a courtesy, a renewal notice will be sent to you prior to your expiration date; however, it is your responsibility as the Principal Investigator to timely request renewal of your approval from the committee.

If you submitted a proposed consent form with your renewal request, the approved stamped consent form is attached to this re-approval notice. Only the stamped version of the consent form may be used in recruiting of research subjects. You are reminded that any change in protocol for this project must be reviewed and approved by the Committee prior to implementation of the proposed change in the protocol. A protocol change/amendment form is required to be submitted for approval by the Committee. In addition, federal regulations require that the Principal Investigator promptly report in writing, any unanticipated problems or adverse events involving risks to research subjects or others.

By copy of this memorandum, the Chair of your department and/or your major professor are reminded of their responsibility for being informed concerning research projects involving human subjects in their department. They are advised to review the protocols as often as necessary to insure that the project is being conducted in compliance with our institution and with DHHS regulations.

Cc: Nancy Rogers, Advisor HSC No. 2011.6316

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FSU Behavioral Consent Fonn Listener perception of segmentation and closure in music

You are invited to be in a research smdy on how listeners segment musical experience. Please read this fomt and ask any questions you may have before agreeing to be in the study.

This study is being conducted by Crystal Peebles from the College ofMus ic.

In this study, you v.

There are no foreseeable risks or discomforts ifyo u decide to participate in this study. You tvil1 be able to adjust the music to a comfortable voltune level. While you will not receive any personal benefits front this study, you ｶＮｾｕ＠ be contributing to the field ofmusic cognition. Participants who are c-urrently enro11ed in Introduction to Psychology and participate in this experinlent through the Psychology Department tviU receive the appropriate antount of course credit.

The records of this study will be kept private and confidential to the eA"tent permitted by law. In any sort of report I might publish, I will not include any infonnation that wi11make it possible to identify a subject. Research records tviU be stored securely.

Participation in this smdy is voltmtary. Your decision whether or not to participate will not affect your current or fi.tture relations tvith the University. You may temlinate your participation in this smdy at any tinte ｶＮｾｴｨｯｵｴ＠ penalty. You tviU still receive the research credits that you have earned ｶＮｾｴｨ＠ your participation to that point in the study.

The researcher conducting this study is Crystal Peebles You may ask any questions you have now. Ifyo u have a question later, you are encouraged to contact the researcher at .. The adviser for this study is Nancy Rogers, 644-4142, [email protected].

If you have any ｱｵ･ｳｴｩｯｮｾ＠ or concerns regarding this study and would like to talk to someone other than the researcher, you are encouraged to contact theFSU IRB at 2010 Levy Street, Research Building B, Suite 276, Tallahassee, FL 32306-2742, or 850-644-8633, or by entail at [email protected].

You will be given a copy ofthis infomJation to keep for your records.

Statement of Consent:

I have read the above infonnation. I have had the opportunity to ask questions and have received answers. I consent to participate in the study.

SigrJature Date FSU Human Subjects Committee Approved 6/23/10. Void after 6/22/11 HSC# 2010.4328

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BIOGRAPHICAL SKETCH

Crystal Peebles received a B.M. in Music Education from East Carolina University and a M.M. and Ph.D. in Music Theory from The Florida State University. Crystal has presented research at a variety of conferences including the International Conference for Music Perception and Cognition, the Annual Meeting for the Society for Music Theory, and numerous regional conferences. She currently teaches Music Theory at Northern Arizona University.

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