Perceived Closure in Philip Glass’ The Hours An experimental assessment of two predicting factors

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Perceived Closure in Philip Glass’ The Hours

An experimental assessment of two predicting factors

Master Thesis by Joy Huijskens (11956488)

MA Musicology

University of Amsterdam

Spring 2019

Dr. M. Beirens as first reader

Dr. J.A. Burgoyne as second reader

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1. Introduction

1.1 Motivation

During the past semester the title of our course kept buzzing through my head: How Music Works. We have looked at how music is processed, but we haven’t looked so much at the workings music elements by themselves. This led me to the question “how does music create a certain effect? And which elements contribute to the feeling that arises? Can we actually see significant differences in what is experienced based on the mere musical features defined by their theoretical basis?”

The affective power of music has mesmerized me during my whole scholarly career. Particularly the ability to evoke emotion, touch or move people, and power to connect people. At first, I was interested to investigate if music features could help to predict when people are affected by music. However, it is quite complex to answer such a question. The psychological experience of being touched by music is rather complex and involves more than just music structure and listener. Memories, performance, and state of mind all matter. Hence, I decided it was too complex to understand the role of music structure in explaining this feeling.

So, I chose to try to explain another feeling that music can provide: the feeling of closure. However, the feeling of closure seemed to me a relatively clear experience that could be related to certain musical elements and structures. Furthermore, this concept is more feasible for an online survey experiment, which is the best option due to monetary and time limitations. Furthermore, the concept of an ending might have more construct validity than the concept of being touched or moved by music.

1.2 Context

Musicology is a broad field of study, ranging from historical descriptions of music scores, to accounts of the practical performance practices per culture, and to the search for the explanation of musical skills by brain scanning. The current study draws from two different types of musicological research. Music theory and cognitive musicology. The former focuses on the analysis of written music, deriving structures, relationships and meaning from there. The latter focuses on the psychological experience that arises when one listens to music, along with the cognitive skills and parts of the brain engaged during this experience. Cognitive musicology research maps the process of music listening in the listener with psychological tests, computer modeling and by scanning the brain. Skills like beat perception, pitch perception and musical memory have been discovered in this field of research.

So, it has been researched what structures people listen to and how they process it; however, when music listening has one or the other outcome, is less well studied. To investigate if music structure predicts a certain experience, it is helpful to specify the input (type of music, music characteristics, performance) and the reference framework of the listener (musical background, musical preference, culture) as factors that likely modulate and thereby help to explain the response (outcome/experience). So, combining music analysis with the understanding of the psychological experience could be beneficial for understanding what factors predict certain musical experiences.

The main goal of this thesis is to investigate the relative importance of theoretical music features (anything that could be found in the sheet music) in predicting a certain experience. The study focuses on a relatively concrete and relatable experience that is present over a wide variety of musical styles: closure. This term is used to describe the feeling that arises when a musical piece is complete and there is no need for anything further (Sears, Chaplin, McAdams, 2014, 404).

A theoretical model is presented in which the contribution of multiple factors – the music features, the listener and external factors – are included to explain when an experience of closure may or may not occur. This theory will be tested with an experiment that investigates if a certain set of music characteristics can predict the experience of closure.

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Previous work often points to tonal resolution or harmonic closure as the main predictor of closure (Rosner & Narmour, 1992; Sears et al., 2014). However, it is difficult to imagine that in a world with such great diversity of music, this would be the only possible mechanism to reach closure. This study examines whether listeners can also experience closure in the absence of traditional tonal closing formulae.

The repertoire chosen for this study has parts with and without traditional closure formulae. In this way, the presence versus the absence of tonal closure on the experience of closure can be investigated, while music examples remain comparable on nearly all other aspects. The work The Hours from Philip Glass is chosen as the material for the current research. In his later work he uses tonal relationships but combines them in non-traditional ways. Sometimes phrases conclude with a harmonic dominant to root progression (V – I progression), and sometimes they use very different harmonic material to end a phrase (e.g. III-II or V7-III), as will become clear in later sections on music analysis (see Operationalization Independent Variables4.1 and 10.4).

It will be investigated if listeners can experience closure in The Hours, and if so, if harmonic closure is the main predictor of perceived closure, even in a music style that does not clearly follow tonal traditions. In practice, theories on closure will be related to the findings of an experiment where participants rate the perceived completion of selected sound fragments.

1.3 Importance and implications

Whereas closure has been defined, debated and redefined, the exact mechanisms that underlie closure have been discussed only sparsely (Anson-Cartwright, 2009). In addition, closure has mostly been investigated in very small numbers of musical works by experienced music theoreticians who have not linked this closure to listeners (ibid.).

This work aims to bridge the gap between theoretical music analysis and music psychology. The theoretical background focuses on music pieces and identifies various music characteristics that composers often use as a tool to create closure to music phrases, segments, or to the entire piece. Hand in hand theories on perception of endings in music and expectations in music will be discussed. The main aim is to link the theoretical structures in music endings to their effect on the listeners. Do listeners also experience the ending of a piece as an ending? And if so, what factors play a role there?

So, the current study aims to bridge this gap by reviewing these theories hand in hand and providing empirical findings that indicate whether a music piece that is characterized as having a ‘strong tendency to close’, according to music theorists, is also perceived this way by listeners. Many theorists are certain about certain markers indicating closure. But whether they function as closure markers or not could also depend on whether they are recognized as closure markers by the listeners. So, if these markers are present in a new context, such as Philip Glass’ music, it is debatable if they are still recognizable in the same way.

An implication of this research is that we start to understand whether closure markers are style specific or also applicable to other types of music. It highlights whether general theories about musical closure (Pebbles, 2006) are correctly capturing this process, or if musical style plays such a big role that any attempt at a generic theory about musical closure would do short to the process of closure.

Implications of this work are mainly to further explore other musical elements that could affect closure. The current work is not the first work to do so, whilst experimental studies already linked music structure and music perception (Boltz, 1989; Bigand, 1996; Knötsche, 2005; Sears et al., 2018).

However, these studies often use abstracted forms of music, like isolated melodies, chords or cadences. Their rationale is to more solidly link music characteristics to effects. However, their external validity is quite low; these experiments do not translate or represent music and music experiences from real life strongly. The current experiment is new in this respect. It focuses more on being representative of real musical experiences by using actual music compositions and neutralizing fewer

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variables. The original key, meter, tempo, number of notes, note lengths, range, contour, chords and order will be used. However, the fragments of about 13 seconds are still brief segments, isolated from their context. Neutralized elements were the performative aspects (ritardando and dynamics) and the instrument (midi piano). Hence, the fragments are not completely representative of real music, but they are more representative than in previous studies.

1.4 Approach

This work aims to connect music theory with music psychology. It will be investigated if assumptions and theories about closing formulae in music structure predict the psychological experience of closure. Since musical structure and the perception of it are closely interrelated, studies and concepts from music theory and music psychology will be discussed hand in hand throughout the theoretical background.

Firstly, music theoretical analysis and definitions will be explored. What musical features could contribute to closure will be identified on a theoretical basis. It will be discussed which of these apply in music in general and which in minimal music specifically. Thereafter, a music theoretical analysis of Philip Glass music will be presented. A theoretical model is proposed in which the relationships and expected effects of various factors on perceived closure are visualized, along with the hypotheses. Following is the documentation of the experiment that was designed and conducted to test whether theoretically defined closure predicts perceived closure as indicated by the participants’ ratings. Finally, it is discussed if closure is also perceived more strongly at those moments where we would expect it from the mere characteristics in the sheet music, regardless of performance. The experimental stimuli, survey and data recollection were entirely designed for this study, which can all be found in the operationalization and methods sections.

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2. Theoretical Background

2.1 Definitions

Before we dive into workings of closure, testing when and how it occurs, it must be clear what closure means. Therefore, the current section starts with a review of definitions of closure.

Closure in Music

In musicology, closure is mainly defined as a characteristic of the stimulus music. So, whether closure is present can be found by carefully examining the music characteristics in the sheet music or audio. Most recent work on closure in the field of musicology is from Anson-Cartwright and colleagues (2009). They investigated closure within the classical repertoire. In addition, they identified three concise definitions of closure in tonal music.

Firstly, it can be regarded as “that condition of rest or finality which a piece or movement attains at the moment of structural (tonal) resolution” (Anson-Cartwright, 2009, 3), claiming closure only happens when the harmonic progressions in music conclude. Where this moment takes place is irrelevant, it can be at the end of a musical phrase somewhere in the work, or at the end of the entire piece, only if the tonal structure reaches closure.

Secondly, the term has been used as: “that condition of imminent rest of finality which begins near the chronological conclusion of a piece of movement, and lasts until such rest is achieved” (ibid), suggesting closure is not just the feeling of rest after the piece, but rather a concluding process near the end that signals the ending is awaiting and ready to take place. The moment when such a closure phase starts, remains ambiguous when employing this definition. Rather, Anson-Cartwright claims, the moment when the concluding phase begins is defined by the expectation and realization of the listener, who feels the end is nearing for a while, instead of simply after the piece has ended. Since it includes the notion of the listener, it seems a more wholesome definition.

Finally, the term closure has been defined as “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” (ibid). He consciously employs immanent here instead of imminent to shift the emphasis. Imminent means approaching or awaiting, whereas immanent means unavoidable, or inherent to the piece. Here, Anson-Cartwright proposes closure is the expectation that a piece will end. He points out every piece has closure potential, the potential to end, from the very first moment it has begun. Interestingly, scholars who employed this definition, do not merely look at the ending of a piece when investigating its closure mechanisms. Instead, the focus lies on all musical events that show the tendency to close.

Altogether, these definitions offer insight in how and when closure may occur, but they do not seem compatible. The notion closure being tied to specific moments in time, and of it being tied to certain music characteristics in the first definition, the notion of closure as a process that takes some time to unfold, and which is defined by the listener’s expectations in the second definition and the notion of closure as something that is not time-bound but which mainly depends on tendencies to close of the third definition all contradict one another.

So, the definitions elucidate closure is about a sense of expectation, that increases, and decreases when fulfilled. But when this occurs, in reaction to what factors, remains unspecified. In the theoretical background that follows, factors that could play a role in closure will be discussed. Thereafter, the focus will lie more on explaining when the psychological definition of closure: feeling completion, this will be discussed after the musical factors responsible for closure.

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2.2 Mechanisms

Scholars investigated closure in different languages and music genres, resulting in many closure factors. For example, when melodies (Boltz, 1989), cadences (Caplin) or phrases (Knötsche, 2005) are perceived as complete, it would be due to different factors. These studies all presented music that varied in certain ‘closure factors’ that supposedly influenced how complete or not the piece was, and let participants rate how completed they experienced the music to be. Afterwards, correlations were drawn between which music characteristics seemed to predict the experience of musical closure. Music Features associated with Closure

Anson-Cartwright (2007) notes that the definition of closure does not explain how closure is achieved. The following section will discuss the means composers use to create closure.

Many common forms exist to conclude a musical piece, like the outro, coda, or repeat and fade. Still, within this form, the musical content such as the thematic or tonal information may determine how complete this fragment may be (Pellegrino, 2002: 148).

Music analyses have identified many plausible characteristics in the music that influence closure. For example, the amount of musical tension (Bigand, 1996; Monahan 2011), melodic completion (Boltz, 1989; Meyer, 1956, 131) repetition in the musical form (Monahan, 2011; Pellegrino, 2002), dynamics (Kraus, 2013, 133), and acoustic cues that indicate phrase boundaries such as silences or prefinal slowing (Knötsche, 2009, 268), or tonal closure (Kraus, 2013; Rosner & Narmour, 1992). These scholars were mostly interested in the Western tonal tradition and emphasized the role of harmony in closure perception. Music analyses of tonal music support this idea, which resulted in a merge of the term closure with harmonic closure.

The following section will discuss the following music features and their association with closure in respective order: harmony, rhetoric or acoustic cues indicating a boundary of a segment.

Harmony

Rosner and Narmour go into depth in their analysis of what musical factors make up harmonic closure (1992). They let listeners rate which two-chord progression was more closed. All sets of two chords had different characteristics (1992, 386). By systematically presenting every possibility, they could recognize which characteristics seem to contribute to closure the most. This is one of the first studies that experimentally assess theoretical claims about what ‘ought to provide closure’ is also experienced that way. They investigate if V-I really is the most closed progression, if it matters which tone of the chord is in the soprano voice, if the number of common tones between chords predicts how closed the event feels and if the outer-voice motion strengthens perception of closure. They found that learned stylistic structures best explained closure (ibid, 385-386). Harmonic factors such as the voice leading (inversion of the chord, soprano position and scale-step motion) were less relevant (ibid, 383). They found that the greater the change between the chords, the larger the feeling of closure.

Like Rosner & Narmour, a study by Chaplin and colleagues (2010) underlines that harmony contributes to closure. They investigated various types of cadences - a music structure known as the key to attaining closure by music theorists – and found listeners also perceived them as so. Especially the V-I progression gave the strongest sense of perceived closure. So, findings from experiments support the idea that listeners often rely on tonal information to assess closure.

Bigand and colleagues (1996) tested some musical factors that could underlie musical tension in an experimental paradigm. They created a test with short music fragments of three consecutive chords. The first and last chord was always C major, whereas the chord in between differed per trial. Over the entire experiment, major triads, minor triads, dominant seventh chords and minor seventh chords build on all other 11 scale degrees were presented as the second chord. Participants were asked to rate the tension the second chord created. Bigand and colleagues concluded that “tension arose

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from a combination of cognitive and psychoacoustic factors, whose relative importance varied depending on musical training” (ibid, 138), suggesting multiple factors together contribute to a sense of closure, both in the music and in the listener. Furthermore, chords on the scale degrees I, IV and V created the least tension. Diatonic chords created some tension and non-diatonic chords created the most tension. Bigand’s study shows harmony plays an important role in creating tension, and thereby also in creating closure.

Many different scholars seem to agree that closure is tied to harmonic elements that raise the anticipation something is about to close. Hence, not all endings are closed, but only the expected endings. Various music pieces have an open ending – they have stopped but still give the feeling they were not complete yet. For example, Pellegrino claims that a simple return of material from the beginning cannot create closure, it must contain tonal or structural closure to provide this feeling (ibid, 163). She claims that an ending is only an ending when it is anticipated, such as the 1st_{scale degree is}

the predetermined end in tonal music (2002:150). Her idea of closure is rather influenced by how common-practice tonality defines closure. This type of closure, which mainly points to the music characteristics, we could also call Harmonic Closure. This means the characteristic harmonic progression associated with completion is part of the music.

Rhetoric

Other scholars have disputed the role of the V-I progression in closure. For tonal pieces, harmonic closure is likely the most present characteristic, but other musical features could contribute to a sense of goal-direction and the perception of closure. For example, some pieces rely on rhetorical signs of closure, which are the signals of a work’s finality or closure which are not tonal in nature (Peebles, 6). In that case, often decreases in intensity can establish closure (Peebles, 2011:10).

This brings us to the next aspect of closure, the psychological aspect. The listener is an important aspect of closure. Without anyone experiencing a sense of anticipation, there is no sense of closure either, although it may seem complete in theory. So, Perceived Closure, the sense of closure that is felt by the listener, is a different aspect of closure that helps to define and understand this concept.

Analyses of modernist or minimalist works highlight different factors that may contribute to closure, likely due to their different way of analyzing pieces. Pellegrino’s analysis of John Adams’ work assesses closure on a more global scale (2002). She indicates that repetition of a ‘theme’ at the end of the piece, after having been encountered before, can provide closure. This type of closure, called formal closure, can only be experienced if a larger section of music is read or listened to. For example, a palindromic structure in Phrygian Gates suggests its own completion when all the material has been repeated backwards (ibid, 153). She notes formal closure (closure of a section of music) often coincides with tonal closure (a return to the root chord or tone of the home key) and rhetorical closure (gestures in dynamics and tempo). However, in John Adams’ music, these different types of closure often seem to contradict one another. Exemplary is the final section of The Chairman Dances, in which the key remains ambiguous, sometimes centering around B and sometimes around D (ibid, 158). If the tonal center is unclear, the arrival at the final chord feels less conclusive.

Pellegrino acknowledges harmonic closure plays in important role. Still, she describes elements that enable listeners to know right away that the piece is about to end, without having heard the preceding parts. She calls this Rhetoric Closure. Often the conclusion is signaled by a change in intensity of the piece. Either dynamics, tempo, register and orchestration become softer, lower and slower, or it becomes louder, higher and faster in comparison to the rest of the work (2002:166). These changes form a fade out or a climactic ending, respectively. These elements can come to light with a description of musical texture. So far not much experimental evidence is present to support musical texture aids closure, but it seems hard to negate that compositional elements like dynamics, tempo, register and orchestration could be contributing factors to closure. Findings from other fields such as boundary

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perception in language, Gestalt psychology in vision, we can assume similar mechanisms for boundary perception apply in segmenting music.

From Pellegrino’s work we can learn that many different factors can contribute to the feeling of completion, and likely closure is only perceived once various factors complete simultaneously. So, closure is unlikely to be only due to harmonic closure. Rather, it is more likely to be the product of multiple elements working together.

Acoustic boundaries

Another way to articulate the point of closure is by interrupting the rhythmic, melodic or harmonic patterns that have been established so far, to “signal a change in a static system has occurred” (Pellegrino, 2002:169). Anson-Cartwright supports this idea that in case of continuous repetitions, closure can only be attained by breaking the cycle, not by reaching a cadence that leads back into the repetition (2007:7). So, a change in form can be a signal of completion. When a pattern is repeated in a cycle, the change in pattern could be the completion of a goal (Pellegrino, 2002:150). A study by Knötsche investigated phrase boundary markers in music (2005). The main components that were identified are note lengthening and post-sound silence length, similar to phrase boundary markers in language (ibid). They let participants listen to two melodies: a phrased and an un-phrased one. Afterwards, the participants were asked to rate the number of phrases with closure. Perception of phrase boundaries in language also depends on certain aspects of the stimulus. Similarly, to the cues in language that help to keep phrases apart, they expected to find phrase boundary markers in music as well. Knötsche’s results indicated that small breaks after strong beats and lengthening of notes were the main characteristics that defined the end of a phrase. From their findings we can conclude that the length of the silence after a phrase is important to control, since it can strongly affect if the phrases are perceived as ended, which people may confuse with the psychological experience of closure or completion, which depends on more than just the silence after a sound, see the abovementioned definition of closure.

Interesting parallels can be found between boundaries in phrase perception in music and in language. This is possibly relevant for understanding the perception of closure at the end of musical phrases (Steinbeis & Koelsch, 2007). Interestingly, these studies do not merely ask for the experience of closure, but they let their participants indicate where an uninterruptedly repeating sound fragment should be cut in segments. Most participants cut the fragments in segments after moments of experiencing closure. Logically, closure and segmentation fall on the same moments, because recognizing an event or sound as a whole means one experienced it as complete.

This paragraph was devoted to describing when closure occurs how this process might work. Musical characteristics associated with closure were pointed out. The following sections will focus on how these music factors could lead to a sense of closure in the listener.

Music Psychology: Feeling Completion

One of the first published works on closure in scholarly literature was in a general psychological context rather than a music analytical one. For example, closure involved testing if participants could still recognize partially camouflaged images or recognize words with omitted letters (Mooney, 1954). Such perceptual tests required the listener to mentally fill in gaps, which was called closure (ibid). Basically, closure denoted a cognitive skill to complete or solve perceptually difficult constellations (Botzum, 1951), applicable to all senses and not just auditory information:

“Closure may be described in a more general sense as the moment of perceptual resolution; as the terminal phase of an act of perceptual contemplation; as the tension-relieving instant when meaning is or is recognized as emerging from a compelling constellation of objects or events” (Mooney, 1954).

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Basically, this view on closure is in line with Gestalt theory, where closure means the resolution of any kind of configuration that has created tension (Mooney, 1954:51). Although not specific to music perception, this definition does provide interesting key information that touches upon the core of musical closure as well, namely that it is a terminal phase, and that it provokes an experience of resolution, or relief of tension.

Not much later, a first discussion of closure in music was written by Leonard Meyer (1956:128-156), a music psychologist. Although he had a strong interest in music theory, he also incorporated the importance of the listener in the process. Although he had little music-related research to base his theories on or empirical evidence to support his claims; he succeeded in defining and theorizing ideas about musical expectations that still are regarded valuable and accurate till this day. In his renowned work Music & Meaning he describes closure as follows: closure is not just silence after music, but when the discontinuation makes sense (1956, 129). Closure can be a product from patterns in the piece, because when repetition occurs one could expect the music to end again in a similar way. Also, it depends on the style (ibid, 128) or culture (ibid, 131), because from all the music once heard one creates expectations about future endings.

Music cognition researchers have really started to embrace closure defined in terms of expectation (Narmour, 1990; Huron, 2006; Peebles, 2011) a feeling of the listener when he or she correctly anticipated the music’s end. Before this anticipated end, our expectation of continuation is very high, and after our predictions have been confirmed, our expectation of continuation is very low. To frame it differently, during this prospected ending phase, uncertainty of what will come is low; we know the end is coming up and foresee it. After the end has happened, uncertainty is high, because we do not know if a new section will start, and if so, what it will sound like

The idea that closure is something produced in the minds of listeners, and not just a characteristic of the object. Also, it is seen as a product of learning. Exemplary is Peebles quote “Closure is experienced when a listener is accurately able to anticipate the end of a musical segment, on any hierarchical level”, (p. xii) asserting that closure is the product from musical expectations that arose previous experiences. Meyer (1956, 138) expresses a similar sentiment.

Peebles points out that closure is a completion of a goal-directed process resulting in an arrival of relative stability or rest. Closure segments a continuous musical stream into discrete events. The strength of closure depends on many musical variables and plays an integral role in the hierarchic construction of a composition and closure is stylistically dependent.

The explanation for this phenomenon boils down to statistical learning. Listeners have likely learned what to expect in response to certain music parameters simply by being exposed to many similar patterns often enough. Even if they do not consciously realize it, the brain draws information from music and creates associations. So, statistical learning predicts that after hearing tremendous amounts of tonal music employing a cadence near the end of a piece, brains have started to associate this with completion. Statistical learning could help to understand that music features can be coupled with certain expectations of such as closure, the expectation of something be complete. The role of statistical learning in creating music expectations is confirmed by the model of Sears, Pears, Caplin & McAdams (2018).

This notion is important for understanding how closure works, and when it may occur or not. If closure is something a listener learns to expect from all previous exposure to music, it means 1) the idea of closure may be different for listeners from a different background who listened to different music, 2) closure is not just something in the music, but also something that is activated in the minds of listeners. Now we have a notion of what music elements elicit closure and how it feels, we will turn to some studies that modelled closure perception. At the end, I will propose a model that poses how closure could work, and what factors would be part of the process.

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Models of Closure Perception

Whereas some researchers really focused on what stimuli close music or provide closure, others are more interested in the mental and neurological mechanisms behind closure. What happens, when one perceives closure? Writers concerned with musical expectation (Hellmuth Margulis, 2007; Huron, 2006) and anticipation (Levitin, 2006) hypothesize what may affect whether music is perceived as closed. They try to fill in the gap of what happens in the mind or brain, but often remain more in a theorizing stage than providing clear empirical data to accompany their theories. All these writers note the importance of musical expectations, just like Leonard Meyer already suggested in the 50s.

Sears, Caplin and McAdams (2014), however, do provide a clear experimental paradigm on cadence perception and how to test this with real listeners. A few years later, Sears, Pearce, Caplin, & McAdams, developed a computational model to test what musical expectations may be created by passively listening to music (2018).

Sears and colleagues created a computer model that simulates musical expectations, namely the Information Dynamics of Music model (IDyOM). The aim is to simulate what expectations may form about music structure simply by exposure, assuming we calculate chances of something occurring again based on how often it has occurred before. Their 2018 study uses IDyOM to simulate what schematic expectations may come to play when listening to tonal cadences. Since cadences are associated with closure, this relates to how expectations play a role in perceiving closure too.

In a preparatory phase the computer model was given music with cadences to derive rules and expectations from. In a test phase, the model was presented comparable music excerpts and computed if the final note or sequence was predictable or not. By looking at the melody and labeling the chords it was determined if the music sequence ended in a predictable or unpredictable way.

By letting IDyOM listen to lots of endings, they could also conclude what patterns need to be present to give the feeling predicted conclusion. It presents the predictability of a continuation as the probability of another musical event to occur next. After a cadence for example, the probability for continuation is often low, hence it is seen as a recognizable pattern that helps a listener to classify a passage as closed. Still, cadences by themselves, without the correct context, did not rise predictions like this. Only if the cadence was anticipated, the music was experienced as closed, and not if the cadence happened at an unpredictable moment.

In that sense, closure is something that occurs in music that we can recognize from certain characteristics, and consequently that we anticipate. After closure is reached, we seize to have expectations for a moment. Final events of cadence sequences gave the lowest unpredictability scores. Cadential deviations, on the contrary, had the highest unpredictability scores. Together, these results suggest the most complete sequences are also the most predictable.

Their idea is that with low uncertainty there is more an experience of closure. It was found that cadential contexts were more predictable than non-cadential contexts. Half-cadences, sequences that end on V, were even unpredictable as any other dominant harmony chosen at random. This suggests that the half-cadence does not raise clear expectations in comparison to the other cadences, or that the effect of this cadence is keeping the listener in uncertainty and full of expectation of continuation. During a cadence, various musical factors such as melody, harmony, rhythm, all come to an end around the same time. Usually segments are distinguished by changes, and the discontinuities of a cadence clearly form such a segment boundary.

In addition, they tried to show whether closure could stem from learned expectations (Sears, Pearce, Caplin & McAdams, 2018). Their idea begins with the assumption that the brain is a predictive machine, which over time learns from all previous experiences which events are likely to happen in the future. In this way, the brain builds up schemata; specific predictions about how an event will continue. Similarly, listeners can build music schemata from exposure to music. Consequently, these schemata guide us to expect music to develop in a certain way. It has been argued that cadences are

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learned and remembered as closing schemata (Sears, Pearce, Caplin & McAdams, 2018:29). It has been called a “compositional device that suppresses expectations for further continuation” (ibid, p.30).

Sears and colleagues found that the Prospective Schema explains the probabilities best. This schema proposes listeners form expectations in advance and foresee what will happen. Subsequent realization of correct predictions will reinforce the strength of the perception cadences (2018, 32). Model

Until now we have seen many approaches to closure, and we know the music characteristics, the interpretation of the listener and the expectations learned by previous exposure to music all affect Perceived Closure. This is exactly why we would like to propose that the process of perceiving closure can be understood in terms of the stimulus-response model. This model views Perceived Closure as the result of a chain process, which allow us to include all the factors that have just been identified as important.

The stimulus-response model attempts to explain behavior or an outcome (the response) by influencing the preceding stimuli (the signal). Specifically, music with certain closure characteristics is the stimulus, which – if it is recognized by the listener – can give the feeling of closure as seen by a reported response (see Figure 1). In this sense, Perceived Closure is something that arises from the combination of the music and the listener, depending on his/her previous experiences with music which alters his/her expectations and thereby colors his/her perception of the current music having closure or not. It merely correlates variations in responses with the stimuli, without attempting to explain what happens in the minds of people between what they hear or see and how they respond to it.

Figure 1: Stimulus-Response Model of Experiencing Closure

After a review of closure in minimal music, we will revisit the stimulus-response model and discuss in more detail which music factors predict highly perceived closure in minimal music.

2.3 Closure and Minimal Music

The feeling of closure could be experienced through a combination of several factors: various music characteristics, exposure to music, and expectations. In tonal music, a sense of closure may be primarily linked to the moment of tonal resolution. Therefore, scholarly inquiry has mainly focused on tonal closure as the main predictor of perceived closure. However, if tonal closure is very dominantly present, it may complicate investigating other closure factors. So, a repertoire that moves away from tonal music allows other closure factors to come to light. Minimal music by Philip Glass was chosen as suitable for this purpose, for several reasons that will be explained below.

Who: Philip Glass

Glass encountered a vast amount of music from early age onwards. He listened to the records of his dad, played various instruments, and joined the Peabody Conservatory’s preparatory division.

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He grew up in a time when modernist music was developing, yet not an established part of the educational institutions. So, he was taught traditional tonal composition while he learned about serialist music in his spare time (Schwartz, 2008). When he travelled to India, his compositional style changed dramatically. His work from then onwards was largely influenced by Indian sitar music.

He is now known as a composer that composed both minimalist and post-minimalist works. Characteristic of his work are multilayered ostinatos, arpeggiated triads, simple harmonic progressions, slowly changing tonal or modal structures, and consonance. His works range from ensemble to opera, symphonies and film music (Burkholder, Grout & Palisca, 1980:973).

Glass’ knowledge of vastly different music traditions through his upbringing, education, interests, and travels allowed him to create compositions that also unite musical characteristics in a new way. Therefore, this composer has the repertoire in which tonal elements are included, but not used in the same predicting manner. His background from different musical traditions allows him to combine things in a new manner and to surprise. Therefore, Philip Glass’s music is an interesting case study to look at closure. Tonal elements are included yet treated and used differently. Hence, Philip Glass music offers the opportunity to study if tonal schemata are the only (or main thing) that creates closure, or which other parameters could provide a sense of completion.

When & What: Minimalism and post-minimalism

A combination of influences has led to the style we nowadays call minimalism. Likely, minimalism was a response to modernist music (Gann, 2013:59; Gann, 2001a; Burkholder, Grout & Palisca, 1980:969). In this context, modernist music refers to serial music and chance music, which was complex, incoherent, rapidly changing and difficult to follow for a listener. In the post-war era, music was overflowing with new scales, instruments, non-western timbres. The tradition was set forth in the music schools and by the established composers. The belief existed that music should be complex, dissonant, and difficult to understand to be valid (Gann, 1998).

In response to modernist complexity, composers started to experiment with creating music with a more audible structure and without too many things going on (Burkholder, Grout & Palisca, 2001:970). Works ranged from short to long, formal to informal and from ensemble to operatic works. Though, common characteristics among most performances and works were the use short melodic patterns, drones, repetitive figures and a slow rate of harmonic change (Potter, Gann, & Ap Siôn, 2013). Musical patterns were often gradually transformed by additions, subtractions or tempo alterations, which would drive the melodic lines apart. Often one main musical idea or sound was explored per piece (Burkholder, Grout & Palisca, 2001:972). The harmonic material was often reduced to a few chords, one scale or mode. With initially simple building blocks, they created complex sounds and rhythms.

“But where serialist syntax was abrupt, discontinuous, angular, arrhythmic, and opaque, post-minimalist syntax was precisely the opposite: smooth, linear, melodic, gently rhythmic, comprehensible.” – Gann, 1998.

Minimal music originated in the 60’s, but only reached the grand public in 1974 when Steve Reich’s Music for Eighteen Musicians was put on record and when his book Writings About Music was released. Early minimal works were loud, extremely long and unconventional. The style developed into repetitive, smooth, ambient music with simple tonality (Potter, Gann, & Ap Siôn, 2013). This shift can be seen from the 80s onwards, when minimalistic composition techniques were applied to create music with religious of expressive aims. These works have been characterized as post-minimalist works. Likely, the shift stems from composers who felt limited by the minimalist style (Gann, 1998), and consequently started to make more varied and expressive compositions including climaxes and build-ups (Burkholder, Grout & Palisca, 2001:972).

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The minimalistic approach was criticized as simple and void, and not as prestigious as the serialist and art music of that time. It was minimal, which means it was less than what listeners were used to. Less variety, change, or events happening over the time span of the music. Near harmonic stasis, very small changes and drones make the music seem repetitive. However, the sober approach helped to create a clearer and simple structure; listeners could truly get back to attentively listening to the music. With nearly contrast-free continuity, one had the time to observe gradual changes and small differences throughout the piece (Gann, 1998).

Unlike minimalist concerts that were often evening-long events where people could lie down and walk in or out whenever they wanted, post-minimalistic concerts moved back to a more conventional format. The event took place in a concert hall, the pieces were usually 5 to 25 minutes, and they were usually chamber works with a classical format (Gann, 2013:40). Orchestra, ensemble and some opera has also been composed. This style was never a united musical scene, but it can be recognized as a body of work with many common characteristics in hindsight.

Gann has summarized the main forms and characteristics of post-minimalistic music (2001b). Like early minimal works, the music is still clear, based on a steady pulse continuous throughout the entire piece, and used additive and subtractive processes to create musical patterns. Characteristically it uses diatonic scales, it is mostly consonant, but it avoids traditional functional tonality.

However, the compositions were less repetitive than minimal music compositions. Whereas minimalists were seeking for new structures of composition, post-minimalists sought to create new texture and timbre by repetition and layering of musical ideas (Gann, 2013). Strict processes were combined with free composition, intuitive alterations and adaptations (ibid:47). Conventional timbres and chords were used, but musical ideas from various styles, genres or cultural background were combined. Influences of African, Indian, and Balinese music can be recognized in the rhythmic complexity and the timbres present.

Typical for post-minimalist music are abrupt transitions to a following section without a pause, melodic stasis, and rhythmic complexity (Gann, 2013:52). Although the pieces often express an emotion or move the listener, they are low in contrast and cohesive. The mood and momentum often remain the same within a piece. Consequently, post-minimalism still has a static sound that makes it difficult for a listener to form expectations about where it is heading (ibid: 55). With a regard to closure, these characteristics could be problematic. If a listener has difficulty forming expectations where the music is heading, can a listener experience closure?

Teleology and Goal-directedness in Minimal Music

The characteristics of minimalist music make it less teleological or goal directed. Minimal music is often static, continuous, and with the same mood or texture throughout. Therefore, it does not have clear boundaries to highlight separate phrases, sections or parts. Without boundaries and events articulated in time, the passage of time becomes less clear. Some scholars propose minimal music lacks the sense that time is moving forward completely, and suggest it provokes a sense of timelessness. Lee notes that minimalist composers often exclude musical elements that articulate linear time, such as phrasing and articulation, and actively create a sense of timelessness by incorporating elements such as repetition, pulse, and audible structure (2013). Schwartz agrees that minimal music rejects the goal-oriented model of common-practice tonality by minimizing change in instrumentation, rhythm, tempo or dynamics (2008, 123).

When the music barely changes, the contrast free continuity that arises can lead to a lost sense of time. The music just goes, and a listener has very few clues where one is in the piece, or where it

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will go next. This new sense of time in minimal music was described as “a potentially infinite ‘now’ that nonetheless feels like an instant” (Lee, 20131₎

The feeling of timelessness and a lack of goal-direction is in direct antithesis with closure, which is strongly associated with a moment in time where a development towards a goal (finishing) unfolds. A sense of time is often indicated by moments that pass. When the present moves to the past, one knows time moves forward. In cases of timelessness, such boundaries that indicate something is over, do not appear clearly. Since minimal music often gives a feeling of timelessness, there may not be markers that indicate endings or beginnings. Thus, it could be questioned whether closure is present in minimal music. To say the least, a sense of goal-direction is complicated in minimal music.

From theories on closure we know that anticipation of the end contributes to the feeling of closure. When there is little development over time, listeners could have trouble forming expectations. Hence, without a sense of time, it is difficult to experience closure. Therefore, it is likely that listeners may find it difficult anticipate endings and feel closure in response to minimal music.

Pellegrino specifically objects that an analysis of phrases is impossible in minimalist music from John Adams, since there are no cadences or recognizable melodies in her case study of the piece Phrygian Gates by John Adams (2002:161). Without these boundaries, it is difficult to find moments of closure. If we look strictly to sheet music, it can be confirmed that minimal music does not show many signs of closure. Tonal relationships are present, but cadences are much less likely to occur. Other factors that help creating an ending, like ritardando or accentuations, are less present. Most minimalistic music has a rigidly set underlying pulse, so slowing down to mark closure is not present in the early works.

Although it has been claimed that minimalist music lacks the goal-directedness of tonal music (Gann, 1998), Evans questions if minimalist music truly lacks teleology and narrativity. The music may not always be working towards a harmonic conclusion but analyzing different aspects may illuminate other types of goal-direction and conclusions (2013:243).

Similarly, Robert Fink, an expert on minimalist music, argues minimal music is not without directionality. It may not be the goal, but that does not mean it is completely void of teleology either. The teleology is just of a different kind, which makes it less recognizable (Fink, 2005). He describes his idea with the term recombinant teleology, for which he uses a sexual analogy to demonstrate it. Western music is as goal-directed towards a single climax, alike doing the sexual act to reach an orgasm. Eastern music, however, has a very gradual progress with minor changes, which does not clearly lead to a climax but cyclically goes on and, like the meditative state of continuous sensory enjoyment without the aim to reach a climax. This is like an experience of tantric sex, trance, or meditations, that seems without a clearly identifiable climax. Yet, it can lead to a state of ecstasy even more thrilling than an anticipated conclusion that ends the ecstatic experience. Fink notes that although the music may seem without a goal, a new idea of goal directedness may help us to understand minimal music may have a goal. It could function to induce a state that provides pleasurable sensations, rather than giving only one satisfactory moment at the end of the piece.

Furthermore, a lack of tonal closure does not negate that the music can provide a sense of closure through completion of rhythmic or melodic patterns. Beyond tonal closure, or “the cadential orgasm”, different types of closure can be present if we reconsider goal-directedness in music.

For example, Fink’s ‘disguised’ form of goal-directedness can be recognized in multiple aspects of minimalist music structure. The gradual development in the pieces, the cyclic movements of the music (repetitions), or the rhythmical musical conclusions, for example. Also, when multiple cyclic processes of slightly different length reach synchrony after a while of seemingly disorganized coexistence, as during phasing, this can result in a sense of completion.

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Similarly, Lee brings up Tom Johnsons analysis of An Hour for Piano, which demonstrates some minimal music contains (elements of) linearity, such as transitions that anticipate the arrival of a new section. Furthermore, some melodic lines create a sense of tension and resolution, through dissonance and consonance at downbeats. The resolution can provide a sense of closure when it is to a note that is more stable, so less dissonant in the context, or when the note accentuates a new pattern (Lee, 20132_{). Such brief moments could be used to investigate closure.}

Altogether, minimalist and post-minimalist music has a great combination of characteristics to investigate closure. Since the composers uses different kinds of conclusions to their musical phrases and sections, sometimes with a return to the tonic, and sometimes not. So, we can see if harmonic closure is necessary to provide a feeling of completion, or if other factors like dynamics and rhythmic completion can fulfill this role as well. Furthermore, the music sometimes ends on the tonic chord, but approached from an unpredictable angle. With such examples, we could find out if completion is signaled by a return to the tonic, or if the preceding context is essential.

In the pitch realm, one could look for harmonies that can show when the tonal journey is completed. To do so, traditional Schenkerian analysis to chart the chords and voice leading (Evans, 2013:244) is helpful to gain insight in the harmonic progressions of the piece, which often reveal the goal of tonal completion. One could also analyze melodies to find markers of completion, by looking at when they reach the tonic or start to repeat a similar pattern. Beyond pitch, one could look for goal-direction in rhythm. Analysis of the rhythmical structure could show boundaries of musical sections, such as those marked by rests.

Beyond music theory, computational analysis offers new ways to understand goal-direction. Pearce and colleagues defined it in terms of entropy; the potential to change. If there is high entropy, a listener is highly uncertain of what is coming next, and vice versa (Evans, 2013:243). If a listener is very certain about the next note, for example just before the final note of a segment is struck, the music is clearly goal-directed (low entropy). However, if the listener is very uncertain about the next note, because the previous section has just been completed and any new directions are possible, the music has a low sense of goal direction (high entropy). Basically, certainty correlates with anticipations and uncertainty with a difficulty in having expectations. In these terms, closure is understood as a moment preceded by a low potential to change and followed by a high potential to change. It is preceded by certainty, and when the anticipations are met followed by uncertainty.

This theory offers a more general approach, because it does not specify which elements cause high entropy. Therefore, it could apply to minimal music as well.

2_{The reference is a webpage without page numbers. The citation refers to}_{“Melodic Sources of Linear Time”,}_§5

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3. The current study

3.1 The Repertoire

Philip Glass’s album The Hours will be taken as a case study to investigate closure. This album is composed as the soundtrack for Stephen Daldry’s movie The Hours (2002) which is based on Michael Cunningham’s novel. This work is more in line with the post-minimalistic tradition than with the minimalistic tradition. As explained before, post-minimalist music offers the possibility to investigate the influence of non-tonal music elements on closure. Still, there are tonal elements in the music too, which offers possibilities for control fragments. This makes it a suitable repertoire for the current research.

The Hours is minimal music written for film. Philip Glass’ minimal works often provide a sense of continuity, which makes this style very suitable for connecting scenes and shots in film. In particular, the music provides continuity between rapidly alternating storylines of three women in different year and location. Not only are the shots connected in a smooth way, the similarities between three women are also underlined by the similarities in the music that repeats cyclically (Crisp & Hillman, 2010).

The music supports the story that is visible on the screen, yet without using themes or motifs to represent something or someone in specific. Neither is there clear harmonic or thematic development in most of the pieces. Rather, the melodies often consist of repeated patterns. The underlying harmonic structure can mostly be understood as triads or seventh chords that repeat (in a more elaborate way) instead of developing in new directions (ibid). We know that the density of the arrangement, range and dynamics do develop over the piece, creating climax and development by different means than harmonic or thematic progression. In this way, the development of the narrative is supported, but not in a common harmonic or thematic way.

Hence, characteristics of minimal music are clearly present in The Hours. Still, it is less like previous minimal music works by Glass, where musical patterns repeat over a much longer time span, and for example teleological development could take more than half an hour (e.g. like in Glass’ work Einstein on the Beach). Because these compositions were made for the film, music from The Hours must develop and complete within a limited time frame to suit the tempo of the movie. For example, before characters start to talk, the music must fade or conclude. The length of the music and the moments when conclusion needs to be reached is shaped by the scenes; hence, being shorter. The Hours has some strange meters changes and unconventional chord progressions that do not align with rules in tonal harmony, but much less than in Glass’ earlier and more experimental minimalist works.

Post-minimalistic characteristics of The Hours are clearly established key, chords progressions mostly start and end on the tonic, chords formed on the diatonic scale degrees are used, and most works are in four-four time. Another characteristic is the sense of smooth continuity throughout the works, probably due to the abundant use of the chord on the 5th_{scale degree at the end of a phrase}

or chord sequence, which initiates the repetition of the following segment that begins with the tonic chord.

To identify the closure factors in The Hours, the fragments were analyzed. Section 4.1 discusses a few exemplary fragments, where music analysis is used to show that closure factors investigated in this study are represented in these fragments. In the Appendices 10.4 sheet music of all fragments can be found organized by their characteristics, along with a short music analysis for each piece. Section 10.5 is a table with the fragment properties in one clear overview. To provide more context to what music was chosen and how it was analyzed, the theoretical model and specific research questions will be introduced next.

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The original music composition for the film was arranged for orchestra3_{. However, for the}

current study the simplified arrangement by Michael Riesman & Nico Muhly4_{for piano solo was}

chosen. This simplified arrangement is still comparable to the entire composition, yet it has fewer confounding factors. Differences in timbre, instrument preferences or reverberation are all minimized by having this piano solo arrangement. This way, one of the variables that could influence closure, timbre, can be controlled. The sheet music of The Hours will be analyzed to make a good selection of musical phrases. The parameters of interest were easy to manipulate in this set up and investigate with these fragments. The choice to include only music from The Hours and not from another work or music style was to control variation within the sample.

Suitability

For the current day listener (between 18 and 60 years of age, because this is the age group that is most likely to participate in the experiment) it may be difficult to perceive closure in serialist music from the 12-tone tradition, because it is overwhelming and changeable (Gann, 2001). Minimal music opposes the abrupt discontinuous, arrhythmic and dissonant serialist music, by making smooth ongoing sounds and using diatonic scales again. Such characteristics make minimalist music more relatable for the current day listener, and hence for measuring closure.

Early minimalist music could be too static and repetitive, lacking goal-directionality that is needed for closure. However, post minimalist music seems very suitable for this study music because it is more conventional and accessible than serialist or early minimalist music, but not too conventional. It includes traditional tonal elements that could provide closure but combines and arranges them in a new way. Hence, it gives the perfect opportunity to investigate closure aspects in music beyond tonal closure. If music is completely void of harmonic closure, it could stray too far from current day listeners’ expectations to provide any closure. Consequently, most fragments could to be rated as ‘incomplete’, which informs us the music is not experienced as complete, but not so much about the relative contributions of closure factors. On the contrary, music with moderate amounts of harmonic closure allows us to discover more about the relative contribution of music characteristics to perceived closure.

More specifically, Glass’ work The Hours is suitable because music fragments with and without harmonic closure can be found, providing perfect control fragments for the experiment. These are in the same style, by the same composer, from the same era and for the same instruments. This helps to keep many factors constant, so the effect that those of interest have on closure can be investigated.

This repertoire decision is especially interesting because we can find out if closure can be perceived in response to Glass’ music, a style in which this hasn’t been investigated.

Furthermore, after performing harmonic analysis to the work it is confirmed that tonal relationships are present in this work, whilst tonality is not strongly used to sign completion. To illustrate, even after I follows V, the music often continues. The discrepancy between tonal closure and a busy arrangement offers an interesting opportunity. Such fragments can clarify if tonal closure by itself gives a feeling of tonal closure, regardless of the arrangement and rhetoric, or if it cannot. Furthermore, in cases were harmonic closure lacks, we can see if listeners can perceive closure without tonal closure.

Approach

Riemannian theory is often used by music theorists to analyze minimal music. Neo-Riemannian theory proposes that transitions between chords in a progression can be understood in terms of pitch space, where proximity defines the smoothness of the transition. Chords being close in

3_{For the original soundtrack, see https://www.youtube.com/watch?v=N4YuenZYHm0}

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space (with e.g. two common tones, small steps to new tone) give smooth transitions as compared to those far apart (e.g. no common tones, large leaps to next tone). Two chords unrelated according to tonal theory and not related by scale, such as G-minor (consisting of G, Bb and D) and Gb (consisting of Gb, Bb and Db), can still give a smooth transition because they are close in space.

Although neo-Riemannian theory is a useful tool to analyze minimal music, it remains unclear how proximity of chord-transitions relates to perceived closure. Hence, this type of analysis is not performed in the current study.

Some scholars think it is misleading to perform harmonic analysis on a piece that is not based on harmonic progressions, such as minimal music (Bernard, 2002). Yet, performing harmonic analysis is helpful for this study, because harmonic closure affects the listeners’ perceived closure. Therefore, it is important to perform analysis to map any harmonic progressions present in the music, to make sure harmonic closure is not confounding the level of perceived closure.

3.2 Theoretical Model

An experiment will be designed to test whether closure in the music of Philip Glass as defined by harmonic closure/music(?) will also be experienced as closure. This section offers a theoretical model of what factors are expected to influence closure, how this process works, and highlight other relationships that could be at work.

This study assumes that music characteristics can influence the reported levels of closure, and different music characteristics may lead to different responses. As can be seen in Figure 2, the theoretical model used to investigate closure assumes that a different signal can lead to a change in processing and thereby to a different outcome. For example, an increase in harmonic closure (signal) could activate the expectation that the music is likely to end (processing in the mind) and thereby let the participant to rate the music as more closed (outcome). In this, the signal is the independent variable that can be altered to investigate the effect on the closure rating: the dependent variable.

Figure 2: Theoretical model

More specifically, the musical factors hypothesized to affect the response are harmonic closure, note density and the midi-format. Harmonic closure refers to the chord progressions. A specific progression, V-I, has been identified as the key to closure. Hence, it is expected that the type of chord progression changes the reported levels of closure. Note density is a concept that captures the

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difference between busy and sparse arrangements. Since music often slows down or is brought to a point of rest the end, we expect low note density to be associated with closure.

Furthermore, it must be considered that the signal is not the only influence on the outcome, because people could answer differently based on their reference framework. With this term I mean the way the participant views the music (middle column in Figure 2). Factors that could change their framework that are accounted for are their music skills, their familiarity with the music, if they liked the music, and some demographics. These individual differences are covariates in the model, because they could lead to variations in the outcome. For example, high familiarity with the music fragment could mean the participant knows the fragment and knows how the end is supposed to sound. Therefore, the participant has learned that this is the end, and is therefore likely biased in reporting how complete the fragment is. Hence, the covariates will be monitored per question, to make the sure the effect they have can be discerned in analysis afterwards.

In addition, confounding variables are part of the model. The participant could answer differently due to distractions, a lack of concentration, fatigue, the quality of the headphones or (problems with) the internet connection. All of these could lead to differences between participants that have nothing to do with the music characteristics. Therefore, they could hinder good understanding of the factors that predict the reported levels of closure. Hence, these variables need to be assessed and incorporated in statistical analysis to make sure of their effect.

3.3 Research Questions & Hypotheses

Before investigating the relative contribution of variables on Perceived Closure in Philip Glass works, it must be established whether listeners can experience closure when listening to them. This leads to the first hypothesis:

H1: Listeners can perceive closure when listening to Philip Glass’ The Hours

Thereafter, the effect of two variables on Perceived Closure will be investigated more closely, with the following research question as an anchor: Is harmonic closure the main predictor of perceived closure, also in a music style that does not clearly follows the tonal traditions?

More specifically, it will be tested whether Harmonic Closure (as defined by music theory) and Note Density predict perceived closure of Philip Glass’ music, as indicated by self-reported ratings on a Likert Scale. The predictions are as follows:

H2: Fragments that have harmonic closure will be rated as more complete than fragments with a lack of harmonic closure.

H3: Fragments with low note density are rated more complete than those with high note density.

H4: Harmonic closure and note density combined show an additive effect on perceived closure or the perceived lack of closure

H5: High harmonic closure in combination with low note density will predict the highest perceived closure.

Perceived Closure in Philip Glass’ The Hours An experimental assessment of two predicting factors