AN EMPIRICAL STUDY EVALUATING THE PRINCIPLES OF THE
IMPLICATION REALIZATION MODEL
A thesis submitted to the Faculty of Humanities of the University of Amsterdam in
partial fulfillment of the requirements for the degree Master of Arts in Musicology by Heather Pinkham
Copyright by Heather Pinkham
2015
Supervisor:
The Implication Realization Model, theorized by Eugene Narmour (1989/1990/1992), describes tone to tone expectancies for melodic continuation. The basis of the theory is that when listeners hear a melody they typically form expectations about its continuation. These expectations are derived from a combination of learned and innate factors. The innate factors described by Narmour have been supported by several studies as accurate predictors of perception of melodic expectancy across different genres and different levels of training (Schellenberg, 1996, 2002; Thompson et al, 1997). However, more recent studies (e.g., von Hippel, 2002; Vos & Pasveer, 2002; Carlsen, 1981) have shown that there may be differences of melodic expectancy across levels of training and/or different cultures. For the present study, 21 participants of varying degrees of musical training and background were tested using Narmour’s (1990) principles of melodic expectancy. Participants were asked to complete three tasks: an interval completion task, a melody completion task, and a perception task. In the production tasks (interval and melody completion tasks), participants were asked to produce what they perceived would be the most likely and least likely continuation tone after a given implicative interval and melody. In the perception task, listeners were asked to rate how likely (on a sliding scale from 0 to 1) the last note of a three-note fragment was to occur following the initial, implicative, interval. Mixed model and two-way ANOVAS were conducted to assess the level that responses could be predicted by Narmour’s (1990, 1992) principles. The Implication Realization Model was found to be an accurate predictor of both production and perception tasks, except when harmonic implications were very strong with the implicative interval. Responses from participants with high and low degrees of training
ACKNOWLEDGMENTS
I would like to acknowledge my thesis advisor, Professor Makiko Sadakata, for her patient answers to my incessant questions. I would also like to thank my friends and family (both near and far) for their support and understanding through this process.
PREFACE………... ….1 1 INTRODUCTION 1.1. Background……….……. ………3 1.1.1. Expectations in Music………..3
1.1.2. Meaning and Emotion in Melodic
Expectancy……….4
1.1.3. The Perspective of Rhythm and
Meter……….5
1.1.4. Empirical Studies of Melodic
Expectancy………...……….5
1.2. Purpose………
…………7
2. THE IMPLICATION REALIZATION MODEL
2.1. Principles of
Implication………..8 v
2.3. Partial Realizations of Process………... ………..10
2.4. Full Realization for Large Intervals: Reversal………..10
2.5. Partial Realizations of
Reversal………...11
2.6. Summary………
………11
3 MATERIALS AND METHODS
.1 Participants………. …………....12 3.2 Stimuli………..……. ….13 3.2.1 Interval Completion Task………....13 3.2.2 Melody Completion Task………14 3.2.3 Perception Task………...14 3.3 Procedure………. ………....16 3.4 Statistical Analysis………... ……….17
4 RESULTS OF PRODUCTION DATA
4.1 Interval Completion
Task………17
4.1.1 Higher Education Completed for Descending Intervals. ……….18
4.1.3 Implicative Intervals in Descending Direction……….20
4.1.4 Implicative Intervals in Ascending Direction………. ………..23
4.2 Melody Completion Task………... ………...25
4.2.1 Analysis of Melody Completion Task………26
5 RESULTS OF PERCEPTION DATA
5.1 Perception Task………27
5.1.1 Mean Expectancy Ratings in Descending and Ascending Directions………...27
5.1.2 Implicative Intervals in Descending Direction ………..……..28
5.1.3 Implicative Intervals in Ascending Direction ……….. ……….…...32
6 DISCUSSION
6.1 Summary……...……….……….. ……….36
6.1.1 Findings from the Interval Completion Task..……….………... ………..37
6.1.2 Findings from the Melody Completion Task………...39
6.1.3 Findings from the Perception
Task……….39
6.2 Implications……….……….... ………..40
7 CONCLUSIONS...……….. …..41 References……… ...43 Appendix 1: Intake Questionnaire………...46
Appendix 2: Instructions for Interval and Melody Completion Tasks………..47 Appendix 3: Information Brochure………..48 Appendix 4: Informed Consent………...50 Appendix 5: Perception Stimuli………....51
Appendix 6: Implied and Realized Tonalities in Perception Task……….52
Appendix 7: The Circle of
Fifths……….54
Appendix 8: Definition of Terms….
………...55
3.1 Intervals used in the experiment………13
3.2 Melodies used in the
experiment………14
2.1 The combination of principles that make up a full realization
(i.e., process) for small
intervals……….9
2.2 Melodic patterns which qualify as
processes………...10
2.3 Different types of partial realizations: intervallic process (IP), intervallic duplication (ID), and registral process (VP) ………...10
2.4 Illustrations of reversal (R), intervallic reversal (IR), and registral reversal (VR)………..11
2.5 Illustrations of each kind of realization discussed: process (P), intervallic process (IP), intervallic duplication (ID), registral process (VP), reversal (R), intervallic reversal (IR), and registral reversal (VR) ………11 4.1.1 Mean full realizations in likely and unlikely conditions for education
completed, descending direction.
………...…..18
4.1.2 Mean full realizations in likely and unlikely conditions for education
completed, ascending direction
……….20
4.1.3 Mean full realizations in likely and unlikely conditions for implicative
interval, descending
direction………. .21
4.1.4 Descending interval M6 as notated in the interval completion task………..22
4.1.6 Mean full realizations in likely and unlikely conditions for implicative
interval, ascending direction
……….23
4.1.7 Ascending interval m3 as notated in the interval completion task………24
4.1.8 Ascending interval P5 as notated in the interval completion task……….25
4.1.9: Ascending interval M7 as notated in the interval completion task………...25
4.2.1 Mean full realizations in likely and unlikely conditions for Melodies 1 and 2………....26
5.1.1 Mean expectancy ratings of the perception task in full realization, partial realization, and denial; ascending and descending directions ………...28
5.1.2 Mean expectancy ratings for in full realization, partial realization, and
denial; descending direction
………...…...29 5.1.3 Descending interval M3 in partial realization and denial as heard in the perception task…..…30
5.1.4 Descending interval P5 in full and partial realizations as heard in the perception……….31
5.1.5 Descending interval m6 in partial realization and denial as heard in the perception task……..32
5.1.6 Descending interval m6 in partial realization and denial as heard in the perception task……..32
5.1.7 Mean likelihood ratings in full realization, partial realization, and denial;
ascending
direction………..33
5.1.9 Ascending interval P5 in full and partial realizations as heard in the perception task………....34
5.2.0 Ascending interval m6 in partial realization and denial as heard in the perception task………35
5.2.1 Ascending interval M6 in partial realization and denial as heard in the perception task………35
5.2.2 Ascending interval M7 in partial realization and denial as heard in the perception task……....35
As music is found in all known cultures (Patel, 2008), it is unsurprisingly a topic that has often been studied, philosophized, theorized, listened to, and practiced. In other words, in various ways and in various times and in various places, it is something that we have tried to understand. Though the possibility that we will never fully understand all the numerous and heterogeneous factors that allow us to appreciate music is great, the search for understanding will undoubtedly continue. Music theorists have tried to understand music through one of its most fundamental properties: the melodic interval and its implied expectancies. In the 20th century these properties have both been studied extensively. To understand expectancy as it relates music, it is perhaps necessary to understanding the full meaning of expectancy in general. Expectancy is defined as an event based on its probability of occurring (Chaplin, 1985). Human beings are constantly anticipating future events; these anticipations can be determined either by learned associations (nurture) or by cognitive predispositions (nature) (Schellenberg, 2002). Expectancies are categorized on the basis of the source of the expectancy (i.e., a stimulus or a behavior) and whether the expected consequence is a response to that consequence or simply another stimulus (Maddux, 1999). That is, whether the second stimulus merely followed the first, or whether the second stimulus was caused by the first. Expectancies give rise to a great range of emotions. Feelings of surprise, anxiety, disappointment, fear, hope, and closure can all be experienced from the fulfillment or denial of expectancies in music. There have been many psychological theories about expectation, but only a few which can be empirically tested. As empirical information is necessary for gaining further insights, however, it is necessary to find ways in which melodic expectancies can be tested.
In recent years, David Huron (2006) elaborated on previous research by Leonerd Meyer (1956, 1957) and hypothesized that listeners have four different types of expectation. These are veridical expectations, which are derived from episodic memory and contain knowledge of the progression of a specific piece. Schematic expectations, which arise from being exposed to certain musical styles and contain information about general event patterns of different musical styles and music in general (based on semantic memory). Dynamic expectations, which are built up through knowledge stored in short-term memory about a specific piece that one is currently listening to and are updated in real time through listening. Huron also described conscious expectations that contain listeners’ thoughts about how the music will sound (Huron, 2006). What Huron describes as schematic expectations was of particular interest in the present study. Through exposure by listening and practicing music, as well as studying music theory, musicology students in university and jazz and classical students at the conservatory undoubtedly have certain schematic expectations when it comes to musical style and presentation. The degree of strength for these schematic expectations would depend on the amount of exposure to these styles (Huron, 2006). The goal of this study is to further investigate this relationship. Though there have been many studies on the perception of melodic expectancy between musicians and non-musicians and between musicians of varying degrees of musical training, (e.g., Cuddy & Lunney, 1995; Schellenberg, 1996/2002; Krumhansl, 1995; Schmuckler, 1989) there have been fewer that have investigated the production of melodic expectancy within these groups (Thompson et al, 1997; Carlsen, 1981; Unyk & Carlsen, 1987). There have even fewer studies that have investigated both production and perception data of melodic expectancy from musicians of varying degrees of training (Schmuckler, 1989). The present study has precisely this within subject design.
1 INTRODUCTION
1.1 Background
1.1.1 Expectations in Music
Because of the role of expectancy to cognitive processes, it perhaps comes as no surprise that almost all contemporary music-theoretic analyses have adopted implicit or explicit (i.e., intra-musical or extra-musical) ideas of expectation (Siegmeister, 1965; Ratner, 1966; Piston, 1978). Schenker (1935) was perhaps the first music theorist to write about implicit uses of expectation in forming structures of melodic motion. In Schenker’s analysis, the foreground, middleground, and background all contain certain events that connect with later events. The earlier events or sequences, then, anticipate the sequences that come later on, creating a foreshadowing of events to come (Schmuckler, 1989).
Narmour (1990), building on existing theories of expectation (e.g., Schenker, 1935; Meyer, 1956) conceived of a model which contains basic principles that thus can and have been used for empirical testing (e.g., Schellenberg, 1996/2002; Cuddy & Lunney, 1995; Thompson et al, 1997; Schmuckler, 1989). Narmour (1990) theorized five basic principles of melodic expectancy that are claimed to be innate factors across all cultures and training. These “bottom-up,” universal principles are as follows: the first principle is registral direction, which states that small intervals imply continuations in the same direction (i.e., ascending to ascending), while large intervals imply a change in direction (i.e., ascending to descending). The second is intervallic difference, which states that small intervals imply a subsequent interval that is similar in size (± two semitones if direction changes and ± three semitones if direction continues), while large intervals imply a consequent interval that is smaller in size (at least three semitones smaller if direction changes and at least four semitones if direction continues). The third is registral return, which is a general implication for both small and large intervals of a return to the general pitch region (± two semitones) of the implicative interval. The fourth principle is proximity, which describes a general implication for small intervals (five semitones or less) between any two tones. The implication is graded according to the size of the interval. The final principle, closure, is determined by two conditions: first, a change in direction; and second, movement to a smaller-sized interval. Combinations of these principles occur in full and partial realization of the Implication Realization Model, to be discussed in full in the following chapter. This model was chosen for the present study as its basic principles have proven to be a useful and accurate predictor for empirical testing (e.g., Cuddy & Lunney, 1995; Schellenberg, 1996/2002; Krumhansl, 1997; Thompson et al, 1997).
In the 1950s, Leonard Meyer theorized about the relationships between musical structures and listener’s expectations (Meyer, 1956/1957). According to Meyer, emotion and meaning conveyed by music depend on whether expectancies are fulfilled or denied (Meyer, 1956). When an unexpected musical event happens, one of three events may follow: (1) judgment will be suspended in an act of trusting that what will follow will clarify the meaning of the unexpected event; (2) if there is no clarification, the mind may reject the whole stimulus and irritation will set in; (3) the expected consequent may be seen as a purposeful blunder (Meyer, 1956). For Meyer, musical stimuli cannot make us expect extra-musical concepts but instead can make listeners expect other musical events which are about to happen. That is, one musical event (be it a tone, a phrase, or a whole section) has meaning because it makes us anticipate another musical event (Meyer, 1956).
Meyer regards learned factors (such as schematic expectations or knowledge of music theory) as the most important phenomenon underlying musical expectations and experience. He does put forth a few innate components, however, which grow out of the basic principles of Gestalt psychology; that is, the whole is different than the sum of its parts1 (Koffka, 1935). These innate processes include grouping (the general observation that humans tend to perceive objects as organized patterns), closure (the mind’s tendency to see complete forms or figures even when the form or figure is incomplete), and good continuation (when there is an intersection between two or more objects, the tendency to perceive each object as a single uninterrupted object), as they apply to music (Meyer, 1956). Another innate process that Meyer writes about is the gap fill (Meyer, 1956). That is, a large melodic interval is “filled in” with a note that is in between the first 1 Gestalt psychology describes the phenomenon that we perceive groupings of objects differently than the individual objects themselves. For example, notice that a series of flashing lights (such as Christmas lights) appears to be moving rather than individual lightbulbs. According Gestalt psychology, this is because our minds fill in missing information. For full explanation of Gestalt psychology, see Koffka (1935).
interval. According to Meyer, the human mind, striving for stability and completeness, expects this melodic gap to be filled in (Meyer, 1956).
1.1.3 The Perspective of Rhythm and Meter
Other theories have suggested that our melodic expectations are shaped by rhythm or metric pattern (Jones, 1981, 1982, 1990). Jones, in her two part essay, Music as a Stimulus for Psychological Motion: Part I and II (1981 & 1982), criticizes the implementation of “vague,” Gestalt-like principles and proposes instead the use of a theory that provides a basis for determining if and how musical interval recognition is affected by the surrounding musical context (Jones, 1981). She argues that, because a musical interval rarely occurs in isolation in music, the omission of context is quite a constraining factor. Jones states (and is supported by evidence from Cuddy et al, 1977) that a listener who encounters an interval (e.g., C4-G4) before the occurrence of another interval (e.g., C4-E4) may be affected by these earlier notes. Jones’ main criticism of similar theories (e.g., Meyer, 1956/1997) is that they are based solely on psychological assumptions, and not the context or style of the musical material. She proposes instead an incorporation of time into the definition of expectancy, as, she claims, it helps to explain the preparatory functions of a stimulating context (Jones, 1981).
1.1.4 Empirical Studies of Melodic Expectancy
One of the first empirical studies of musical expectancy was performed by Carlsen and her colleagues (Carlsen, 1981/1982; Carlsen et al, 1970). Carlsen et al. (1970) reported a study in which subjects provided one-note continuations for two-note intervals. Using the same technique, Carlsen (1981) performed a more thorough study of melodic expectancies, using all two-note ascending and descending intervals, plus the unison. In this study,
listeners sang a continuation tone which felt the most “natural” depending on the interval (Carlsen, 1981). Carlsen presented the first 2 notes of a melody to musically trained singers from the United States, Germany, and Hungary, and asked them to sing notes that might continue the melody. Unyk and Carlsen (1981) then used a similar procedure with musicians from the United States only. The researchers examined the frequency with which different continuation notes were sung, and introduced the notion that different melodic intervals generated different expectancies, which is in line with Narmour’s (1990) principles. Completions were analyzed by counting the number of times each realized interval (the response interval of the participant) occurred. Results showed that responses from participants clustered around two or more pitches; there was no single pitch expectancy from a given implicative (that is, initial) interval. Results further showed that small response intervals of three semitones or less were more likely than large intervals. Finally, expectancy responses varied depending on the culture of the listener (American, German, or Hungarian), but not on the basis of explicit musical training (Carlsen, 1981). Though this study was not a test of Narmour’s (1990) bottom-up principles (indeed, it was before Narmour’s principles were theorized), they can be used to analyze the data.
Another empirical study was done by Cuddy & Lunney (1995), who performed a study of melodic expectancy using predictors based on the bottom-up principles of Narmour’s (1990) model of melodic expectancy against continuity ratings collected for a note that followed an initial melodic interval. In this study, twenty-four musically trained and untrained subjects were presented with eight melodic intervals that they were asked to consider the beginning of a melody. The eight intervals were presented in ascending and descending order, and all had a tonal center around either C4 or F#4. Two versions of each of the eight ascending and descending intervals were created around C4 and F#4 so as not to create a top-down sense of tonality. For the full list of intervals used, see Cuddy & Lunney
(1995), p. 455. Each melodic interval was followed by a third tone, which was one of the 25 chromatic notes within the range on octave below or above the second tone of the interval. Subjects were asked to rate how well the third tone continued the melody. Support was found for three of Narmour’s principles (intervallic difference, registral return, and proximity) and a modified version of a fourth (registral direction). The study found no significant difference in responses between levels of musical training.
Building on Carlsen (1981) and Cuddy & Lunney’s (1995) models of testing, Thompson et al (1997) performed a comprehensive study of the Implication Realization Model in a study of 100 participants (50 with high training in music; 50 with low training). The study was a re-examination of the same eight intervals examined by Cuddy & Lunney (1995), but participants were asked to perform a production task rather than a perception task. The same eight intervals were presented, and participants were asked to use the initial interval as the beginning of a melody. The first note following the initial interval was analyzed. Support was found for all of Narmour’s (1990) principles, as well as two additional predictors based on implied tonal structure. Again, there was no significant difference in responses between levels of musical training.
While the Implication Realization Model has proven to be a good general predictor of melodic expectancy and in most cases has not seen a difference between musicians with varying degrees of training (e.g., Cuddy & Lunney, 1995; Thompson et al, 1997), some more recent studies have shown differences in melodic expectancy between degrees of training (e.g., von Hippel, 2002; Vos & Pasveer, 2002; Von Hippel & Huron, 2000). Von Hippel (2002) conducted an experiment in which 28 trained musicians and 12 untrained participants were asked to make perspective judgments for a set of unknown (read: generated) melodies. The expectations of the trained listeners exhibited the influence of the principles of registral reversal and
registral direction. The expectations of the untrained listeners, however, showed significantly weaker influences of these principles. In a similar study of melodic expectancy (Vos & Pasveer, 2002), results showed that the responses of untrained listeners exhibited a greater influence of the principle of registral direction than those of the trained listeners. It should also be noted that in some cases (Carlsen, 1981), differences between cultural groups in observed patterns of expectations have been found.
1.2 Purpose
Narmour (1990) asked whether the definitions he outlined of the principles of intervallic similarity and intervallic difference are constant from listener to listener and style to style, or whether they varied according to degree of learning. The current study is an attempt to answer these and other questions. The specific goals of the present study are threefold. The first goal is to utilize the so-called universal principles of the Implication Realization Model as a basis for further investigation of melodic expectancy in production and perception tasks. As the results from previous studies of melodic expectancy have been conflicting, the second goal is to further investigate the relationship between degree of musical training and melodic expectancy. The third goal is to investigate the influence of possible tonal implications of certain intervals on response ratings and production.
In order to achieve these goals, the present study was designed using similar models of testing melodic expectancy by Cuddy & Lunney (1995) and Thompson et al (1997). The present investigation differed from these studies in four ways. First, participants were presented with sixteen intervals instead of eight, in ascending and descending direction. Second, the intervals used did not have a tonal center, so as to examine as best as possible the harmonic implications of each implicative interval. Third, as production and perception tasks have yielded different results (e.g., perception: Cuddy & Lunney, 1995; production: Thompson et al, 1997), this
study implemented the use of both production and perception tasks. The fourth and final difference is that participants were asked, in the production task, to produce what they perceived as the most likely and least likely (i.e., most expected and least expected) continuation note after the initial interval.
Although Narmour’s (1990) model of melodic expectancy has been criticized for being overly complex and redundant (Schellenberg, 1997), and there exists a simplified two factor model developed by Schellenberg (1997), the complete five factor model was used in the analysis of this data. This is because the simplified two factor model lacks some more complex components of the Implication Realization Model (Pearce & Wiggins, 2006) which were necessary for analysis of the production tasks. The present study attempts to provide answers for the above-mentioned goals. In order to fully understand the results of this study, however, a solid understanding of the Implication Realization Model is necessary. For this reason, an explanation of the model is discussed in detail in the following chapter. A complete analysis and interpretation of the results will follow, and finally, the study concludes with a general discussion of the results, their implications and some directions for potential future development of this research.
2 THE IMPLICATION REALIZATION MODEL
2.1 Principles of Implication
Building on the work of melodic expectancy by Meyer (1956, 1957), Narmour (1990, 1991, 1992) developed a theory of melodic expectancy called the Implication Realization Model. The theory is based on two perceptual systems – the bottom-up principles and the top-down principles of melodic implication. The theory further separates different implications for small intervals, defined as ≤ 5 semitones, and large intervals, defined ≥
7 semitones (Narmour, 1990). While the bottom-up principles that Narmour outlines are held to be innate and universal, the top-down principles are learned and dependent on degree of musical training. According to Narmour,
“…the analysis of melody rests on the perception of implications of continuation and reversal. Continuation is said to be governed hypothetically by the bottom-up Gestalt laws of similarity, proximity, and common direction (common fate); whereas reversal is hypothesized as a symmetrical construct. The hypotheses are context-free and scalable, producing several archetypal realizations (process, duplication, reversal, [and] registral return).” (Narmour, 1990)
The Implication Realization Model hypothesizes that intervallic similarity, registral direction, and proximity are all separately subject to cognitive prediction and thus dependent on laws of implication and expectancy (Narmour, 1990). The theory hypothesizes, for instance, that a pattern such as F4-G4-A4, shown in Figure 2.1 below, implies a continuation of registral direction (i.e., up to up), a continuation of intervallic similarity (M2 to M2), a continuation of duration (quarter to quarter), a realization on the level of the beat, and satisfies the principles of proximity. The model also states, however, that all small intervals like major 2nd tend to be implicatively governed by the bottom-up by the Gestalt laws of proximity, similarity, and common direction (sometimes called common fate) (Narmour, 1990). The major 2nd implies a similar interval and the ascending direction implies registral continuation. Narmour implements the Gestalt laws for three main reasons: (1) they have been shown to be resistant to learning and may perhaps be innate (Gleitman, 1981); (2) the Gestalt laws of similarity, proximity, and common direction are measurable, formalizable, and open to empirical testing (Pomerantz, 1981); and (3) in the cases that Narmour puts forth, they are bottom-up as nonclosural hypotheses (Narmour, 1990). The bottom-up principles of registral direction, intervallic difference, registral return, proximity, and closure are governed by larger patterns in which combinations of these principles occur. Chapter 2.2 and 2.3 will outline how
these principles combine to make up full and partial realizations for small intervals.
Figure 2.1: The combination of principles that make up a full realization (i.e.,
process) for small intervals
Source: Narmour, 1992; p. 3
2.2 Full Realization for Small Intervals: Processes
Patterns in which both intervallic similarity (M2 to M2) and registral direction (F4-G4-A4), and proximity are satisfied are called registral intervallic processes, or simply processes (symbolized by the letter P) (Narmour, 1990). Given an interval without any top-down processes (i.e., melodic or harmonic context, or knowledge of style), Narmour (1992) hypothesizes that all small intervals imply a continuation of registral direction in the mode of the implicative interval. Figure 2.2 below shows some examples of process (P). Realizations of this type will later be referred to as full realizations for small intervals.
Figure 2.2: Melodic patterns which qualify as processes
Source: Narmour, 1992; p. 4
Some three-note patterns only satisfy part of the intended principles of process, and thus are called partial realizations. A registrally zigzagging up-down pattern, (e.g., F#4-B4-G) realizes only the intervallic similarity (i.e., a small implied interval followed by a small realized interval), but not the registral direction (F#4 followed by B4 implies a realized interval in the same direction). These partially realized patterns are known as intervallic processes (IP). Melodic patterns such as F4-A4-F4, where the first and third notes are exactly the same, are known as intervallic duplications (ID). Patterns like the ones on the far right of the figure, where the registral direction is continued but intervallic similarity does not occur called registral processes (VP, V=vector or direction) (Narmour, 1990). All three types can be seen below in Figure 2.3.
Figure 2.3: Different types of partial realizations: intervallic process (IP),
intervallic duplication (ID), and registral process (VP)
Source: Narmour, 1989; p. 48
2.4 Full Realization for Large Intervals: Reversal
Larger intervals are not governed by the Gestalt laws of similarity, proximity, and common direction. Intervallic-registral reversal, or simply reversal (R) is a full realization of large intervals. It is a pattern that creates closure in and of itself (Narmour, 1990). The principles regarding reversal are fairly simple: when a listener hears a large interval (≥P5), he or she expects a change in registral direction and intervallic difference. That is, when a listener hears a large leap upwards, he or she expects the next interval to change direction and contain an interval smaller than the first. Because of the change of direction and interval size, this type also satisfies the principles of closure. Examples of reversal can be seen in the first two measures of Figure 2.4.
Figure 2.4: Illustrations of reversal (R), intervallic reversal (IR), and registral
reversal (VR)
Source: Narmour, 1989; p. 50
2.5 Partial Realizations of Reversal
Similar to the principles of process, reversal implications can be realized in full or in part for large intervals. For example, some principles of reversal can be realized, while registral implication (that direction should reverse) can be denied. These types of partially realized patterns are called intervallic reversals, or IR. An example of this kind of pattern can be seen above in Figure 2.4 and below in Figure 2.5. The opposite of this can also be true. That is, given a large initial leap, implied registral direction (that direction should reverse) can be realized while intervallic difference (that a small interval is expected to follow a large interval) is denied. This pattern is called registral reversal, symbolized as VR. Examples of this kind of partial realization can be found above in Figure 2.4 and below in Figure 2.5.
Figure 2.5: Illustrations of each kind of realization discussed: process (P),
intervallic process (IP), intervallic duplication (ID), registral process (VP), reversal (R), intervallic reversal (IR), and registral reversal (VR)
Source: Narmour, 1989; p. 52
2.6 Summary
The Implication Realization Model has been the most used model for melodic expectancy in empirical testing (e.g., Cuddy & Lunney, 1995; Schellenberg, 1996; Krumhansl, 1995; Thompson et al, 1997). It has been
tested in both production and perception tasks (Cuddy & Lunney, 1995; Thompson et al, 1997), making it a suitable model for the present study. Though recent studies have shown that differences may occur depending on degree of musical training (e.g., von Hippel, 2002; Vos & Pasveer, 2002), this model still has relevance because it adheres to general perceptual principles that are precisely and quantitatively specified and therefore lend themselves to empirical investigation (Krumhansl, 1995; Schellenberg, 1996). Narmour (1990) provides five principles that are theoretically innate and bottom-up across cultures and genres. These principles can further be grouped into full or partial realizations of the model. Although this model may not be able to predict melodic expectancy for every case, for the purposes of this study this model provides an important general guideline for the analysis of production and perception responses.
3 MATERIALS AND METHODS
3.1 Participants
Twenty-one musicians with varying degrees of training participated in the experiment. All participants had some training in music, ranging from 6-30 years of experience (M=16.9, SD=6.5). The nationalities of the subjects were as follows: 12 Dutch, 2 British, 2 American, 1 Taiwanese, 1 Greek, 1 Italian, 1 Latvian, and 1 Australian. The participants were 11 males and 10 females, with an age range from 20-40 years (M=25.6, SD=5.0). Eight participants had formal training in composition, ranging from 1-12 years (M=3.3, SD=3.7). Eleven participants claimed their main instrument to be piano, 5 voice, 1 violin, 1 cello, 1 trumpet, 1 clarinet, and 1 bass guitar. Seven participants were current students of the Conservatory of Amsterdam (CvA), 3 students in their 4th year in the Jazz department, and 4 Master’s students (3 in the Classical department and 1 in the Live Electronics department). Two were graduates with a Master of Music (MM) degree
from the Classical department from CvA, and 1 participant was a graduate with a Bachelor of Music (BM) degree from the Jazz department. 6 participants were graduates with an MA in Musicology from the University of Amsterdam (UvA), and 3 were current students in the MA Musicology program at UvA. Finally, 2 participants had some formal training and private lessons, but did not continue their musical training in higher education. There were 10 participants who attended universities or higher education music schools other than or in addition to CvA or UvA. These schools were: Northwestern University, National Taiwan Normal University, National Taiwan University of Art, Oxford University, University of Turin, University of London, Conservatory of Tilburg, Trinity Christian College, and the University of California at Berkeley.
3.2 Stimuli
3.2.1. Interval Completion Task
This task was to determine how participants would produce realized intervals given a set of implied intervals. The intervals chosen for these tasks were based on the relative implications set forth by interval size and direction outlined by Narmour (1990). According to the model, the implication gets stronger as intervals become larger. Thus, four small intervals (≤P4) and four large intervals (≥P5) were used. These were major second (M2), minor third (m3), major third (M3), perfect fourth (P4), perfect fifth (P5), minor sixth (m6), major sixth (M6), and major seventh (M7). The augmented 4th/dimished 5th, or tritone, was omitted as its implication is ambiguous. The unison and octave were also omitted because of ambiguous and/or complex implications (Narmour, 1990), and minor 2nd and minor 7th
were omitted in an effort to keep tasks relatively short. So as not to give a sense of overall tonality in the task, most intervals started on a different note. The intervals provided had a range a little over an octave (C4-D#5). To account for sequential intervallic implication, three separate tasks were made in which the order of intervals was randomized. The 8 intervals were presented in ascending and descending direction. Furthermore, each interval was repeated on the tasks in order for a realized note in a most likely and least likely condition to be produced. This made a total of 32 intervals per interval completion task (8 intervals x 2 directions (up/down) x 2 repetitions (likely/unlikely)). The eight intervals used in ascending and descending direction can be seen below in Table 3.1.
The given notes were chosen so as to have even tonal implication amongst implied intervals. Four intervals had implied tonalities which contained sharps (m3, P4, M6, M7), three intervals implied tonalities which contained flats (M3, P5, m6) and one interval implied a C Major tonality (M2).
3.2.2 Melody Completion Task
This task was to determine how participants would end a given melody. The task contained two melodies, outlined below in Table 3.2.
Attempts were made to make one melody with strong tonal implications (first melody) and one melody with more ambiguous tonal implications (second melody). The first melody was chosen because it has strong tonal implications of Bb Major, outlining the first four notes of the Bb Major scale. The second melody was chosen because a downward gesture in g minor has more ambiguous tonality and thus lends itself to more possible continuation tones. As most melodies in the classical canon begin with an upward gesture (Vos & Troost, 1989), the downward beginning could lead participants to give more varied answers. For example, if the figure is thought of as the end of a melody, G4 would be a reasonable answer, though this does not coincide with Narmour’s (1990) theory of registral continuation, and thus would not count as a full realization of the Implication Realization Model. For this reason, the answers for the second melody were hypothesized to be less clear than the answers to the first melody. Furthermore, the two melodies can be thought of as the start of a melody or figure (first melody) and the end of a melody (second melody). The current experiment tested whether this made a difference on production of the Implication Realization Model.
3.2.3 Perception Task
Participants heard the same 8 intervals presented in the interval completion tasks. In this task, however, following each implied interval was a continuation tone (Thompson et al, 1997), or realized interval. Participants heard three types of realized intervals in the task: (1) a full realization of the Implication Realization Model, (2) a partial realization of the model, and (3) a denial of the model. This resulted in a total of 48 ((8 x 2 (up/down) x 3 (full realization/partial realization/denial)) melodic fragments. For full realizations and denials of the Implication Realization Model, the perception
task either followed or denied Narmour’s (1990) universal, bottom-up implicative principles2. However, even by following these principles, there are still many possible notes to choose from. In order to choose the specific note that occurred in this task, the perceived tonal implication of the implied interval was taken into account. For full realizations, notes that were in accordance with implied tonalities, in addition to the principles outlined by Narmour (1990), were chosen. For example, the full realization of the implicative interval from F4-A4 was a continuation note of C5. The implied tonality of the Major 3rd starting on F was F Major, and the full realization outlined the F Major chord. For denials, the continuation note that was chosen had no common tones with the implied tonality. If we take the same example as above, the denial of the implicative interval from F4-A4 was a continuation tone of C#4. Notes for denials of the Implication Realization Model were the farthest away tonality in the circle of fifths from the implied tonality. The note C#5 was chosen as it is within the key of B Major, which is on the opposite side of the spectrum from F Major in the circle of fifths3. Thus, this choice denies the principles of the Implication Realization Model outlined by Narmour (1990) and contains a note that is far away from the original implied tonality4. For partial realizations, only some of Narmour’s principles were observed. Partial realizations for small intervals that were used were intervallic processes (IP) and registral processes (VP), while partial realizations for large intervals were intervallic reversal (IR) and registral reversal (VR). Again, however, specific note choices became an issue. Specific note choices were made by using a note that was in the key of the relative major or minor of the implied tonality, except in cases where these realized intervals sounded too much like denials or full realizations5. In this case, notes were chosen from keys that
2 These are registral direction, intervallic difference, registral return, and proximity (Narmour, 1990).
3 See Appendix 7 for the circle of fifths.
4 It should be noted that the implied tonality is what was perceived as implied by the author of this paper and not by an outside source.
were one step away from the implied tonality on the circle of fifths. If the implied tonality was in Major, the continuation tone would be a note contained in the relative minor of the key one step away from the implied tonality. While most partial realizations followed the protocol outlined above, there was one partial interval which differed from the full realization by only a half-step6. This was done to test if participants would be able to perceive very slight melodic differences.
3.3 Procedure
After having consented to participate in the experiment, the subjects were seated in a quiet room with minimal distraction. First, participants filled out an intake questionnaire with demographic information7. Through verbal and written instructions, participants were informed on how to proceed with the interval and melody completion tasks. Any questions were answered before taking the test. For the interval completion task, participants were informed to fill in a continuation tone following each implicative interval in a set of 32 trials. For the melody completion task, participants were informed to fill in a continuation tone following the two melodies given in a set of 4 trials. They were asked to produce a separate continuation tone for each given interval, according to what they would consider the most likely and least likely (i.e., most expected and least expected) answer. Participants were asked to answer based on their intuition, and not necessarily based on their music theory training, though undoubtedly this played a heavy role. Interval completion tasks were randomized per participant. Under supervision, participants were told to take as much time as needed with the interval and melody completion tasks. Participants varied in time taken to complete the tasks, though on average participants took around 30 minutes to complete the task. A keyboard was available so that participants could hear the given 6 Given notes were G#4-B4-D#5 and G#4-B4-E5. For visual, see figure 6 in Chapter 4.3.2 or Appendix 6
intervals if desired. All but 6 participants made use of the keyboard during the study. Three of these participants were UvA students, 2 were current CvA students, and 1 was a graduate of CvA.
Once finished with the interval and melody completion tasks, the perception task was conducted. In the same quiet environment, participants were seated in front of a laptop with headphones. Instructions of the listening portion were presented on the screen of the laptop. Participants read that they were to listen to 48 three-note melodic fragments. Similar to other studies of melodic expectancy (Cuddy & Lunney, 1995; Krumhansl, 1991/1995), participants were asked to rate how likely the continuation tone was to occur. These studies both used a 7-point Likert scale for expectancy rating. In the present study, however, participants were able to measure the continuation tone’s expectancy on a sliding scale from 0 to 1 (0 being not at all likely and 1 being very likely). Before starting, a test was done to measure the volume, and participants were told that they could adjust the volume as necessary. The presentation order of the perception task was randomized by PsychoPy, so all participants listened to a different sequence of intervals during testing. Any questions after testing were answered thoroughly.
3.4 Statistical Analysis
Repeated measures and mixed model ANOVAs were calculated for the production and perception tasks, and pairwise comparisons and simple effect analyses were examined. Possible factors entering the ANOVAs were condition, (likely, unlikely) interval, (M2, m3, P4, P5, m6, M6, M7) higher education completed, (0, 3, 4, 5, 6) direction, (up, down) melody ID, (melody 1 or melody 2) and expectation (full realization, partial realization, and denial). Perception data was collected and archived using PsychoPy, and all statistical analyses were run on SPSS version 23. The Greenhouse-Geisser
correction was applied for repeated measures ANOVAs and corrected p values are reported.
4 RESULTS OF PRODUCTION DATA
4.1 Interval Completion Task
The collected data yielded 32 responses per subject. Responses for the interval completion tasks were coded into numbers (C=1, C#=2, D=3, D#=4, E=5, etc.) and analyzed for degree of realization of the Implication Realization Model. Many participants had partial realizations (including intervallic processes (IP), intervallic duplications (ID), registral processes (VP), intervallic reversal (IR), and registral reversal (VR)), but only answers which are considered full realizations (i.e., for small intervals, satisfying the principles of registral direction, intervallic similarity, and proximity, and for large intervals, satisfying the principles of registral return, intervallic difference, and closure) were analyzed. As the results were significantly different in the ascending intervals and descending intervals, two separate analyses were done for each direction. The partial realizations in the descending direction accounted for 60.7% of answers, while in the ascending direction partial realizations accounted for only 54.5% of answers. For this reason, only full realizations (processes (P) and reversals (R)) which gave statistically meaning interactions were used to calculate statistics (full realizations for descending direction accounted for 49.4% of answers, while in the ascending direction they accounted for 47.0%). For analysis, mean full realizations were computed for each of the following factors: higher education completed (in years 0, 3, 4, 5, 6) and implied interval (M2, m3, M3, P4, P5, m6, M6, M7) in likely and unlikely conditions.
The first analysis was calculated to see the effects of years of higher education completed on means of full realizations (for small intervals process (P); large intervals reversal (R)) in the descending direction. The effects of years of higher education completed on full realizations of the Implication Realization Model were computed. From the data collected, type of education (that is, CvA, UvA, or Other) did not significantly influence the way participants responded with regard to full realizations in any of the analyzed factors. The amount of time some form of higher music education, whether conservatory or university, however, did have significant effect. A mixed model ANOVA was performed, with condition (likely, unlikely) as within subject factor and education completed (in years 0, 3, 4, 5, 6) as between subject factor on averaged full realization score. The analysis indicated the significant main effect of condition (F(1,16)=36.635, p<.001, Partial Eta Squared=.696). Effect of education completed was not significant (F(4,16)=1.176, p=.358, Partial Eta Squared=.227). There was, however, significant interaction between the two factors (F(4,16)=2.964, p=.052, Partial Eta Squared=.426). The resulting data is represented below in Figure 4.1.1.
Figure 4.1.1: Mean full realizations in likely and unlikely conditions for education completed, descending direction.
Simple effect analysis indicated that when education was shorter (i.e., 0 and 3), the full realization score for the two conditions (likely, unlikely) did not differ, but when participants indicated more years of higher education (4,5,6) the values for the two conditions differed significantly. This trend is visible in the above Figure 4.1.1.
The mean values for the unlikely condition in years 4, 5, and 6 are much lower than the rest of the mean values. The likely mean values, however, stay relatively similar through the number of years of higher education completed. These results indicate that the more higher education completed (≥4 years), the more likely it is to deny the principles of the Implication Realization Model in an unexpected case. That is, the more education you have does not necessarily coincide with a higher rate of full realizations of the Implication Realization Model, but rather a lower rate of full realizations of the Implication Realization Model in the unlikely condition. This suggests that as exposure to a certain type of music increases, the ability to ascertain what sounds unexpected also increases.
4.1.2 Higher Education Completed for Ascending Intervals
For the analysis of the effects of higher education completed on the averaged full realization scores in the ascending condition, another mixed model ANOVA was performed. Again, condition (likely, unlikely) was the within subject factor, and education completed (in years 0, 3, 4, 5, 6) was the between subject factor on averaged full realization score. The analysis indicated again a significant main effect of condition (F(1,16)=36.536, p<.001, Partial Eta Squared=.695). Effect of education completed was not significant (F(4,16)=.835, p=.523, Partial Eta Squared=.173). There was no significant interaction between the two factors (F(4,16)=.699, p=.603, Partial Eta Squared=.149). The data is represented below in Figure 4.1.2.
Figure 4.1.2: Mean full realizations in likely and unlikely conditions for education completed, ascending direction
Though Figure 4.1.2 shows a slightly downward slope for the unlikely condition along the x-axis, simple effect analysis found no significant difference between likely and unlikely conditions, unlike the results from the descending direction. This could perhaps be partly due to the fact that many melodies in the classical canon begin with an upward gesture, as was found in a study by Vos & Troost (1989). In this study, statistical analysis of 469 indexed beginnings of melodies by 13 composers (Bach, Bartok, Beethoven, Brahms, Chopin, Debussy, Dvorak, Mozart, Schubert,
Schumann, Shostakovich, Johann Strauss, and Stravinsky) and The Beatles was done. They examined the distribution of ascending versus descending intervals on the first five interval positions of all melodic patterns in the collected material. The only statistically significant feature found was the predominantly ascending nature of the intervals on the first interval position in the melodic patterns (Vos & Troost, 1989). As most of the participants of this study were inclined towards the classical style, it follows that they would have certain schematic expectations in regards to this style. This suggests that, as Western classical music listeners and practitioners, it becomes more difficult to deny Narmour’s (1990) bottom-up principles of melodic expectancy.
4.1.3 Implicative Intervals in Descending Direction
To test the effect that the implicative intervals in the descending direction had on the averaged full realization score, a two-way repeated measures ANOVA was performed. The implicative interval (M2, m3, M3, P4, P5, m6, M6, M7) was the independent variable and condition (likely, unlikely) was the within subject factor. The analysis indicated the significant main effect of interval (F(1,16)=5.018, p<.001, Partial Eta Squared=.715). Effect of condition was significant (F(1,16)=35.163, p<.001, Partial Eta Squared=.637). There was also significant interaction between the two factors (F(4,16)=7.656, p<.001, Partial Eta Squared=.793). In the pairwise comparisons between condition and interval, it was shown that every interval except M6 had significant differences between likely and unlikely conditions (p=.258). This would suggest that participants were successful in producing full realizations of Narmour’s (1990) bottom-up principles with every interval in the descending direction except M6. However, looking at a visual representation of the data shown below in Figure 4.1.3, it is clear that there was another type of interaction effect with M7. In addition, looking at the trend in the graph shown below, mean
full realizations in the unlikely condition became higher as the intervals got larger.
Figure 4.1.3: Mean full realizations in likely and unlikely conditions for implicative interval, descending direction
In an examination of which principles were realized, it was shown that the most frequent responses for small intervals in the likely condition contained the principles of registral direction, intervallic similarity, and proximity, making them fully realized according to the model (type P). The most frequent responses for large intervals in the likely condition satisfied the principles of registral return, intervallic difference, and closure (type R). That is, except for the interval of M7. M7 satisfied the principle of intervallic difference, but not registral return (type IR). In the unlikely condition, most responses for small intervals satisfied the principles of intervallic similarity and proximity, but not of registral direction (type IP). The most frequent responses for large intervals in the unlikely condition, on the other hand, were of type R. In the unlikely condition in the descending direction, therefore, large intervals mostly satisfied full realizations of the Implication Realization Model. All intervals were found to have significant difference in condition aside from M6. M7, on the other hand, had significant difference but in the opposite direction as the rest of the intervals. A closer examination of M6 and M7 will follow. Figure 4.1.4
shows the given notes in descending direction for M6 in the interval completion task.
Figure 4.1.4: Descending interval M6 as notated in the interval completion task
The M6 in descending direction was an ambiguous interval for participants. This suggests that the downward direction of the interval had an effect on the participants’ ability to reproduce the principles of the Implication Realization Model. This particular interval was chosen in the ascending direction partly for its connotations (at least amongst Western – specifically, U.S. listeners) as the NBC logo. Because of this, the implied tonality was thought of as B Major. This proved to be not very clear with participants, however, as only 29.0% of participants answered in this way. The most frequent response for M6 in both the unlikely and likely condition was of type R, a full realization. For the likely condition, responses of this type were 81.0%, and for the unlikely condition, responses of this type were 61.9%. It is clear from these results that for this interval, participants were unsure of how to differentiate between likely and unlikely.
The M7 interval also had similarly confusing results from participants. Similar to the M6, in the ascending direction, the M7 has a very clear tonal implication as the leading tone to E. In the descending direction, however, the implication is less clear. Figure 4.1.5 shows the M7 as written in the interval completion task.
Figure 4.1.5: Descending interval M7 as notated in the interval completion task
In the likely condition, the most frequent responses for the M7 was of type IR, the partial realization satisfying intervallic difference and closure, but
not registral return. In the unlikely condition, however, the most frequent responses for M7 was a full realization, type R. This could have been because the tonal implication for the M7 was unclear in the descending direction for participants. While the ascending M7 (E4-D#5) is heard as a clear leading tone to the E5, the descending interval does not have implications that are as clear. The tonal implication could be C# Major or E Major, or their parallel minors. For the interval of M7, participants were seemingly unable to produce an unlikely condition successfully.
4.1.4 Implicative Intervals in Ascending Direction
For the analysis of the effects of implicative intervals in the ascending direction on the averaged full realization score, another two-way repeated measure ANOVA was performed. Implicative interval (M2, m3, M3, P4, P5, m6, M6, M7) was the 1st within subject factor and condition (likely, unlikely) was the 2nd within subject factor. The analysis indicated the significant main effect of condition (F(1,16)=70.949, p<.001, Partial Eta Squared=.780). Effect of interval was not significant (F(1,16)=1.556, p=.228, Partial Eta Squared=.438). There was, however, significant interaction between the two factors (F(4,16)=3.849, p<.05, Partial Eta Squared=.658). In the pairwise comparisons between condition and interval in the ascending direction, all interactions were found to have significant differences between likely and unlikely conditions except for the intervals m3 (p=.056) and P5 (p=.329). The representation of this data can be seen below in Figure 4.1.6.
Figure 4.1.6: Mean full realizations in likely and unlikely conditions for implicative interval, ascending direction
In an examination of principles realized, the most frequent responses for small intervals in the likely condition again satisfied the principles of registral direction, intervallic similarity, and proximity, making them fully realized according to the model (type P). For the large intervals m6 and M6, the most frequent responses satisfied the principles of registral return, intervallic difference, and closure (type R). The intervals P5 and M7 in the likely condition, however, satisfied the principles of intervallic difference and closure, but not registral return (type IR). The responses for the unlikely condition were less focused. The most frequent response for the interval M2 in the unlikely condition satisfied the principles of proximity and registral direction, but not intervallic similarity (type VP). For the intervals M3 and P4, the most frequent responses satisfied the principles of proximity and intervallic similarity, but not of registral direction (type IP). The minor 3rd, however, had the most frequent responses of Process (P). For the large intervals in the unlikely condition, P5 and m6 had the most frequent answers of type IR. The M6 had equal frequency of answers between type IR and R, and M7 had the most frequent answers of type R. There was no significant difference between likely and unlikely condition between m3 and P5, and M7 had a similarly different effect as it did in the descending direction. That is, the unlikely condition satisfied more mean full
realizations than the likely condition. These intervals (m3, P5, and M7) will be evaluated in further detail below.
In Figure 4.1.7, the m3 in ascending direction can be seen as it appeared on the interval completion task.
Figure 4.1.7: Ascending interval m3 as notated in the interval completion task
The m3 in the ascending direction did not have significant difference between the likely and unlikely conditions. For a full realization of the Implication Realization model, the next note of Figure 4.1.7 would have to be a D# or something close in proximity (e.g., C, C#, D, D#, or E are all possible). Participants were less sure of how to make a differentiation between likely and unlikely in the m3 example. Many participants (42.9%) had full realizations in the unlikely condition, and there was no overall trend in answers. However, 38% of participants answered with a D#5, creating a g# minor chord in the likely condition. In the unlikely condition, however, there was no clear agreement on a single note or even note proximity.
In Figure 4.1.8, P5 is shown in ascending direction as it appear on the interval completion task.
Figure 4.1.8: Ascending interval P5 as notated in the interval completion task
In the likely condition, 52.0% of participants answered with an Eb5, which is only a partial realization of the model (type IR), satisfying the principles of intervallic difference and proximity, but not closure or registral return (Narmour, 1990). This accounts for the fact that there is no significant difference between conditions in the interval P5. Harmonically, however, the
Eb5 as a realized interval makes musical sense. This phrase, Eb4-Bb4-Eb5, could be interpreted as being the end of a melody, in which this sequence of notes is very common, especially in the classical canon. Regarding it in this way, it could be seen harmonically as a Perfect Authentic Cadence8. This could indeed be an explanation of the high percentage of Eb5 notes as continuation notes.
Again, as in the descending direction, the M7 in the unlikely condition had more full realizations than the likely condition. This time, the M7 interval involves a true leading tone to E5, as can be seen in Figure 4.1.9.
Figure 4.1.9: Ascending interval M7 as notated in the interval completion task
Many participants (81.0%) treated this as a leading tone in E Major or e minor, and answered with an E5. For this interval, the tonal implications were stronger than the principles of registral return and closure. Though this answer does not satisfy all of the bottom-up principles of the Implication Realization Model, which Narmour (1990) declares should be dominant in implicative intervals, the answer was very clear to participants, as it had a very strong tonal implication.
4.2 Melody Completion Task
Responses were coded into numbers for the melody completion task, as they were for the interval completion tasks. Again, only full realizations were used, as these answers gave statistically significant interactions (partial realizations for descending direction accounted for 29.4% of answers, while the ascending direction accounted for 42.9%). Full realizations (descending direction accounted for 70.6% of answers, and ascending direction
8 I.e., I64-V7-I (Major tonic chord in second inversion going to a dominant seventh chord and back to a root position tonic chord).
accounted for 51.0%) of the model were calculated for melody identification (melody 1 or 2) in likely and unlikely conditions.
4.2.1 Analysis of Melody Completion Task
To see the effects of melody on condition in the melody completion task, a two-way repeated measure ANOVA was performed. Melody (melody 1, melody 2) was the 1st within subject factor and condition (likely, unlikely) was the 2nd within subject factor. The analysis indicated the significant main effect of condition (F(1,4)=30.00, p<.001, Partial Eta Squared=.600). Effect of melody was not significant (F(1,4)=.087, p=.771, Partial Eta Squared=.004). There was no significant interaction between the two factors (F(1,4)=.1.447, p=.261, Partial Eta Squared=.063). From the data, as is shown clearly in Figure 4.2.1, participants were successful in creating statistically significant means of full realizations in the likely condition.
Figure 4.2.1: Mean full realizations in likely and unlikely conditions for Melodies 1 and 2
The aim of the first melody was to have a very clear tonal implication of Bb Major, while the aim of the second melody was to be more tonally ambiguous, or at the very least have a less clear implication for a continuation note. Though there is a slight difference in answers in the
