Running Head: MODELING OF MUSICAL ENCULTURATION 1 Computational modeling of musical enculturation: An investigation of multicultural music learning using self-organizing maps Jesse Pazdera Haverford College Advisors: Marilyn Boltz & Jane Chandlee Author Note: The author would like to thank advisors Marilyn Boltz and Jane Chandlee for providing year-long guidance and feedback on this research project. The author also thanks Shu-wen Wang and Steven Lindell for providing additional feedback during the writing of this document. Finally, the author would like to recognize Richard Freedman and Adam Crandell for assistance in locating the musical datasets utilized in the present study. MODELING OF MUSICAL ENCULTURATION 2 Table of Contents I Introduction & Literature Review 8 1. An Introduction to Musical Syntax 9 2. Universals of Musical Syntax 10 i. Consonance, dissonance, and octave equivalence 10 ii. Pitch classes and keys 10 iii. Syntactic relations between keys 11 iv. Uneven scale intervals 11 v. Variable stability of pitches 12 3. Cross-Cultural Differences in Melody 13 4. Musical Systems of the Present Study 14 i. Western music 14 ii. Hindustani music 16 iii. Chinese music 17 5. Implicit Knowledge of Melodic Syntax 18 i. Chord and pitch priming 19 ii. Perceptions of stability 21 6. The Developmental Trajectory of Musical Enculturation 23 7. Enculturation for a Novel Musical System 27 i. Learning an artificial musical grammar 27 ii. Exposure to an unfamiliar culture 28 8. Introduction to the Computational Modeling of Human Learning 30 9. Models of Implicit Musical Knowledge and Learning 32 MODELING OF MUSICAL ENCULTURATION 3 i. N-gram models 32 ii. Connectionist models 34 iii. Self-organizing maps 37 10. Introduction to the Present Study 43 i. Selections of musical cultures 43 ii. Goals and hypotheses 43 II Experiment 1 47 III Method 47 1. Design 47 2. Materials 48 i. The model 48 ii. Musical training sets and stimuli 48 iii. Software and data collection 52 3. Procedure 53 4. Accuracy Measures 55 i. Pitch accuracy 55 ii. Activation level 55 IV Results 56 1. Topographical Organization 56 i. Western condition 57 ii. Chinese condition 57 iii. Hindustani condition 57 2. Pitch Accuracy 59 MODELING OF MUSICAL ENCULTURATION 4 i. Accuracy for native systems 60 ii. Cross-cultural accuracy 61 3. Activation Level 61 i. Accuracy for native systems 62 ii. Cross-cultural accuracy 63 4. The Nature of Learned Keys 64 V Discussion 67 1. Map Organization 67 2. Native System Accuracy 69 3. Cross-Cultural Performance Effects 71 VI Experiment 2 73 VII Method 74 1. Design 74 2. Materials 74 3. Procedure 74 4. Accuracy Measures 75 VIII Results 75 1. Topographical Organization 75 i. Western/Chinese 75 ii. Western/Hindustani 76 iii. Chinese/Hindustani 78 iv. Western/Chinese/Hindustani 79 2. Pitch Accuracy 79 MODELING OF MUSICAL ENCULTURATION 5 i. Initial scores 79 ii. Multicultural learning 81 3. Activation Level 81 i. Initial scores 83 ii. Multicultural learning 83 IX Discussion 84 1. Map Organization 84 2. Success of Multicultural Learning 85 X Experiment 3 87 XI Method 87 1. Design 87 2. Materials 88 3. Procedure 88 4. Accuracy Measures 89 XII Results 89 1. Topographical Organization 89 i. Western & Chinese 89 ii. Western & Hindustani 93 iii. Chinese & Hindustani 93 2. Pitch Accuracy 93 i. Changes with novel exposure 95 ii. Within-system accuracies 95 3. Activation Level 96 MODELING OF MUSICAL ENCULTURATION 6 i. Changes with novel exposure 96 ii. Within-system accuracies 98 XIII Discussion 99 1. Model Organization 99 2. Success in Learning a New System 100 XIV General Discussion 102 XV Conclusion 109 XVI References 111 MODELING OF MUSICAL ENCULTURATION 7 Abstract Past research has shown that children are able to implicitly learn the underlying melodic structure of their native culture's musical system, even without formal musical training. Although implicit musical learning has been well studied, little is known about non-Western and multicultural musical enculturation. The present study addressed these issues though three experiments using self-organizing maps (SOMs), a type of neural model, to simulate implicit musical learning. Experiment 1 used SOMs to simulate Western, Chinese, and Hindustani musical enculturation, each learned independently from one another. Experiment 2 simulated a child growing up in a multicultural context, to investigate whether they might learn the structure of multiple native systems. Experiment 3 simulated an adult encountering an unfamiliar culture, to examine whether adults – not only children – may implicitly acquire the syntax of new musical systems. Results generally supported the plausibility of successful multicultural learning, with the caveat that certain systems disrupted the learning of others. Our findings led to further discussion of cross-cultural similarities between musical systems and the implications of these connections. MODELING OF MUSICAL ENCULTURATION 8 Computational modeling of musical enculturation: An investigation of multicultural music learning using self-organizing maps The ability to detect and learn patterns in environmental stimuli is critical for an organism's survival. Recognizing the early signs of danger can allow one to prepare an appropriate survival response, with enough time to avoid harm (Pearce & Wiggins, 2012). Similarly, identifying patterns as to where food and water can be found allows one to better locate such life-sustaining resources. For some species, especially humans, pattern-detection plays a crucial role in social interaction. Recognizing the emotions indicated by a particular combination of body language, facial expression, and vocal intonation enables a person to better interpret the feelings and intentions of others, and to generate expectancies about how they will act. It is important, therefore, that the human brain be able to naturally learn statistical regularities among stimuli and events, and to generate expectancies based on these learned associations. Music plays a central role in human culture, and sees near-universal use in contexts such as festivals and religious rituals (Brown & Jordania, 2011). It is notable in relation to statistical learning, in that music tends to follow a set of established syntactic rules, unique to each musical culture, which govern the melodic and rhythmic patterns that can manifest themselves in a given musical context. These syntactic rules generate statistical regularities across musical pieces, which the human brain can naturally learn and recognize. Based on these learned rules, the brain can generate expectancies about how a given song will unfold (Pearce, Ruiz, Kapasi, Wiggins, & Bhattacharya, 2010), and identify when a performer violates these rules – either intentionally or otherwise. MODELING OF MUSICAL ENCULTURATION 9 In the current study, we seek to explore the particulars of this musical learning process computationally using self-organizing maps, a type of artificial neural network. We will use the models to simulate the processes by which humans implicitly learn the musical structures of Western, Hindustani (North Indian), and Chinese culture, with the goal of addressing gaps in the literature as to how non-Western musical syntax is learned. Additionally, we will investigate whether it is possible for humans to learn the structures of multiple musical cultures, or to acquire the syntax of a novel system in adulthood. An Introduction to Musical Syntax Before proceeding to discuss the particulars of humans' musical learning, it will be useful to review the basics of musical structure. Although musical structure consists of several different dimensions, such as rhythm, tempo, and melody, the present study will focus primarily on melody and melodic syntax. While rhythm has been demonstrated to affect a person's processing of the melodic patterns in a song, and is known to affect listeners' expectancies of how a melody will proceed (Bharucha & Krumhansl, 1983; Boltz, 1993; Schmuckler & Boltz, 1994), little research has been conducted into the processes by which humans may learn the rhythmic tendencies of their native musical culture. In contrast, the developmental trajectory of melodic syntax learning is well understood (see Trainor, 2005), which will provide a strong theoretical basis against which our neural model's learning can be compared. Furthermore, several computational models developed in previous studies have successfully learned Western melodic syntax (e.g. Pearce et al., 2010; Tillmann, Bharucha, & Bigand, 2000), offering a framework from which to build. Therefore, the present study will specifically target melody, in isolation from rhythm. MODELING OF MUSICAL ENCULTURATION 10 Which musical features, then, does melodic syntax govern? Generally speaking, melodic syntax can be defined as a culture's set of rules as to which musical notes can be used together in context or sequence, as well as the functional properties associated with each tone. Although musical cultures differ greatly from one another in their specific melodic rules and organization, there are numerous universal features present across all musical systems (Brown & Jordania, 2011). Universals of Musical Syntax Consonance, dissonance, and octave equivalence. First, all cultures distinguish consonant and dissonant intervals between tones, and prefer consonance over dissonance (Hannon & Trainor, 2007; Trainor & Corrigall, 2010; Trainor, Tsang, & Cheung, 2002). Universally, two tones whose frequencies form small integer ratios are considered