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26. Musical Syntax II: Empirical Perspectives

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26. Musical Syntax II: Empirical Perspectives 487 26.Musical Musical Syntax II: Empirical Synt Perspectives a Marcus Pearce, Martin Rohrmeier 26.1 Computational Research.................... 487 Efforts to develop a formal characterization of mu- 26.1.1 Foundations ..................................... 487 sical structure are often framed in syntactic terms, 26.1.2 Early Approaches: Pattern Processing... 488 sometimes but not always with direct inspiration 26.1.3 Markov Modeling............................... 489 from research on language. In Chap. 25,wepresent 26.1.4 Beyond Simple Markov Models: Hidden syntactic approaches to characterizing musical Markov Models structure and survey a range of theoretical issues and Dynamic Bayesian Networks ........ 490 involved in developing formal syntactic theories 26.1.5 Hierarchical Models ........................... 491 of sequential structure in music. Such theories 26.1.6 Neural Networks................................ 493 are often computational in nature, lending them- 26.2 Psychological Research...................... 494 selves to implementation and our first goal here 26.2.1 Perception of Local Dependencies ....... 494 is to review empirical research on computational 26.2.2 Perception of Nonlocal Dependencies.. 495 modeling of musical structure from a syntactic point of view. We ask about the motivations for 26.3 Neuroscientific Research.................... 496 implementing a model and assess the range of 26.3.1 Introduction ..................................... 496 approaches that have been taken to date. It is im- 26.3.2 Neural Basis of Syntactic Processing portant to note that while a computational model in Music............................................ 496 may be capable of deriving an optimal structural 26.3.3 Syntax in Music and Language ............ 497 description of a piece of music, human cognitive 26.3.4 Grouping Structure ............................ 497 processing may not achieve this optimal perfor- 26.4 Implications and Issues..................... 498 mance, or may even process syntax in a different 26.4.1 Convergence Between Approaches ...... 498 way. Therefore we emphasize the difference be- 26.4.2 Syntax, Semantics and Emotion .......... 498 tween developing an optimal model of syntactic References................................................... 499 processing and developing a model that simu- lates human syntactic processing. Furthermore, we argue that, while optimal models (e.g., op- musical syntax from the perspective of compu- Part C | 26.1 timal compression or prediction) can be useful tational modeling, experimental psychology and as a benchmark or yardstick for assessing human cognitive neuroscience. There exists a large num- performance, if we wish to understand human ber of computational models of musical syntax, but cognition then simulating human performance we limit ourselves to those that are explicitly cog- (including aspects that are nonoptimal or even nitively motivated, assessing them in the context erroneous) should be the priority. Following this of theoretical, psychological and neuroscientific principle, we survey research on processing of research. 26.1 Computational Research 26.1.1 Foundations of representing. Therefore, there is a direct link between the theoretical characterization of musical syntax (dis- Different approaches to building computer models of cussedinChap.25) and the implementation and testing musical structure can be characterized, and distin- of these theories as computational models of cogni- guished, in terms of how expressive they are in terms tion, discussed here. Implementing a theory of musical of the degree of structural complexity they are capable syntax and processing has several potential advantages, © Springer-Verlag GmbH Germany 2018 R. Bader (Ed.), Springer Handbook of Systematic Musicology, https://doi.org/10.1007/978-3-662-55004-5_26 488 Part C Music Psychology – Physiology following well-known examples in cognitive science: ers form. Nonetheless, it is often useful to identify theoretical bounds on structural complexity using an 1. Implementing a theory as a computer program optimal model. Furthermore, theoretical models of mu- (which must run, generating output from the data sical structure can help us understand the hypothesis and parameters supplied as input) ensures that it space that human learners are faced with when they takes as little as possible for granted and any as- acquire the syntactic structure of a musical style. In sumptions are explicitly stated [26.1–3]. artificial intelligence research, we distinguish between 2. Experiments can be run to evaluate the implemented the representation defining the search space and algo- theory by comparison of its behavior with the output rithms for traversing the space. Similarly in machine expected from theoretical accounts or directly with learning, we distinguish between the hypothesis space human behavior given the same inputs [26.3, 4]. and learning mechanisms for traversing the space. In the case of musical syntax, the hypotheses correspond It is important to distinguish between models whose to potential stylistic grammars generating structural de- knowledge is provided to them by a human expert (in scriptions of music and we can think of the learning as the style of good, old-fashioned artificial intelligence, traversing the space of possible grammars, specifying GOFAI) and those that acquire knowledge about musi- the parameters distinguishing those grammars along the cal structure by learning (either supervised or unsuper- way. vised) from experience of music, given some predefined The following sections illustrate these points, using structural representation, the parameters of which are different kinds of computational models that have been learned (in the tradition of machine learning), be it proposed for understanding musical syntax. a neural network, a Markov model or grammatical in- ference. The appropriate approach depends on the goal 26.1.2 Early Approaches: Pattern Processing of the modeling. However, in many cases the two ap- proaches are complementary in that successfully learn- We begin with a review of two early approaches that ing complex representations (e.g., context-free rules) is are of historical importance because they laid the extremely challenging but the alternative approach can foundations for symbolic models that subsequently be- result in models that do not generalize far beyond the came influential. One early approach was based on musical domain for which they were developed (e.g., the assumption that listeners use pattern induction pro- Steedman’s [26.5, 6] grammars for blues harmony). In cesses to develop predictions for successive events in the past, tasks that required context-free representa- melodies [26.10, 11]. These models attempt to define tions have usually been hand coded while tasks that formal languages for describing the patterns perceived require simpler representational relationships have been by humans in temporal sequences (such as music) and able to benefit from the flexibility of machine learning. use them to explain how these patterns are applied for However, methods have now been developed in compu- prediction. Simon and Sumner [26.11], for example, be- Part C | 26.1 tational linguistics to learn certain kinds of context-free gin with ordered alphabets for representing the range representation [26.7]. Note that if we are interested in of possible values for a particular musical dimension cognitive representations of music, there is the addi- (e.g., note names, note durations). Simon and Sum- tional issue of the extent to which the representations in ner restrict their attention to the dimensions of melody, question are actually learned or inherited (i. e., innately harmony, rhythm and form and use alphabets for dia- specified) by human beings ([26.8] as, e.g., discussed in tonic notes, triads, duration, stress and formal structure. the poverty of the stimulus debate [26.9]). The operations they consider are same (when the subse- As mentioned above, we must also emphasize the quent symbol is identical to the previous one) and NEXT distinction between finding an optimal structural de- (the subsequent symbol is obtained by taking the next scription of a piece of music and modeling the cognitive symbol in the specified alphabet a specified number of representation of that piece in the mind of a lis- times). Sequences of symbols may then be described tener. The former bounds the latter but listeners are more compactly as a sequence of these operations. likely to be subject to constraints of perception and Deutsch and Feroe [26.10] extended the model of cognition (e.g., limitations of working memory load), Simon and Sumner in several ways, in particular defin- which would prevent them reaching an optimal struc- ing structures as sequences of elementary operators and tural description. Note also that it is problematic to sequence operators such as prime, retrograde, inver- assume the existence of an average listener without sion and alternation. They apply their pattern language understanding all the factors (e.g., musical training, to various alphabets, corresponding to collections of environmental context, degree of attention etc.) that pitches, such as the major and (natural, harmonic and could influence the structural descriptions that listen- melodic) minor scales, major, minor and diminished tri- Musical Syntax II: Empirical Perspectives 26.1 Computational Research 489 ads, and seventh chords. They argue that the pattern how unexpected the next
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