473 25.Musical Musical Syntax I: Theoretical Synt Perspectives a Martin Rohrmeier, Marcus Pearce 25.1 Outline............................................. 473 The understanding of musical syntax is a topic of fundamental importance for systematic musicol- 25.2 Theories of Musical Syntax................. 474 ogy and lies at the core intersection of music theory 25.2.1The Concept of Musical Syntax ............ 474 and analysis, music psychology, and computa- 25.2.2Foundations of Musical Syntax............ 475 tional modeling. This chapter discusses the notion 25.3 Models of Musical Syntax................... 477 of musical syntax and its potential foundations 25.3.1Building Blocks ................................. 477 based on notions such as sequence grammat- 25.3.2Structure Building ............................. 478 icality, expressive unboundedness, generative capacity, sequence compression and stability. Sub- 25.4 Syntactic Models of Diferent Complexity ..................... 478 sequently, it discusses problems concerning the 25.4.1Finite-Context Models........................ 478 choice of musical building blocks to be modeled 25.4.2Finite-State Models ........................... 479 as well as the underlying principles of sequential 25.4.3Context-Free or Equivalent Models...... 479 structure building. The remainder of the chapter 25.4.4Beyond Context-Free Complexity ........ 481 reviews the main theoretical proposals that can be characterized under diferent mechanisms of 25.5 Discussion ........................................ 482 structure building, in particular approaches using 25.A Appendix: The Chomsky Hierarchy ..... 483 fnite-context or fnite-state models as well as 25.A.1Type 3(Regular)................................. 483 tree-based models of context-free complexity (in- 25.A.2Type 2(Context Free) .......................... 483 Part C | cluding the Generative Theory of Tonal Music) and 25.A.3Type 1(Context Sensitive).................... 483 beyond. The chapter concludes with a discussion 25.A.4Type 0(Unrestricted) .......................... 483 25 . of the main issues and questions driving current 1 References................................................... 483 research and a preparation for the subsequent empirical chapter Musical Syntax II. The idea that there is a grammar of music is prob- ably as old as the idea of a grammar itself. Mark Steedman [25.1,p.1] 25.1Outline What distinguishes music from other sounds? One an- tional, and psychological/neuroscientific approaches, swer is to be found in the manner in which the elements questions about musical structure and the perception are organized and related within a structural frame- of it facilitate a close link across traditional divisions work and, most importantly, the apprehension of this between disciplines [25.2]. Note that we use the term structure by a listener, so that the sound is experienced computational to describe a theory that is expressed in as music by that listener. Therefore, discovering the computational terms, whether or not it is actually im- principles of musical structure building is one of the plemented as a computer program. central questions for theoretical and empirical music Exploring the principles of musical structure build- research. Despite the strong historical (and method- ing naturally requires us to distinguish between the goal ological) divide between music-theoretical, computa- of uncovering rules governing the structure of music (an ©Springer-VerlagGmbHGermany2018 R. Bader (Ed.), Springer Handbook of Systematic Musicology, https://doi.org/10.1007/978-3-662-55004-5_25 474 Part C Music Psychology – Physiology external goal) and the cognitive principles of the per- with computational modeling since the search for an ception and production of these structures (an internal optimal structural description (that relates to structures psychological goal). Yet both aspects form two sides as heard)stronglyimpliesmodeling the internal struc- of the same coin: the capacities and limitations of hu- ture of the music (whether it is a single composition, man perception and cognitive processes influence the a part thereof, or a corpus). Since music is an inherently possible structures that composers can use (for a sim- psychological phenomenon, we often use psychological ilar argument about language, the reader is directed understanding to guide the development of structural to [25.3]) and, together with other constraints (e.g., models of music, just as we use structural models of those imposed by cultural factors or the physical prop- music to guide the development and testing of psycho- erties of instruments, constraints of the hands or the logical theories of the perception of musical structure. body, constraints of the performance and so on [25.4]) The disciplines involved in research on musical syn- give rise to the musical structures that we find in mu- tax range from musicology and music theory, through sic. In turn, musical structure is acquired implicitly by computational modeling, to psychology and neurobiol- listeners from mere exposure and musical interaction ogy. Although the disciplinary perspectives are distinct and represented internally [25.5, 6]and,ultimately,re- (e.g., it is possible to develop a structural theory that is produced in compositional practice (since composers optimal according to some criterion, such as simplicity, are listeners before they become composers). However, but not according to the criterion of matching human there can be no learning without a hypothesis space perception and cognition), in this contribution, we fo- and therefore theoretical models of musical structure, cus on a converging picture that emerges when musical especially those grounded in computational modeling, syntax is examined by triangulating between theory, provide a useful approach to understanding the hypoth- computational modeling, and cognitive research. Here esis space that human learners are faced with when they we focus on theoretical approaches to musical syntax acquire the syntactic structure of a musical style. while empirical research using computational models, Finding a formal characterization of musical struc- psychological experimentation, and neuroimaging are ture brings traditional music theory in close connection covered in the companion chapter, Musical Syntax II. Part C | 25 25.2Theories of Musical Syntax . 2 25.2.1The Concept of Musical Syntax the concert is an English sentence, whereas Icon- cert went the to is not. Similarly, I-VII6-I6-II6-V7-I Berwick et al. [25.7,p.89]giveabriefaccountofsyn- [. ] is a coherent progression of chords, whereas tax as: I-I6-VII6-II6-I-V7 [. ] is not, as you can hear if you play through the two examples. In the study of the rules for arranging items (sounds, words, word language, the word syntax is used to refer to the ar- parts, phrases) into their possible permissible com- rangement of words to form sentences; word order binations in a language. is a very important component of syntax. In study- In human language the set of items (alphabet of sym- ing music, we can use the term harmonic syntax to bols) may be words and morphosyntactic units, in refer to the arrangement of chords to form progres- birdsong they may be pitches, slides and other sounds. sions; the order of chords within these progressions In music the symbols may be melodic notes, chords, is at least as important as the order of words in lan- voice-leading patterns or relationships between voices, guage. (Other components of harmonic syntax are timbral qualities and so on. Many music-theoretical the position of chords within phrases, the prepara- approaches constitute informal, verbal accounts of syn- tion and resolution of dissonances, and the relation tactic models of music. Although the use of strict and of chord progressions to melody and bass lines.) well-defined formalisms is not (yet) common in music theory, there are some accounts that employ the notion Asyntactictheorymightbeappliedtoanyaspectof of syntax in music theory. For instance, Aldwell and musical structure – melody, harmony, rhythm, metre, Schachter write the following in order to characterize grouping structure, form, or even aspects such as timbre harmonic syntax [25.8,p.139]: and dynamics. In practice, syntactic approaches have typically been applied to what happens in a musical One way that music resembles language is that sequence – e.g., predicting (combinations of) pitches the order of things is crucial in both. Iwentto and chords – rather than when it happens. Conversely, Musical Syntax I: Theoretical Perspectives 25.2 Theories of Musical Syntax 475 theories of rhythm and metre often do not take an ex- grammaticality judgements), the fact that the space of plicitly syntactic approach. By analogy, metrical and possible musical compositions is theoretically infinite rhythmic features of language are often studied from (or unbounded), the idea that we want to be able to de- the perspective of phonology rather than syntax. A well- scribe structural relationships within musical sequences formed harmonic sequence, for instance, may be as- (i. e., focus on strong generative capacity compared to signed to metrical structure in a regular or irregular weak generative capacity). Syntax is also relevant to way. It is important to note that despite the predom- tasks such as compression, identifying the stability of inance of Western music in theoretical and cognitive events at different levels within music, and measuring research [25.9], the