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This chapter summarizes the goals, idealizations, and rule system of the predecessor volume, A Generative Theory of Tonal Music, whose overall goal is to model and explain the musical intuitions of an experienced listener. The theory assumes the musical surface and idealizes to final-state listening. Features of well-formedness and preference rules are reviewed. The components of grouping structure, metrical structure, time-span segmentation, time-span reduction, and prolongational reduction are presented through an analysis of a Bach chorale. Particular attention is paid to the derivation of prolongational structure. On this foundation, ideas within the framework of the prolongational theory are advanced, including prolongational good form, the strict-branching constraint, polyphonic groupings, and abstractions and transformations of underlying events.

This chapter makes additional comments on the discussion in Chapter 2. The theory of metrification presented by Fabb and Halle (F&H) seems to be flawed in a number of respects. At the root of the problem is F&H's assumption that metrical structure is projected from the surface syllables of a linguistic text. It is argued that an alternative view not discussed by F&H is superior. This view — shared in its essentials by Kiparsky (1991), Lerdahl (2001), Hanson (2006), J. Halle (2008), and Deo (2007) among others — holds that metrification proceeds via the mapping of linguistic structures onto a pre-determined metrical template. It is shown that this view leads to more natural accounts of many of the relevant phenomena, especially with regard to mismatches between text and metrical structure, such as catalexis, anacrusis, anceps, and syncopation. This alternative has the advantage of allowing for poetic and musical metre and performance to be accounted for with a unified set of straightforward mechanisms. It is argued, contra the fourth section of F&H, that this is a desirable and feasible move.

Prosodic structure features prominently in work on metrical stress, in intonational phonology and prosodic phonology (where it provides the domain for segmental and supra-segmental processes), but specifics vary widely in the literature. Following Truckenbrodt, a simple version of the prosodic hierarchy, using phonological phrases, intermediate phrases, and intonational phrases above the word level is used, related to syntax by a small set of ranked, violable constraints; a prosodic constituent’s metrically strongest element, its head, may serve as an anchoring point for pitch accents, subject to a single ‘stress-to-accent’ constraint. Sometimes a more articulated structure is called for, involving a limited kind of recursion in prosodic categories, or perhaps even label-less recursion of a single unspecific category. The rules of syntax-to-prosody mapping actually predict when these more complex structures arise. Generalizations introduced earlier—integration, nuclear accent placement, optional accenting—find their proper place in this prosodically more elaborate setting.

A Linear Structure can be enhanced with an affine (straight line) substructure, which in turn can be invested with a metric. This chapter discusses how to define metrical structure, using the notion of an anthyphairetic ratio between lines. Metrics can be of different strengths, reflecting the classes of straight lines whose lengths can be compared. Methods for defining the length of curved lines are considered.

It is particularly significant to examine the intonational systems of typologically diverse languages in light of renewed interest in ‘intonational universals’. As yet, only a handful of indigenous Australian languages possess significant intonational descriptions. This chapter examines the intonational phonology of six closely-related varieties of a Northern Australian language, Bininj Gun-wok, also known as Mayali. It then outlines transcription conventions that are designed to transcribe significant prosodic events in this language and its various dialects.

In terms of metrical structure, Tiberian Hebrew has long been problematic due to its apparent lack of metrical coherence. The simplified bracketed grid theory offers a more elegant alternative to previous approaches for analyzing the metrical structure of Tiberian Hebrew. This chapter examines stress assignment in Tiberian Hebrew and argues that the evidence previously considered to be supporting inconsistent metrical constituents does not actually require the construction of entire constituents, and that the same evidence can be taken into account by the construction of more minimal single brackets. It shows how the assignment of aspects of metrical structure interacts with phonological processes to create surface opacity. The chapter also discusses the Main Stress Rule, pretonic lengthening, pausal stress, and stress retraction.

At many levels of linguistic structure, units at one level are organized into a group, forming a unit at a higher level. This is the basis of hierarchical structure that organizes units from the phonetic to the discourse level. In many areas of Linguistics, it has emerged that the rules of combination that organize units hierarchically are local in nature, even though the structures that emerge have a wider more global span. This paper builds on work by John Goldsmith and Gary Larson on computational networks that organize syllables into feet based on local interaction between the neighboring syllables, and that build global metrical structures that are typologically well-attested using dynamical systems analysis. The goal of the paper is to establish exactly what kind of dynamical system the Goldsmith/Larson is, and to introduce, in a tutorial style, the necessary background in dynamical systems analysis, difference equations, and green’s function analysis to make clearer the import of the Goldsmith/Larson networks for metrical structure analysis, as well as for the general motif of hierarchical patterning in language.

This book explores foundational questions in phonology, such as the sorts of phenomena that comprise the explananda of the field, how phonological objects should be represented, or the optimal architecture for phonological theory. It examines computation and representation, the distinction between phonetics and phonology, modularity within phonology, and modularity producing emergent phenomena. It looks at core aspects of phonology and interactions within and among modules, the status of phonological features, and contemporary theories of syllabification in phonology. It also discusses metrical structure, the overall architecture of the phonological component, and various sorts of interaction among components of phonology.