William E. Caplin

Simulating melodic and harmonic expectations for tonal cadences using probabilistic models

Abstract This study examines how the mind’s predictive mechanisms contribute to the perception of cadential closure during music listening. Using the Information Dynamics of Music model (or IDyOM) to simulate the formation of schematic expectations—a finite-context (or n-gram) model that predicts the next event in a musical stimulus by acquiring knowledge through unsupervised statistical learning of sequential structure—we predict the terminal melodic and harmonic events from 245 exemplars of the five most common cadence categories from the classical style. Our findings demonstrate that (1) terminal events from cadential contexts are more predictable than those from non-cadential contexts; (2) models of cadential strength advanced in contemporary cadence typologies reflect the formation of schematic expectations; and (3) a significant decrease in predictability follows the terminal note and chord events of the cadential formula.

Theories of musical rhythm in the eighteenth and nineteenth centuries

Everyone agrees: it is difficult to talk about rhythm in music, or, for that matter, the temporal experience in general. Compared with spatial relations, which appear to us as fixed and graspable, temporal ones seem fleeting and intangible. As a result, the language of time and rhythm is complex, contentious, and highly metaphorical. Considering that theorists today continue to have difficulty dealing with the metrical and durational organization of music from the eighteenth and nineteenth centuries – our most familiar music – it should come as no surprise that theoretical writings from those centuries often present themselves as perplexing and in need of explication. Though their manner of formulation may at times seem odd or convoluted, these theorists nonetheless ask many of the same questions about musical rhythm that underlie current concerns: What is a metrical accent? How do the profusion of time signatures relate to each other? Do the groupings of measures create a sense of larger-scale rhythm? Can various durational patterns be organized according to some scheme or another? How does our understanding of musical rhythm affect performance, especially tempo, phrasing, and articulation? Like many other domains of music theory, rhythmic theories are largely formulated in relation to a distinct compositional practice. Thus when compositional styles change, theorists respond by modifying their conceptions and formulating new ones in order better to reflect such transformations in practice. The high Baroque style, with its motoric pulses, regularized accentuations, and dance-derived rhythms, induced early eighteenth-century theorists to focus in detail on the classification of various metrical and durational patterns and to begin accounting for that most elusive concept – metrical accent.

Expecting the end: Continuous expectancy ratings for tonal cadences

Cognitive accounts for the formation of expectations during music listening have largely centered around mental representations of scales using both melodic and harmonic stimuli. This study extends these findings to the most recurrent cadence patterns associated with tonal music using a real-time, continuous-rating paradigm. Musicians and nonmusicians heard cadential excerpts selected from Mozart’s keyboard sonatas (perfect authentic cadence [PAC], imperfect authentic cadence [IAC], half cadence [HC], deceptive cadence [DC], and evaded cadence [EV]), and continuously rated the strength of their expectations that the end of each excerpt is imminent. As predicted, expectations for closure increased over the course of each excerpt and then peaked at or near the target melodic tone and chord. Cadence categories for which tonic harmony was the expected goal (PAC, IAC, DC, EV) received the highest and earliest expectancy ratings, whereas cadence categories ending with dominant harmony (HC) received the lowest and latest ratings, suggesting that dominant harmony elicits weaker expectations in anticipation of its occurrence in cadential contexts. A regression analysis also revealed that longer excerpts featuring dense textures and a cadential six-four harmony received the highest ratings overall.

Recent Research in the History of Theory: The Eighteenth and Nineteenth Centuries

I am very pleased to have been asked to speak on recent research in the history of theory of the eighteenth and nineteenth centuries. All of us working in this field are surely proud of the record of accomplishment compiled since the founding of our Society. I would like to review some of the major changes and developments that have characterized our endeavors over the past decade. I also want to consider some topics that have been relatively little explored of late and are thus deserving of our further attention.