Individual Project – Proposal


QUESTION: What can expressive timing tell us about how performers delineate formal boundaries in passages that exhibit form-functional fusion?

SPECIFIC QUESTION: How do different performers interpret, through expressive timing, the structure of the main theme-transition complex of Mozart’s Piano Sonata in C, K. 545, Allegro?


1) Form-functional fusion: the merging of two formal functions within a single unit
MT-TR complex: a formal unit in which the cadence typically found between MT and TR is eliminated, thus giving rise to the the fusion of main theme and transition functions (the point is that the formal boundaries are blurred, at least from a theoretical perspective)

IMPORTANCE OF QUESTION: The current theoretical perspective on form-functional fusion (Caplin 1997) provides no insight into the point at which MT function becomes TR function in a MT-TR complex. A study of performances of Mozart’s K. 545, which contains such a complex, promises to give us some idea of how performers interpret this transitional moment.


The project I’m proposing is analytical. In other words, I’m interested in applying the results of current research to a specific case study (K. 545, Allegro).


I will first determine how performers group the first 12 measures of K. 545 by extracting timing profiles (IOIs) from a large body of commercial recordings.
I will then compare the grouping structure(s) that emerge from this data to musical characteristics in the score.


The format of the final project will be in two main parts: 1) the experiment and its attendant formalities; 2) discussion, which will branch out into the music-theoretical literature (particularly Caplin’s theory of formal functions)

The final product will analyze the results to see if a normative timing profile emerges, from which we can then extract a more nuanced idea of how MT-TR complexes work from a structural standpoint.


PALMER, C. (1989). “Mapping musical thought to musical performance.” Journal of Experimental Psychology: Human Perception and Performance”, 15 (2), 331-346. (PSYCNET)

ABSTRACT: Expressive timing methods are described that map pianists’ musical thoughts to sounded performance. In Experiment 1, 6 pianists performed the same musical excerpt on a computer-monitored keyboard. Each performance contained 3 expressive timing patterns: chord asynchronies, rubato patterns, and overlaps (staccato and legato). Each pattern was strongest in experienced pianists’ performances and decreased when pianists attempted to play unmusically. In Experiment 2 pianists performed another musical excerpt and notated their musical intentions on an unedited score. The notated interpretations correlated with the presence of the 3 methods: The notated melody preceded other events in chords (chord asynchrony); events notated as phrase boundaries showed greatest tempo changes (rubato); and the notated melody showed most consistent amount of overlap between adjacent events (staccato and legato). These results suggest that the mapping of musical thought to musical action is rule-governed, and the same rules produce different interpretations (Palmer, 1989).

RELEVANCE: Palmer’s work concludes that there is a general consensus among performers on how to express phrase boundaries. More specifically, she finds a correlation between such boundaries and tempo variation, indicating that timing is intimately related with the expression of musical form. And so it gives me reason to look at timing profiles for signs of such expression.

REPP, B. H. (1997). The Timing Implications of Musical Structures. In D. Greer (Ed.), Musicology and Sister Disciplines: Past, Present, Future. Paper presented at The 16th International Congress of the International Musicological Society, London (pp. 60–70). London: Oxford UP. (PART OF MY SPECIAL TOPIC READINGS)

ABSTRACT: For the last decade or so, the author has been engaged in empirical research on the small, unnotated variations in musical sound patterns that convey what is commonly referred to as expression in performance. The work has focused on piano performance, in part for methodological reasons and in part because the author is a pianist himself. Among the several parameters of expression, timing (rubato) has received the greatest attention. This paper summarizes the results of recent studies which have yielded four kids of empirical evidence converging on a single hypothesis: that musical structures have specific timing implications which constrain the considerable variety of expressive timing patterns observed in individual performances.

RELEVANCE: This paper addresses the potential results of my experiment in that it posits the existence of normative timing profiles that are suggested by the music itself. In other words, specific musical features constrain the expressive possibilities available to the performer. Greer’s findings suggest that by analyzing performances we can come to understand features inherent in the musical structure. More specifically, if normative timing profiles emerge, they will tell us something about the internal structure of Mozart’s MT-TR complex.


TODD, N. P. (1985). A Model of Expressive Timing in Tonal Music. Music Perception, 3, 33–58. (JSTOR)

ABSTRACT: During a performance, a pianist has direct control over only two variables, duration and intensity (Seashore, 1938). Other factors such as pitch and timbre are determined largely by the composer and the mechanics of the instrument. Thus expressiveness imparted to a performance lies in the departures from metrical rigidity and constant intensity. In this article, the first of the two variables is considered and it is shown how a duration structure can be generated, corresponding to the rubato in a performance, from the musical structure.The main input to the model is the time-span reduction of Lerdahl and Jackendoff’s theory (1977, 1983). Also shown is an interesting analogy between this model and the algorithms of Grosjean, Grosjean, and Lane (1979). Thus the hypothesis that expression is largely determined by musical structure, and the formal parallel between time-span reduction and prosodic structure are given empirical support.

RELEVANCE: Todd places musical phrase-final lengthening into a larger context, noting parallels in speech and other motor sequences. And so the impetus for using this tendency to slow down at a phrase’s end as a way of gleaning one’s conception of a formal structure is given a more universal significance. Todd’s formalization of phrase-final lengthening is also potentially useful in terms of how it might be represented both mathematically and graphically.

A reformulation of my previous questions into a new project

It has been shown that performers use small variations in performance parameters—inter-onset timing, intensity, and articulation—to communicate aspects of intended musical structure (Clarke 1988). Thus in theory, by monitoring these parameters, we can determine how performers interpret the formal ambiguity presented by the so-called continuous exposition (i.e., an exposition that, due to the lack of a medial caesura, does not have a subordinate theme).

This ambiguity is reflected by two competing theories of sonata form: Hepokoski and Darcy’s sonata theory and Caplin’s theory of formal functions. Whereas Hepokoski and Darcy acknowledge the existence of continuous expositions, Caplin rejects the notion, claiming instead that the constituent form-functional units of subordinate-theme function are present even in the absence of a medial caesura.

In the spirit of Dodson 2008, which finds a correlation between performance and  Schenkerian readings of musical form, this paper asks whether performance trends align with a sonata-theory reading, a form-functional one, or neither.

Perceiving the so-called continuous exposition

QUESTION: To what extent does the lack of a medial caesura affect out judgment of grouping structure in Hepokoski and Darcy’s so-called continuous exposition?

SOME PRELIMINARY QUESTIONS: Do we actually perceive these as continuous units that lack the clear delineation of a subordinate theme, or are form-functional considerations enough for us to group this music into distinct units (i.e., a transition that is separate from a subordinate theme)? How do similarity relationships factor in? E.g., Are we more likely to identify a subordinate theme if is it begins with a presentation phrase, which by definition contains the immediate repetition of a unit and would thus encourage us to group the two together (see Drake 2003 & references)?

Perception of Intrinsic Formal Functionality – Critique

VALLIÈRES, Michel et al. (2009). Perception of Intrinsic Formal Functionality: An Empirical Investigation of Mozart’s Materials. Journal of Interdisciplinary Music Studies, 3(1/2), 17–43.

The study cited above found that listeners were able to distinguish between beginnings, middles, and ends in the absence of temporal context. This result is attributed to the theorized existence of intrinsic formal functionality. In short, specific combinations of musical features are associated with the three basic temporal functions of beginning, middle, and end. According to the study, these features alone provide sufficient information for listeners (both musicians and non-musicians) to determine the temporal location of a given excerpt within a score.

As an individual project, I propose to examine the authors’ assumptions (they seem to imply, for instance, that intrinsic form functionality is constant and universal) and questionable methodology, which I suspect will cast doubt on the findings. I will also discuss the general conclusions of this article in light of recent literature on the perception of musical form.