Musicians have to make many interpretive decisions when performing a piece. For example, the grace note, a one-note musical ornament, has no precise duration written in the score; it has to steal its duration from either the preceding or following melody notes. This study addressed several empirical questions: What duration are grace notes given? Does this vary depending upon musical context or individual preferences? And, are the durations of grace notes taken from the preceding or subsequent melody note, or is time added? In an experiment, 16 professional pianists performed three musical fragments (from a Beethoven theme) "with" and "without" grace notes in seven different tempi. The timing of the grace notes was found not to be proportional to changes in global tempo for most, but not all performers, which replicates findings in earlier studies. In the majority of cases, increases in bar duration were matched by relative increases in grace-note duration that were smaller than predicted by a proportional tempo model, with a minority of subjects performing grace notes with fixed duration over tempo. In most cases, grace-note duration was "stolen" from the preceding melody note, with a small contribution from the following (main) note and with minimal disturbance to local tempo. Conversely, where grace notes were played as appoggiatura , the main source of their duration was the main note. The type of grace note performed depended both on its musical context and on individual differences between performers. A model of grace-note duration is proposed to account for these results.

We investigated whether and how the timing of musical rhythms changes with tempo. Twelve skilled pianists played a monophonic eight-bar melody in 21 different rhythmic versions at four different tempi. Within bars, the rhythms represented two isochronous patterns and all possible ordered pairs and triplets of different note values with ratios from the set {3, 2, 1}. The three-note rhythms also occurred in each of two meters (3/4 and 6/8). Significant deviations from the notated interval ratios were observed in performances of most rhythms, even at the slowest tempo. The observed ratios of the two-note rhythms changed little with tempo. By contrast, those of the three-note rhythms showed increasing assimilation of the two longer intervals as tempo increased, while the relative duration of the short interval was barely affected by tempo. These results replicate previous findings of Fraisse (1956), obtained in a nonmetrical and non-musical context. At fast tempi, the distinction between three different interval durations seems difficult to maintain.

A number of attempts have been made in the past 10 to 15 years to construct artificial systems that can simulate human expressive performance, but few systematic studies of the relationship between model output and comparable human performances have been undertaken. In this study, we assessed listeners' responses to real and artificially generated performances. Subjects were asked to identify and evaluate performances of two differently notated editions of two pieces, played by a panel of experienced pianists and by an artificial performer. The results suggest that expressive timing and dynamics do not relate to one another in the simple manner that is implemented in the model (Todd, 1992) used here, that small objective differences in the expressive profiles of different performances can lead to distinctly different judgments by listeners, and that what appears to be the same expressive feature in performance can fulfill different functions. Although one purpose of such a study is to assess the model on which it is based, more important is its demonstration of the general value of comparing human data with a model. As is often the case, it is what the model does not explain that is most interesting.

This paper compares timing and key-velocity data collected from a skilled performance of Schubert's G♭-major Impromptu (Opus 90) with a number of performances generated by a version of a musical expression algorithm proposed by Todd (1992). Regression analysis is used to demonstrate both the shortcomings of this model as a complete explanation of musical expression and how it might be more successfully used as a tool for analyzing data from real performances. Used in this second manner, the algorithm is shown to provide a general expressive baseline against which other aspects of expression may be highlighted. It is also suggested that such a baseline provides a method of decomposing performances into continuous and discrete forms of expression. It is concluded that using algorithmic models as heuristic tools, rather than as explanations in themselves, may better serve our increased understanding of the flexible and multiple nature of musical expression.