Penel, A., Desain, P., Maris, E., and Windsor, W. L. (1999) A decomposition model of expressive timing. In Proceedings of the 1999 SMPC, 21. Evanston.

We are interested in systematic timing variations observed in music performance. Two basic assumptions are made. First, we accept the dominant idea that timing variations are related to the musical structure processed by the performer and communicated to listeners. Second, we assume that the timing variations highlighting the different components of the musical structure are additive. In Penel and Drake (1998), timing variations possibly highlighting various structural components were measured from the timing profile and the timing profile was regressed against them. This method presents the drawback that some measured timing variations may originate from multiple structural components, not just from the one under consideration. For example, phrase-final lengthening may be influenced by the phrase structure but also by the metrical structure. Taking a different, concept-driven approach, Todd (1995) proposed a model of expressive timing which gives a central role to the hierarchical grouping structure: at all levels in the hierarchy, each group results in a parabolic timing pattern (accelerando/ritardando). Parabolas of all groups at all levels are added towards a final timing pattern that can be compared to those produced by humans (Windsor & Clarke, 1997).

The present study retains the data-driven approach chosen in Penel & Drake (1998), while overcoming the difficulty mentioned above. A decomposition model is proposed, in which various aspects of the musical structure are coded, the timing profile being regressed against this coding. Thus, the timing profile is decomposed into independent timing variations corresponding to different structural components. Compared to Todd's model, it has the advantage of allowing components of the musical structure other than the hierarchical grouping structure to be taken into account. Furthermore, timing variations related to any structural component may have any shape: parabolic, linear, purely local (the lengthening or the shortening of one single note), etc. This model was used to analyze timing variations in performances of Beethoven's theme of his theme and variations on "Nel cor più non mi sento" by G. Paisiello, at three different tempi.

In the future, this decomposition model may be used to analyze expressive timing in a larger musical corpus. It will allow a better understanding of timing variations produced, and in turn will enable the conception of improved concept-driven models of expressive timing.

References

Penel, A. et Drake, C. (1998). Sources of timing variations in music performance: A psychological segmentation model. Psychological Research, 61, 12-32.

Todd, N. P. McAngus (1995). The kinematics of musical expression. Journal of the Acoustical Society of America, 97, 1940-1949.

Windsor, W.L. & Clarke, E.F. (1997). Expressive timing and dynamics in real and artificial musical performances: using an algorithm as an analytical tool. Music Perception, 15, 127-152.

More on components of musical expression