Phase-plane Representation and Visualization of Gestural Structure in Expressive Timing

Abstract

For the past few decades there has been considerable scientific interest in expression in music performance (Gabrielsson, 2003). A particularly relevant aspect of music performance is expressive timing, that is, the intentional fluctuations of tempo during a performance. Accordingly, expressive timing has been one of the major topics in music performance research. As an expressive parameter, timing is used to clarify the musical structure of the piece (Clarke, 1988), among other things. The problem of explaining expressive timing in music performances can be regarded as a special case of a very wide range of problems where we want to learn experimentally about the temporal behaviour of some dynamical system based on limited observation. A common way of studying data in dynamical systems theory is by phase-plane representation. In this paper we argue that phase-plane representations of expressive timing provide a useful way of visualizing data, and furthermore, we show that such representations are promising in the context of performer characterization and identification.

Acknowledgements

This work is funded by the Austrian National Research Fund (FWF) under project number P19349-N15. We are grateful to Bruno Repp for providing the expressive timing data for the performances of Schumann's Träumerei.

Notes

¹The phase-plane visualization method was introduced in Grachten et al., (2008). With the current paper, we extend this work, by a quantitative and qualitative evaluation of the phase-plane representation.

²We interpret the curves as tempo curves, although these remarks of course hold independently of the interpretation of the dimensions.

³The data used here originates from that study.

⁴A common practice in spline fitting is to put a breakpoint at each data point.

⁵The pieces are selected to contain at least three occurrences of a single musical fragment.

⁶The analysis was performed on the IIPG measure rather than F-score since the F-score data, by repeated summarizing of intermediate results, is too sparse to make a reliable claim.