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

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.