Linear Basis Models for Prediction and Analysis of Musical Expression

Abstract

The quest for understanding how pianists interpret notated music to turn it into a lively musical experience, has led to numerous models of musical expression. Several models exist that explain expressive variations over the course of a performance, for example in terms of phrase structure, or musical accent. Often however expressive markings are written explicitly in the score to guide performers. We present a modelling framework for musical expression that is especially suited to model the influence of such markings, along with any other information from the musical score. In two separate experiments, we demonstrate the modelling framework for both predictive and explanatory modelling. Together with the results of these experiments, we discuss our perspective on computational modelling of musical expression in relation to musical creativity.

Acknowledgements

This research is supported by the Austrian Research Fund (FWF, Z159 ‘Wittgenstein Award’). We are indebted to Mme. Irene Magaloff for her generous permission to use the data of her late husband's performances for our research. For this research, we have made extensive use of free software.

Notes

¹We use the term framework to refer to the general modelling methodology, including techniques to estimate parameters, and to predict new performances. By model, we mean an instantiation of this methodology, using a fixed selection of basis functions.

²The loudness of a note depends on several factors, and the relation between the MIDI velocity of a note performed on the Bösendorfer piano and its loudness is far from straightforward. The relation between sound pressure level and MIDI velocity on computer controlled pianos has been investigated by Goebl and Bresin (2003). For the Bösendorfer piano this relation is roughly linear from MIDI velocities 40 upwards, although it depends on pitch.

³Listening to synthesized model predictions revealed that a second-order pitch model tends to overemphasize higher pitches.

⁴Narmour's concept of closure is subtly different from the common notion of musical closure in the sense that the latter refers to ‘ending’ whereas the former refers to the inhibition of the listener's expectation of how the melody will continue.

⁵To meet the assumptions of ANOVA, the data set was restricted to the pianists for which performances of all four pieces are available, namely Pollini, Rubinstein, and Ashkenazy.

⁶See http://www.cp.jku.at/research/TRP109‐N23/BasisMixer/midis.html for sound examples.