On the control of virtual violins : Physical modelling and control of bowed string instruments

Abstract:   This thesis treats the control of sound synthesis of bowed string instruments based on physical modelling. The work followed two approaches: (a) a systematic exploration of the influence of control parameters (bow force, bow velocity, and bow-bridge distance) on the output of a physical model of the violin, and (b) measurements and analyses of the bowing parameters in real violin playing in order to model and parameterize basic classes of bowing patterns for synthesis control.First a bowed-string model based on modal solutions of the string equation is described and implemented for synthesis of violin sounds. The behaviour of the model is examined through simulations focusing on playability, i.e. the control parameter space in which a periodic Helmholtz motion is obtained, and the variations of the properties of the simulated sound (sound level and spectral centroid) within this parameter space. The response of the model corresponded well with theoretical predictions and empirical expectations based on observations of real performances. The exploration of the model allowed to define optimal parameter regions for the synthesis, and to map sound properties on the control parameters.A second part covers the development of a sensor for measuring the bow force in real violin performance. The force sensor was later combined with an optical motion capture system for measurement of complete sets of bowing parameters in violin performance.In a last part, measurements of the control parameters for basic classes of bowing patterns (sautillé, spiccato, martelé, tremolo) are analyzed in order to propose a realistic control of the sound synthesis. The time evolution of the bowing parameters were modelled by analytical functions, which allowed to describe and control simulated bowing patterns by a limited set of control parameters. For sustained bowing patterns such as détaché, control strategies for basic elements in playing (variations in dynamic level, bow changes) were extracted from exemplary measurements, and simple rules deduced, which allowed extrapolation of parameters to modified bow strokes with other durations and at different dynamic levels.