On the control of virtual violins - Physical modelling and control of bowed string instruments
Résumé
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.
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.
Cette thèse porte sur le contrôle de la synthèse sonore par modélisation physique des instruments à corde frottée. Elle se base, d'une part, sur l'exploration systématique de l'influence des paramètres de contrôle (pression d'archet, vitesse de l'archet et distance au chevalet) sur le comportement du modèle, et d'autre part, sur la mesure du contrôle effectif qu'exerce l'instrumentiste afin d'obtenir un contrôle réaliste du modèle physique. Un modèle physique basé sur la résolution modale de l'équation de la corde est d'abord présenté et implémenté pour la synthèse sonore du violon. Le comportement du modèle physique est ensuite examiné en effectuant des simulations et se concentre sur deux aspects: la ``jouabilité", c'est-à-dire l'espace des paramètres de contrôle dans lequel un mouvement de Helmholtz périodique est obtenu, et les variations des propriétés du son synthétisé (fréquence d'oscillation, niveau sonore et centroïde spectral) à l'intérieur de cet espace de paramètres. La deuxième partie de ce travail concerne la mise au point d'un capteur pour mesurer la force d'appui de l'archet sur la corde dans un contexte de jeu réel. Le capteur est ensuite combiné avec un système optique de capture du mouvement afin de mesurer l'ensemble complet des paramètres de jeu du violoniste. La dernière partie présente l'analyse des mesures de ces paramètres de contrôle pour des modes de jeu typiques (sautillé, spiccato, martelé, tremolo, détaché). Ces mesures permettent de décrire certaines propriétés du geste instrumental et de proposer un contrôle réaliste de la synthèse sonore pour différents modes de jeu et différentes tâches musicales.
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