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%0 Conference Proceedings %A Serafin, Stefania %A Vergez, Christophe %A Rodet, Xavier %T Friction and application to real-time physical modeling of a violin %D 1999 %B ICMC: International Computer Music Conference %C Pekin %F Serafin99b %K friction %K physical model %K violin %X One key point in physical modeling of bowed string instruments is to find a suitable equation that describes the friction force between the bow and the string. This force is a highly non-linear and eventually discontinuous function of bow parameters and dynamics of the model. The friction mechanism gives rise to the well known stick-slip phase alternation, characteristic of the so-called Helmholtz motion. In this paper we propose different models of bow string interaction. Evaluations of the models' influence on the quality of the synthesis is done with a complete physical model of a violin. We have chosen an hyperbolic friction function that fits measurements carried out in real instruments. Solving the coupling of the bow and the string usually requires to cope with a system of two equations. This is often done by numerical methods or by table-lookup techniques. However, we have shown that an hyperbolic friction function allows us to obtain an analytical solution. When the solution is not unique but triple, we choose the one that is given by a physically based hysteresis rule: the system follows the current state (stick or slip) continuously as long as it can and the middle solution is not chosen. We have furthermore refined the classical basic model of violin-like instruments. Starting from a single bow hair, we then consider a bow with many hairs. The strings are represented by fractional delay lines, and losses are lumped into low-pass filters. All the filter coefficients are estimated according to impulse response of violin's strings. Losses are adapted to the length of the vibrating part, and refined in order to take into account the influence of terminations and fingers. Finally, the body resonances are estimated on a measured transfer function. All our simulations are performed using the real-time environments jMax or Max/MSP interchangeably. We built a graphical interface which allows us to see the coupling between the non linear bow string interaction and the linear wave propagation in the string. In fact, we display the friction curve, (the shape of which depends on the force exerted by the player on the bow), and the previously mentioned analytical solution at each time, which moves on the friction curve according to the coupling with the string. >From a sound and musical point of view, the simulation results are very satisfactory. Sound synthesis is even more realistic when the model with many bow hairs is included. The model 's musical capabilities will be highlighted at the conference using a real time implementation and playing interface. %1 7 %2 3 |