Physics-based guitar synthesis

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Supervisor:
Dr. Bank Balázs Lajos
Department of Measurement and Information Systems

In the past few decades, physics-based sound synthesis of musical instruments has started to evolve rapidly. This thesis is about the physical modeling of the acoustic guitar, which allows the synthesis of the guitar sound. First, the structure of the guitar is described and the mechanism is shown how the sound is produced. Next, an outline of the physical model of the guitar is presented: the string model, the body model and the radiation model. Various methods are described which are used to model the string in the literature and then the solution is shown which is based on the finite difference method. The presented solution differs from the common one, as the discretization of the string is irregular in space. The numerical dispersion and stability of the method is also examined. The stiffness and damping factors of the strings are determined by measurements. Guitar playing techniques are explained, and their implementation in the model are shown. In the next part of the work, modeling of the soundboard is described, which is based on the Kirchhoff-Love plate theory. The main element of the theory is the differential equation of the plate, which is extended with other factors to model damping. Finite difference method is used to solve the equation with proper handling of the boundary conditions. An algorithm is presented which makes the modeled plate to be of any shape. The struts of the soundboard are modeled by locally altering the physical parameters of the soundboard. The simulation is validated by using results from the literature. A simple radiation model is presented which is derived from the model of the baffled piston. Admittance and sound pressure measurements are taken on a guitar, and these results are compared with the corresponding parts of the simulated guitar. In the last chapter, further development possibilities are outlined, and the sound quality of the model is evaluated.

The presented phyiscal model is implemented as a software synthesizer, written in C++. The program receives parameters of the physical model and a score, and creates a wave file. The software does not work in real-time due to the complexity of the model, but it includes a simplified model which can calculate the generated sound in real-time.

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