Physical model real-time auralisation of musical instruments : analysis and synthesis

Abstract

Physical modelling is a widely applied method for researching acoustical properties of musical instruments. In recent years the ever rising computational power of standard personal computers and the accessibility of dedicated accelerating hardware has fuelled manifold developments in this field of research. Most physics based methods that directly solve the underlying differential equations have the severe drawback of a high computational cost, so many simplifications of the physical models are proposed and utilised to make physical schemes faster or capable of real-time. But, with simpler descriptions of the modelled instruments, less information about the actual physical behaviour can be gained from the model. This, in turn, directly influences the sound quality of the physical model. A method that could retain high structural accuracy while being capable of calculating and synthesizing instrument models in real-time would be highly beneficial for several reasons:

a) For musicological research of the influence of physical parameters on the timbre and the radiated sound of the instrument. b) For instrument makers who could test the influence of geometrical alterations on the vibrational behaviour of the respective instrument without the time delay of crafting a new instrument. c) For musicians who are interested in physics based synthesis of musical instruments. d) For composers who want to compose and perform music for a new class of instruments with changeable geometrical features in real-time. (Imagine a piano that can be manipulated in size while playing.)

This thesis presents a methodology and working implementation of real-time physical models of four musical instruments. The models are developed by using measurements taken on real instruments as a basis and implementing all acoustically relevant parts of the instruments in software and hardware. The physical models are computed using symplectic and multi-symplectic time integration methods iterating Newton's equation of motion in time. All models are implemented in C/MATLAB and on Field Programmable Gate Array Hardware. The final instrument models can be controlled from a Graphical User Interface running on a standard PC.