Physical modelling of brass instruments using finite-difference time-domain methods
Harrison-Harsley, Reginald Langford
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This work considers the synthesis of brass instrument sounds using time-domain numerical methods. The operation of such a brass instrument is as follows. The player's lips are set into motion by forcing air through them, which in turn creates a pressure disturbance in the instrument mouthpiece. These disturbances produce waves that propagate along the air column, here described using one spatial dimension, to set up a series of resonances that interact with the vibrating lips of the player. Accurate description of these resonances requires the inclusion of attenuation of the wave during propagation, due to the boundary layer effects in the tube, along with how sound radiates from the instrument. A musically interesting instrument must also be flexible in the control of the available resonances, achieved, for example, by the manipulation of valves in trumpet-like instruments. These features are incorporated into a synthesis framework that allows the user to design and play a virtual instrument. This is all achieved using the finite-difference time-domain method. Robustness of simulations is vital, so a global energy measure is employed, where possible, to ensure numerical stability of the algorithms. A new passive model of viscothermal losses is proposed using tools from electrical network theory. An embedded system is also presented that couples a one-dimensional tube to the three-dimensional wave equation to model sound radiation. Additional control of the instrument using a simple lip model as well a time varying valve model to modify the instrument resonances is presented and the range of the virtual instrument is explored. Looking towards extensions of this tool, three nonlinear propagation models are compared, and differences related to distortion and response to changing bore profiles are highlighted. A preliminary experimental investigation into the effects of partially open valve configurations is also performed.