Bore optimisation and impedance modelling of brass musical instruments
Alistair C. P. Braden · ERA · 2006
The input impedance of a brass musical instrument is a good representation of its resonance characteristics. Methods of calculating input impedance for a known instrument shape, or bore-profile, are reviewed, and an extension to existing theory for bent waveguides is given. These input impedance methods form the basis for consideration of the inverse problem; to find a bore-profile with given impedance characteristics. Such problems can be formulated as bore reconstruction – finding an unknown bore from its impedance, and performance optimisation – altering certain characteristics of a known bore. The inverse problem is solved by means of optimisation, using either genetic algorithms or the Rosenbrock direct-search method. A number of new techniques are used to improve convergence speed by minimising both the size of the search space and the number of design variables. These techniques are incorporated into an elegant object-oriented instrument representation, allowing convenient and flexible problem definition and forming the basis of an integrated application in C++. Experimental impedance measurements on a series of trombones are conducted, and typical results presented. These data are used to formulate optimisation targets. The optimiser is then used for bore reconstruction and performance optimisation to solve real-world trombone design problems.