This paper presents how the shape of a brass instrument can be optimised with respect to its intonation and impedance peak magnitudes. The instrument is modelled using a one-dimensional transmission line analogy with truncated cones. The optimisation employs the Levenberg-Marquardt method, with the gradient of the objective function obtained by analytic manipulation. Through the use of an appropriate choice of design variables, the optimisation is capable of rapidly finding smooth horn profiles.
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