A hybrid scheme for bore design optimization of a brass instrument

This paper presents how the shape of a brass instrument can be optimized with respect to its intonation properties. The instrument is modeled using a hybrid method between a lossy one-dimensional transmission line analogy for the slowly flaring part of the instrument, and a two-dimensional finite element model for the rapidly flaring part. The optimization employs gradient-based algorithms, and allows for a large number of design variables. Through the use of an appropriate choice of design variables, the algorithm is capable of rapidly finding horn profiles that are optimal subject to various geometric constraints, such as increasing or convex bell flares. It is found that under a convexity constraint, brass wind bells that are optimal with respect to an intonation condition can be constructed of piecewise conical sections.