A computer program for optimization of brass instruments. Part I. Concept, implementation

Abstract

Computer optimization is used to improve characteristics of real world systems. Different strategies are known and have successfully been applied in areas like filter design, circuit synthesis, layout, etc. Common to all optimization methods is the need for mathematical models and target functions evaluating to a single number, reflecting the sum on all deficiencies depending on variables to be varied. In a brass instrument optimizer these variables are representing physical dimensions which later on can be changed by the instrument maker (e.g., by inserting sleeves or modifying the bore). In the target function, differences between actual and desired characteristics like intonation or responsiveness are calculated, weighted, and added. Because these characteristics can only be derived from the instrument’s calculated input impedance, physical modeling is required. Systematically and algorithmically, the optimizer approaches the best possible instrument step by step, varying optimization variables. It is directed by the result and tendency of the target function which is evaluated after each step. The brass instrument optimization program introduced here makes computer optimization available for musical instrument manufacturers. Much expert knowledge like defining target functions, specifying optimization variables, and modeling instruments are hidden from the user, making the tool easy enough to work with.