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

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 ...