Trombone Synthesis by Model and Measurement

A physics-based synthesis model of a trombone is developed using filter elements that are both theoretically-based and estimatedfrom measurement. The model consists of two trombone instrument transfer functions: one at the position of the mouthpieceenabling coupling to a lip-valve model and one at the outside of the bell for sound production. The focus of this work is onextending a previously presented measurement technique used to obtain acoustic characterizations of waveguide elements forcylindrical and conical elements, with further development allowing for the estimation of the flared trombone bell reflection andtransmission functions for which no one-parameter traveling wave solution exists. A one-dimensional bell model is developedproviding an approximate theoretical expectation to which estimation results may be compared. Dynamic trombone modelelements, such as those dependent on the bore length, are theoretically and parametrically modeled. As a result, the trombonemodel focuses on accuracy, interactivity, and efficiency, making it suitable for a number of real-time computer music applications.