Trombone Synthesis by Model and Measurement
© Tamara Smyth and Frederick S. Scott. 2011
Received: 29 August 2010
Accepted: 24 January 2011
Published: 20 February 2011
A physics-based synthesis model of a trombone is developed using filter elements that are both theoretically-based and estimated from measurement. The model consists of two trombone instrument transfer functions: one at the position of the mouthpiece enabling coupling to a lip-valve model and one at the outside of the bell for sound production. The focus of this work is on extending a previously presented measurement technique used to obtain acoustic characterizations of waveguide elements for cylindrical and conical elements, with further development allowing for the estimation of the flared trombone bell reflection and transmission functions for which no one-parameter traveling wave solution exists. A one-dimensional bell model is developed providing an approximate theoretical expectation to which estimation results may be compared. Dynamic trombone model elements, such as those dependent on the bore length, are theoretically and parametrically modeled. As a result, the trombone model focuses on accuracy, interactivity, and efficiency, making it suitable for a number of real-time computer music applications.
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