Abstract
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.
Highlights
Instrument synthesis involving real-time interactive sound often faces trade-offs between accuracy and computational efficiency to provide both parametric control and quality sound production
If the goal is to extract physical parameter values from an instrument during performance, the model’s produced sound when played with proper parameter values will likely require a higher degree of actual similarity to the instrument being modeled. In this application, which is gaining increasing attention in the physical modeling community [1,2,3,4,5,6,7,8], the virtual model must often account for the frequency characteristics of any variables involved in the acquisition of data, such as instrument radiation, mic placement, or inclusion of any measurement device/apparatus that may alter the acoustic behaviour of the instrument being modeled
The trombone model presented here consists of two trombone instrument transfer functions, one taken at the position
Summary
Instrument synthesis involving real-time interactive sound often faces trade-offs between accuracy and computational efficiency to provide both parametric control and quality sound production. EURASIP Journal on Advances in Signal Processing produced sound may be seen as the coupling of the pressure input from the lips (the product of the volume velocity and the bore opening’s characteristic impedance) with the instrument bore and bell—a convolution of the lip-valve signal and the trombone impulse response With this view, isolation of the lip-valve signal is a matter of obtaining and deconvolving the instrument’s transfer function, as well as any measurement variables, from the instrument’s produced sound. The focus is on obtaining a parametric model of the trombone’s transfer function in two positions: one tapped at the position of the mouth and the other outside the bell The former may be coupled to a lip-valve model, providing feedback of bore resonances and the pressure difference across the lip valve (required for dynamic models in which the bore pressure influences the behaviour of the vibrating lips [9]), while the latter may be convolved with the lip-valve signal to provide the instrument’s produced sound. The method is extended and applied here to measure instrument structures that are more difficult to account for theoretically, and which are not expected to change during performance, such as the reflection and transmission of the trombone’s bell, with comparison to classic modeling techniques showing consistency in the results
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