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Other Instruments

One of the most interesting aspects of building virtual musical instruments is that every instrument has its own unique characteristics and modeling considerations. One disadvantage of this, however, is that it is not feasible to cover all cases in a single book. This section provides some literature pointers that can hopefully serve as a starting point for further research in some of the instrument areas not discussed here. While these pointers are neither complete nor up to date, the most recent papers and dissertations by the cited researchers can help fill in the gaps. (This is true of the preceding sections as well.)

Singing Voice

An historical summary of voice modeling and synthesis appears in §A.6.3. In [290], a model is proposed for the singing voice in which the driving glottal pulse train is estimated jointly with filter parameters describing the shape of the vocal tract (the complete airway from the base of the throat to the lip opening). The model can be seen as an improvement over linear-predictive coding (LPC) of voice in the direction of a more accurate physical model of voice production, while maintaining a low computational cost relative to more complex articulatory models of voice production. In particular, the parameter estimation involves only convex optimization plus a one-dimensional (possibly non-convex) line search over a compact interval. The line search determines the so-called ``open quotient'' which is fraction of the time there is glottal flow within each period. The glottal pulse parameters are based on the derivative-glottal-wave models of Liljencrants, Fant, and Klatt [133,257]. Portions of this research have been published in the ICMC-00 [291] and WASPAA-01 [292] proceedings. Related subsequent work includes [250,213,251,214,212] Earlier work in voice synthesis, some summarized in Appendix A, includes [40,81,87,90,206,257,389,492]; see also the KTH ``Research Topics'' home page.

Flutes, Recorders, and Pipe Organs

A chapter on the fundamental aero-acoustics of wind instruments appears in [196], and a comprehensive treatment of the acoustics of air jets in recorder-like instruments is given in [530]. A comprehensive review article on lumped models for flue instruments appears [130] in a special issue (July/August 2000) of the Acustica journal on ``musical wind instrument acoustics.'' An overview of research on woodwinds and organs appears in [129]. Follow-up publications by this research group include papers concerning the influence of mouth geometry on sound production in flue instruments [108,418].

Percussion Instruments

While sample-playback synthesis is especially effective for percussion instruments that are supposed to play ``in the background,'' some form of parametrization is needed for the more expressive performances, or for highly variable percussion instruments such as the Indian tabla. Highly efficient computational models of 2D membranes and 3D volumes may be built using the digital waveguide mesh [146,520,518,521]. More recently, Lauri and Välimäki have developed a frequency-warping approach to compensating for dispersive wave propagation in a variety of mesh types [398,399,401]. The 2001 thesis of Bilbao [54] provides a unified view of the digital waveguide mesh and wave digital filters [136] as particular classes of energy invariant finite difference schemes [481]. The problem of modeling diffusion at a mesh boundary was addressed by [268].
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