We have visited some basic methods for computational acoustic modeling with applications in digital audio effects and musical instrument modeling. Topics visited included acoustic echo simulation, artificial reverberation, chorus and flanging effects, digital waveguide modeling of strings and winds, lumped modeling, transfer-function modeling, plucked and struck strings, electric and acoustic guitars, piano, woodwinds, bowed strings, and brass instruments.

The remainder of this book consists of a series of appendices which extend and supplement the material introduced thus far. First, some historical background is filled in, followed by a tutorial appendix on underlying physical principles. The next appendix discusses further extensions of the digital waveguide modeling paradigm, followed by an introduction to finite difference schemes, and a discussion of equivalences between the two modeling approaches. Finally, the closely related topic of wave digital filters is introduced, followed by some pointers on the Internet.

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A History of Enabling Ideas Leading to Virtual Musical Instruments
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Virtual Musical Instruments