Alberto Torin

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Percussion Instrument Modelling In 3D: Sound Synthesis Through Time Domain Numerical Simulation

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Ch. 6 - Virtual instruments

This chapter presents the ultimate contribution of this thesis. Three different virtual instruments are presented: a system of multiple plates in 3D, the nonlinear double membrane drum (a model for bass drums and tom toms), and finally the snare drum. All these instruments are embedded in the 3D acoustic field. They are obtained by combining together in a modular way the components presented in the previous chapters. As such, the resulting numerical schemes possess a numerical energy that can be used to guarantee their stability. For each of these virtual instruments, a description of the physical model is given, together with the implementation details and simulation results. The implementation of these instruments as energy conserving algorithms is original.

Multiple plate environment in 3D

Double membrane drums - the bass drum

Snare drum



Sound examples

One of the perks of numerical physical modelling is the ability to play with the parameters of the system, pushing sound synthesis to its limits. Here is an example of a square, 2x2 m gong played in a 3D space.

Here is a short piece that I made just for fun, putting together sounds generated with different virtual percussion instruments I created.



Table of contents

Abstract

Chapter 1 - Introduction

Chapter 2 - Linear plate vibration

Chapter 3 - Nonlinear plate vibration

Chapter 4 - Collisions

Chapter 5 - Coupling with the acoustic field in 3D

Chapter 6 - Virtual instruments

Chapter 7 - Summary and conclusions

Appendix A - Experimental investigation of nonlinearities in drum membranes

Appendix B - Finite precision effects in FDTD schemes

Appendix C - Iterative methods for linear systems