The Changing Picture of Nonlinearity in Musical Instruments: Modeling and Simulation
Stefan Bilbao · 2014
A natural starting point for the study of any physicalsystem is linearisation—leading to great simplification isterms of analysis, and also, in the computer age, to designflexibility and algorithmic simplification in simulation. T heacoustics of musical instruments is no exception. Onequestion, then, is: how much of the behaviour of a giveninstrument can be linearised? The only clear answer is:definitely not all of it. The production of musical soundby an instrument, whether it is struck, blown, or bowed,relies critically on a nonlinear excitation mechanism. Onestandard model of the musical instrument, then, relies ona subdivision of the instrument into a nonlinear excitationmechanism, which is to a good approximationlumped, and alinear resonator which is distributed, and characterized by anumber of natural frequencies, or modes. Such a model hasbeen employed, for many particular cases, for some time—apowerful unified picture emerged, however, with the articleby McIntyre, Schumacher and Woodhouse [1]. See Figure1. Such a characterisation has been enormously useful, notonly in investigations in musical acoustics, but also as ameans of arriving at efficient synthesis methods, using modalrepresentations [2, 3], methods based on transfer functiondescriptions [4], or to spectacular effect for certain systemsin 1D when a traveling wave formulation is available,leading to the digital waveguide formalism [5, 6].