Linearity And Nonlinearity In Musical Instruments

Abstract

Basic understanding of musical instruments relies upon the fact that the primary vibrating element is, in nearly all cases, a simple linear extended vibrator with well defined mode frequencies. Some instruments, such as bells, guitars, and harpsichords, can be almost completely understood in.this approximation, though the discussion may necessarily be quite complicated because of the number of coupled linear systems involved. Instruments producing sustained sound, however, such as violins, clarinets, and trumpets, depend essentially for their operation upon nonlinear phenomena. These nonlinear phenomena largely determine the radiated acoustic power, the frequency spectrum, and the transient behaviour of the instrument. There has been great advance in our understanding of these matters over the past twenty years, and this paper will give an overview of musical instrument behaviour from this point of view.