Nonlinear theory of musical wind instruments

While many important features of the design and playing of musical wind instruments can be appreciated from a linear theory of their acoustical operation, an understanding of tone quality, loudness, and transient behavior depends almost entirely upon the essential nonlinearity of the sound generation mechanism and its interaction with resonances of the horn. This has been appreciated in a general way since the time of Bouasse, early this century, while Benade has led the renaissance of interest in the topic over the past 25 years. Until recently, available theoretical methods allowed the calculation of behavior only for rather soft playing conditions and consequently for limited nonlinearity. The development of time‐domain and mixed‐domain “frequency‐balance” techniques during the past few years, however, now allows all regimes of playing to be investigated. This paper reviews available theoretical methods and their application to typical instruments.