Computational study of the piccolo: Evidence for chaotic tones.

ABSTRACT

Direct numerical solutions of the Navier-Stokes equations have been used to compute tones produced by a model of the piccolo. The behavior depends on the angle at which the air jet is directed at the embouchure hole and the displacement of the jet center from the embouchure edge. Values of the jet angle and displacement are found that produce pure tones with spectra similar to those of real piccolo tones. The behavior of calculated tones as a function of the blowing speed u is studied, and it is found that unsteady behavior can occur depending on the value of u, the jet angle, and the jet displacement. Detailed analysis of these unsteady tones suggests that the model piccolo studied here exhibits chaotic behavior with a positive Lyapunov exponent. The implications for piccolo tones produced with real piccolos by real piccolo players are discussed.