Effects of nonlinear sound propagation on the characteristic timbres of brass instruments.

The capacity of a brass instrument to generate sounds with strong high-frequency components is dependent on the extent to which its bore profile supports nonlinear sound propagation. At high dynamic levels some instruments are readily sounded in a "cuivré" (brassy) manner: this phenomenon is due to the nonlinear propagation of sound in ducts of the proportions typical of labrosones (lip-reed aerophones). The effect is also evident at lower dynamic levels and contributes to the overall tonal character of the various kinds of brass instrument. This paper defines a brassiness potential parameter derived from the bore geometries of brass instruments. The correlation of the brassiness potential parameter with spectral enrichment as measured by the spectral centroid of the radiated sound is examined in playing tests using musicians, experiments using sine-wave excitation of instruments, and simulations using a computational tool. The complementary effects of absolute bore size on spectral enrichment are investigated using sine-wave excitation of cylindrical tubes and of instruments, establishing the existence of a trade-off between bore size and brassiness potential. The utility of the brassiness potential parameter in characterizing labrosones is established, and the graphical presentation of results in a 2D space defined by bore size and brassiness potential demonstrated.