A Simulation Tool For Brassiness Studies, Preliminary Results Obtained From Brass Instrument's Bores

Abstract

The brightness of the sound generated by brass instruments at high dynamic level is mainly due to the essential nonlinearity of the wave propagation in the pipe. The bright instruments such as the trumpet and the trombone (high brassiness) are different from more mellow brass instruments such as saxhorns or flugelhorns (low brassiness). The bright instruments have an almost cylindrical pipe segment just downstream of the mouthpiece. The conical bore of the saxhorns in this region implies a faster decay of the wave which reduces the nonlinear wave steepening. To investigate the differences between the brassiness of different instruments, crescendos have to be played (experiments) or simulated (theory). Then a spectral enrichment parameter, characterising the rate of spectral enrichment with increasing dynamic level, can be extracted for each instrument. A frequency‐domain numerical model of brass instrument sound production is proposed as a tool to predict the spectral enrichment parameter (brassiness characterisation). It is based on generalized Burger's equations applied to weakly nonlinear wave propagation in non uniform ducts. The relevance of the present tool is evaluated by doing simulations of periodic regimes using typical brass instrument's bores, from which the spectral enrichment parameters are calculated, and compared to measured ones.