Comparison of Trumpets' Sounds Played by a Musician or Simulated by Physical Modelling

This paper addresses the use of sound simulations for instrument characterization. It focuses on the ability of simulations by physical modelling to create sounds characteristic of a given instrument. The harmonic balance technique is used to generate trumpet sounds in permanent regime. The input parameters of the simulations are the input impedance of the trumpet (resonator), the control parameters are the characteristics of the virtual musician (excitator), and the outputs of the simulations are the playing frequency and the magnitude of the 6 first harmonics of the notes. Three different trumpets, obtained by small geometrical variations of the leadpipe, are first simulated using several virtual musicians, and second played by a “real” musician. These two populations of sounds, generated with different dynamics, are characterized by the playing frequency, the spectral centroid and the spectral irregularity, and their spectrum in permanent regime. Results show first that even for steady dynamics, the spectra of the two populations are very different. But convergent differences between the instruments for the simulated and the played sounds can be noticed. Principal Component Analysis (PCA) and Discriminant Analysis (DA) are used to study the influence of the musician, virtual or real, on the spectrum of the sounds. For steady dynamics sounds, the simulated sounds are clearly differentiated. For sounds played by the musician, the variability due to the musician is in the same order than those of the instruments. The similarities between the simulated sounds and those played by a musician are next studied for different dynamics. To compare the influence of the instrument, an ANOVA (Analysis of Variance) model is fitted to the data for the 3 descriptors of the sounds (playing frequency, spectral centroid and spectral irregularity). Results show interesting similarities in the influence of the instrument on these 3 descriptors. Simulations could be used to predict certain characteristics of the sounds of an instrument, opening the door to virtual acoustics for instrument making.