A methodological and preliminary study on the acoustic effect of a trumpet player's vocal tract

Numerical continuation of a physical model of brass instruments: Application to trumpet comparisons

The system formed by a trumpet player and his/her instrument can be seen as a non-linear dynamic system and modeled by physical equations. Numerical tools can then be used to study these models and clarify the influence of the model parameters. The acoustic input impedance, for instance, is strongly dependent on the geometry of the air column and is therefore of primary interest for a musical instrument maker. In this study, a method of continuation of periodic solutions based on the combination of the Harmonic Balance Method (HBM) and the Asymptotic Numerical Method (ANM) is applied to a physical model of brass instruments. It allows the study of the evolution of the system where one parameter of the model (static mouth pressure) varies. This method is used to compare different B♭ trumpets on the basis of two descriptors (hysteresis behavior and dynamic range) computed from the continuation outputs. Results show that this methodology enables the differentiation of instruments in the space of the calculated descriptors. Calculations for different values of the lip parameters are also performed to confirm that the obtained categorization is independent of variations of lip parameters.

Acoustical interaction between vibrating lips, downstream air column, and upstream airways in trombone performance

This paper presents experimental results on the acoustical influence of the vocal tract in trombone performance. The experimental approach makes use of measurements at the interface between the player and instrument, allowing a relative comparison between upstream airways and the downstream air column impedances, as well as an estimation of the phase of the impedance of the upstream and downstream systems. Measurements were conducted over the full traditional range of playing, during sustained tones with varying dynamic, as well as in special effects such as pitch bending. Subjects able to play over the full range demonstrated significant upstream influence in the higher register of the instrument. These players were categorized in two groups according to their ability to control the phase of the upstream impedance and their ability to generate powerful downstream acoustic energy. Sustained tones played with varying dynamics showed a general tendency of a decrease in vocal-tract support with increase in loudness. Although pitch bends did not involve significant upstream influence at f0, results suggest modification of the lip behavior during bending. Vocal-tract tuning at tone transitions was also investigated and found to potentially contribute to slur articulations.