Session: 01-06-01: AI and Machine Learning in Acoustics and Vibrations

Paper Number: 166610

Determination of Sound Production Maps for a Trumpet Acoustic Model As a Function of a Player’s Control Parameters 

The trumpet is a difficult instrument to play, as creating desired sounds on the instrument requires a musician to set their lips (i.e, embouchure) and blowing strength with fine precision. Small changes in these control parameters can lead to the absence of sound, out of tune pitches, or spurious sounds. Determining conditions under which desirable sounds are produced is important for characterizing the process of trumpet playing, but doing so involves accurately classifying regions in a potentially high dimensional parameter space.

 

This work proposes to identify the regions of a player’s control parameters that would lead to satisfactory sounds. For this purpose, this study introduces a computational model of a trumpet as well as an approach to explicitly identify the “playability” regions.

 

This work is based on a trumpet model that involves a resonator with a trumpet’s experimentally measured acoustic impedance. Trumpet sound production results from three interconnected phenomena: oscillation of a player’s lips, driven by pressure from the player’s mouth and from within the trumpet’s mouthpiece; air flow between the lips into the trumpet; and the interaction of the player’s blown air with the air column in the trumpet. The proposed model represents the lip as a two degree of freedom damped oscillator, considers the air that the musician blows as incompressible, inviscid fluid flow, and approximates the trumpet’s acoustic impedance using a modal decomposition scheme. This system of ordinary differential equations can either be solved numerically for the acoustic pressure or linearized near equilibrium points. Both methods can be used for sound classification.

 

In order to identify the playability regions in the parameter space, this work uses a support vector machine classifier that is trained on labels qualifying whether or not a given parameter configuration leads to sound production. Sound production can be determined through a criterion based either on the growth or decay of the pressure time series or on a spectral analysis of the Jacobian around equilibrium points. The proposed approach is able to accurately identify the playability regions using an adaptive sampling scheme that minimizes the number of necessary model evaluations by selecting the important parameter configurations to test. The approach is applied to cases involving three player-controlled parameters: the “stiffness” of the player’s lip, described by the natural frequency of the lip oscillator; the player’s blowing strength, described by the pressure in the player’s mouth; and the at-rest lip opening, described by the rest height of the lip oscillator.

Presenting Author: Harry Mayrhofer The University of Arizona

Presenting Author Biography: Harry Mayrhofer is a graduate student in the physics department at the University of Arizona.

Authors:

Harry Mayrhofer The University of Arizona
Samy Missoum The University of Arizona
Christophe Vergez Laboratorie de Méchanique et d'Acoustique