Identification of lip-parameters associated to different trumpets using constrained continuation

Abstract

The relationship between the player's global perception and acoustical characteristics of a musical instrument is very complex but nevertheless an important topic of interest for musical instrument makers. One of our hypotheses is that some aspects of the biomechanical control required by the player to achieve a given task (embouchure adjustments for instance) can contribute to explain the player's perception of an instrument: for an exact same musical task, if two instruments require different lip adjustments, there are likely to be perceived as different in terms of "blowing feeling" by the player. In this study we follow this idea in order to compare numerically two trumpets. Our strategy is based on the application of constrained continuation where the physical model studied is enriched with target trajectories for some of the output variables, and where two lip parameters of the physical model are relaxed. These constraints are established from playing measurements on one player and two trumpets. The evolutions of the relaxed parameters along the solution branches are then compared between the two instruments, and confronted to the blowing feeling reported by the player.