Woodwind instrument design optimization based on impedance characteristics with geometric constraints

Augustin Ernoult (1) , Christophe Vergez (2) , Samy Missoum (3) , Philippe Guillemain (4) , Michael Jousserand (5)

1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
2 Sons
3 University of Arizona
4 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
5 Buffet Group

Computational optimization algorithms coupled with acoustic models of wind instruments provide instrument makers an opportunity to explore new designs. Specifically, they give the possibility to automatically find geometries exhibiting desired resonance characteristics. In this paper, the design optimization of woodwind instruments with complex geometrical features (e.g., non-cylindrical bore profile and side holes with various radii and chimney heights) is investigated. Optimal geometric characteristics are searched to obtain specific target frequencies or amplitude characteristics. However, woodwind instruments exhibit complex input impedance whose features might change drastically for a small variation of the geometry, thus hampering gradient-based optimization. For this reason, this paper introduces new formulations of the impedance characteristics (resonance frequencies and amplitudes). The approach is applied to an illustrative instrument subjected to geometric constraints similar to the ones encountered by manufacturers (a key-less pentatonic clarinet with two-registers). Three optimization problems are considered, demonstrating a strategy to simultaneously adjust several impedance characteristics on all the fingerings.

Mots clés: Musical instrument design; Impedance characteristics; Woodwind instruments; Bore profile optimization; Musical acoustics

Domaines: Acoustique [physics.class-ph]

Augustin Ernoult, Christophe Vergez, Samy Missoum, Philippe Guillemain, Michael Jousserand. Woodwind instrument design optimization based on impedance characteristics with geometric constraints. 2020. ⟨hal-02479433v2⟩