Cartography of a trombone sound regimes using a python implementation of a Support Vector Machine-based Explicit Design Space Decomposition

¹ Laboratoire Manceau de Mathématiques, Le Mans, France
² Laboratoire d’Acoustique de l’Université du Mans (LAUM), UMR CNRS 6613, Institut d’Acoustique – Graduate School (IA-GS), CNRS, Le Mans Université, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 1 April 2025
Accepted: 25 July 2025

Abstract

Self-sustained musical instruments are non-linear dynamical systems that can produce a large number of sound regimes, whose existence and stability depend on both design and a number of control parameters. Determining which regimes exist for given parameters and which one is reached in practice when several stable regimes coexist for identical parameters is of importance from both the making and playing points of view. In this article, we consider a physical model of a trombone, and produce cartographies of the sound regimes in the space of playing parameters associated to the musician, namely the blowing pressure and the lips parameters. In practice, boundaries of the parameters space regions corresponding to different regimes are defined explicitly using Support Vector Machines. This approach is implemented in an open-source python library pyEDSD which is presented here. Importantly, the method is not specific to the considered application and the library may be of interest for other applications, in particular in engineering.