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Numerical simulation of woodwind dynamics:investigating nonlinear sound production behavior in saxophone-like instruments

Abstract : This work links features of sound production in woodwinds to the action of the musician, through numerical simulation of a physical model supported by experiments. It focuses on the nonlinear dynamics of the model, as one of the missing links between the acoustical features of the instrument, and how easy it is to play. The results are intended to facilitate future instrument development endeavors that would use a physical model as a virtual prototype. Two fundamentally different simulation methods are used conjointly to provide a robust understanding of the mechanisms governing sound production in woodwind instruments. On the one hand, time-domain synthesis allows large-scale direct investigations into the transients and steady-state oscillations, with the advantage of being interpretable directly in terms of musician actions. On the other hand, the Harmonic Balance Method associated with continuation (Asymptotic Numerical Method) provides a precise, in depth investigation of stable and unstable periodic solution branches throughout the parameter space. This method highlights bifurcations which signal the apparition or disappearance of oscillation regimes: Neimark-Sacker, period doubling, Hopf and fold. These last two are followed by continuation, in codimension two. Experimental results constitute the initial foundation and final validation of numerical simulations. Input impedance measurements allow simulations to be based on the acoustical parameters of real saxophones. This justifies subsequent comparisons of simulated dynamics with phenomena observed in playing situation using an instrumented saxophone mouthpiece. Archetypes of oscillating regimes are explored and connected to musician control parameters, such as the blowing pressure and action on the reed. The so-called standard, inverted and double two-step regimes are revealed and analyzed both experimentally and numerically. The influence of geometrical and modal parameters of the resonator on the instrument’s dynamics is detailed. The dynamic system is characterized globally, by mapping out its oscillation thresholds and regime production regions. Maps representing types of oscillation regimes produced depending on the control parameters constitutes a more detailed way to compare two instruments or fingerings. They are applied to compare two alto saxophones, demonstrate the effect of the register key, and assess sound production on a virtual prototype of bicylindrical resonator. This virtual prototype's geometry is optimized based on the input impedance of a saxophone, using a differentiable cost function well-suited to gradient-based optimization procedures. A more fundamental investigation of woodwind dynamics tackles multistability (different regime being stable for the same control parameter values), which is shown to be ubiquitous on saxophones. The initial conditions leading to different regimes are grouped as attraction basins. Multistability is also characterized in a more musically interpretable way, via a variable blowing pressure transient affecting the obtained steady-state regime. These considerations are applied to improve the regime maps and avoid bias that may be due to overlooking multistable regimes. Improved regime maps are used to demonstrate that the ratio between the first two resonance frequencies leading to the most first register production is not exactly two, but a slightly higher value. The results of this dissertation and the related analysis tools further the understanding of a complex dynamic, that of the saxophone, and open the door to quantitative studies and direct application in virtual prototyping.
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Contributor : Tom Colinot <>
Submitted on : Wednesday, January 27, 2021 - 9:16:59 AM
Last modification on : Friday, January 29, 2021 - 3:27:12 AM


  • HAL Id : tel-03122454, version 1


Tom Colinot. Numerical simulation of woodwind dynamics:investigating nonlinear sound production behavior in saxophone-like instruments. Acoustics [physics.class-ph]. Aix-Marseille Université (AMU), 2020. English. ⟨tel-03122454⟩



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