arXiv subjects

Tom Colinot

Publications and source records attributed to Tom Colinot.

7 recordsLinked to original sources

arXiv2026

How localized nonlinear losses condition the acoustical design of a self-sustained oscillator: the clarinet and its register hole

The register tube marks the invention of the clarinet in the early eighteenth century, tripling the range of its ancestor, the chalumeau, and giving it the widest range among wind instruments. Opening this narrow tube causes the fundamental frequency of the played note to increase by a factor of three, from the first to the second register of the resonator. The geometry and location of the register hole condition not only this mode selection mechanism, but also the global tuning of the second register. However, existing self-sustained nonlinear models of reed instruments fail to predict whether a register transition can occur, limiting optimization of the register hole geometry. Here, we introduce a sparse self-oscillating clarinet model that includes localized nonlinear acoustic losses in the register hole. This nonlinear mechanism is shown to be necessary to reproduce register transitions observed experimentally. Using systematic exploration of the control and design parameter spaces, we identify combinations of register hole diameter, position, and chimney length that ensure reliable register transitions. We show that the competing demands of playability and tuning are only satisfied by a long and narrow tube. Our findings provide a predictive tool for instrument making, assisting manufacturers in refining clarinets as well as other reed instruments, including oboes, bassoons, and saxophones.

physics.class-ph↗

arXiv2025

Influence of the basins of attractions in the register jumps of the clarinet

When playing the clarinet, opening the register hole allows for a transition from the first to the second register, producing a twelfth interval. On an artificial mouth, the blowing pressure range where the second register remains stable can be determined by gradually varying the blowing pressure while keeping the register hole open. However, when the register hole is opened while the instrument is already producing the first register, the range of blowing pressures that lead to a stable second register is narrower than the full stability zone of the second register. This phenomenon is investigated numerically by performing multiple hole openings at different times for each blowing pressure value. The evolution of the probability of reaching the second register is computed, and its relationship with the structure of the basin of attraction of the second register is analyzed.

physics.class-ph↗

arXiv2025

Geometric sensitivity of modal parameters in wind instrument models: a case study on saxophone intonation

The Transfer Matrix Method is a practical approach for modeling plane wave propagation in one-dimensional waveguides. Its simplicity makes it especially attractive for accounting for viscothermal losses, enabling realistic simulations of complex waveguides such as wind instruments. Another strength of this method lies in its fully analytical formulation of wave propagation. Modal parameters naturally arise as by-products of the model, obtained by numerically solving analytical expressions. In this work, the analytical potential of the method is extended by deriving the sensitivity of modal parameters to changes in the geometry of the resonator. These analytical gradients are applied in the context of wind instrument design. A simplified model of a soprano saxophone is used to investigate how octave harmonicity can be optimized through small geometric adjustments. The proposed approach enables predictive adjustments of geometry and offers valuable insight for both sound synthesis and instrument making.

physics.class-ph↗

arXiv2025

Register jumps on the clarinet: numerical and in-vitro investigation into basins of attraction and phase-tipping

When playing the clarinet, opening the register hole allows for a transition from the first to the second register, producing a twelfth interval. On an artificial player system, the blowing pressure range where the second register remains stable can be determined by gradually varying the blowing pressure while keeping the register hole open. However, when the register hole is opened while the instrument is already producing the first register, the range of blowing pressures that lead to a stable second register is narrower than the full stability zone of the second register. This phenomenon is investigated numerically by performing multiple hole openings at different times, for various values of the blowing pressure and the embouchure parameter. In some narrow regions of the control parameters space, the success of a register transition depends on the phase at which the hole is opened. This illustrates an instance of phase-tipping, where the limit cycle of the closed-hole regime may intersect multiple basins of attraction associated with the open-hole regimes. Furthermore, to assess the robustness of the basins of attraction, random noise is introduced to the control parameters before the register hole is opened. Results indicate that the equilibrium regime is more robust to noise than the other oscillating regimes. Finally, long-lasting transient quasiperiodics are investigated. The phase at which the hole is opened influences both the transient duration and the resulting stable regime.

physics.class-ph↗

arXiv2024

Oscillation threshold of a Raman clarinet with localized nonlinear losses at the open end

Localized nonlinear losses are taken into account in a simple Raman clarinet model.The complete system is expressed as an iterated map, enabling to study the stability of the different playing regimes. A parametric study is carried out with respect to three major parameters: blowing pressure, embouchure and nonlinear losses coefficient.The model exhibits the well-known effect of reducing the maximum blowing pressure until the oscillations stop (extinction threshold) when nonlinear losses increase.Furthermore, the stability analysis also shows that increasing nonlinear losses increases the minimal blowing pressure for which the oscillations start (oscillation threshold).

physics.class-ph↗

arXiv2024

Second register production on the clarinet: nonlinear losses in the register hole as the decisive physical phenomenon

This study investigates the role of localized nonlinear losses in the register hole on the production of second-register notes. First, an experiment is conducted to study the ability of a register hole to produce second register. A cylindrical tube is drilled with holes of increasing diameter. Five are at the same level as the register hole of a B-flat clarinet, and five are at the same level as the thumb hole. Participant clarinetists are then asked to play with constant control parameters. At the beginning of each measurement, all holes are closed. The operator then opens randomly one of the ten holes.The resulting register is noted. The experiment is replicated numerically by time integration of two different models. The first is the state-of-the-art model based on the modal decomposition of the input impedance of the resonator. The second accounts for localized nonlinear losses in the register hole, through the model from Dalmont and Nederveen (2002). These losses are handled through a variable modal coefficients method. For the first model, simulations never produce second register, for any of the open holes. For the second, the proportion of second-register production is close to the experiment for upstream holes, but remains at zero for downstream holes.

physics.class-ph↗

arXiv2023

Amplitude-dependent modal coefficients accounting for localized nonlinear losses in a time-domain integration of woodwind model

This article develops the design of a sound synthesis model of a woodwind instrument by modal decomposition of the input impedance, taking into account viscothermal losses as well as localized nonlinear losses at the end of the resonator. This formalism has already been applied by Diab et al. (2022) to the study of forced systems. It is now implemented for self-oscillating systems. The employed method extends the denition of the input impedance to the nonlinear domain by adding a dependance on the RMS acoustic velocity at a geometric discontinuity. The poles and residuals resulting from the modal decomposition are interpolated as a function of this velocity. Thus, the pressure-ow relation dened by the resonator is completed by new equations which account for the dependence with the velocity at the end of the tube. To assess the ability of the model to reproduce a real phenomenon, comparisons with the experimental results of Atig et al. (2004) and Dalmont et al. (2007) were carried out. Simulations show that the model reproduces these experimental results qualitatively and quantitatively.

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