Multiple two-step oscillation regimes produced by the alto saxophone

Colinot, Tom; Guillemain, Philippe; Vergez, Christophe; Doc, Jean-Baptiste; Sánchez, P.

doi:10.1121/10.0001109

Cited by 8 publications

(8 citation statements)

References 20 publications

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“…The signal is extracted from the same blowing pressure ramp as in Figure 4, between c = 0.45 and c = 0.51 (at first occurrence of oscillation). [52] emerges. This coexistence zone is not shaded on the figure, as it could represent less of a musical issue, since double two-step regimes have roughly the same frequency as standard first register regimes.…”

Section: Overlapping Stability Zones On the Bifurcation Diagrammentioning

confidence: 98%

“…The written D] produces the heard note F]3 at 185 Hz as its first register regime. This intermediate fingering of the first register is chosen as test case because it exhibits both first and second register regimes, but no stable third register regime and few double two-step phenomena [52]. Figure 3 shows the L 2norm of the pressure signal:…”

Section: Overlapping Stability Zones On the Bifurcation Diagrammentioning

confidence: 99%

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Multistability of saxophone oscillation regimes and its influence on sound production

et al. 2021

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The lowest fingerings of the saxophone can lead to several different regimes, depending on the musician’s control and the characteristics of the instrument. This is explored in this paper through a physical model of saxophone. The harmonic balance method shows that for many combinations of musician control parameters, several regimes are stable. Time-domain synthesis is used to show how different regimes can be selected through initial conditions and the initial evolution (rising time) of the blowing pressure, which is explained by studying the attraction basin of each stable regime. These considerations are then applied to study how the produced regimes are affected by properties of the resonator. The inharmonicity between the first two resonances is varied in order to find the value leading to the best suppression of unwanted overblowing. Overlooking multistability in this description can lead to biased conclusions. Results for all the lowest fingerings show that a slightly positive inharmonicity, close to that measured on a saxophone, leads to first register oscillations for the greatest range of control parameters. A perfect harmonicity (integer ratio between the first two resonances) decreases first register production, which adds nuance to one of Benade’s guidelines for understanding sound production. Thus, this study provides some a posteriori insight into empirical design choices relative to the saxophone.

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Section: Overlapping Stability Zones On the Bifurcation Diagrammentioning

confidence: 98%

Section: Overlapping Stability Zones On the Bifurcation Diagrammentioning

confidence: 99%

Multistability of saxophone oscillation regimes and its influence on sound production

et al. 2021

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“…In musical acoustics literature, the static bifurcation point of the trivial solution is often called oscillation threshold [14]. In this "static" context, periodic solutions and their stability can be also determined using for example the harmonic balance method [18,12] or orthogonal collocation [37,19]. Control parameters are changed over time only in the very special context of time simulations, e.g.…”

Section: Introductionmentioning

confidence: 99%

Analytical prediction of delayed Hopf bifurcations in a simplified stochastic model of reed musical instruments

Bergeot

Vergez

2022

Nonlinear Dyn

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This paper investigates the dynamic behavior of a simplified single reed instrument model subject to a stochastic forcing of white noise type when one of its bifurcation parameters (the dimensionless blowing pressure) increases linearly over time and crosses the Hopf bifurcation point of its trivial equilibrium position. The stochastic slow dynamics of the model is first obtained by means of the stochastic averaging method. The resulting averaged system reduces to a non-autonomous one-dimensional Itô stochastic differential equation governing the time evolution of the mouthpiece pressure amplitude. Under relevant approximations the latter is solved analytically treating separately cases where noise can be ignored and cases where it cannot. From that, two analytical expressions of the bifurcation parameter value for which the mouthpiece pressure amplitude gets its initial value back are deduced. These special values of the bifurcation parameter characterize the effective appearance of sound in the instrument and are called deterministic dynamic bifurcation point if the noise can be neglected and stochastic dynamic bifurcation point otherwise. Finally, for illustration and validation purposes, the analytical results are compared with direct numerical integration of the model in both deterministic and stochastic situations. In each considered case, a good agreement is observed between theoretical results and numerical simulations, which validates the proposed analysis.

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“…The oscillation threshold of a clarinet as a function of model parameters has been investigated in [15]. Properties of saxophone bifurcation diagrams have been investigated in [16,17]. A bifurcation diagram based classification of different models of trumpets has been proposed in [18].…”

Section: Introductionmentioning

confidence: 99%