Iterated maps for clarinet-like systems

Taillard, Pierre-André; Kergomard, Jean; Laloë, Franck

doi:10.1007/s11071-010-9715-5

Cited by 21 publications

(45 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2, and with a supplementary parameter, corresponding to frequency-independent losses in the resonator. 3,4,5 Comparison with experiments shows a good agreement for the bifurcation scheme. 6 Therefore, thanks to these extremely simplified models, basic features of the sound production can be understood, while refined details of the waveform, that are important for the high frequencies and the external sound perception, cannot be predicted.…”

Section: Introductionmentioning

confidence: 56%

Idealized digital models for conical reed instruments, with focus on the internal pressure waveform

Kergomard

Guillemain

Silva

et al. 2016

The Journal of the Acoustical Society of America

Self Cite

View full text Add to dashboard Cite

Two models for the generation of self-oscillations of reed conical woodwinds are presented. They use the fewest parameters (of either the resonator or the exciter), whose influence can be quickly explored. The formulation extends iterated maps obtained for lossless cylindrical pipes without reed dynamics. It uses spherical wave variables in idealized resonators, with one parameter more than for cylinders: the missing length of the cone. The mouthpiece volume equals that of the missing part of the cone, and is implemented as either a cylindrical pipe (first model) or a lumped element (second model). Only the first model adds a length parameter for the mouthpiece and leads to the solving of an implicit equation. For the second model, any shape of nonlinear characteristic can be directly considered. The complex characteristics impedance for spherical waves requires sampling times smaller than a round trip in the resonator. The convergence of the two models is shown when the length of the cylindrical mouthpiece tends to zero. The waveform is in semiquantitative agreement with experiment. It is concluded that the oscillations of the positive episode of the mouthpiece pressure are related to the length of the missing part, not to the reed dynamics.

show abstract

Section: Introductionmentioning

confidence: 56%

Idealized digital models for conical reed instruments, with focus on the internal pressure waveform

Kergomard

Guillemain

Silva

et al. 2016

The Journal of the Acoustical Society of America

Self Cite

View full text Add to dashboard Cite

show abstract

“…However for clarinet-like instrument, a negative flow rate is usually not encountered (see Ref. [10]). The simplest control parameters that can be defined with such a model are the mouth pressure p m and the reed channel opening area S c at rest.…”

Section: Reed and Mouthpiece Coupled To The Resonatormentioning

confidence: 99%

The effect of the size of the opening on the acoustic power radiated by a reed woodwind instrument

Guilloteau

Guillemain

Kergomard

et al. 2015

Journal of Sound and Vibration

View full text Add to dashboard Cite

a b s t r a c tFor a given note, the maker of woodwind instruments can choose between different sizes for the toneholes under the condition that the location is appropriate. The present paper aims at analyzing the consequences of this choice on the power radiated by a hole, which depends on the coupling between the acoustic resonator and the excitation mechanism of the self-sustained oscillation, thus on the blowing pressure. For that purpose a simplified reed instrument is investigated, with a cylindrical pipe and a unique orifice at the pipe termination. The orifice diameter was varied between the pipe diameter and a size such that the instrument did not play. The pipe length was in each case adjusted to keep the resonance frequency constant. A simple analytical model predicts that, for a given mouth pressure of the instrumentalist, the radiated power does not depend on the size of the hole if it is wide enough and if resonator losses are ignored. Numerical solution of a model including losses confirms this result: the difference in radiated power between two diaphragm sizes remains smaller than the difference obtained if the radiated power would be proportional to the orifice cross section area. This is confirmed by experiments using an artificial mouth, but the results show that the linear losses are underestimated, and that significant nonlinear losses occur. The measurements are limited to the acoustic pressure at a given distance of the orifice. Experiments also show that rounding edges of the orifice reduces nonlinear losses resulting in an increase of the power radiated and of the extinction threshold, and resulting in a larger dynamical range.

show abstract

“…Due to the non-linear nature of the system, the oscillation cannot grow forever, of course, and it stabilises in a periodic solution. (---) Exponential envelope deduced from the function (6). The following parameters are used: γ = 0.42 (constant) and ζ = 0.5.…”

Section: Local Stability Of Non-oscillating Solutionsmentioning

confidence: 99%

“…In a static-parameter context, the oscillation would eventually stabilise in an oscillatory regime between values given by the 2-branch part of the static bifurcation diagram (an extensive discussion is given by Taillard et al [6]).…”

Section: Local Stability Of Non-oscillating Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Determination of the Attack Transient in a Clarinet With Time-Varying Blowing Pressure

Almeida¹,

Bergeot²,

Vergez³

et al. 2015

Acta Acustica united with Acustica

View full text Add to dashboard Cite

This article uses a basic model of a reed instrument, known as the lossless Raman model, to determine analytically the envelope of the sound produced by the clarinet when the mouth pressure is increased gradually to start a note from silence. Using results from dynamic bifurcation theory, a prediction of the amplitude of the sound as a function of time is given based on a few parameters quantifying the time evolution of mouth pressure. As in previous uses of this model, the predictions are expected to be qualitatively consistent with simulations using the Raman model, and observations of real instruments. Model simulations for slowly variable parameters require very high precisions of computation. Similarly, any real system, even if close to the model would be affected by noise. In order to describe the influence of noise, a modified model is developed that includes a stochastic variation of the parameters. Both ideal and stochastic models are shown to attain a minimal amplitude at the static oscillation threshold. Beyond this point, the amplitude of the oscillations increases exponentially, although some time is required before the oscillations can be observed at the "dynamic oscillation threshold". The effect of a sudden interruption of the growth of the mouth pressure is also studied, showing that it usually triggers a faster growth of the oscillations.

show abstract

Iterated maps for clarinet-like systems

Cited by 21 publications

References 18 publications

Idealized digital models for conical reed instruments, with focus on the internal pressure waveform

Idealized digital models for conical reed instruments, with focus on the internal pressure waveform

The effect of the size of the opening on the acoustic power radiated by a reed woodwind instrument

Analytical Determination of the Attack Transient in a Clarinet With Time-Varying Blowing Pressure

Contact Info

Product

Resources

About