Influence of the "Ghost Reed" Simplification on the Bifurcation Diagram of a Saxophone Model

Colinot, Tom; Guillot, Louis; Vergez, Christophe; Guillemain, Philippe; Doc, Jean-Baptiste; Cochelin, Bruno

doi:10.3813/aaa.919409

Cited by 16 publications

(13 citation statements)

References 11 publications

(15 reference statements)

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“…where h 0 is given in Table 1, x 0 ¼ Im s 4 ð Þ=4 is the quarter of the fourth resonance angular frequency of the resonator (chosen as so because the fourth resonance frequency appears to be quite similar between instruments of the same tube length, such as a trombone and a euphonium for instance), so that p 0 can be defined in a similar way as the closure pressure for woodwind instruments [18]:…”

Section: Conflict Of Interestmentioning

confidence: 99%

Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments

et al. 2021

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In this study, an acoustic resonator – a bass brass instrument – with multiple resonances coupled to an exciter – the player’s lips – with one resonance is modelled by a multidimensional dynamical system, and studied using a continuation and bifurcation software. Bifurcation diagrams are explored with respect to the blowing pressure, in particular with focus on the minimal blowing pressure allowing stable periodic oscillations and the associated frequency. The behaviour of the instrument is first studied close to a (non oscillating) equilibrium using linear stability analysis. This allows to determine the conditions at which an equilibrium destabilises and as such where oscillating regimes can emerge (corresponding to a sound production). This approach is useful to characterise the ease of playing of a brass instrument, which is assumed here to be related – as a first approximation – to the linear threshold pressure. In particular, the lower the threshold pressure, the lower the physical effort the player has to make to play a note [The Science of Brass Instruments. Springer-Verlag, 2021]. Cases are highlighted where periodic solutions in the bifurcation diagrams are reached for blowing pressures below the value given by the linear stability analysis. Thus, bifurcation diagrams allow a more in-depth analysis. Particular attention is devoted to the first playing regime of bass brass instruments (the pedal note and the ghost note of a tuba in particular), whose behaviour qualitatively differs from a trombone to a euphonium for instance.

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Section: Conflict Of Interestmentioning

confidence: 99%

Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments

et al. 2021

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“…The harmonic balance method (Sect. 2.3) can also be applied to this model to study its dynamic behavior, for instance to quantify the effect of neglecting reed contact [29].…”

Section: Numerical Simulation Framework 21 Saxophone Modelmentioning

confidence: 99%

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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“…The choice of an appropriate frequency range will be discussed in Section 3.4. Matrix M is written as a block matrix for compactness in equation (8). As indicated by equation ( 9), the rows of each block correspond to the frequencies contained in m, whereas the columns correspond to the modal components.…”

Section: Estimation Of Modal Amplitudesmentioning

confidence: 99%

“…The input impedance of a wind instrument can be mathematically represented using a modal expansion [1]. By carrying out modal identification from a measured input impedance, it is therefore possible to model the resonator of an existing instrument by a set of ordinary differential equations which can be directly plugged into numerical methods for analysing the emergence of self-sustained oscillations, such as time-domain simulations [2], linear stability analysis [3][4][5] or numerical continuation [6][7][8]. This approach is facilitated by the fact that well-established experimental devices and procedures exist for measuring the input impedance of wind instruments [9,10].…”

Section: Introductionmentioning

confidence: 99%

Peak-picking identification technique for modal expansion of input impedance of brass instruments

Ablitzer

2021

Acta Acust.

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The paper presents a method to obtain the modal expansion of the measured input impedance of a brass instrument. The method operates as a peak-picking procedure, which makes it particularly intuitive for users who are not experts in modal analysis. To bypass the limitation of usual peak-picking approaches, which are valid only for well separated resonances, the present method is based on a semi-local optimization problem. It consists in adjusting the frequency and damping of one mode at a time while taking into account the presence of all other modes in the basis. The practical application of the method involves four elementary actions, which can be chained in different ways to progressively approximate a measured input impedance. This procedure is illustrated through the approximation of the input impedance of a bass trombone. The supervised nature of the method allows the user to favour modes that have a physical meaning, i.e. that can be associated with a resonance peak. A single spurious mode can however be deliberately introduced to approximate the input impedance curve beyond the last visible peak. The method applies directly to the frequency-domain data provided by an impedance sensor and does not require any preprocessing. Nevertheless, it is fairly robust to noisy data. Since the method allows a reconstruction of the input impedance using either complex modes or real modes, results obtained with each approximation are critically compared.

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Influence of the "Ghost Reed" Simplification on the Bifurcation Diagram of a Saxophone Model

Cited by 16 publications

References 11 publications

Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments

Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments

Multistability of saxophone oscillation regimes and its influence on sound production

Peak-picking identification technique for modal expansion of input impedance of brass instruments

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