Sound production on a “coaxial saxophone”

Doc, Jean-Baptiste; Vergez, Christophe; Guillemain, Philippe; Kergomard, Jean

doi:10.1121/1.4967368

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…where The bicylindrical resonator, as defined in [21], is composed of a cylindrical mouthpiece (i.e. a mouthpiece with cylindrical chamber) followed by the parallel association of two cylinders (see figure 1).…”

Section: Introductionmentioning

confidence: 99%

“…The influence of the long cylinder on the 211 radiation of the short one is neglected, which corre-212 sponds to a plane-wave approximation. A compar-213 ison with a flanged impedance radiation model [24] 214 for the output of the short cylinder yields almost no impedance models of the bicylindrical resonator are 217 validated by comparison with impedance measure-218ment carried out on a bicylindrical resonator prototype in[21].…”

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confidence: 99%

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Numerical Optimization of a Bicylindrical Resonator Impedance: Differences and Common Features Between a Saxophone Resonator and a Bicylindrical Resonator

Colinot¹,

Guillemain²,

Doc³

et al. 2019

Acta Acustica united with Acustica

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This paper explores the analogy between a saxophone resonator and a bicylindrical resonator, sometimes called transverse saxophone or cylindrical saxophone. The dimensions of a bicylindrical resonator are optimized numerically to approximate a saxophone impedance. The target is the impedance measured on an usual saxophone. A classical gradient-based non-linear least-square fit function is used. Several cost functions corresponding to distances to the target impedance are assessed, according to their influence on the optimal geometry. Compromises appear between the frequency regions depending on the cost function. It is shown that the chosen cost functions are differentiable and locally convex. The convexity region contains the initial geometrical dimensions obtained by crude approximation of the first resonance frequency of the target. One optimal geometry is submitted to further analysis using descriptors of the impedance. Its deviations from the target saxophone are put into perspective with the discrepancies between the target saxophone and a saxophone from a different manufacture. Descriptors such as harmonicity or impedance peak ratio set the bicylindrical resonator apart from saxophone resonators, despite a good agreement of the resonance frequencies. Therefore, a reed instrument with a bicylindrical resonator could be tuned to produce the same notes as a saxophone, but due to differences in the intrinsic characteristics of the resonator, it should be considered not as a saxophone but as a distinct instrument.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Numerical Optimization of a Bicylindrical Resonator Impedance: Differences and Common Features Between a Saxophone Resonator and a Bicylindrical Resonator

Colinot¹,

Guillemain²,

Doc³

et al. 2019

Acta Acustica united with Acustica

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“…The simplest model, based upon the analogy with bowed string instruments, was studied by many authors [6,7,8,9,10,11,12], and a result is the waveshape approximation of the mouthpiece pressure by a rectangle signal, i.e., the waveshape of the ideal Helmholtz motion. Formerly, some authors explained that an approximation of the natural frequency of reed conical instruments is equal to that of an "openopen" cylinder whose length is the length of the truncated cone extended to its apex [13,14,15].…”

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confidence: 99%

“…The playing frequencies are in the range [209Hz, 438Hz] for c = 340 ms −1 . The issue of the regime stability is complicated, and is out of the scope of the present paper (see[9,12,27]).…”

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confidence: 99%

Role of the Resonator Geometry on the Pressure Spectrum of Reed Conical Instruments

Kergomard¹,

Guillemain²,

Sánchez³

et al. 2019

Acta Acustica united with Acustica

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Spectra of musical instruments exhibit formants or 2 anti-formants which are important characteristics of 3 the sounds produced. In the present paper, it is shown 4 that anti-formants exist in the spectrum of the mouth-5 piece pressure of saxophones. Their frequencies are 6 not far but slightly higher than the natural frequen-7 cies of the truncated part of the cone. To determine 8 these frequencies, a first step is the numerical deter-9 mination of the playing frequency by using a simple 10 oscillation model. An analytical analysis exhibits the 11 role of the inharmonicity due to the cone truncation 12 and the mouthpiece. A second step is the study of 13 the input impedance values at the harmonics of the 14 playing frequency. As a result, the consideration of 15 the playing frequency for each note explains why the 16 anti-formants are wider than those resulting from a 17 Helmholtz motion observed for a bowed string. Fi-18 nally numerical results for the mouthpiece spectrum 19 are compared to experiments for three saxophones 20 (soprano, alto and baritone). It is shown that when 21 scaled by the length of the missing cone, the anti-22 formant frequencies in the mouthpiece are very similar 23 for the three instruments. The frequencies given by 24 the model are close to the natural frequencies of the 25 missing cone length, but slightly higher. Finally, the 26 numerical computation shows that anti-formants and 27 formants might be found in the radiated pressure. 28 85 spectively. 86 It is still the only model that yields analytical ex-87 pressions for the sound produced, and therefore it is 88 used as a reference for the present study. In a pa-89 per written by some of the present authors, it was 90 shown that a simple numerical model can largely im-91 prove the model of the Helmholtz motion [16]. We call 92 it the "Reed-Truncated-Cone" model (RTC model). 93 The difference between the two models lies in the res-94 onator model. Example of waveshapes obtained with 95 the two models are shown in Fig. 2. Using the RTC 96 model for the present investigation on the spectrum, 97 the paper aims at further understanding of the exis-98 tence of formants or anti-formants in the mouthpiece 99 pressure spectrum, and, to some extent, of the exter-100 nal pressure. The computation is done ab initio in the 101 time domain. 102 The study is limited to the first register, which re-103 sembles the Helmholtz motion (periodic regime, one 104 positive pressure and one negative pressure episodes). 105 The RTC model is based upon the observation that 106 in practice the mouthpiece volume is approximately 107 equal to that of the missing cone [17], entailing a weak 108 0, which depend on the note; ii) the solutions of 231 sin(kx 1) = 0, which do not depend on the note. Fig. 232 3 shows an example of input impedance curve. For 233 this figure, realistic visco-thermal losses (for an aver-234 age cone radius) have been taken into account in Eq.

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Improved multimodal formulation of the wave propagation in a 3D waveguide with varying cross-section and curvature

Guennoc

Doc

Félix

2021

The Journal of the Acoustical Society of America

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An efficient method is proposed to solve the multimodal wave propagation within a three-dimensional waveguide bounded by a hard wall with varying cross section and curvature. This is achieved by first turning the original problem, in a complex-shaped waveguide, into a cylindrical waveguide with unit radius, by means of an adapted and flexible geometrical transformation. Then supplementary modes are defined to enrich the standard modal basis that is usually considered in such methods and to help restore the right boundary condition. It is shown through various numerical applications that the introduction of these supplementary modes, whatever the complexity of the waveguide geometry, significantly enhances the multimodal method, notably by increasing its convergence rate, whether one's aim is to solve the wavefield or the scattering problem.

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Sound production on a “coaxial saxophone”

Cited by 3 publications

References 11 publications

Numerical Optimization of a Bicylindrical Resonator Impedance: Differences and Common Features Between a Saxophone Resonator and a Bicylindrical Resonator

Numerical Optimization of a Bicylindrical Resonator Impedance: Differences and Common Features Between a Saxophone Resonator and a Bicylindrical Resonator

Role of the Resonator Geometry on the Pressure Spectrum of Reed Conical Instruments

Improved multimodal formulation of the wave propagation in a 3D waveguide with varying cross-section and curvature

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