Jean-Baptiste Doc

A Minimal Model of a Single-Reed Instrument Producing Quasi-Periodic Sounds

Summary Single-reed instruments can produce multiphonic sounds when they generate quasi-periodic oscillations. The aim of this article is to identify a minimal model of a single reed-instrument producing quasi-periodic oscillations. To better understand the influence of model parameters on the production of quasi-periodic regimes, the mapping between parameters and quasi-periodic regimes is explicitly identified using a support vector machine (SVM) classifier. SVMs enable the construction of boundaries between quasi-periodic and periodic regimes that are explicitly defined in terms of the parameters. Results and conclusions obtained from the numerical model are compared to published experiments related to t he the production of quasi-periodic oscillations with an alto saxophone. This qualitative comparison highlights the influence of key parameters on the production of multiphonic sounds.

Oscillation regimes produced by an alto saxophone: Influence of the control parameters and the bore inharmonicity

The aim of this work is to highlight experimentally how inharmonicity of the bore resonance frequencies of an alto saxophone influences the nature of the oscillation regimes. A variable volume branching from the neck of an alto sax at an appropriate position allows one to change the frequency of the first resonance independently from the second. A blowing machine with artificial lips is used to make the saxophone play while controlling independently the control parameters: the blowing pressure and an embouchure parameter. Values of these parameters are estimated experimentally through the measurement of the nonlinear characteristics linking the mean air flow blown into the instrument to the static pressure difference across the reed. Experiments with different values of the control parameters as well as of the inharmonicity produce different kinds of oscillation regimes. These regimes are categorized through the analysis of the pressure signal inside the mouthpiece. The resulting maps demonstrate that the emergence of quasi-periodic regimes, and their extent, depend on the level of inharmonicity, but also on the values of the control parameters. Periodic regimes playable by choosing appropriate values of the control parameters also differ according to the level of inharmonicity, a higher inharmonicity facilitating the emergence of the third register.

Three-dimensional parabolic equation model for low frequency sound propagation in irregular urban canyons

A three-dimensional wide-angle parabolic equation (3DPE) is used to model low frequency sound propagation in irregular urban canyons at low computational cost. This one-way wave equation is solved using the Alternating Direction Implicit method. A finite difference scheme adapted to the geometry of the urban environment is then developed. Abrupt variations of the street width are treated as a single scattering problem using the Kirchhoff approximation. Numerical results are compared with experimental data obtained on a scale model of a street. Comparisons show the ability of the 3DPE model to provide reliable transmitted fields even for large irregularities.

Coarse-grid computation of the one-way propagation of coupled modes in a varying cross-section waveguide.

A one-way approximation is investigated for the computation of wave propagation in varying cross-section waveguides. The proposed method derives as a basic approximation of the extensively studied multimodal admittance method. When integrated with a Magnus scheme, this matrix one-way equation exhibits an unexpected behavior, as the deviation from the exact solution is minimum when only two discretization points per wavelength are taken. This peculiar property makes this method efficient to compute the wave propagation for a large variety of geometries, beyond the initially stated framework of weakly non-uniform waveguides.

Explicit mapping of acoustic regimes for wind instruments

This paper proposes a methodology to map the various acoustic regimes of wind instruments. The maps can be generated in a multidimensional space consisting of design, control parameters, and initial conditions. The boundaries of the maps are obtained explicitly in terms of the parameters using a Support Vector Machine (SVM) classifier as well as a dedicated adaptive sampling scheme. The approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria. Examples of computation of the probability of occurrence of a specific acoustic regime are also provided. In addition, the approach is demonstrated on a design optimization example for optimal intonation.

Descriptive maps to illustrate the quality of a clarinet

Generally, subjective opinions and decisions are made when judging the quality of musical instruments. In an attempt to become more objective, this research presents methods to numerically and experimentally create maps, over a range of control parameters, that describe instrument behavior for a variety of different sounds features or “quality markers” (playing regime, intonation, loudness, etc.). The behavior of instruments is highly dependent on the control parameters that are adjusted by the musician. Observing this behavior as a function of one control parameter (e.g., blowing pressure) can hide diversity of the overall behavior. An isovalue quality marker can be obtained for a multitude of control parameter combinations. Using multidimensional maps, where quality markers are a function of two or more control parameters, can solve this problem. Numerically: in two dimensions, a regular discretization on a subspace of control parameters can be implemented while conserving a reasonable calculation time....