A Digital Synthesis Model of Double-Reed Wind Instruments
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A Digital Synthesis Model of Double-Reed Wind Instruments Ph. Guillemain Laboratoire de M´ecanique et d’Acoustique, Centre National de la Recherche Scientifique, 31 chemin Joseph-Aiguier, 13402 Marseille cedex 20, France Email: [email protected] Received 30 June 2003; Revised 29 November 2003 We present a real-time synthesis model for double-reed wind instruments based on a nonlinear physical model. One specificity of double-reed instruments, namely, the presence of a confined air jet in the embouchure, for which a physical model has been proposed recently, is included in the synthesis model. The synthesis procedure involves the use of the physical variables via a digital scheme giving the impedance relationship between pressure and flow in the time domain. Comparisons are made between the behavior of the model with and without the confined air jet in the case of a simple cylindrical bore and that of a more realistic bore, the geometry of which is an approximation of an oboe bore. Keywords and phrases: double-reed, synthesis, impedance.
1.
INTRODUCTION
The simulation of woodwind instrument sounds has been investigated for many years since the pioneer studies by Schumacher [1] on the clarinet, which did not focus on digital sound synthesis. Real-time-oriented techniques, such as the famous digital waveguide method (see, e.g., Smith [2] and V¨alim¨aki [3]) and wave digital models [4] have been introduced in order to obtain efficient digital descriptions of resonators in terms of incoming and outgoing waves, and used to simulate various wind instruments. The resonator of a clarinet can be said to be approximately cylindrical as a first approximation, and its embouchure is large enough to be compatible with simple airflow models. In double-reed instruments, such as the oboe, the resonator is not cylindrical but conical and the size of the air jet is comparable to that of the embouchure. In this case, the dissipation of the air jet is no longer free, and the jet remains confined in the embouchure, giving rise to additional aerodynamic losses. Here, we describe a real-time digital synthesis model for double-reed instruments based on one hand on a recent study by Vergez et al. [5], in which the formation of the confined air jet in the embouchure is taken into account, and on the other hand on an extension of the method presented in [6] for synthesizing the clarinet. This method avoids the need for the incoming and outgoing wave decompositions, since it deals only with the relationship between the impedance variables, which makes it easy to transpose the physical model to a synthesis model.
The physical model is first summarized in Section 2. In order to obtain the synthesis model, a suitable form of the flow model is then proposed, a dimensionless version is written and the similarities with single-reed models (see, e.g., [7]) are pointed out. The resonator model is obtained by associating several elementary impedances, and is described in terms of the acoustic pressure and flow. Section 3 presents the digital synth
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