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The internal and external spectra of woodwind reed instruments are partially determined by the tonehole lattice cutoff and reed resonance frequencies. Because they can impact the spectrum in similar ways, a study of one without accounting for the other risks incomplete or false conclusions. Here, the dual effects of the cutoff and reed resonance frequencies are investigated using digital synthesis with clarinet-like academic resonators. It is shown that the odd and even harmonics have similar amplitudes at and above the cutoff frequency or reed resonance frequency, whichever is lowest. However, because the resonators radiate efficiently at the cutoff, it has the additional role of reinforcing the amplitude of both the odd and even harmonics in the external spectrum. The spectra are analyzed using the single value descriptors playing frequency, spectral centroid (SC), odd/even ratio (OER), and brightness as a function of the musician mouth pressure. Higher reed resonances correspond to higher values for all descriptors. The OER and brightness increase with resonator cutoff frequency, whereas the SC exhibits more complicated trends. The reed resonance has a larger impact on the "playing condition oscillation threshold," implying that it may have a more important role in sustaining auto-oscillation.

Computational optimization algorithms coupled with acoustic models of wind instruments provide instrument makers with an opportunity to explore new designs. Specifically, they enable the automatic discovery of geometries exhibiting desired resonance characteristics. In this paper, the design optimization of woodwind instruments with complex geometrical features (e.g., non-cylindrical bore profile and side holes with various radii and chimney heights) is investigated. Optimal geometric designs are searched so that their acoustic input impedance has peaks with specific target frequencies and amplitudes. However, woodwind instruments exhibit complex input impedance whose features, such as resonances, might have non-smooth evolution with respect to design variables, thus hampering gradient-based optimization. For this reason, this paper introduces new formulations of the impedance characteristics (resonance frequencies and amplitudes) using a regularized unwrapped angle of the reflection function. The approach is applied to an illustrative instrument subjected to geometric constraints similar to the ones encountered by manufacturers (a key-less pentatonic clarinet with two-registers). Three optimization problems are considered, demonstrating a strategy to simultaneously adjust several impedance characteristics on all fingerings.

A saxophone mouthpiece fitted with sensors is used to observe the oscillation of a saxophone reed, as well as the internal acoustic pressure, allowing to identify qualitatively different oscillating regimes. In addition to the standard two-step regime, where the reed channel successively opens and closes once during an oscillation cycle, the experimental results show regimes featuring two closures of the reed channel per cycle, as well as inverted regimes, where the reed closure episode is longer than the open episode. These regimes are well-known on bowed string instruments and some were already described on the Uilleann pipes. A simple saxophone model using measured input impedance is studied with the harmonic balance method, and is shown to reproduce the same two-step regimes. The experiment shows qualitative agreement with the simulation: in both cases, the various regimes appear in the same order as the blowing pressure is increased. Similar results are obtained with other values of the reed opening control parameter, as well as another fingering.

When designing a wind instrument such as a clarinet, it can be useful to be able to predict the playing frequencies. This paper presents an analytical method to deduce these playing frequencies using the input impedance curve. Specifically there are two control parameters that have a significant influence on the playing frequency, the blowing pressure and reed opening. Four effects are known to alter the playing frequency and are examined separately: the flow rate due to the reed motion, the reed dynamics, the inharmonicity of the resonator, and the temperature gradient within the clarinet. The resulting playing frequencies for the first register of a particular professional level clarinet are found using the analytical formulas presented in this paper. The analytical predictions are then compared to numerically simulated results to validate the prediction accuracy. The main conclusion is that in general the playing frequency decreases above the oscillation threshold because of inharmonicity, then increases above the beating reed regime threshold because of the decrease of the flow rate effect.

A simplified physical model mainly devoted to the reproduction of some transients of clarinet-like instruments is presented. From time-frequency analyses of natural clarinet sounds, it is shown that the vocal tract can play a significant role in some attacks as well as in the permanent regime. The model proposed consists in supplying a pressure source at the entrance of a cylindrical bore attached to the mouthpiece, allowing one to reach various vocal tract configurations. For real-time synthesis purposes, a digital scheme solving the physical problem is proposed. It is shown that this synthesis model is able to reproduce some of the complex features observed during the attacks of the natural sounds analyzed, as well as known effects of the vocal tract in permanent regime.

A real-time synthesis model of wind instruments sounds, based upon a classical physical model, is presented. The physical model describes the nonlinear coupling between the resonator and the excitor through the Bernoulli equation. While most synthesis methods use wave variables and their sampled equivalent in order to describe the resonator of the instrument, the synthesis model presented here uses sampled versions of the physical variables all along the synthesis process, and hence constitutes a straightforward digital transposition of each part of the physical model. Moreover, the resolution scheme of the problem (i.e., the synthesis algorithm) is explicit and all the parameters of the algorithm are expressed analytically as functions of the physical and the control parameters.