Collisions play an important role in manyaspects of the physics of musical instruments. The striking action of ah ammer or mallet in keyboard and percussion instruments is perhaps the most important example, buto thers include reed-beating effects in wind instruments, the string/neck interaction in fretted instruments such as the guitar as well as in the sitar and the wire/membrane interaction in the snare drum. From asimulation perspective, whether the eventual goal is the validation of musical instrument models or sound synthesis, such highly nonlinear problems pose various difficulties, not the least of which is the risk of numerical instability.Inthis article, anovel finite difference time domain simulation framework for such collision problems is developed, where numerical stability follows from strict numerical energy conservation or dissipation, and where ap ower lawf ormulation for collisions is employed, as ap otential function within ap assive formulation. The power laws erves both as amodel of deformable collision, and as amathematical penalty under perfectly rigid, non-deformable collision. Va rious numerical examples, illustrating the unifying features of such methods across awide variety of systems in musical acoustics are presented, including numerical stability and energy conservation/dissipation, bounds on spurious penetration in the case of rigid collisions, as well as various aspects of musical instrument physics.

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are nonanalytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton's equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton's method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument. (Vasileios Chatziioannou), m.vanwalstijn@qub.ac.uk (Maarten van Walstijn)

Articulation on the clarinet is achieved by a combination of precise actions taking place inside the player's mouth. With the aim to analyse the effects of tonguing and blowing actions during playing, several physical variables are measured and parameters related to articulation are studied. Mouth pressure, mouthpiece pressure and reed displacement are recorded in an experiment with clarinet players to evaluate the influence of the player's actions on the selected parameters and on the sound. The results show that different combinations of tongue and blowing actions are used during performance. Portato and legato playing show constant blowing throughout the musical phrase, which varies according to the dynamic level. In portato, short tongue-reed interaction is used homogeneously among players and playing conditions. In staccato playing, where the tongue-reed contact is longer, the mouth pressure is reduced significantly between notes. Such a mouth-pressure decrease might be used to stop the note in slow staccato playing. It is hereby shown that when the note is stopped by the action of the tongue both the attack and release transients are shorter compared to the case where the vibration of the reed is stopped by a decrease of mouth pressure.

Analysis of the acoustical functioning of musical instruments invariably involves the estimation of model parameters. The broad aim of this paper is to develop methods for estimation of clarinet reed parameters that are representative of actual playing conditions. This presents various challenges because of the difficulties of measuring the directly relevant variables without interfering with the control of the instrument. An inverse modelling approach is therefore proposed, in which the equations governing the sound generation mechanism of the clarinet are employed in an optimisation procedure to determine the reed parameters from the mouthpiece pressure and volume flow signals. The underlying physical model captures most of the reed dynamics and is simple enough to be used in an inversion process. The optimisation procedure is first tested by applying it to numerically synthesised signals, and then applied to mouthpiece signals acquired during notes blown by a human player. The proposed inverse modelling approach raises the possibility of revealing information about the way in which the embouchure-related reed parameters are controlled by the player, and also facilitates physics-based resynthesis of clarinet sounds.

Previous work has demonstrated that structural vibrations of brass wind instruments can audibly affect the radiated sound. Furthermore, these broadband effects are not explainable by assuming perfect coincidence of the frequency of elliptical structural modes with air column resonances. In this work a mechanism is proposed that has the potential to explain the broadband influences of structural vibrations on acoustical characteristics such as input impedance, transfer function, and radiated sound. The proposed mechanism involves the coupling of axial bell vibrations to the internal air column. The acoustical effects of such axial bell vibrations have been studied by extending an existing transmission line model to include the effects of a parasitic flow into vibrating walls, as well as distributed sound pressure sources due to periodic volume fluctuations in a duct with oscillating boundaries. The magnitude of these influences in typical trumpet bells, as well as in a complete instrument with an unbraced loop, has been studied theoretically. The model results in predictions of input impedance and acoustical transfer function differences that are approximately 1 dB for straight instruments and significantly higher when coiled tubes are involved or when very thin brass is used.