Paper Archive

Slide-string instruments allow continuous control of pitch by articulation with a slide object whose position of contact with the string is time-varying. This paper presents a method for simulation of such articulation. Taking into account sensing and musical practice considerations, an appropriate physical model configuration is determined, which is then formulated in numerical form using a finite difference approach. The model simulates the attachment and detachment phases of slide articulation which generally involve rattling, while finger damping is modelled in a more phenomenological manner as a regionally induced time-varying damping. A stability bound for the numerical model is provided via energy analysis, which also reveals the driving power contributions of the separate articulatory sources. The approach is exemplified with simulations of slide articulatory gestures that involve glissando, vibrato and finger damping.

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In physical modelling synthesis, articulation and tuning are effected via time-variation in one or more parameters. Adopting hammered strings as a test case, this paper develops extended forms of such control, proposing a numerical formulation that affords online adjustment of each of its scaled-form parameters, including those featuring in the one-sided power law for modelling hammerstring collisions. Starting from a modally-expanded representation of the string, an explicit scheme is constructed based on quadratising the contact energy. Compared to the case of time-invariant contact parameters, updating the scheme’s state variables relies on the evaluation of two additional analytic partial derivatives of the auxiliary variable. A numerical energy balance is derived and the numerical contact force is shown to be strictly non-adhesive. Example results with time-variant tension and time-variant contact stiffness are detailed, and real-time viability is demonstrated.

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Collisions are an integral part of the sound production mechanism in a wide variety of musical instruments. In physics-based realtime simulation of such nonlinear phenomena, challenges centred around efficient and accurate root-finding arise. Nonlinearly implicit schemes are normally ill-suited for real-time simulation as they rely on iterative solvers for root-solving. Explicit schemes overcome this issue at the cost of a slightly larger error for a given sample rate. In this paper, for the case of lumped collisions, an alternate approach is proposed by approximating the contact potential curve. The approximation is described, and is shown to lead to a non-iterative update for an energy-stable nonlinearly implicit scheme. The method is first tested on single mass-barrier collision simulations, and then employed in conjunction with a modal string model to simulate hammer-string and slide-string interaction. Results are discussed in comparison with existing approaches, and real-time feasibility is demonstrated.

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