In the design of real-time spring reverberation algorithms, a modal architecture offers several advantages, including computational efficiency and parametric control flexibility. Due to the complex, highly dispersive behavior of helical springs, computing physically accurate parameters for such a model presents specific challenges. In this paper these are addressed by applying an implicit higher-order-in-space finite difference scheme to a two-variable model of helical spring dynamics. A novel numerical boundary treatment is presented, which utilises multiple centered boundary expressions of different stencil width. The resulting scheme is unconditionally stable, and as such allows adjusting the numerical parameters independently of each other and of the physical parameters. The dispersion relation of the scheme is shown to be accurate in the audio range only for very high orders of accuracy in combination with a small temporal and spatial step. The frequency, amplitude, and decay rate of the system modes are extracted from a diagonalised form of this numerical model. After removing all modes with frequencies outside the audio range and applying a modal amplitude correction to compensate for omitting the magnetic transducers, a light-weight modal reverb algorithm is obtained. Comparison with a measured impulse response shows a reasonably good match across a wide frequency range in terms of echo density, decay characteristics, and diffusive nature.

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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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