Numerical Calculation of Modal Spring Reverb Parameters

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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.
Original languageEnglish
Title of host publication 23rd International Conference on Digital Audio Effects: (online)
Publication statusEarly online date - 30 Sep 2020
Event23rd International Conference on Digital Audio Effects: (online) - hosted at Vienna University of Music and Performing Arts, Vienna, Austria
Duration: 09 Sep 202011 Oct 2020

Publication series

NameProceedings of the 23rd International Conference on Digital Audio Effects
ISSN (Print)2413-6700
ISSN (Electronic)2413-6689


Conference23rd International Conference on Digital Audio Effects
Abbreviated titleeDAFx2020
Internet address


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