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In discrete-time digital models of contact of vibrating objects stability and therefore control over system energy is an important issue. While numerical approximation is problematic in this context digital algorithms may meat this challenge when based on exact mathematical solution of the underlying equation. The latter may generally be possible under certain conditions of linearity. While a system of contacting solid objects is non-linear by definition, piece-wise linear models may be used. Here however the aspect of “switching” between different linear phases is crucial. An approach is presented for exact preservation of system energy when passing between different phases of contact. One basic principle used may be pictured as inserting appropriate ideal, massless and perfectly stiff, “connection rods” at discrete moments of phase switching. Theoretic foundations are introduced and the general technique is explained and tested at two simple examples.

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In this paper the problem of the synthesis of plucked strings by means of physically inspired models is reconsidered in the context of the player’s interaction with the virtual instrument. While solutions for the synthesis of guitar tones have been proposed, which are excellent from the acoustic point of view, the problem of the control of the physical parameters directly by the player has not received sufficient attention. In this paper we revive a simple model previously presented by Cuzzucoli and Lombardo for the player’s touch. We show that the model is affected by an inconsistency that can be removed by introducing the finger/pick perturbation in a balanced form on the digital waveguide. The results, together with a more comprehensive model of the guitar have been implemented in a VST plugin, which is the starting point for further research.

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