Numerical simulations of piano strings. II. Comparisons with measurements and systematic exploration of some hammer-string parameters

Abstract

A physical model of the piano string, using finite difference methods, has recently been developed. [Chaigne and Askenfelt, J. Acoust. Soc. Am. 95, 1112-1118 (1994)]. The model is based on the fundamental equations of a damped, stiff string interacting with a nonlinear hammer, from which a numerical finite difference scheme is derived. In the present study, the performance of the model is evaluated by systematic comparisons between measured and simulated piano tones. After a w•rification of the accuracy of the method, the model is used as a tool for systematically exploring the influence of string stiffness, relative striking position, and hammer-string mass ratio on stri.ng waveforms and spectra.

Sound timbre interpolation based on physical modeling

“…The exciter and the vibrator model used here is basically the same as that reported by Hiller and Ruiz [19,20], and further elaborated by Chaigne and Askenfelt [21,22] for the simulation of the vibration of a piano string struck by a hammer. This struck-string model is modified to enable us to interpolate sound to obtain a timbre between striking and plucking.…”

Geometric-integration tools for the simulation of musical sounds

“…to [3,4,18]. As it is shown below, when the damping terms are ignored, that is, μ = d 1 = d 3 = 0, the above model is a separable Hamiltonian system, which is a system with a remarkable Hamiltonian structure from a viewpoint of numerical analysis.…”

“…Appropriate fitting parameters can be integrated, which enables the design of more realistic models. Previous research in this direction includes the modeling and simulation of the hammer [11,12,19,53], the key action [31,44,45,48,49], string vibrations [3][4][5]17,18,54], and the soundboard [20,21,36]. The interactions between the components are also considered in the literature; in particular, Chabassier et al established a model and a numerical method for simulation of the whole piano [14,16].…”

Musical Acoustics and Computational Science

“…Calculations of this type are also at the forefront of current research in musical acoustics, as witnessed by the increasing interest in physical modeling of musical instruments [3,17,18,19,20,21,2].…”