Toward a physical model of the clavichord

Abstract

String excitation by the tangent in the clavichord is a unique mechanism. The tangent, keeping in contact with the string after the initial strike, controls continuously the string tension. Four main flexible subsystems are considered in the clavichord: the tangent/key subsystem, the strings subsystem, the bridge-soundboard subsystem, the string damper subsystem. A modal description of the dynamics of these subsystems is proposed. Parameters of the subsystems are estimated on a copy of a historical instrument by Hubert (1784). The different subsystems and their couplings are modeled using a modal Udwadia-Kalaba formulation. The string-tangent interaction is modeled via the intermittent contact dynamics, using the Kirchoff-Carrier string model. Realistic string, soundboard and tangent motions are obtained using a time-domain synthesis scheme that computes the dynamics of the uncoupled subsystems and the constraints resulting from coupling between them. Simulated motions of the model in response to a driving force on the key are analysed. The results are consistent with experimental measurements and published data on the dynamics of the clavichord. The model is able to reproduce the main acoustic features of the instrument: force on the key for intonation control, key velocity for dynamic nuances control, constant spectral slope for varying dynamic nuances.

Physical modelling of a harp from Central Africa

“…Indeed, the soundboard being driven by the force exerted by the string at the attachment point, an underestimation of the driving point accelerance will inevitably lead to an underestimation of its dynamic response. A study of the clavichord 19 based on the U-K formalism confirmed the strong influence of modal truncation on the high frequency content of physical simulations. As shown in Figs.…”

“…In the time domain, Antunes and Debut recently adapted the Udwadia-Kalaba (U-K) formulation 15,16 , originally suited for rigid multibody systems, to flexible coupled systems by describing them through their uncoupled modal basis 17 . Recent studies showed the ability of this formulation to include string nonlinearities 18 (guitar), collisions 19 and sympathetic vibrations 20 in the case of the clavichord. Following these results, it seemed appropriate to include multiple string polarizations as well as coupling with the instrument's body at both ends.…”

Whistling in the clavichord

“…Numerical simulation is proposed to overcome these limitations. Time-domain simulation of the string motion in a recently proposed model of the clavichord shows energy transmission from the P-string to the S-string (see the video example in 22 ). In this section a reduced clavichord model using the Udwadia-Kalaba (U-K) formalism is developed.…”

“…Marin Mersenne 3 and Jakob Adlung 4 discussed noted the effect of the sympathetic string. The tonal consequences of S-strings and comparison with room reverberation data have been investigated in previous works [5][6][7] . Significant effects of sympathetic strings on the instrument's tonal quality are found.…”

Experimentally-Tuned Synthesis of a Thin Plate

“…The numerical simulation of acoustic instruments and devices is a growing subject of research. 1 Applications range from model-aided instrument making, [2][3][4][5] to virtual instrument and effect design, [6][7][8][9] to virtual reality applications. 10,11 A faithful reproduction of the underlying system may be realised via signal-based analysis and resynthesis, 12 starting usually from a recorded sample.…”