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.

The vibratory and acoustic modeling of musical instruments is important for several purposes in cultural heritage preservation, performance studies and musical creation. On the one hand, building a model helps understanding the key features of an instrument, and then is useful for evaluation, documentation and preservation of historical models. On the other hand, modeling and simulation can help for improving existing instruments, or even designing new instruments by extension of the model. The clavichord is an early keyboard instrument equipped with a very simple mechanics. The strings are excited by small metal wedges or blades (the tangents) placed at the end of the keys. The tangent remains in contact with the strings for the duration of the note, defining the vibrating length of the string. All strings are coupled at a same bridge. A string is divided into three sections: a damped section (DS) between the hitch-pin and the tangent; the played section (PS), excited by the tangents, between the tangent and the bridge; and the resting section (RS) between the bridge and the tuning pin. Because of the coupling through the bridge of the PS and RS, the RS is set into vibration, acting as sympathetic strings. The vibratory responses of the RS is modelled using a modal approach based on the Udwadia-Kalaba formulation. Firstly, a review of the method is presented, accompanied with measurements performed on an instrument (copy of a Hubert 1784 fretted clavichord), which include an experimental modal analysis at the instrument bridge and measurements of string motions. Then, simulation results are reported and compared with experimental measurements.

Sympathetic string vibration plays an essential role in the clavichord's sound quality and tonal identity. Sympathetic vibration comes from the undamped string segments between the bridge and tuning pins. Under some conditions, a specific note, a whistling tone, stands out of the reverberation halo due to sympathetic vibration. It is hypothesized that this whistling tone comes from resonance between played and sympathetic segments of strings that are coupled through the bridge. Vibratory measurements for three pairs of excited and sympathetic strings are conducted on a copy of a historical instrument built by Hubert in 1784. The influences of bridge mobility and tuning on sympathetic string frequency and damping are studied. The results show a significant increase in vibratory amplitude, frequency veering, and damping increase in the string segments when tuning approaches frequency coincidence. Numerical simulations of a reduced clavichord model corresponding to the experiments are conducted using the modal Udwadia–Kalaba formulation. Simulation gives a more accurate picture of the veering phenomenon. Simulation and experimental results are in good agreement, showing that whistling in the clavichord comes from string resonance. It is favored by frequency coincidence between excited and sympathetic string segments and by higher bridge mobility.