Institut Jean Le Rond d'Alembert, Équipe Lutheries-Acoustique-Musique, Sorbonne Université, CNRS, F-75005 Paris, France.
Applied Dynamics Laboratory, Instituto Superior Técnico, Centro de Ciências e Tecnologias Nucleares, Bobadela, Portugal.
J Acoust Soc Am. 2021 Oct;150(4):2350. doi: 10.1121/10.0006438.
String excitation by the tangent in the clavichord is a unique mechanism. The tangent, keeping in contact with the string after the initial strike, continuously controls the string tension. Four main flexible subsystems are considered in the clavichord: the tangent/key subsystem, the string subsystem, the bridge-soundboard subsystem, and 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 analyzed. 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, and constant spectral slope for varying dynamic nuances.
古钢琴的琴键通过切弦来激发琴弦，这是一种独特的机制。在初始敲击后，琴键持续与琴弦接触，从而不断控制琴弦的张力。古钢琴中有四个主要的弹性子系统：琴键/琴槌子系统、琴弦子系统、琴马-音板子系统和琴弦制音器子系统。提出了这些子系统的动力学模态描述。通过对胡贝特（Hubert）（1784 年）的一件历史乐器的复制品进行参数估计，确定了各子系统的参数。使用模态 Udwadia-Kalaba 公式对不同的子系统及其耦合进行建模。通过使用 Kirchoff-Carrier 弦模型来模拟琴弦-琴键之间的间歇性接触动力学，从而实现琴弦-琴键的相互作用建模。使用基于时域的综合方案来获得琴弦、音板和琴键的实际运动，该方案计算未耦合子系统的动力学以及它们之间耦合产生的约束。分析了模型对琴键上驱动力的响应的模拟运动。结果与古钢琴动力学的实验测量和已发表的数据一致。该模型能够再现乐器的主要声学特征：用于音准控制的琴键上的力、用于动态细微差别控制的琴键速度以及用于变化的动态细微差别的恒定谱斜率。
