Multibody dynamics as a tool for historical research. Study of an 18th century piano action of Johann Andreas Stein

Ancient musical instruments can tell us much about the way composers of the past centuries wrote their music. Indeed, the sound and playing characteristics of historical instruments are often very different from those of the instruments we are used to. For example, in the case of the Viennese piano actions used by Mozart and his contemporaries, the so-called “escapement height” largely conditions the response of the instrument to the pianist’s touch. In this contribution, we aim to define how the Viennese action behaves when the escapement height, usually tuned by piano technicians, is changed. To do this, a multibody model containing the frame, the key, the hammer, the pawl, and the string has been developed. This paper describes how the model has been carried out; a special focus is put on the detection of the intermittent contacts between bodies, which may look easy in the real action, but is rather complex to model. The model is compared with high-speed imaging data and a parametric study of the escapement height is performed by adjusting the rest position of the pawl. The high sensitivity of this regulation is revealed as a shift of 1 mm of the pawl seems to induce a displacement of the escapement height of 20 mm. It is also shown that a strong but linear decrease of the maximal force between the hammer and the string appears when the escapement height increases