Characterizing the Feel of the Piano Action

The array of keys that the piano presents to a musician seems at first glance quite innocent: a one-to-one mapping from 88 neatly laid-out locations to 88 discretely pitched tones. While the pianist’s first challenge in playing a note is to navigate a finger into position within this field of black and white levers, the second challenge is to depress that key in a manner that produces the particular loudness and timing the pianist has in mind. Thus, in addition to the mapping from spatial location to pitch, the pianist must negotiate a second mapping: that from keypress (a trajectory over a brief time period) to hammer strike velocity and strike time (two scalars describing an event). Each key is not, after all, a trigger for the release of stored sound energy. Rather, each key is a means for converting mechanical work performed by a finger into acoustic energy radiating from the soundboard, as incited by a hammer strike on strings.

The mapping from keypress to hammer strike event is realized by the piano action, the system of levers linking key to hammer. Three levers known as the whippen bottom, jack, and repetition lever intervene between the key and hammer (see Figure 1). Within this system, various contacts are made and broken in the course of a keypress, and the kinematic chain linking key to hammer undergoes significant changes in character. These changes support the various functions performed by the piano action, including escapement, check, and repetition. For example, escapement begins when a key is depressed and the jack tender contacts the let-off button. This causes the jack fly to pivot out from under the hammer shank knuckle, as the keypress continues to raise the assembly and propel the hammer toward the string. Subsequently, the contact between the jack fly and the hammer shank knuckle transitions from pushing to sliding and is then broken, causing the hammer to travel the remaining 1–1.5 mm distance to the string in free flight.

Upon striking the string, the hammer is then thrown against the backcheck, which is attached at the rear (raised) end of the depressed keystick, suspending the hammer in a position approximately 12–15 mm from the string. Meanwhile, as the jack rotates, the drop screw depresses the repetition lever, compressing the repetition spring and priming the repetition lever to push the checked hammer upward again. With only a slight relaxation of finger pressure on the fully depressed key, the backcheck releases the hammer from its suspended position and the repetition lever pushes upward on the hammer shank, allowing the jack fly to quickly slide back underneath the knuckle. Once the jack fly is thus repositioned, the pianist can execute a rapid re-strike of the string, a function called repetition.

The timing and even the sequence of these changing contact events depend on the keypress trajectory (Askenfelt and Jansson 1990; Hayashi, Yamane, and Mori 1999). Thus, the mapping from keypress to strike event is by no means simple. The mapping cannot even be described as constant, because the kinematic chain linking key to hammer changes character within even a single keypress. A complete description of the piano action requires a hybrid dynamical model, one combining continuous and discrete variables (Gillespie 1994; Oboe 2006). Although the mechanical realization of escapement, check, and repetition in the piano action are not of concern for the typical pianist, their function (i.e., the manner in which a keypress is mapped to a hammer strike event) is of paramount concern. Knowledge of this mapping is the means for gaining control over the sounds produced.

Figure 1.

Schematic of the grand piano action.

The interface realized by the piano action, however, includes more than the mapping from mechanical input to strike event. There is another mapping involved: the mapping from keypress (mechanical input) to mechanical response. The mechanics of the piano action also determines the feel of each key. Gillespie (1996) and Oboe (2006) have emphasized that the mechanical or haptic response...