Characterizing the Feel of the Piano Action, Board (Sensoray 626)

R. Brent Gillespie,∗ Bo Yu,∗ Robert Grijalva,† and Shorya Awtar∗ Characterizing the Feel ∗Department of Mechanical Engineering of the Piano Action University of Michigan 2350 Hayward Street Ann Arbor, MI 48109-2214 USA †Piano Technology Department School of Music, Theatre, and Dance University of Michigan 1100 Baits Drive Ann Arbor, MI 48109-2085 USA {brentg, ybo, pianoman, awtar}@umich.edu The array of keys that the piano presents to a to raise the assembly and propel the hammer toward musician seems at first glance quite innocent: a one- the string. Subsequently, the contact between the to-one mapping from 88 neatly laid-out locations to jack fly and the hammer shank knuckle transitions 88 discretely pitched tones. While the pianist’s first from pushing to sliding and is then broken, causing challenge in playing a note is to navigate a finger the hammer to travel the remaining 1–1.5 mm into position within this field of black and white distance to the string in free flight. levers, the second challenge is to depress that key in Upon striking the string, the hammer is then a manner that produces the particular loudness and thrown against the backcheck, which is attached timing the pianist has in mind. Thus, in addition at the rear (raised) end of the depressed keystick, to the mapping from spatial location to pitch, the suspending the hammer in a position approximately pianist must negotiate a second mapping: that from 12–15 mm from the string. Meanwhile, as the jack keypress (a trajectory over a brief time period) to rotates, the drop screw depresses the repetition hammer strike velocity and strike time (two scalars lever, compressing the repetition spring and priming describing an event). Each key is not, after all, a the repetition lever to push the checked hammer trigger for the release of stored sound energy. Rather, upward again. With only a slight relaxation of finger each key is a means for converting mechanical work pressure on the fully depressed key, the backcheck performed by a finger into acoustic energy radiating releases the hammer from its suspended position from the soundboard, as incited by a hammer strike and the repetition lever pushes upward on the on strings. hammer shank, allowing the jack fly to quickly slide The mapping from keypress to hammer strike back underneath the knuckle. Once the jack fly is event is realized by the piano action, the system of thus repositioned, the pianist can execute a rapid levers linking key to hammer. Three levers known re-strike of the string, a function called repetition. as the whippen bottom, jack, and repetition lever in- The timing and even the sequence of these tervene between the key and hammer (see Figure 1). changing contact events depend on the keypress Within this system, various contacts are made and trajectory (Askenfelt and Jansson 1990; Hayashi, broken in the course of a keypress, and the kinematic Yamane, and Mori 1999). Thus, the mapping from chain linking key to hammer undergoes significant keypress to strike event is by no means simple. changes in character. These changes support the The mapping cannot even be described as constant, various functions performed by the piano action, because the kinematic chain linking key to hammer including escapement, check, and repetition. For changes character within even a single keypress. A example, escapement begins when a key is depressed complete description of the piano action requires a and the jack tender contacts the let-off button. This hybrid dynamical model, one combining continuous causes the jack fly to pivot out from under the and discrete variables (Gillespie 1994; Oboe 2006). hammer shank knuckle, as the keypress continues Although the mechanical realization of escapement, check, and repetition in the piano action are not of concern for the typical pianist, their function Computer Music Journal, 35:1, pp. 43–57, Spring 2011 c 2011 Massachusetts Institute of Technology. (i.e., the manner in which a keypress is mapped to Gillespie et al. 43 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/COMJ_a_00039 by guest on 02 October 2021 Figure 1. Schematic of the grand piano action. a hammer strike event) is of paramount concern. models range from the complex (Gillespie and Knowledge of this mapping is the means for gaining Cutkosky 1992; Hirschkorn 2004; Pineda 2005; control over the sounds produced. Van den Berghe, De Moor, and Minten 1995) to The interface realized by the piano action, the relatively simple (Hayashi, Yamane, and Mori however, includes more than the mapping from 1999). Modeling the map from keypress to hammer mechanical input to strike event. There is another strike event is motivated by the need for improved mapping involved: the mapping from keypress electronic instruments with full-key motion sensing (mechanical input) to mechanical response. The (Van den Berghe, De Moor, and Minten 1995) mechanics of the piano action also determines or improved designs for automatic (self-playing) the feel of each key. Gillespie (1996) and Oboe pianos (Hayashi, Yamane, and Mori 1999). Also, (2006) have emphasized that the mechanical or models that capture the driving point impedance haptic response felt at the finger carries valuable (mapping from mechanical input to mechanical information for the pianist, and pianists might well response) support the design of haptic-enabled or view this assertion as self-evident. The feel at the force-reflecting electronic musical instruments key is a signal that carries information about the inspired by the piano (Cadoz et al. 1984; Gillespie current state or mode of the kinematic chain. It also 1992; Oboe 2006). Models of the piano action informs the pianist about the sequence of contact also support a fuller understanding of the piano’s events occurring in response to a given keypress. In manufacture, performance practice, history, and this regard, the human/machine interface embodied acoustics (Hirschkorn, McPhee, and Birkett 2006; in each key is quite unlike the interface in a Izadbakhsh, McPhee, and Birkett 2008). computer keyboard or mouse, whose mechanical Precisely because the acoustic piano requires responses do not carry information that significantly mechanical work input at the key to produce sound complements visual feedback from a screen. The energy, the mechanical impedance that it presents piano action is more akin to a manual interface like to each finger is, by design, well matched to typical a hand tool or surgical instrument, in which haptic finger impedance. The piano is not like a piece response informs the user about the state of the of ideal measurement instrumentation, able to linkage with the environment or the state of the produce its response as a function of applied force tool itself. alone using an exceptionally high input impedance Several research groups have been active in or as a function of motion alone using a vanishingly the construction and experimental verification of low input impedance. Likewise, the human finger is computational models of the piano action. These not capable of exhibiting a particularly high or low 44 Computer Music Journal Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/COMJ_a_00039 by guest on 02 October 2021 source impedance. Instead, the piano key exhibits a dence to the adoption of a family of simple, linear finite “give” under an applied force, coupling its own models. dynamics to the biomechanics and neuromuscular But we have a secondary aim, one not explored dynamics of the pianist. What eventually produces in Hayashi, Yamane, and Mori (1999). We aim to the hammer strike is the evolution of a coupled unravel the dynamic coupling that takes place dynamical system involving both piano action and between piano action and finger/arm biomechanics human finger. It is important to note that neither and even neuromechanics. Thus, we excite the the behavior of the piano action nor the finger can be piano action for system identification while coupled observed in isolation without changing the coupled to a mechanized impedance modeled after the behavior. That is, when the dynamics are decoupled, biomechanics of the finger. As a result, the operating the normal, coupled behavior cannot be reproduced conditions, in particular the force and motion at the without emulating the original driving conditions, finger/key interface, are similar to normal playing because linearity (scaling and superposition) does conditions, and in effect our “linearization” is about not hold. the appropriate operating point by construction. Given that the mappings realized by the piano By exciting the coupled dynamics, we avoid such action are many-to-one, non-constant, and certainly behaviors as the hammer-double strike shown to nonlinear, specialized techniques are required for occur in response to a mechanized and unlikely step characterization of the action. In particular, its velocity input (Hayashi, Yamane, and Mori 1999). driving point impedance cannot be extrapolated Instead, we can expect to produce motion and force from measurements made under an excessively high trajectories reminiscent of those measured under or low source impedance. Measurements must be human input by Askenfelt and Jansson (1991) and made at the operating point that characterizes the similar studies (Goebl, Bresin, and Galembo 2005). magnitude and type of mechanical coupling between Naturally, the designer of a new musical instru- piano action and finger. ment is interested in the construction, in the mind In this article, we begin our construction of of the musician, of an internal representation of the a piano action model by adopting an empiri- instrument dynamics that determine how physical cal technique—specifically, a frequency-domain action maps to the loudness and timing of a tone. system-identification method. Using insight made Such a representation is presumably the basis for available from a frequency-domain presentation of planning and executing the actions that make up a set of non-parametric empirical models, we fit a musical performance with a given instrument.

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