Control index of the upright and grand piano actions
Xavier Boutillon, Robert Grijalva · The Journal of the Acoustical Society of America · 1999
The motion of the piano hammer between its resting position and the contact with the strings follows two phases. At first, the motion is imposed by the pianist’s finger on the key. When it escapes from the main action, within 2 mm from the string, the hammer possesses the velocity ve. During the second and brief phase before impact, the hammer is only subject to gravity, friction of its pivoting axis, and to the action of an additional spring in the case of the upright piano. Finally, the hammer hits the strings with velocity vi. The difference between ve and vi, and the threshold on ve below which the hammer does not even touch the strings, are a nuisance for the musician. Although inevitable, this second phase also affects the aptitude to control nuances, so important in music. To quantify this notion, the control index ic=dve/dvi is introduced, which can be easily calculated. Its limit is 1 for fortissimo but it approaches 0 for pianissimo. For the pianist, this corresponds to a steeply increasing difficulty to phrase music at low rather than at high dynamic levels. Differences between the grand and the upright piano will be discussed.