Modeling of the part-pedaling effect in the piano

Anatoli Stulov , Vesa Välimäki , Heidi-Maria Lehtonen

This study presents the theoretical modeling of the part - pedaling effect in the piano. Part – pedaling means a common use of the sustain pedal where the pedal is not fully depressed, but pressed somewhere between the two extremes. The model implies to consider the distributions of the string deflection and the string velocity along the string as functions created by the traveling nondispersive waves generated by the hammer impact and moving in both directions. The damper restricts the amplitude of the string deflection in the region of its position, and also suppresses the "up" velocity of the string. Such nonlinear model gives possibility to calculate the spectrograms of the string vibration tone, and to compare the numerical calculations with the measured example tones of the string. To obtain the appropriate decay rates of the string vibrations, the damping factor at one termination of the string is induced. The modeling confirms that in the bass range the nonlinear amplitude limitation causes energy transfer from the lower partials to higher partials, which can excite missing modes during the damper-string interaction.

Mots clés: nonlinear system; physical model; piano

Domaines: Acoustique [physics.class-ph]

Anatoli Stulov, Vesa Välimäki, Heidi-Maria Lehtonen. Modeling of the part-pedaling effect in the piano. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810856⟩