Regimes of Piano-String Vibration

In general, more complex synthesis models are needed at higher dynamic playing levels. The main three regimes of vibration are as follows [27]:

1. The simplest piano-string vibration regime is characterized by linear superposition in which transverse and longitudinal waves decouple into separate modes, as implied by Eq.(9.30). In this case, transverse and longitudinal waves can be simulated in separate digital waveguides (Ch. 6). The longitudinal waveguide is of course an order of magnitude shorter than the transverse waveguide(s).

2. As dynamic playing level is increased, transverse-to-longitudinal coupling becomes audible [26].

3. At very high dynamic levels, the model should also include longitudinal-to-transverse coupling. However, this is usually neglected.

Other regimes arise depending on whether tension can be assumed to be uniform along the string [27].

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.