Sound synthesis for fretted instruments, such as the guitar, has a long history because of numerous challenges; the interaction between the finger, string and fretboard under variable playing conditions is a delicate one, leading to many subtle features difficult to emulate using standard synthesis methods. A physical modeling approach thus becomes an attractive option. A vibrating string is subject to intermittent contact/recontact phenomena along the length of the fretboard, and the string is driven by a plucking interaction and stopped by a finger, the position of which and force applied by are gestural parameters. In this research, a finite-difference time-domain method is developed with a penalty potential allowing for a convenient model of distributed collision. Implementation details are discussed and simulation results and visualizations are presented illustrating a variety of typical playing gestures. Finally, given that such methods for highly nonlinear systems are prone to numerical instability, a brief description of an energy-balanced or Hamiltonian framework is provided, allowing for convenient numerical stability conditions.
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