A physical model of a highly nonlinear string and its use in the music composition Quartet for Strings

A real-time virtual string model is created that supports two modes of haptic force-feedback interaction. Using one haptic controller, the string can be plucked, and using a second haptic controller, the virtual stringu0027s pitch can be continuously varied by applying pressure to the string. Via both controllers, the vibrations of the virtual string can be felt while it is played. These functionalities are achieved by modeling the string as a finite sequence of interleaved masses and stiffening springs. For artistic purposes, a nonlinear spring force characteristic function is selected that limits the effective stiffness of each spring to a range between k and (k + ks). This function is F(x) = kx + (ksx3)/(β2+xu003e + x2), where x is the displacement of the nonlinear spring and β approximately adjusts the displacement at which the stiffness becomes significantly nonlinear. For small displacements, the stringu0027s undamped fundamental frequency is tuned by k, and for sufficiently large displacements, the stringu0027s un...