Abstract:
Nonharmonic components in a string vibration generate beats, effect the sound quality of a musical instrument, and become a harmful component in the tuning. Therefore, one needs to grasp in detail the influence of various parameters such as inherent elasticity. In the present paper, influence of tension change acting as nonlinear with the displacement of the stiff string on vibration frequencies is analyzed by constructing a discrete model. In numerical calculations of the string vibration affected by a disturbance such as elasticity, it is impossible to get a rigorous solution from a finite-difference scheme, and particular consideration in evaluating vibration frequencies affected by nonlinear ingredients is needed. Because of this influence of vibration, frequencies are expected to be very small; the analysis has to be carried out with a sufficient grasp of digitizing errors. First string vibration frequencies of the discrete model are analyzed and then evaluated with a rigorous value for an ideal string and the case including inherent elasticity. In addition, the simulation of nonlinear string vibration is conducted by correcting the digitizing error. The vibration frequencies of the simulated response are obtained from the period of numerical solution by applying a digital filter. The results show that vibration frequencies fall slightly due to the effects of nonlinear components.