Thanks for sharing that article. My understanding is that this bridge effect is actually what is happening across the entire length of the string; it's just th

Thanks for sharing that article. My understanding is that this bridge effect is actually what is happening across the entire length of the string; it's just that the boundary condition makes the effects of stiffness clearer. Stiffness causes there to basically be a radius of curvature in the string when you apply a force. The boundary condition of a guitar string is that the displacement and first derivative of displacement of the string are zero at both ends. So, this radius of curvature will be visible there. But, even when plucking a string, rather than having a sharp peak at the plectrum, it will necessarily be similarly smoothed out. (Though, through time in a frequency-dependent way.) In the wave equation, stiffness involves a factor with a coefficient proportional to Young's modulus. Based on the stress/strain graphs I could find, Young's modulus of a guitar string increases with tension, increasing inharmonicity. Of course, the pitch of the string also increases with tension, so there's a lot going on. (I have to admit that the zero-first-derivative boundary condition having no additional effect is coming from my intuitions about linearity of solutions to the wave equation, but maybe it still has some interesting effect. I think the overall effect of stiffness would dominate this one, however.) Some things I was looking at: https://www.dsprelated.com/freebooks/pasp/Dispersive_1D_Wave_Equation.html https://www.dsprelated.com/freebooks/pasp/Dispersive_1D_Wave... https://www.dsprelated.com/freebooks/pasp/Stiff_String.html https://www.dsprelated.com/freebooks/pasp/Stiff_String.html