Real string stiffness makes higher partials travel faster than the ideal thin-string model predicts

Evidence

This equation, although it is derived assuming an infinitely thin string, is applicable to most strings that one is likely to meet in practice. But it is applicable to only pure transverse vibration; it does not apply to other modes of vibration. However, transverse waves are the dominant form of vibration for thin strings. The main error in Equation 1.7 is due to the inherent stiffness in real materials, which results in a slight increase in velocity with frequency. This effect does alter the timbre of percussive stringed instruments, like the piano or guitar, and gets stronger for thicker pieces of wire. — David Howard, Jamie Angus, coustics and Psychoacoustics, 84

Categorization

• XREF: Explains inharmonicity in piano and guitar — the physical source behind stretched tunings; connects to how digital piano synthesis must model stiffness for realistic timbre.