Real strings show slightly sharp partials because tight curvature stiffens them like bars

Evidence

The partials of a plano string are slightly sharp compared to the integer multiples of the lowest partial. This effect is weak for the first few partials, but grows more important for the higher partials. The higher partials possess shorter wavelength oscillations on the string, bending it in tighter curves. If the diameter of the string gets to be noticeable on the scale of the wavelength on the string, it starts to act a little like a bar rather than a string, stiffening its bending resistance and raising its frequency. — Eric J. Heller, Why You Hear What You Hear- An…, 876

Categorization

• XREF: Directly explains inharmonicity — connects to piano tuning practice where higher partials are deliberately stretched. — connects to: Real strings produce inharmonic partials whose deviation grows steeply with thickness — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1095