Mark Schecter wrote:
> ...inharmonicity is due to the material's stiffness at the attachment
> points only?...
No, inharmonicity is affected by the material's stiffness anywhere that it bends - which is mostly at the termination points and at the nodes. That is why the effect is more pronounced for higher partials. They bend in more places than the fundamental or lower partials.
The model of a vibrating string that produces pure harmonics (no inharmonicity) is one where the string has some mass and some longitudinal spring constant, but no transverse stiffness - i.e. no resistance to bending. The frequency of each resonance is determined by how a displaced mass responds to a restoring force. In the case of the ideal string, the restoring force is entirely made up of the transverse component of the string tension when the string is displaced. But when you add stiffness (resistance to bending) into the picture, the restoring force for a displaced mass is partly due to that stiffness, which is in addition to the restoring force due to string tension. That raises the pitch of those resonances that engage in more bending.
Robert Scott
Ypsianti, Michigan
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