Robert, Thanks for this explanation. It confirms my general sense of the matter. -Mark Schecter Robert Scott wrote: > 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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