A stiff piano string has overtones which are sharper than multiples of its fundamental. This inharmonicity is very important characteristic on the tuning and on the tone quality of a piano. This study deals with the problem of controlling the inharmonicity of a piano string by attachment of a small mass. The mass attachment lowers the frequency of each normal mode except that for mass in the node.
In the analysis of the frequency of each normal mode, the Dirac delta function is employed in describing concentrated mass. The magnitude of the attached mass and the location of attaching point are determined by the constant of making the 2nd partial harmonic to the fundamental.
According to experimental results, the mass attached string has longer initial decay time than the original string and overtones of the former have stronger relative tonal intensity than those of the latter. So that, the inharmonicity of the string can be reduced to 2-40 cent by attachment of mass of a fraction of one gram. The experimental values agree well with analytic solutions.
