Inharmonicity of Piano Bass Strings

Abstract

Piano bass strings are made by winding copper or iron wire over a core of plain steel music wire to increase the linear density so that the length of the string can be kept within the space available. The core itself is stiff and causes inharmonicity (i.e., departure of the natural frequencies of the string from a harmonic series), and the covering winding increases the stiffness still more. A theory has been developed for the limiting stiffness resulting from the covering wire. Experiment indicates that the covering wire does stiffen the string somewhat, but that the stiffening is not nearly as great as it would be if the coils of covering wire just touched each other with the string at rest. Inharmonicity data are presented for the bass strings of a concert grand piano, a medium grand piano, and an upright piano. The inharmonicity is greatest in the extreme bass strings. The inharmonicity is twice as great in the upright as in the medium grand piano, and for the lowest eight strings of the medium grand (which are single) the inharmonicity is, in turn, roughly twice that for the concert grand piano.