Basic Elements in Piano Scale Design with Plain Strings
Earle L. Kent · The Journal of the Acoustical Society of America · 1971
Consideration must be given to space limitations, string tension, string diameter, inharmonicity coefficients, tensile strength of wire, and the musical character of the tones produced by the strings, in establishing the scale design for the plain strings in a piano. Mathematical expressions involving these basic elements are well known, but a study of several commercial pianos indicates that it is probable that empirical and graphical methods are relied upon for scale design more than the use of mathematics that relate all of the basic elements. Modern computers provide means for optimizing smooth string-to-string relationships in scale design without the drudgery that would be involved otherwise. A flexible mathematical tool for smooth scale design is provided when expressions are developed that correlate vibration frequencies, string mass, string length, string tension, the energy in the vibrating string, tensile strength, and the inharmonicity due to string stiffness.