The Clang Tone of the Pianoforte
Armand F. Knoblaugh · The Journal of the Acoustical Society of America · 1944
This phenomenon occurs in the bass section of all pianofortes and is termed a “clang” or “wolf” tone by piano makers. It comprises a distinctly audible, high pitched sound, emitted with the bass tone when the string is struck in the usual manner. Its pitch, varying from 500 to 3000 c.p.s. throughout a piano, is constant for any one string but varies with string dimensions, being higher for the shorter, lighter bass wires. The fundamental tones of the corresponding bass strings range from 30 to 100 c.p.s. With the aid of a tone analyzer and other apparatus, the effect has been shown to be due to a longitudinal vibration of the bass string. The velocity along the string has been found to be (AE/M)12 where A = the cross-sectional area of the core wire, E = the modulus of elasticity of the core wire material, and M = the total mass (core+wrapping) per unit length of the string. Dividing the velocity by twice the length of the string yields the frequency of the clang, confirmed by observation and experiment. The clang has its own system of partials, substantially harmonic. The component of hammer motion tangential to the string is probably an exciting cause and the complex motion of the bass bridge probably permits transfer of energy to the soundboard.