Fundamental theory and computer simulation concerning the decay characteristics of piano sound

Abstract

It is shown by theory and computer simulation that the decay characteristics of piano sound are dependent upon the degree of coupling between the strings. String and soundboard vibration are calculated using an equivalent circuit. Each string is comprised of resonance circuits that correspond to partials, and the behaviors of individual partials are described independently of each other by these circuits. When the most simplified version of only one partial is considered, the equivalent circuit is expressed by the two resonant circuits coupled with the soundboard impedance. The degree of coupling between the two strings is dependent on the ratio of two constants: the degree of mistuning and the ratio of soundboard impedance to string impedance. If the former is smaller than the latter, the two strings are closely coupled with each other and a double decay characteristic results. If the relation between the two constants is reversed, the coupling is loose and a beat type of decay characteristic results. The decay characteristics are changed by the above two constants. The results show that the degree of tuning and the characteristics of the strings and the soundboard determine the decay characteristics of piano sound.