Abstract:
Previous work in the study of coupled piano string behavior, e.g., by Weinreich and Nakamura, has focused analytically on the interaction of a pair of coupled modes, noting that the rest of the string modes couple similarly. The coupling of three or more modes, as occurs in sets of unison piano strings, is studied. Equivalent circuits (modeling a finite number of modes) of coupled piano strings can be written in state-space form and their eigenvalues analyzed at various levels of detuning and coupling. Alternatively, the transfer functions of the system can often be written in a root-locus analysis form, which lends a control-theory perspective to the analysis. Often, an intuitive understanding of pole movement under variations in a single parameter, such as a single-mode frequency or coupling coefficient, can be developed. Many effects, for example, two-stage decay, can be understood in terms of system pole location. Three-mode coupling is explored and interpreted, as is variation in coupling behavior at different string harmonics.