A Musicological Study of the Japanese Koto using Heuristic Finite Element Models

Abstract

This musicological study investigates the sound of the Japanese koto, a 13-string zither, using heuristic finite element models. It aims firstly to test a new integrated analytical approach with finite element methods; these methods have become more accessible to scholars across many disciplines including systematic musicology in recent decades. This thesis demonstrates how these methods can provide powerful analytical tools for technical studies of musical instruments as part of organological research. Secondly, it applies this method in a heuristic study of the koto to characterise its sound envelope by using a series of models; these models range from a simple box to a more complex and geometrically accurate lofted model developed as part of this study. These models permitted the continual development of the integrated analytical approach during the period of investigation. COMSOL Multiphysics®, the finite element method software used to develop the models, also enabled specialist analysis of sound from the instrument including its qualitative visual representation. Results of these models in turn were validated by comparison with the limited existing literature on the koto’s acoustics and additional physical experiments. During this process initial tests on a plank of paulownia wood were undertaken in order to understand the paulownia wood from which the koto is made. These results then informed more complex, subsequent models. Findings from the study reveal that the anisotropic nature of paulownia significantly influenced predicted resonances when compared to a simple isotropic model. Key characteristics of the koto body that help to explain the relationship between sound production and geometry of the instrument were also identified, for example, the significant influence of the curvature of the top plate and the arching down the length of the instrument on the sound envelope produced. These findings contribute to the understanding of the acoustical behaviour of the koto in particular and East Asian zithers in general. The methods identified and validated in this study also serve more broadly as a template for future organological and acoustical investigations of geometrically complex wooden musical instruments.