The design and analysis of new musical bells
Neil M. McLachlan · The Journal of the Acoustical Society of America · 2004
The design and analysis of a series of new musical bells will be presented in this paper. Modal analysis of a wide range of bell-like geometries using FEA revealed the presence and significance of transverse axial modes in unconstrained bell models, leading to a new understanding of the relationships between bell geometry and modal behavior. This understanding was used to adjust simple parametric models of bell geometry to arrive at appropriate geometries to begin numerical shape optimization for the design of bells with a range of desired overtone tunings. Pitch salience is well known to depend on the degree of harmonic relationships between pure tones in complex stimuli. Bells intended to produce a single, highly salient pitch were designed and manufactured with up to the first 7 overtones tuned to the harmonic series. Other bells with overtones tuned to subsets of two or three harmonic series were also designed and manufactured. These bells were intended to produce multiple pitch perceptions of approximately equal strength. Spectral analysis and range of numerical psycho-acoustic models are used to evaluate the sounds of manufactured bells against these design objectives. [I would like to acknowledge the close collaboration of Dr. Anton Hasell of Australian Bell.]