Musical instruments – Sound synthesis of virtual idiophones

The design of tuned idiophones, such as bells, gongs, and metallophones, has undergone centuries of development, pushed forward by instrument makers. All these improvements have the purpose of optimizing the sound such that it is pleasing to the human ear, resulting in complex geometries of the instruments. This empirical process is rather similar to the work of structural engineers who also optimize physical structures. In general, an idiophone can be described by its elastic properties, where eigenmodes and corresponding eigenfrequencies correspond to the overtones of the sound. However, this alone is not sufficient to evaluate sound. In particular, it is most important to take into account the time behavior of striking instruments like the vibraphone. It is the novel contribution of this paper to provide a systematic approach for synthesizing sound from vibrating structures with arbitrary geometries just from their surface vibrations. In case of musical instruments, the resulting sound can be evaluated and rated by psychoacoustic criteria to define a target function for their numerical optimization. The method is applied to a bar modeled according to the design of typical vibraphone bars. The sound resulting from the synthesis algorithm is validated against the boundary element approach and results from microphone measurements.