Vibration of clipped strings in the bundengan musical instrument

摘要

Bundengan is a musical instrument from the Wonosobo Regency in Central Java, Indonesia. It has a distinctive half-dome structure, and its unique sound, which imitates the sound of gongs and cow-hide drums of the gamelan, is produced by plucking a number of clipped strings and long, thin bamboo plates fitted on the dome. Using computer simulations, this paper investigates the vibration of the clipped strings as affected by variations of the number, mass and position of the bamboo clips, as well as the location of plucking. Our results show that, upon plucking, the bamboo clips cause multiple vibrations of non-harmonic frequencies to occur at different sections of the string separated by the clips, thus resembling the non-harmonic spectra commonly found in metallic percussion instruments. Shifting the clips along the string results in changes in the vibration spectra, which are manifested as shifts of both the frequency values and their magnitudes. The frequency spectra can be related to Mersenne's law when the clip mass is extremely small or extremely large. In the former case, the frequencies will be the same as that of a string with no clips. In the latter case, the frequency will go to zero for mode 1 if there is only one clip, and for modes 1 and 2 if there are two clips on the string. For the next mode, the frequency is dictated by Mersenne's law corresponding to the length of the longer string section. For clip masses in between these two extremes, the vibration frequencies generate graphs resembling sigmoid curves. The results provide insights that may enable us to systematically predict how the frequencies of the clipped bundengan strings are influenced by the properties of the bamboo clips. (C) 2019 Elsevier Ltd. All rights reserved.