Acoustical properties of ancient Chinese musical bells

Ancient Chinese music bells can be traced back to the Shang dynasty (1600–1100 B.C.). In addition to their significance in history and metallurgy, they provide much insight into the design of musical instruments in the early years and continue to make important contribution to acoustics due to their unique acoustical properties and rich physical mechanisms. These music bells differ from carillon/church bells and oriental temple bells by their almond-shaped cross sections, which result in two distinct strike tones (normal and side) in one bell. Through the analyse of the resonance frequencies of 64 music bells cast 2400 years ago, frequency relations are rediscovered between the normal and side-strike tones in individual bells and between the normal-strike tones of adjacent bells. Acoustical qualities of each strike tone are characterised using frequency ratios between the partials and fundamental, as well as the spectrogram of the tone. The study on the scaling rules for achieving the required frequency intervals between adjacent bells also sheds light on our understanding of music scales and sound balance principles in bell acoustics already recognized in ancient times. INTRODUCTION Previous studies in the acoustics of ancient Chinese music bells were mainly focused on the two-tone [1] and shortdecay properties [2] of individual bells and their dependence on the nature of the bell’s modal vibration and sound radiation. In practice, a set of music bells were performed together in groups as a single music instrument. It is thus necessary to investigate the acoustical properties of the entire set of bells and to identify the roles played by individual bells in determining the music scales, sound quality and balance of the instrument. Information available for this study are the dimensions and the measured fundamentals and partials [3] of both the normal and side-strike tones of each of the 64 Marquis Zeng Yi's musical bells (see Figure 1), which were cast from more than 2400 years ago. The measured time signals of vibration and sound of the normal and side-strike tones of other 64 music bells (see Figure 2) at the Beijing bell museum are used to generate the spectrogram for tonal quality analysis. The later set of bells was made in 1990 using identical dimensions and material compositions (Cu 83%, Sn 14%, Pb 2~4%) of the former set. Signal processing techniques, boundary and finite element analysis are employed as tools in this study. Figure 1. Marquis Zeng Yi's musical bells. I3.3 I3.1 J3.4 J3.6 J2.12 K1.1 J1.1 . I1.1