Pitch of a set of ancient Chinese bells: Piao-shi Bian Zhong

Abstract

The precise pitch and size are measured for a set of 12 ancient Chinese bells, named “Piao-shi Bian Zhong” and made probably in 404 B.C., which have been preserved at the Sen-Oku Hakko Kan Museum in Kyoto. The complete set consists of 14 bells, including the 12 bells measured in this paper and two other bells preserved at the Royal Ontario Museum in Canada. Zhong, a kind of Chinese bell with an almond-like cross section, emits two tones according to the position struck. The bells are all constructed in a similar shape except for the thickness. The frequencies of the 12 lower tones were found to be inversely proportional to the squared distance between the two tails of the lateral spines, called “xian,” of the bells. This was the same with the upper tones. This relation suggests that ancient craftsmen should probably have taken advantage of such an empirical formula to determine the size of each bell to produce two specified pitches of a musical scale.