Ancient Chinese Bells Research Articles

A “set” of ancient bronze bells excavated in Changsha, Hunan Province, China

This article explores the criteria used to ascertain whether or not, and how, ancient Chinese bronze bells might form sets of musical instruments, thus clarifying their original intended use by ancient musicians. The focus is on ten bells unearthed from Changsha city in Hunan province in China, which date to the twelfth century BCE. A range of diverse relationships between these bells provide valuable insights that can be explored. Debate is ongoing among music historians regarding the nature of the bells. Some argue that the ten bells do not constitute a set of musical instruments because their designs and acoustic properties lack sufficient similarity and correlation. Conversely, another group of historians suggests that nine of the ten bells could indeed be seen as a set, but with the tenth bell being an outlier due to its distinct design. The third group of historians contends that the ten bells should be considered a musical set because of their organized sequence of consecutive semi-tones, while the design differences of the bells are less significant and can be overlooked if we focus on their musical functions. In this study, we scrutinize the assumptions made by these music historians, including their definitions of design similarity and the sequence of progressive pitches. Further previously overlooked criteria, such as the geographical proximity of these ten bells and others found in neighboring areas, and the incremental changes in the bell sizes, are also considered. Through the use of these criteria we aim to explore a wide range of relationships between ancient Chinese bells and to reassess what other new evidence the bells may offer to the study of ancient Chinese musical concepts. The concept of the chromatic scale discovered by ancient Chinese musicians was embodied on the casting of bronze bells.

Acoustics of Western and Eastern bells, old and new

The modes of vibration and sound radiation from tuned church bells, carillon bells, handbells, ancient Chinese two-tone bells, and temple bells will be compared. Most bells have a circular cross section, but many ancient Chinese bells do not, and thus they have two different strike notes, depending upon where they are struck. The musical interval between these two strike notes is often near a minor third or a major third.

A theoretical study of the vibration and acoustics of ancient Chinese bells.

In this paper, the acoustics of an ancient Chinese bell, which was made some 3000 years B.C., is studied theoretically. In ancient times, a set of the bells was used as a musical instrument. Unlike a western church bell and an ancient Indian bell, an ancient Chinese bell has two interesting acoustics. First, two tones can be heard separately as the bell is struck at two special points. The interval between the two pitches is always a minor or major third. Second, tones of the bell attenuate quickly, which is necessary for a musical instrument. So, an ancient Chinese bell is sometimes called a two-tone bell or a music bell. Although a three-dimensional model should be used to simulate the acoustics of the bell, a simplified model proposed in this paper does give some insight. Based on the lens-shaped cross section of an ancient Chinese bell, two tones of an ancient Chinese bell can be simulated by the vibration of a double-circular arch and the quick attenuation of tones can be simulated by acoustics of a cylinder with the lens-shaped cross section like a double-circular arch. Numerical results on the vibration and acoustics of the models are presented.

Acoustics of ancient Chinese bells

Many ancient Chinese bells, some more than 3000 years old, remain from the time of the Shang and Zhou dynasties. Most of these bells, being oval or almond shaped, sound two distinctly different musical tones, depending upon where they are struck. Studies of these bells have provided us with much knowledge about the musical culture of Bronze age China. Results are reported from our investigations of original bells in the Shanghai Museum and the Sackler Gallery at the Smithsonian Institution, as well as replica bells in our own laboratory. Modes of vibration in original bells, obtained by experimental modal testing in the museum, compare very well with holographic interferograms of replica bells. Our results are compared with our catalogue of data on ancient Chinese bells gathered by other investigators. Although acoustical studies have revealed a great deal about ancient Chinese music and casting practices, several questions still remain unanswered.

Modal analysis of noncircular cylinders and bells

In oval cylinders, the familiar vibrational modes of a circular cylinder are split into doublets, one new mode having a node in the region of greatest curvature and the other having an antinode there. Since increasing the curvature increases the effective stiffness and thus raises the speed of bending waves, the bending wavelengths are generally longer (and the nodes further apart) in the region of greater curvature. This phenomenon is the basis of the ‘‘two‐tone’’ phenomenon in ancient Chinese bells. The mode splitting in a variety of noncircular cylinders and bells, observed by means of holographic interferometry and experimental modal testing with impact excitation, is described. By using two mirrors, it is possible to view simultaneously the front, end, and top of a vibrating cylinder in holographic interferograms.

Scaling of bells

The fundamental frequency of a bell has roughly the same dependence on thickness and diameter as flexural vibrations in a circular plate, and thus in designing a bell chime or ensemble of bells, it would be possible, in principle, to scale all dimensions proportional to 1/f. Tonal considerations often dictate otherwise, however, and in practice different scaling laws are found in ensembles of large and small carillon bells, church bells, handbells, and ancient Chinese bells that have been studied.

Sound spectra of ancient Chinese bells in the Shanghai Museum

Sound spectra were obtained from ten bells from the 5th–12th centuries BC by striking them at the appropriate sui and gu locations. Although considerably different in size, shape, and ornamentation, all the bells had oval cross sections and thus exhibited two‐tone behavior [T. D. Rossing et al., J. Acoust. Soc. Am. 83, 369 (1988)]. Frequency ratios of the two fundamental (2,0) modes range from 1.11–1.31 (181–473 ¢). In most spectra, it is possible to identify two partials most likely associated with two (3,0) modes that have frequencies 2.32–3.29 times the lowest (2,0) mode. The spectra of these bells are compared to those of other Chinese bells, including those of the renowned Zenghou Yi.

Acoustics of Eastern and Western bells, old and new.

Bells have many modes of vibration whose modal shapes are characterized by the numbers of nodal meridians and nodal circles. In Western church bells and carillon bells, the bell is shaped so that the lowest mode frequencies are harmonically related. The subjective strike note is determined by three strong partial tones with frequencies nearly in the ratios 2: 3: 4. The pitch of a handbell, on the other hand, is determined by the frequency of the fundamental tone. In ancient Chinese bells, the vibrational modes occur in pairs, and two different tones result from striking at the sui and gu strike points. A new type of carillon bell has been developed in which the traditional minor third partial is replaced by a major third partial, thus changing the timbre of the bell.

Size-frequency relation and tonal system in a set of ancient Chinese bells: Piao-shi bianzhong.

Resonance frequencies and tonal system are investigated on a set of ancient Chinese bells named “Piao-shi bianzhong.” According to the measurement of 12 bells preserved in Kyoto, it is found that a simple relation between frequency and size holds well. The relation tells frequency of a bell inversely proportional to square of its linear measure. It is reasonable to conclude that the set was cast for a heptatonic scale which is very similar to F# major in our days. Preceding studies in history and archaeology on Piaoshi bells are also shortly reviewed.

Acoustics of Eastern and Western bells, old and new

Bells have belonged to nearly every culture in history. The oldest surviving bells from the Near East and China are thought to be over 3000 years old. Many ancient Chinese bells, by virtue of their oval shape, have two distinctly different strike notes, separated in pitch by about a major or minor third. Bells developed as Western musical instruments in the 15th and 16th centuries when bell founders learned how to tune their partials harmonically. The acoustical behavior of Western church bells, carillon bells, and handbells are compared to those of ancient Oriental bells. Recently carillon bells with a major third replacing the traditional minor third partial have been developed [A. Lehr, Music Percept. 4, 267 (1987)].

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

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.

Dependence of vibrational modes of a handbell on thickness and added mass

The vibrational modes of a large tuned handbell (G2) are compared with those of an untuned bell casting having the same shape but with twice the thickness. Doubling the wall thickness is found to raise the frequencies of the various modes by factors ranging from 1.4 to 2.4 (flat plate theory predicts a factor of 2 for all modes). Unlike the tuned G2 handbell, whose pitch coincides with the frequency of the fundamental mode of vibration, the thick bell has two prominent strike notes, depending upon where it is struck. These subjective tones appear to be created by groups of three nearly harmonic partials radiated by the (m,l) and (m,l♯) families of modes, respectively. The acoustical effects of attacking up to twelve 35‐g brass cylinders have also been observed, both in a symmetrical pattern and in clusters similar to the clusters of mei found on ancient Chinese bells [Rossing et al., J. Acoust. Soc. Am. Suppl. 1 77, S102 (1985)]. The additional masses lower the frequencies of certain modes but have relatively little effect on modal decay rates.

Vibrational modes of Chinese two-tone bells

The vibrational modes of a modern copy of an ancient Chou dynasty bell have been studied by means of holographic interferometry and by scanning the sound field near the bell. The modes are compared to those observed in church bells, carillon bells, and handbells, as well as other ancient Chinese bells. Modes tend to occur in pairs, one with a node at the xian or spine, and one with an antinode there; the frequencies of the two doublet members differ by about 3% to 10%. Bells of this type emit two distinctly different notes, depending upon where they are struck.

Acoustics of Ancient Chinese Bells

In 1978 a set of 65 chinese bronze chime bells was unearthed in hubei province, southern china. The chime, dating from the 5th century bc, covers 5 octaves. A filigree of gold inlaid inscriptions on the bells and their frame indicates the existence of an elaborate theory of music and has prompted the re-writing of acoustical history. Neither the principle nor the practice of this unique bell design was passed down. Single chime bells first began to be discovered some 80 years but their ability to produce dual pitch (1 note if sounded from inside, another if struck on the side) was only rediscovered by chance in 1977. The asymmetric construction which produces these acoustical properties is explained, with diagrams and photographs.

Vibrational modes of a Chinese two‐tone bell

Many ancient Chinese bells, by virtue of their oval shape, sound two distinctly different tones, depending upon where they are struck. These so‐called sui and gu tones usually differ in pitch by about a minor third. The vibrational modes and sound radiation from a carefully dimensioned modern copy of a Chou dynasty (1030—221 B.C.) bell in the Dutch National Carillon Museum have been studied. The lowest modes, and many of the higher ones as well, occur in pairs, with one member having an antinode near the sui strike point and the other near the gu strike point. The frequency separation of these doublets is determined by the shape of the bell. The modal shapes, determined by holographic interferometry, are similar to those observed in round church bells, but with more mixed modes due to the greater damping.