Politics of precision in ancient China

Later this year the General Conference of the International Committee for Weights and Measures is scheduled to meet outside Paris to discuss a major metrological question that has provoked strong passions and extensive research: whether to keep the current artifact-based kilogram standard or replace it with an absolute standard. But discussions of how to connect units and standards have flared passions and inspired research since ancient times—and not only in the West. In the past few years, for instance, scholars of early China have unraveled an episode involving metrological change in the Jin dynasty (AD 265–420) that sheds light on a complex and unique blend of metrology, musicology, and politics in ancient Chinese courts.

Weights and measures have a long and venerable history in China. ¹ Relics showing that the ancient Chinese passion for defining and maintaining proper order extended to their measurement practices date back to the Neolithic era in the third millennium BC. The precise manufacture of jade ritual artifacts as early as 2000 BC reveals the use of systematic measurement practices. ² The earliest linear measures used to make those artifacts were based on body parts, especially fingers and hands. The principal body-derived measures were the chi (pronounced “chur”), a foot measure that could vary from 16 to 24 cm, depending on the time period and geographic region, and the cun (“tswun”), which was once connected to finger width but by 400 BC was regulated at one-tenth of the chi. At least as early as the Neolithic era, however, those units were tied not to the bodies of individuals but to easily duplicated measuring sticks.

The diversity of measures persisted through the Shang dynasty (about 1600–1046 BC) and the Zhou dynasty (1046–256 BC), two long-lasting but not heavily centralized dynasties. In the Shang dynasty, the shapes and sizes of ritual vessels and the ornamental designs on them came to be governed by precise mathematical rules. Those rules were not simply for the sake of proper proportion or even aesthetics; they were symbolically significant, reflecting deeper proportions in the universe. “Structure was an element in the hierarchy of meaning, a metaphor for the moral and spiritual order of the universe made plain for all to see,” wrote Robert Poor, a professor of art history, in an article on the role of measurement in ancient Chinese ritual. ³ Bronze bells were also increasingly important in Chinese life, thanks to technological developments. From about 1200 BC onward, bell foundries sprang up, especially in the south, to satisfy a steady demand for military music and signaling. The bells’ form became standardized, with artisans continually trying to improve their sound.

Bells as standards

In the Zhou dynasty, a truly national Chinese culture and state emerged: The written language was developed to a high level, iron use became common, and China’s great philosophers, including Confucius, Lao Tzu, and Mencius, delivered their teachings. Court policies and practices concerning authoritative rites began to be standardized. They included ideas about proper musical performances and involved specification of the harmonic system. ⁴ Bells began to work their way into the court ritual-religious system and became increasingly important in its emerging musicological component. By 800 BC, court ceremonies of investiture, worship, and liturgies used to mark the ritual calendar and define royal authority came to rely on increasingly elaborate and expensive cast-bronze bells, singly and in arrays. Imperial music masters began to explore note possibilities beyond the 3, 4, or 6 bells that were usually available. When a 12-note system developed, sometime before about 400 BC, it further elevated the ritual importance of bell chimes, because the 12 tones were readily integrated into a mathematical philosophy. “Tuned bell chimes,” says Howard L. Goodman, an American scholar of early China, “could demonstrate to the emperor’s underlings and visitors a totalistic harmony that related to formulas, mathematical completeness, and a mysterious confluence of tunes and numbers, all of which increased the king’s importance and ritual power.”

Most of China’s old capital cities had bell and drum towers that marked off the hours and served as landmarks for city planning. But the ritualized music at imperial courts, which took place in palace rooms or at altars just outside the palace, involved a far more intimate interweaving of music into court culture. The ritual 12-note harmonic scale system was called the lülü—a deceptively simple name for something as serious and elaborate as a sonic system; the name consists of two unique Chinese characters both coincidentally pronounced “lyu.” As archaeologists have discovered, many ancient bell-chime tunings reflected the lülü notes. The lowest of the 12 notes was called the huangzhong (“hwahng-joong”), a term that was often used alone to imply musical correctness. The harmonic system was not equal tempered, with every pair of adjacent notes having identical frequency ratios as in the Western European classical tradition; it would sound out of tune to our ears, and was not the 12-tone scale of Arnold Schoenberg, say, though it consisted of a sequence of 12 relatively evenly spaced steps.

The names of the individual bells developed slowly over hundreds of years until about 400 BC, with different names in different regions. During that time both the bells’ nomenclature and the mathematicization of the harmonic system became standardized. In 1977, bulldozers leveling a hill to build a factory in Suizhou, China, uncovered the tomb of a minor Zhou-dynasty lord named Marquis Yi, dated sometime after 433 BC; the tomb contained a vast collection of bells complete with musical notations explaining the scale and relationships between keys. Research in the wake of the discovery has vastly improved our knowledge of the ancient scale system and its role at court. ⁵

In particular, pitch was important—of “critical importance”—at court, writes University of Pittsburgh physicist and music historian Bell Yung, and often, he adds, it was “exploited in power struggles among the different factions in the preparation of ritual.” ⁶ To set the base pitch for the zithers, flutes, and singers of imperial court orchestras, the 12 steps of the lülü were linked to the dimensions of 12 pitch pipes. Those pitch regulators were cast-metal, straight-walled tubes without finger holes, and their length was specified by court regulations in chi. Thus the chi—the basic unit of length—was inextricably connected with musical pitch, at least at the imperial court. Outside the court little is known and few artifacts exist, though the chi surely was at least loosely governed by the court’s definitions.

Grains as standards

China’s first centralized, imperial regime appeared in 221 BC, when a warlord named Ying Zheng conquered local lords and gave himself the imperial title Qin Shi Huang Di, appropriating the name of the legendary ancestor of Chinese civilization. His first act as emperor was to issue an edict unifying weights and measures in the realm; the edict was carved on or cast into the weights and measures themselves. It was the first unification of weights and measures in China.

The Qin dynasty was succeeded by the Han dynasty (206 BC–AD 220), which also issued edicts for weights and measures, developed harmonic scales and metrological instruments, and began the tradition of creating and preserving documentation of imperial metrology. During the Han era, numerology and mathematics blossomed in court scholarship, with treatises coupling the harmonic system, celestial motions, and the calendar. Having court instruments pitched properly grew in importance in establishing the legitimacy of the dynastic rituals.

The proper pitch was produced by pitch pipes, which had been constructed to classically prescribed lengths. The huangzhong was also involved in the definition of the court’s capacity measure. An important court history titled Hanshu—literally, historical documents of the Han dynasty—defines both the chi and the capacity measure in terms of the number of millet grains placed end to end so as to be equivalent to the length of a huangzhong pitch pipe. Several famous writings around the second to third century BC specify that length as 9 cun, or 0.9 chi. Ninety black millet grains defined the chi, and 1200 grains defined the capacity measure, with yet another measure being the weight equivalent of the number of those seeds that filled a huangzhong pitch pipe. With the use of such definitions during the Han dynasty, metrology became intimately bound up with ritual practices—the court’s religious system, the symbology of court dress and uniforms, astronomical observances, and the lülü musicological system.

The court metrology—the length and weight standards determined by court scholarship—did not always extend outside the palaces into the towns and countryside. Nevertheless, in the court precincts, metrology had a symbolic significance, a social and cultural meaning related to metaphysical ideas, classical texts, and artifacts. The science and execution of measurement standards in a ritual context has been termed metrosophy. ⁷

The life of Xun Xu

In a recent book, ⁴ Goodman describes a remarkable episode in the life of a court official named Xun Xu (AD 221–289) during the Jin dynasty. The episode, which reveals much about the connection between metrology, musicology, and politics in imperial China, concerns Xun’s attempt to introduce a tiny though politically significant change to the chi and the political fallout that ensued.

Xun was from a politically well-connected family in Luoyang, which had become the imperial seat of the Wei dynasty in AD 220. He was a junior scholar for the Wei dynasty, one of several warring kingdoms that succeeded the Han. He was also respected as a portraitist and court archivist and had a keen musical ear. According to an undoubtedly apocryphal story, at some point he realized he needed to re-create a sound he had once heard a cowbell make on a trip he had taken to the north. Later at the capital, he ordered his staff to round up cowbells from that area, and to his delight he was able to pick out the one he had heard decades before.

In AD 265, the Wei dynasty was overthrown, and its leader assassinated, by friends of Xun’s family. Xun was soon an insider in the new Jin dynasty and a leading member of an ambitious faction that sought to influence the court through planning of the royal succession and, in Xun’s case, through politically charged technical reforms. Around 270 an elder cousin recruited him to reform the new dynasty’s musical practices. Such reforms were not uncommon: Each new emperor would order a scholarly reexamination of the inherited ceremonies to make sure they were technically correct, each exercising the virtue of “right conduct” essential to political legitimacy. Most scholars in Xun’s position would have made minor changes. Xun, obsessively ritualistic and politically ambitious, immediately introduced a significant change in the verse lines of the ritual songs. Other court officials opposed him, but Xun replied with aesthetic arguments that his reforms sounded better and with antiquarian arguments that his was the way it had been done in the idealized ancient Zhou times. His reform was both musicological and political: It implied that the practices of the previous Wei rulers were illegitimate, and it cast suspicion on lingering Wei policies and their supporters.

Xun’s court duties also included searching palace storerooms for ancient artifacts, which led him to create another court revolution, this one musical and metrological. In 274 he came across a cache of old bronze pitch-pipe regulators called lüs, used by previous court musicians to establish pitch for the court instruments.

Most court scholars would have simply used the inherited pitch regulators and found some references in classic texts to justify their use. Not Xun. He compared the sound of the ancient lüs with ones currently used at court and found the older ones pitched slightly lower. That inspired him to mount a vast project to collect, identify, and compare standards from earlier dynasties. He concluded not only that the current court instruments were literally out of tune with the ancient orchestras and cosmic harmony but also that the ancient chi itself had become inappropriately long during the last decades of the Han dynasty. “This was not a way to investigate antiquity and honor the sages,” wrote Xun, “nor to provide a system for later generations.”

Goodman terms Xun’s strategy of harking back to the Zhou his prisca Zhou, adapted from the West’s prisca theologia, the belief of Protestant scholars in 16th- and 17th-century Europe that adoption of a pure, Biblical form of theology could improve the world and offer its people a blessed life. Xun provided the Chinese court a similar kind of revisionist critique of the present by appealing to a more distant and authentic past. For example, Goodman writes, imagine if Western religious legitimacy “were to have depended on establishing Christ’s (or Paul’s, or even Gregory I’s) exact pitch for psalmody, whether through some vaguely reconstructable pipe, trumpet, or string-length, or, more abstractly, a radical reading of scripture that might point to specifications of magnitudes” (reference 4, page 211).

Xun’s high status gave him access to workshops and a trained staff. He ordered a new bronze chi standard cast, about 23.1 centimeters according to our measures, about a centimeter shorter than the ones made at the end of the Han dynasty and imitated in the Wei dynasty. It was not difficult for Xun to revise the length standard himself, in the absence of professional metrologists or independent taxation and mercantile agencies, whose interests would be threatened by a change. Nor was there any significant international commerce that might be adversely affected by or pose an obstacle to its implementation. Xun’s change in the length standard, Goodman writes, was his career signature, “a ritualized search for an ancient, or Zhou, truth” (reference 4, page 176). It was as if NIST in the US sought to elevate its political profile by insisting that the government use the feet, inches, and pounds that the founders had used in Philadelphia in the late 1700s.

The Jin emperor happily implemented the measures, though people in the countryside familiar with the existing measures resisted. Xun’s work reinforced the emperor’s legitimacy by showing that the Wei dynasty annihilated by the emperor’s family was ritually incorrect. Xun’s corrections also resonated with the struggles among families jockeying for court control. His newly adjusted tuning system applied only to the ritual court music and did not affect the folk music known as yuefu (“ywe-foo”) that was extremely popular outside court walls after about AD 100. That music had been steadily gaining in popularity in court and had been especially fashionable in Wei times. Goodman’s research suggests that the yuefu style of music at court may have been made to adapt to the new tuning, and Xun’s brilliant maneuver both allowed the popular new music in the court and subjected it to imperial control. His new chi, however, was applied only inside the court walls; outside, in the markets and countryside, the other traditional measures continued to follow their own practical logic. “Xun’s standards,” Goodman writes, “did not flow into the practices of palace clothiers, coin casters, and other craftsmen who did not share the need for a prisca Zhou reform. The foot-rule as a metrological ‘overseer’ did however remain a mainstay of court rites and even court liturgies” (reference 4, page 196).

Xun went even further with musicological reforms. Based on his new chi magnitude, Xun made 12 pitch-pipe tone regulators, which in turn were used to correct the court orchestras’ di (“dee”) flutes. Those instruments in various forms dated back many hundreds of years. Open-ended and made of bamboo, the flutes played pentatonic or heptatonic scales. Using a remarkable algorithmic-like process, Xun adjusted the spacing of the finger holes according to the new chi and its derivative pitch regulators. That process, though it didn’t yet solve the problem of equal temperament, sought to impose the ideal harmonic system of the lülü upon the problems of tone and pitch in real instruments.

In the 1980s and 1990s, Xun’s flute finger-hole spacing system was extensively studied by Chinese music archaeologist Zichu Wang, who used a Stroboconn, an electronic device to measure musical pitch, to compare sounds produced by cylinders constructed with equal hole spacings with sounds from cylinders constructed according to Xun’s algorithm and patterned after the design of ancient flutes. ⁸ Wang was particularly interested in exploring the “end correction”—that is, whether Xun compensated for the fact that the structure of a fundamental pitch is changed by the pressure wave of the escaping sound wave from the finger holes.

In 2008 Goodman, who early in his career studied music at the Juilliard School, teamed up with Y. Edmund Lien, a former engineer who had changed careers and become a graduate student in Chinese literature at the University of Washington, to analyze Wang’s work. They concluded that in the third century Xun had not yet grasped the physical phenomenon of end correction (though some Chinese scholars dispute that); the effect would remain unaddressed by music scholars until Muslim philosopher Abu Nasr al-Farabi tackled it in the 10th century. Nor was Xun seeking equal temperament. Rather, he was seeking through his algorithm how best to accommodate the numerological lülü scheme to the demands of real performance and the need to use the chromatic scale to play in different keys. For the first time, Goodman and Lien write, Chinese court orchestras had “flutes that used the ritual pitch-standard pitches so as to be in tune when responding to mode and key variation.” Through his meticulous attention to detail, Xun in a certain sense brought the court music into “real-world physics and acoustics.” ⁹

Postscript

Xun’s metrological reformations did not last. His strident faction ran afoul of court politics, and he himself was accused of bad scholarship and defective aesthetics—he made the flutes play too high, charged critics. He was forced to transfer to another position with no metrological or musicological power. Archaeological evidence shows that chi standards in various contexts grew longer again within only a generation or so after Xun’s death.

Though Xun’s episode resulted in only a momentary change in the length of the court chi, the volatility of the length measure and its dependence on musicological issues, as deciphered by the various interdisciplinary researches of Goodman, Wang, Lien, and others, reveals much about what was strongly coupled to what in China’s third-century-AD courts—and, in fact, for long stretches of Chinese imperial history.