Speaking of the matter of measurement, the "Book of Han" records it in great detail. In the ninth year of Emperor Wu's reign, Xun Xu, the Minister of the Imperial Library, was responsible for correcting the court's music and found that the eight notes were out of tune. It was then discovered that the rulers from the Eastern Han to the Wei Dynasties were over four fen longer than the ancient ones. Xun Xu instructed Liu Gong, the Imperial Clerk, to remake a ruler based on the standards set forth in the "Rites of Zhou," which represents the true ancient standard!
With this ancient ruler, bronze tuning instruments were recast to calibrate the musical scale. When measuring ancient artifacts with this ruler, the dimensions matched those recorded in the inscriptions perfectly. Additionally, an individual in Ji County illegally excavated the tomb of King Wei from the Warring States period and unearthed jade musical stones, bells, and chimes from the Zhou Dynasty, and, surprisingly, the sound closely resembled that of the newly cast tuning instruments! Around the same time, old bells from the Han Dynasty were discovered in several locations, and when played alongside the newly made tuning instruments, the sound was harmonious. Xun Xu also engraved an inscription on the ruler consisting of eighty-two characters, which states: "In the tenth year of Jin Tai Shi, the Imperial Library verified ancient artifacts, noting that the current ruler is four and a half fen longer. Seven types of ancient standards were established: Guxi Jade Musical Stones, Xiaolu Jade Musical Stones, Xijing Bronze Measuring Vessel, Jincuo Measuring Vessel, Bronze Hu, Ancient Coins, and Jianwu Bronze Ruler. Guxi Jade Musical Stones are slightly higher, Xijing Bronze Measuring Vessel is slightly lower, while the rest match this ruler." This ruler was newly crafted by Xun Xu, while the ruler commonly used today was made by Du Kui.
Xun Xu's newly made bells and music harmonized well with the sounds of ancient instruments, and people at the time praised his craftsmanship. However, the Assistant Cavalry Minister Ruan Xian criticized that the sound was too high-pitched, which sounded desolate; it was not the sound of a thriving kingdom but rather the sound of a fallen one! The sound of a fallen kingdom is sorrowful and laden with melancholy, making listeners feel uncomfortable. Now, this sound fails to meet the standards of refined music, likely due to differences in measurement standards between ancient and modern times. Later, Ruan Xian fell ill and died, and Emperor Wu believed that Xun Xu's tuning matched the instruments of the Zhou and Han dynasties, so he adopted it. Later, during excavations in Shiping County, an ancient bronze ruler was discovered, which had nearly disintegrated over time, and its dynasty remained unknown; it turned out to be four inches longer than the ruler made by Xun Xu! At that moment, everyone recognized Ruan Xian's keen insight, but no one could understand the reasoning behind it.
Historical records state that the standards established by Xun Xu, when viewed over millennia and referencing the systems of various dynasties, were very suitable in terms of measurement and musical pitch, and could be said to be extremely precise and reliable. However, the people at that time had a limited understanding, only focusing on minor details they had heard, neglecting the systems of the Zhou and Han dynasties, and blindly praising or criticizing—this was truly ridiculous! The "Shishuo Xinyu" records, "A farmer found a jade ruler from the Zhou dynasty in the fields, claiming it to be the world's standard ruler." Xun Xu used it to calibrate his own metal and silk musical instruments and found that they were all one meter shorter than it.
Moreover, during the reign of Emperor Zhang of Han, the historian Xi Jing from Lingling discovered a jade ruler beneath the shrine of Emperor Shun in Lingdao and used it for measurement. It was referred to as the "Han Official Ruler." When compared with Xun Xu's ruler, Xun Xu's ruler was four fen shorter than the Han Official Ruler; the Han Official Ruler and the Shiping Ruler were the same length. Also, the tuning ruler used by Du Kui was one chi four fen seven mao longer than Xun Xu's new ruler. In the fourth year of the Wei Jingyuan era, Liu Hui commented in "Nine Chapters on the Mathematical Art" that during the Wang Mang era, Liu Xin's hu and ruler were four fen five mao shorter than the rulers at that time; compared to the rulers of the Wei dynasty, the hu had a depth of nine cun, five fen, and five mao; this aligns with Xun Xu's statement that "the current ruler is four fen and a half longer." After the Yuan Emperor, the rulers found in the Jiangdong region were one chi six fen two mao longer than Xun Xu's ruler. In the fourth year of Guangchu, Liu Yao of the Zhao kingdom cast the Hunyi, and in the eighth year, he cast the Tugui. The ruler he used was one chi five fen longer than Xun Xu's ruler. Xun Xu's new ruler was mainly used for tuning, and it was not widely circulated among the people, so the instruments made in the Jiangzuo region and by Liu Yao were similar to the rulers of the Wei dynasty.
It is said that in the "Rites of Zhou," there exists a measuring instrument known as "Li Shi," which is one chi deep, featuring a square interior with sides measuring one chi, and a round exterior, with a volume of one sheng. Its "tun" (similar to a small handle) is one cun long and has a capacity of one dou; its "ear" (similar to a handle) is three cun long and has a capacity of one sheng; it weighs one jun in total, and its sound is the same as the Huang Zhong. This kind of measuring instrument is exempt from taxation. There is an inscription on it: "Designed with care, striving for perfection; the standard measuring instrument has been completed, available for reference by all countries; benefiting future generations, this instrument serves as a benchmark." In the "Zuo Zhuan," it is also mentioned that prior to the establishment of the Qi kingdom, there were four types of measuring instruments: dou, qu, sheng, and zhong. Four sheng equal one dou, four dou make one qu, four qu make one fu, and ten fu make one zhong.
Next, let's talk about the volume of these measuring instruments. According to the records of the "Zuo Zhuan," one unit is six sheng, one pot is six dou plus four sheng, and one zhong is sixty-four dou. Zheng Xuan believed that the pot had a square shape with each side measuring one chi, with a volume of one thousand cubic inches, which differs slightly from the result calculated in the "Nine Chapters on the Mathematical Art - Grain Calculation," missing two sheng, eighty-one fen, and twenty-two. After calculation, the volume of the ancient hu is approximately one thousand five hundred sixty-two point five cubic inches, with a square base measuring one chi and circular sides, with a diameter of approximately one chi, four cun, one fen, four hao, seven seconds, and two hou, and a depth of one chi. This represents the standard measurement for the ancient hu.
In the "Nine Chapters on the Mathematical Art - Shang Gong," it states that one hu of millet has a volume of two thousand seven hundred cubic inches; one hu of rice has a volume of one thousand six hundred twenty-seven cubic inches; one hu of beans, da, hemp, and wheat has a volume of two thousand four hundred thirty cubic inches. This is primarily determined by the weight and texture of the grains for pricing purposes, so although the prices are the same, the volumes of different grains vary. If we use the hu of rice as a standard, it aligns with what is recorded in the "Book of Han." In the fourth year of Wei Jingyuan, during the time of Prince Chenliu, when Liu Hui annotated the "Nine Chapters on the Mathematical Art - Shang Gong," he said: "The hu currently used by the Grand Minister of Agriculture has a circular shape with a diameter of one chi, three cun, five fen, and five hao, a depth of one chi, and a volume of one thousand four hundred forty-one fen ten fen three. The copper hu from the time of Wang Mang, calculated according to the current ruler, has a depth of nine cun, five fen, and five hao, and a diameter of one chi, three cun, six fen, eight hao, and seven miao. According to my calculations, the volume of the hu from Wang Mang's era is approximately nine dou, seven sheng, and four he." This indicates that the hu during the Wei Dynasty was larger and used a longer ruler, while the hu from Wang Mang's time was smaller and used a shorter ruler.
Speaking of "hengquan," the word "heng" means balance, and "quan" means weight. The purpose of "heng" is to bear weight and achieve balance, that is, to weigh both light and heavy items equally. In ancient times, there were many units of measurement, including shu, lei, chui, zi, huan, jun, lue, and yi, with different names in different dynasties. The "Book of Han" records that the hengquan system of the Han Dynasty was very complete with various units of measurement, but over time, the hengquan system underwent several changes, the specifics of which are unknown to me. During the Yuan Kang era, a man named Pei Wei said that medical prescriptions can affect human lives, but the units of measurement currently in use differ from those in ancient times, which poses significant dangers. The hengquan system should be properly revised, but no one paid attention to him.
In the eighteenth year of Zhao Shile's rule, in July, during the construction of Jiande Hall, a round stone that looked like a water mill was dug out, inscribed with the words "Luquan Stone, weighing four jun, for legal measurement." It was created by the Xin family. Subsequent research revealed that this originated from the era of Wang Mang.
