Ming Shu (míng shù), oh, friends gather together, secretly helping, with favorable winds and timely rains, starting to govern the world, when all things revive, shaking the heavens and the earth, riding on the beautiful season, exuding fragrance, spreading a wonderful atmosphere, bringing joyful news at lightning speed, the ranks of officials grow, sowing seeds everywhere, free and easy, carefree and joyful, benevolent yet dignified, competing to develop southward, as the sun rises in the east, morning arrives, all things grow, each developing, renewed and refreshed.
This part is the "Jia Zhong" melody, consisting of twenty-seven musical phrases.
Next is the "Gu Xia" melody, consisting of thirty-four musical phrases. Good news comes from the south, reminiscing about the hometown, honoring the deities, this demonstrates our unity, erasing old evils, changing the status quo, selecting talents, auspicious energy starts to rise, beautiful clouds (qīng yún), picturesque mountains, smooth roads, the timing is perfect, travelers are constantly on the move, the blazing sun, strong winds, soft branches, starting to bear fruit, punishments become fair, all things prosper, new grass flourishes, fruits are abundant, light shines all around, flourishing growth, (lower life brings peace) following the natural order, (upper life nurtures) developing upwards, embracing all things, selecting a few people, following reason, dressed in crimson robes, gaining fame in the court, maintaining purity.
The "Zhong Lü" melody, consisting of twenty-seven musical phrases. The crimson light heralds new fortunes, the scenery is picturesque, the weather is pleasant and sunny, birds and animals become lively, the southern region says goodbye to spring, beginning to guide farmers in their work, orderly and methodical, the southern region warmly welcomes the changing seasons, coordinating with each other, hearts steadfast, red foliage gleaming, dedicated to great causes, illuminating the fields, at the snake hour the weather is cool and warm, everything is thriving, cautious of lean years, desolate sights fade away, righteous instruments play, may heaven bless the Zhou Dynasty.
"Ruibin" musical mode, comprising twenty-seven musical phrases. The affairs of the South (the Jingfang's final law) are quiet and peaceful, choosing the right moment, adorned with blossoms, full of vitality, subtly transforming, undergoing significant changes, guests feel at peace, reminiscing about the distance, the sound resonates far and wide, the paths are aligned, the sea is calm, disasters are averted, away from chaos, robust tranquility, championing light, looking into the distance, rising to the center, phoenix flying, the sun rising, seizing the opportunity, auspicious signs, the emergence of the Chunhuo star, orderly, with flames soaring and radiating light.
"Linzong" musical mode, comprising thirty-four musical phrases. Serving with humility, advocating morality, following reason, gradually becoming stronger, Yin energy rising, eliminating evil, removing disasters, prosperity fading, friends celebrating, clouds filling the sky, equally sharing responsibilities, looking up to achievements, tolerant and peaceful, passing through peacefully, morally balanced, free from obstacles, etiquette prevailing, deep wisdom, serious responsibilities, unwavering loyalty, returning to goodness, beautiful sounds, warm wind, waiting for the opportunity, Minhua blooming, beautiful mountains and hills, all things unobstructed, beautiful scenery, clear well water, sunshine everywhere, overlapping wheels, prosperity in wealth.
"Yize" musical mode, ... Speaking of this ancient music, it is divided into several parts, just like how we listen to songs in playlists nowadays. Let's start with this part of "Yize", comprising twenty-seven tunes, listening to it is quite refreshing, evoking a sense of clarity and precision, like "Shengshang refreshing and refined, Yinde white hidden imperial decree, fresh punishment sincere gold sky", imbued with righteousness. Then there are "Liu Shen meeting the way of benevolence, Yinlu going south, Yang eliminating soft bitterness, extending Yi and Geng, Mi Hui Ti Jin, dividing accumulation Kong Xiu, nine virtues all respect, Qian Wei Bi Yi" and so on; they instill a sense of calm and comfort.
Next is the "Nan Lu" section, which is quite substantial, comprising thirty-four different tones! The melodies of "Nan Lu" are richer and more varied than those of "Yi Ze," with some strong and some gentle, much like the many facets of life. The intricate lyrics evoke a sense of grandeur and mystery, creating a feeling that is both majestic and enigmatic.
Next is the "Wu She" section, offering a more serene sound, ideal for quiet contemplation. Listening to it evokes the tranquil beauty of autumn scenery, bringing forth a sense of peace and charm.
Lastly, the "Ying Zhong" section has a more solemn tone, as if narrating a grand tale. The profound lyrics convey a sense of hope and resilience, filling the listener with strength and inspiration. In conclusion, these four sections of music each possess unique characteristics and charm.
It is said that in the "Records of the Grand Historian," it is recorded: "King Yu of the Xia used his own body as a measurement standard and used sound to determine musical pitches." The "Book of Rites" also states: "The length of a man's outstretched palm is one foot." The "Rites of Zhou" writes: "The edge of a jade disc serves as a standard for measuring length." Zheng Sinong explains: "'Xian' means long. The diameter of this disc measures one foot and is used as a standard of measurement." The "Yiwai Tonggua Yan" states: "The length of ten horse tails is considered one minute." The "Huainanzi" mentions: "At the autumn equinox, the awns of the grains have taken shape; when the awns are formed, the grains are mature. The number of musical pitches is equivalent to the length of twelve awns, which equals one grain, and twelve grains equal one inch." The awns refer to the bristles on the grain ears. The "Shuoyuan" states: "The standards of measurement are derived from grains, with one grain counting as one minute." The "Sunzi Suanshu" records: "The silk produced by silkworms is known as 'hu,' ten 'hu' equal one 'miao,' ten 'miao' make one 'hao,' ten 'hao' make one 'li,' and ten 'li' make one 'fen.'" All these are the origins of ancient measurements, but the accounts are somewhat contradictory. Only the "Book of Han, Treatise on Music" records more reliably: "Measurement is used to measure length and its fundamental source is the length of the Huangzhong (a large bell). Using medium-sized grains of millet—jiu-shu, the width of one grain of jiu-shu counts as one minute, and the length of ninety grains of jiu-shu is the length of the Huangzhong. One jiu-shu is one minute, ten minutes make one inch, ten inches make one foot, ten feet make one zhang, and ten zhang make one yin, thus five types of length are established." Later authors based their measurements on this account, and because the size of jiu-shu varies, various different methods emerged, though generally they were still in common use. The problem is that the size of millet differs, and in years of abundance and scarcity, the size of millet also varies. The calibration of ancient measurements often resulted in discrepancies, and coupled with oral transmission among the people, errors inevitably occurred, resulting in gradual variations. Now I will now briefly outline fifteen types of measurements from various dynasties, along with their similarities and differences, as follows: The "Han Zhi" records the copper ruler made by Liu Xin during Wang Mang's time; the copper ruler from the Jianwu period of the Eastern Han; the regulation ruler made by Xun Xu in the tenth year of the Taishi era of the Jin dynasty, which was in use prior to the Jin dynasty;
There is also the bronze ruler handed down by Zu Chongzhi. It is said that in the ninth year of the Tai Shi era of the Jin Wu Emperor, the Minister of the Interior, Xun Xu, inspected the musical instruments of the court ensemble and found that the pitch was off. Upon investigation, it was discovered that the rulers from the Eastern Han to the Wei Dynasty were over four and a half inches longer than those from ancient times. Xun Xu immediately sent the official Liu Gong to remake the ruler according to the standards of the "Rites of Zhou," which was the authentic ancient ruler! Using this ancient ruler, they recast the bronze tuning devices to adjust the pitch of the musical instruments. When measuring those antiques with this ancient ruler, the inscriptions matched perfectly! Even more coincidentally, tomb robbers in Jiyun County opened the tomb of King Xiang of Wei and surprisingly found the jade tuning instruments and bells from the Zhou Dynasty, which had pitches remarkably similar to the newly cast tuning devices! At that time, old Han Dynasty bells were also dug up in various locations, and when tested with the newly made tuning devices, they all matched perfectly! The "Bell and Tuning Weave" authored by the Liang Wu Emperor also mentions this matter, stating that the bronze ruler handed down by Zu Chongzhi is inscribed with the following inscription: "In the tenth year of Tai Shi of Jin, the Minister of the Interior verified ancient artifacts and checked the current rulers, which were four and a half inches longer. The ancient standards verified are seven types: the first is the Gu Xia jade tuning instrument, the second is the Xiao Lü jade tuning instrument, the third is the Xi Jing bronze measuring instrument, the fourth is the Jin Cuo measuring instrument, the fifth is the bronze measure, the sixth is ancient coins, and the seventh is the Jianwu bronze ruler. The Gu Xia jade tuning instrument is slightly higher, the Xi Jing bronze measuring instrument is slightly lower, while the rest are the same as this ruler." This inscription contains eighty-two characters. This bronze ruler is the one newly crafted by Xun Xu. The "Bell and Tuning Diagram" by Lei Cizong and He Yinzhi records Xun Xu's verification of the ancient ruler, and it is identical to this inscription. The music score by Xiao Ji claims these are the seven standards verified by the Liang Dynasty, which is inaccurate! We will now use this ruler as the benchmark to verify the rulers from different dynasties. The Liang Dynasty ruler is actually one foot and seven-tenths longer than those from before the Jin Dynasty.
Once upon a time, an old farmer unearthed a jade ruler from the Zhou Dynasty while digging in the fields. It was said to be the standard ruler used throughout the country at that time. Xun Xu used it to calibrate musical instruments and found that the gold, stone, silk, and bamboo he made were all shorter than the standard by a meter. The Liang Emperor also mentioned in his "Book of Bell and Music Regulations" that there was a bronze ruler from the Zhou Dynasty and eight ancient jade tuning pipes that had been preserved in the imperial palace for generations. Later, it was discovered that the Zhou ruler was used as a token by the Eastern Huan Marquis, but unfortunately, the ruler was lost afterward. Regarding the jade tuning pipes, one has gone missing, and the remaining seven were tuning pipes for bells, with previous inscriptions still visible. Thus, the Liang Emperor had people remake a ruler based on these jade tuning pipes for mutual calibration. They also measured millet with fine hairs, recalibrating repeatedly, which could be said to be the most precise measurement method of the era, surpassing Zu Chongzhi's ruler by half a unit. The Liang Emperor then used this new ruler to make four musical instruments called "Tong." He also made a flute according to the new ruler, used it to calibrate ancient bells, adjusted the pitches of the Yize pitch, and determined the pitch of Yin and Yun with the flute, thus establishing the Yize pitch. You see, the lengths of these two rulers are quite similar.
Xiao Ji states in his book, "This method originates from the Sima Method." The Liang Dynasty engraved the ruler's scale on a shadow board to measure the shadow of the sun, referring to the bronze gnomon calculated by Feng Zhao and Qing Zu Tan. Later, when the Chen Dynasty fell, this gnomon entered the court. During the Sui Dynasty's Daye period, someone proposed to restore the ancient standards, thus using this gnomon to calibrate musical scales and create eight types of musical instruments, including bells and chimes.
During the Jin Dynasty, someone in Shiping (now Xianyang City, Shaanxi Province) unearthed an ancient bronze ruler.
Xiao Ji's "Score" states: "During the time of Emperor Zhang of Han, the literary historian Xi Jing from Lingling dug up a set of jade pitch pipes under the Shun Temple in Lingdao County, and based on it, crafted this ruler." Fu Chang's "Praise of the Jin Dukes" states: "The bell pitch made by Ge Xu was considered very accurate at the time, but only Ruan Xian from Chenliu criticized it for being too high. Later, Shi Ping dug up that ancient bronze ruler, which was nearly decayed, compared it to Xun Xu's ruler, and found it to be a quarter shorter. At the time, everyone agreed with Ruan Xian's assessment." The lengths of these two rulers are also similar.
In the fourth year of the Wei Chenliu King Jingyuan, Liu Hui commented on the "Nine Chapters on Arithmetic" and said that during the time of Wang Mang, the hu and ruler that Liu Xin used were four and a half fen shorter than the rulers at that time, and compared to the rulers of the Wei Dynasty, the height of the hu was nine inches and five fen. This aligns with the statement made by Xun Xu of the Jin Dynasty, "Du Kui's ruler is four and a half fen longer than the current ruler."
Xiao Ji noted that this ruler was utilized in the Jiangdong region during the Jin Dynasty. The market ruler of the Later Zhou Dynasty was one chi, nine fen, and three li shorter than the jade ruler. The official ruler of the Kaihuang period, known as the iron ruler, was one chi and two cun long. From the early Wei Dynasty to the division of the Eastern and Western Wei, until the Later Zhou Dynasty stopped using the jade ruler, people commonly used these rulers interchangeably.
A book called "Arithmetic" states that the market ruler of the Zhou Dynasty is equivalent to nine and two fen of the jade ruler. Some say that this ruler was made by a Taoist named Zhigong from the Liang Dynasty and sent to the Zhou Dynasty, given to someone named Duoxu Laoweng. Both the founder of the Zhou Dynasty and the founder of the Sui Dynasty believed that this ruler was made for them, and the people of the Zhou Dynasty used this ruler. By the Kaihuang period of the Sui Dynasty, the official ruler officially designated this ruler as the official ruler, and all departments used it, until the Renshou period. By the Daye period of the Sui Dynasty, some ordinary citizens also used it privately.
Next, let's talk about Yuan Yanming, the Lieutenant of the Wei Dynasty, who made one foot using half the width of a millet seed, and the Qi Dynasty then adopted this standard. Wei Shou recorded in the "Book of Wei · Law and Calendar Records" that Gongsun Chong made a new foot during the Yongping period, using the length of a millet seed added together as the standard for one inch. Later, Liu Fang, the Grand Minister of Ceremonies, was ordered to revise the music, using the width of a medium-sized millet seed as a fen. Yuan Kuang, the Lieutenant, used the width of a millet seed plus two millet seed gaps as a fen. These three differing opinions led to a prolonged debate with no resolution. It wasn't until the nineteenth year of Dahe that Emperor Gaozu ordered that the width of a millet seed be used as a fen, and the length of ninety millet seeds be used as the length of the Huangzhong to determine the standard of the bronze ruler. The relevant authorities reported that Liu Fang's ruler matched that of Emperor Gaozu, so the standard for gold and stone objects was revised according to Liu Fang's ruler. Until the Wuding period, there was no further discussion on the issue of legal measurement.
Eleventh, Cai Yong's bronze ruler. The jade ruler of the Later Zhou Dynasty was one foot, one inch, five fen longer than the rulers before the Jin Dynasty. From ancient times to the present, there has been a bronze ruler passed down, decorated with silver filigree craftsmanship, inscribed: "Ruler, the palace of Huangzhong, nine inches long, nine fen in circumference, capable of holding twelve hundred millet seeds, weighing twelve zhu, with two zhu equaling one he. Three points of gain or loss, transform into twelve laws." Zuxiaosun said, "It is said that this is Cai Yong's bronze ruler."
During the Baoding period of Emperor Wu of the Later Zhou Dynasty, the emperor ordered Dazongbo Lu Jingxuan, Shangdang Gong Changsun Shaoyuan, and Qiguo Gong Husizheng to make rulers by accumulating millet seeds, but the lengths horizontally and vertically were not consistent. Later, while repairing the warehouse, an ancient jade container was discovered, which was believed to be the standard object. Standards for laws, measurements, and weights were established based on the jade container. This ruler was then used, a general amnesty was declared, and the era was renamed Tianhe, and all departments began using this ruler, which continued until the Daixiang era. The Huangzhong law associated with this ruler is the same as that of Cai Yong's ancient ruler.
Twelfth, the Song ruler. The Song ruler is one foot six inches and four fen longer than the ruler used before the Jin dynasty. There is also Qian Lezhi's celestial globe ruler; the iron ruler from the Later Zhou dynasty; the ruler used for adjusting time during the Kaihuang period; and the water ruler used for time adjustments after the Chen dynasty was pacified.
This ruler was commonly used by ordinary people during the Song dynasty, and later it was passed on to the Qi dynasty, the Liang dynasty, and the Chen dynasty, which they used to establish musical standards. Compared to the rulers from the Jin dynasty onward, the rulers used by the common people in the Liang dynasty, as well as the ruler on Liu Yao's celestial globe, are of similar lengths. This is likely because rulers used by everyday people tend to wear out and change over time, resulting in slight discrepancies in length.
In the sixth year of Jiande during the Zhou dynasty, after their victory over the Qi dynasty, this ruler was adopted as the standard measure and promoted for use nationwide. Later, during Emperor Xuan's reign, Da Xi Zhen and Niu Hong held discussions:
I carefully studied the measurements involved. Governing a country requires attention to detail, and one must thoroughly review historical data to find appropriate standards. I examined the iron ruler that is currently in use, which was crafted by Suo Chuo, the Shangshu appointed by Emperor Taizu. It was meticulously inspected and designated as the standard ruler for the former Zhou dynasty. I measured its length and found it to be the same as the ruler from the Song dynasty. It was used at that time to calibrate musical pitch and to measure land area. Currently, we measure using millet from Yangtou Mountain in Shangdang, following the method outlined in the "Book of Han: Treatise on Music and Calendars." If large millet grains are piled up to fill a foot and then placed in the yellow bell tube, it requires vigorous shaking to fit inside. If medium-sized millet grains are piled up to fill a foot, although it looks sparser, when placed in the yellow bell tube, it can be filled without shaking. These two situations are different mainly because the millet grains are uneven in size, so measuring with an iron ruler is more accurate. Moreover, the millet from Shangdang differs from that of other regions, with a very dark color and large, round grains. Using it for measurement is certainly intentional. Due to differences in rainfall and drought conditions in different regions, as well as variations in soil fertility, the varying sizes of millet grains complicate obtaining an average measurement. Xu Shen noted that these millet grains are significantly larger than typical ones. I believe that these large millet grains are the same as those at that time, with one hundred grains filling a foot, which aligns with ancient standards. Apart from the millet grains that fill the bell tube, there are still over ten remaining, which could be due to inaccuracies in measuring the diameter of the millet, or the bell tube not being finely made. The notion that vigorous shaking is needed to fill it also holds true.
Now we examine the ancient coins of the Zhou and Han dynasties, both conforming to the standards in size; the armillary sphere, an ancient astronomical instrument, of the Song dynasty also has no errors in scale. Additionally, according to the "Huainanzi," twelve grains of millet piled together equal one inch. This indicates that the regulations set by ancient emperors, after careful study and examination, are measured by law and standards and are consistent in meaning. The "Book of Han: Treatise on Food and Money" states: "Gold measuring one inch square weighs one pound." We now cast gold to verify, and the iron ruler is the closest to the standard. Based on historical records and practical calculations, there are many places that meet the standards. Moreover, iron rulers have been in use since the Pingqi period, and establishing them now aligns more closely with actual circumstances. As for using a jade ruler to measure millet, taking width as length, when piled full there is still a surplus, but it is not completely filled. Searching through ancient and modern literature, this method seems unreliable. The rulers of the Jin and Liang dynasties were too short; using millet to fill the measuring tube would not fill it at all, and using it to calibrate sound would certainly result in a sharp pitch. The harmony of the eight musical tones is a sign of a prosperous era and wise rulers, while unifying laws and measures is a strategy for governing by enlightened monarchs. We have carefully studied previous literature and combined it with current circumstances, believing that using an iron ruler is the most appropriate. Before we could confirm the details, Emperor Gaozu passed away. Niu Hong, Xin Yanzhi, Zheng Yi, He Tuo, and others discussed it for half a day without reaching a conclusion. After the fall of the Chen dynasty, the emperor felt that the music of Jiangdong was good, saying: "This is the ancient music of Huaxia; although it has changed somewhat with the times, it largely follows the ancient methods." Ancestor Xiaosun said: "After pacifying the Chen dynasty, we abolished the jade ruler and laws of the Zhou dynasty, replacing them with this iron ruler and laws, stipulating that one foot and two inches is the market foot." In the tenth year of the Kaihuang era, the law and water ruler made by Wan Baochang was actually one foot, one inch, eight tenths, and six hundredths longer than the rulers used before the Jin dynasty. "The current Taiyue Warehouse and the internal copper law, a part made by Wan Baochang, is called the water ruler law. It is said that its Huangzhong tuning corresponds to the southern sound of the iron ruler."
Now both the Tai Le Library and the palace have produced a set of copper tuning pipes, which are manufactured by Wanbao, called the Water Scale Pipes. The book states that its Huangzhong pitch is equivalent to twice the pitch of the Nanlv of the iron scale. Nanlv is the feather tone of Huangzhong, hence it is called the Water Scale Pipes.
14. Among various scales, the soil gage scale of Zhao Liuyao's armillary sphere is four fen and three li longer than the official scale of the Liang Dynasty, and it is actually one foot and five fen longer than the scale used before the Jin Dynasty. "The soil gage scale of Zhao Liuyao's armillary sphere is four fen and three li longer than the Liang official scale, and actually one foot and five fen longer than the pre-Jin scale."
15. The commonly used measuring scale among the populace during the Liang Dynasty is six fen and three li longer than the official scale of the Liang Dynasty, two fen longer than the scale of Liuyao's armillary sphere, and actually one foot, seven fen, and one li longer than the scale used before the Jin Dynasty. Emperor Wu of Liang noted in the "Zhonglu Wei": "After Emperor Wu of Song pacified the Central Plains, he sent the armillary sphere and the soil gage, claiming they were made by Zhang Heng. However, upon checking the inscription on the armillary sphere, it was cast in the fourth year of Guangchu, and the soil gage was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. He utilized the soil gage from the armillary sphere as a measuring tool, which is four fen and three li longer than the current standard scale and two fen shorter than the commonly used scale." Here, the 'new scale' refers to the official measuring scale of the Liang Dynasty. "The commonly used measuring scale of the Liang Dynasty is six fen and three li longer than the Liang official scale, two fen longer than the scale of Liuyao's armillary sphere, and actually one foot, seven fen, and one li longer than the pre-Jin scale. Emperor Wu of Liang noted in the 'Zhonglu Wei': 'After Emperor Wu pacified the Central Plains, he sent the armillary sphere and soil gage, claiming they were made by Zhang Heng. Upon examining the inscription on the armillary sphere, it was cast in the fourth year of Guangchu, and the soil gage was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. Utilized as a measuring tool, it is four fen and three li longer than the new scale, and two fen shorter than the commonly used scale.'" The 'new scale' refers to the official measuring scale of the Liang Dynasty.
In ancient times, the measurement system was indeed a complex subject. The "Book of Rites" records that the measuring vessel made by the Yan clan of ancient China was one foot deep, square inside with a side length of one foot, and round outside, with a capacity of one "hu" (a unit of measurement). Its bottom was one inch, with a capacity of one "dou"; its handles were three inches, with a capacity of one "sheng." The total weight was one "jun," and it produced a sound akin to that of a yellow bell. This measuring vessel was exempt from taxes. Inscribed on it were the words: "Through careful thought, we have achieved excellence. This fine measure, established for all to see, benefits future generations as the standard." This means that after repeated deliberation, a refined measuring vessel was finally created for all four nations to see, benefiting future generations; this vessel is the standard.
The "Zuo Commentary on the Spring and Autumn Annals" states that the State of Qi once had four types of measuring vessels: "dou," "qu," "hu," and "zhong." Four "sheng" make one "dou," and so forth, with four "dou" making one "hu," which amounts to six "dou" and four "sheng"; ten "hu" make one "zhong," which equals sixty-four "dou." Zheng Xuan estimated that the area of a square foot was one thousand "cun," which differed from the calculation in "Nine Chapters on the Mathematical Art – Grain" by two "sheng" and eighty-one "fen," specifically one twenty-second. Zu Chongzhi calculated the area to be one thousand five hundred sixty-two and a half "cun." If it were square on the outside and round, removing the edge part, the diameter would be approximately one foot four inches one-tenth four "hao" seven "miao" two "hu," with a depth of one foot; this reflects the design of the ancient "hu."
The "Nine Chapters on the Mathematical Art – Commercial Work" states that the volume of one "hu" of millet is two thousand seven hundred "cun," one "hu" of rice is one thousand six hundred twenty "cun," and one "hu" of beans, peas, hemp, and wheat is two thousand four hundred thirty "cun." This volume is based on the grain's fineness, ensuring prices remain consistent regardless of grain type. The volumes of these measuring vessels, based on the rice "hu," are similar to those recorded in the "Book of Han." The "Sunzi Arithmetic" states: six grains of millet equal one "gui," ten "gui" equal one "miao," ten "miao" equal one "cuo," ten "cuo" equal one spoon, and ten spoons equal one "he." Ying Shao noted that "gui" represents a natural form; four "gui" make one "cuo." Meng Kang said: sixty-four grains of millet equal one "gui."
"The Book of Han" mentions five measuring vessels: yue, he, sheng, dou, and hu, used to measure quantities. Initially, yue was made according to the musical scale of the yellow bell. Its volume was determined using standard measurements, filling it with twelve hundred medium-sized grains and calibrating its capacity with well water. The volume of yue served as the basis for he; ten hes made a sheng, ten shengs made a dou, and ten dous made a hu, completing the five measuring vessels. It was crafted from copper, square in shape with a rounded exterior and protrusions on the sides. The top was hu, the bottom was dou, the handle on the left was sheng, and the handle on the right was he and yue. Its shape resembled a jue, symbolizing nobility. The three parts on top and two parts on the bottom symbolized the three heavens and two earths; the circle containing the square, one part on the left and two parts on the right symbolized yin and yang. The circle represented rules, weighing two jin, encompassing various quantities of heaven, earth, and all things, each with eleven thousand five hundred and twenty. Its sound was akin to that of the yellow bell, starting from the yellow bell and repeating. The hu was inscribed with the inscription: "the Lu Jia measuring hu, square feet with a round exterior, protrusions on the sides nine li and five millimeters, with a measurement of one hundred sixty-two inches, depth of feet, accumulating one thousand six hundred and twenty inches, capacity of ten dous." Zu Chongzhi used pi to calculate; the diameter of this hu was approximately one foot, four inches, three tenths, six millimeters, one hundred ninety-two microns, and the protrusions on the sides were approximately one tenth of a millimeter. Liu Xin's calculation of the protrusions on the sides was about one li and four millimeters less, due to his inaccurate calculation.
In the fourth year of Wei Jingyuan, Liu Hui wrote in "Nine Chapters on the Mathematical Art": The hu used by the Grand Minister of Agriculture now has a diameter of one foot, three inches, five tenths, five millimeters, a depth of one foot, and a volume of one thousand four hundred and forty-one inches thirty-first. The copper hu from the time of Wang Mang, measured using today's standards, had a depth of nine inches, five tenths, five millimeters, and a diameter of one foot, three inches, six tenths, eight millimeters, seven millimeters. Using Liu Hui's calculation method, Wang Mang's hu was only slightly more than nine dou, seven sheng, and four he of the current hu. This indicates that the hu from the Wei Dynasty was larger, and the measuring standards were longer; Wang Mang's hu was smaller, and the measuring standards were shorter.
The Liang and Chen dynasties continued to use the previous measurement system. The Qi dynasty used five ancient sheng units combined to make one dou. In the first year of Emperor Wudi of Later Zhou, which was in the fifth month of the Xinsi year, when Jin was building a granary, they discovered an ancient jade dou. By the fifth year of Bao Ding, which was in the tenth month of the Yixiu year, the emperor ordered the re-establishment of the copper measurement standard, ultimately achieving the unification of measurements. Inscriptions recorded that after repeated measurements with millet, the capacity of this jade dou exactly matched the new copper measurement standard. They then used this jade dou as a standard, cast copper sheng units, and distributed them for use nationwide. The inscription on the copper sheng units read: "In the first year of Bao Ding in Later Zhou, during the month of Zhongguang, when the Jin officials were repairing the granary, they discovered this ancient jade sheng unit, its shape and size were very standardized, similar to the ancient standard measuring instruments. The Grand Preceptor reported this to the Emperor, who ordered it to be stored in the Heavenly Treasury. By the fifth year of Bao Ding, during the month of Xieqia, the Emperor ordered a careful inspection, repeated calibration with millet, ensuring there were no discrepancies. Therefore, a replica of this jade sheng unit was cast in gold and distributed nationwide to unify the country's measurements." The inscription on the copper sheng unit was written as such. The inscription on the jade sheng unit read: "In the first year of Bao Ding in the great Zhou dynasty, during the month of Zhongguang, when the Jin officials were repairing the granary, they obtained an ancient jade sheng unit, its shape and form were correct, like the excellent measurements of the ancients. The Grand Preceptor reported this to the Emperor, who ordered it to be collected in the Heavenly Treasury. By the fifth year, during the month of Xieqia, the Emperor decreed strict inspections, using a measuring stick, examining the ash, ensuring no errors. It was then melted into gold, inscribed and distributed nationwide, to achieve a fair and unified measurement system." Now, calculating with numbers, the estimated volume of this jade sheng unit is approximately 110.8 cubic inches, while the volume of the hu is approximately 1185.73 cubic inches.
Zhen Luan said in "Arithmetic": The capacity of a jade sheng is equivalent to one sheng, three he, and four spoonfuls of the government's dou. In other words, the jade sheng is larger, and the government's dou is smaller. According to calculations, the dou used by the Later Zhou dynasty government that Zhen Luan mentioned has a volume of approximately a little over ninety-seven inches, and the volume of the hu is approximately a little over nine hundred seventy-seven inches. The jade dou from the Later Zhou dynasty, along with the corresponding jin cuo bronze dou and the jin cuo bronze dou produced in the sixth year of Jiande, were all measured by volume using glutinous millet. When using jade scale weights, one sheng weighs six jin and thirteen liang. During the Kaihuang period, it was stipulated that three ancient shengs are equivalent to one modern sheng. By the Daye period, the ancient dou was reinstated.
The term "heng" refers to balance, while "quan" signifies weight. Heng is used to weigh items and assess their lightness or heaviness. The principle behind creating heng is akin to that of a compass, ensuring its accuracy and straightness. Turning left aligns it with a compass, and turning right aligns it with a square. The role of heng in the sky is to support the xuanji (an ancient astronomical instrument) in accurately adjusting the solar terms, allowing the seven celestial bodies (the sun, moon, and five planets) to operate in harmony, hence its name "yu heng." Quan refers to weight units such as zhu, liang, jin, jun, and shi. Using a scale allows one to determine an object's weight. In ancient times, there were also measurement units like shu, zhi, chui, ci, huan, gou, shuo, and yi, but these varied slightly across different dynasties, and I am not very clear about the specifics. The "Book of Han" states that the origin of quan is based on the weight of the yellow bell. One yue (an ancient unit of volume) can hold 1,200 grains of millet, weighing 12 zhu. Twenty-four zhu is one liang, sixteen liang is one jin, thirty jin is one jun, and four jun is one shi. The crafting of these five weights is highly precise, guided by principles and calibrated with reference objects. Other size differences are adjusted based on lightness and heaviness. Creating them round and maintaining uniform thickness allows for an endless cycle. When weight and object achieve balance, heng is formed. The function of heng creates the compass, the circular shape of the compass leads to the square ruler, the square shape of the ruler produces the rope, and the straightness of the rope results in the plumb line. When the plumb line is precise, heng is balanced, and quan is accurate. These five principles are all embodied in weighing instruments, serving as standards for their production.
According to the records in the "Book of Zhao," in the seventh month of the eighteenth year of Shile, while constructing the Jiande Hall, a round stone shaped like a water pounder was discovered. It was inscribed with the words: "Stone of Legal Weights, weighing four jun, used for legal measurements and weights. Made by the Xin family." It is believed this item dates back to the Wang Mang period. During the Jingming era of the Northern Wei, a man named Wang Xianda from Bingzhou presented an ancient copper weight inscribed with 81 characters. The inscription stated: "Stone of Legal Weights, weighing four jun." It also stated: "The Yellow Emperor, the first ancestor, whose virtue extends to Yu. The Yu Emperor, the first ancestor, whose virtue extends to Xin. In the year of Daliang, the dragon gathered at Wuchen. Wuchen set the standard, heaven's decree is with the people. According to the land's virtue received, the correct title is indeed authentic. Rectifying the flawed construction, long life and enduring honor. Same legal measurements and weights, according to the current people. The dragon is in Jisi, the year is truly Shen, the world is initially ordered, and all nations will eternally obey. Generations of descendants will enjoy this for billions of years." This was also made during the Wang Mang period. At that time, the Grand Music Official Gongsun Chong first adjusted the weights and measures based on the "Book of Han," and when he saw this weight, he used the new scale to weigh it, and the weight was one hundred and twenty jin. The new scale and this weight matched perfectly. Therefore, Gongsun Chong was assigned to adjust the musical scales. During the reign of Emperor Xiaowen, the斗 (dou) and尺 (chi) were produced in strict accordance with the "Book of Han."
It is said that during the Liang and Chen dynasties, the old weights and measures were in use. In the Qi dynasty, one jin equaled eight liang of the old weights. In the Zhou dynasty, a four-liang object on the jade scale equated to four and a half liang of the old weights. By the time of the Kaihuang period of the Sui dynasty, it was mandated that one jin equated to three jin of the old weights. During the Daye period of the Sui dynasty, the old weights were reinstated.
Thus, the ancient weights and measures had a chaotic standard, fluctuating from one measure to another, leaving people truly perplexed. The Liang and Chen dynasties used the old weights, in the Qi dynasty one jin equaled eight liang of the old weights, in the Zhou dynasty a four-liang object on the jade scale equated to four and a half liang of the old weights, during the Kaihuang period of the Sui dynasty it was changed to one jin equating to three jin of the old weights, and by the Daye period, it reverted back to the old weights. This ancient system of weights and measures is genuinely bewildering!
