According to the "Book of Han," the Huangzhong has a circumference of nine fen, the Linzhong is six fen, and the Taicu is eight fen. Later, both the "Continuation of the Book of Han" and Zheng Xuan confirmed this: the hollow parts of the twelve pitches have a diameter of three fen and a circumference of nine fen. However, King Anfeng of Northern Wei, according to Ban Gu's "Book of Han," made a Linzhong with a circumference of six fen and a Taicu with a circumference of eight fen, but when blown, the sounds did not match those of Huangzhong, Shang, or Zhi. Eventually, all were standardized to a circumference of nine fen, which then matched the standard sound of bells.
In the ninth year of the Kaihuang era of the Sui Dynasty, after the fall of the Chen Dynasty, a few individuals including Niu Hong, Xin Yanzhi, Zheng Yi, and He Tuo referenced ancient measurements and, based on the prevailing conditions of the time, produced pipes for the Huangzhong, with a diameter of three fen and a length of nine cun. Due to differences in manufacturing techniques, the sounds varied in pitch; the pipes' thickness and length varied from standard sizes, leading to different quantities of grains that could fit inside. Now I will list these data:
Before the Jin Dynasty, rulers measuring the Huangzhong pipe could fit eight hundred eighty grains of millet. The legal ruler of the Liang Dynasty measuring the Huangzhong pipe could accommodate eight hundred twenty-eight grains. Several other rulers from the Liang Dynasty could accommodate nine hundred twenty-five grains, nine hundred ten grains, and one thousand one hundred twenty grains in the Huangzhong pipe, respectively. The official ruler used in the Han Dynasty measuring the Huangzhong pipe could accommodate nine hundred thirty-nine grains. The ancient silver-inlaid Huangzhong pipe could hold one thousand two hundred grains. The Song Dynasty's iron ruler measuring the Huangzhong pipe could accommodate one thousand two hundred grains and one thousand forty-seven grains for two different sizes of pipes. The early Northern Wei ruler could accommodate one thousand one hundred fifteen grains in the Huangzhong pipe. The jade ruler from the Northern Zhou could accommodate one thousand two hundred sixty-seven grains in the Huangzhong pipe. The mid-Northern Wei ruler could accommodate one thousand five hundred fifty-five grains in the Huangzhong pipe. The late Northern Wei ruler could accommodate one thousand eight hundred nineteen grains in the Huangzhong pipe. The Eastern Wei ruler could accommodate two thousand eight hundred sixty-nine grains in the Huangzhong pipe. The Wanbao Changshui ruler could accommodate one thousand three hundred twenty grains in the mother Huangzhong pipe.
During the Liang Dynasty, there were several types of rulers and iron measuring rods used to measure the Huangzhong pipe. The lengths of the pipes and the diameters of their hollow sections were identical, but the amount of grains they could hold varied. This was because the maker intentionally altered the size of the pipe's cavity, leading to variations in the amount of grains inside.
The military officer of the Northern Qi Dynasty, named Xindu Fang, was particularly intelligent and capable. He could predict the weather using the pipes; by simply looking up at the clouds, he could tell what the weather would be like. One time, while talking to others, he pointed to the sky and remarked, "The season of Mengchun has arrived!" When others checked his pipe, they found that the ash had indeed shown a reaction. His monthly weather predictions were always very accurate. He also made twenty-four rotating fans that were buried underground to measure the twenty-four solar terms. Whenever a solar term arrived, one fan would start to rotate while the others remained still, in perfect harmony with the reaction of the ash in the pipe, as if it had been prearranged.
In the ninth year of the Kaihuang era, after defeating the Chen Dynasty, Emperor Yang Jian sent Mao Shuang, Cai Ziyuan, and Yu Puming to observe the solar terms. Following the previously established method, they set up twelve wooden tables in a triple-sealed room. Each table corresponded to a solar term and held the appropriate tuning pipe, which was then buried in soil, with the surface leveled. The inside of the tables was filled with reed ash, and the openings of the tuning pipes were covered with a fine silk cloth. When each month's solar term arrived, if the sound of the tuning pipe was in tune, the reed ash would rise, breaking through the silk and dispersing. However, the timing and quantity of ash released varied; some reacted right at the start of the month, while others only began to react in the middle or later part of the month. Some ash would fly out completely in three to five days, while others would only release a little over the course of the entire month.
Yang Jian found it quite strange and asked Niu Hong what this meant. Niu Hong replied, "When half of the ashes fly out, it signifies peaceful luck; when all the ashes fly out, it signifies strong luck; when the ashes do not fly out, it signifies weak luck. Peaceful luck corresponds to political clarity, strong luck is associated with unrestrained ministers, and weak luck corresponds to the monarch being tyrannical." Yang Jian retorted, "If ministers are unrestrained and the monarch is tyrannical, politics will definitely not be clear. This isn't something that varies every month! The reactions of the twelve months in a year are all different; how can you say that the monarch must be tyrannical and the ministers must be unrestrained? Is it that serious?" Niu Hong was at a loss for words. So Yang Jian had Mao Shuang and others develop a systematic approach. Mao Shuang consulted previous materials and wrote an article titled "Lüpu."
The "Lüpu" probably states: I, Mao Shuang, have verified that the Yellow Emperor sent Ling Lun to collect bamboo in the Yangu Valley and created twelve musical tones under the nest of the Feng bird. This enabled the qi of heaven and earth to correspond, marking the origin of numerical systems. Yang pipes are tones, Yin pipes are modes; their qi can be used to predict the four seasons, and their numbers can be used to record all things. Cloud Li first created a counting method, which likely serves as the foundation of legal systems. The numbers one, ten, hundred, thousand, ten thousand, million, billion, etc., are all derived from this, and measurements also come from it. Therefore, the Yu clan used tones to coordinate music, and Zou Yan modified it to determine the five beginnings. The correct calendar and clothing colors are all determined by this. The Xia dynasty used people as the standard, the Shang dynasty used the land as the standard, and the Zhou dynasty used the heavens as the standard. Confucius said, "I have obtained the calendar of the Xia dynasty," implying that he had grasped the essence of qi and numerical principles.
When the Han Dynasty was just established, Zhang Cang formulated laws and implemented the Five Victories principle, considering it to embody the virtue of water. In fact, it was due to the negligence of officials during the Warring States period and the decline of scholarship after the Qin Dynasty's fall that this principle gradually became lost. Zhang Cang merely repaired it without fully understanding it. It was not until the reign of Emperor Wu of Han that the role of Music Coordinator was created, appointing Li Yannian as the Music Commandant. Although Li Yannian understood some new musical pieces and modulations, he did not truly grasp the fundamental principles of music theory, which meant that the sizes and colors of musical instruments could not be standardized at that time.
By the time of Emperor Yuan of Han, the emperor himself understood music theory, and the official Jing Fang was also proficient in it. Therefore, Emperor Yuan invited Wei Xuancheng and others to consult Jing Fang. Jing Fang introduced himself, saying, "I study the theories of Jiao Yanshou and apply the method of the sixty tones generating one another. The upper generates the lower, with three leading to two; the lower generates the upper, with three leading to four; yang generates yin downwards, yin generates yang upwards, thus returning to the standard practices of palace tuning." Later, Liu Xin compiled and recorded the details of these matters, and music theory gradually underwent deeper research. Ban Gu's "Book of Han: Treatise on Music and Calendar" mainly adopted Liu Xin's results, while Sima Biao's "Continuation of the Book of Han: Treatise on Music and Calendar" mainly adopted Jing Fang's results.
By the Eastern Han, the dimensions of musical tuning had increased slightly. Du Kui of the Wei Dynasty also established musical tones to observe the climate, ensuring that dust remained settled. Xun Xu, a Grand Minister of the Jin Dynasty, obtained ancient bronze tubes and compared them with the musical tones established by Du Kui, realizing that Du Kui's musical tones were inaccurate because of his errors. Consequently, Xun Xu recreated the ancient ruler according to the "Rites of Zhou" to establish the sizes of musical instruments, ultimately ensuring their musical tones were accurate.
After the Jin Dynasty, musical tuning gradually began to have errors. During the reign of Emperor Wu of Liang, there was the Jade Ruler from Jizhong. During the Cangwu period of the Song Dynasty, someone adapted it into a transverse flute, but its length, thickness, and overall structure were still preserved. When I was young, I studied mathematics with Zuxun and learned musical tuning from He Chengtian. I dedicated myself to research for decades and gained a good understanding of musical tuning. Later, when I became the Minister of Ceremonies, in charge of music affairs, I brought the Jade Pipe and the ruler of the Taishi of the Song Dynasty to the court for presentation. The court ordered craftsmen to make musical instruments according to the samples. Since then, the dust of musical tuning has been stirred up again. During the rebellion of Hou Jing, my brother Xi obtained these musical instruments in the Department of Music. Later, when Emperor Xuan of Chen was taken to Jingzhou as a hostage, at the same time as the defeat of Emperor Yuan of Liang, my brother died in Northern Zhou. Just as I was about to present to the court, Emperor Wu of Chen succeeded to the throne. He further developed the twelve pipes into sixty scales, privately studied climate change, and observed its signs and reactions. During the reign of Emperor Taijian of Chen, my brother served as the Minister of Personnel and wanted to present to the court. However, Emperor Xuan passed away, and the subsequent emperor ascended the throne, demoting my brother to the position of Interior Minister of Yongjia. As a result, these musical instruments stayed in the family and were passed down to his descendants. When the Chen Dynasty fell, these musical instruments were eventually lost.
Nowadays, the twelve-pipe instruments used in the court are determined according to the principles of yin and yang. Starting from Huangzhong, the yang energy gradually weakens, while the yin energy gradually strengthens. By the end of Zhonglv, the seasonal climate changes are all encompassed. After Zhonglv is Zhishi, followed by Qumie, and finally Nanshi, completing the cycle of sixty scales.
In midwinter (November), the Yellow Bell's music is played. The Yellow Bell marks the beginning of the winter solstice, symbolizing the onset of yang energy. Its length is nine inches, calculated according to celestial phenomena. In November, the music of the Yellow Bell was established, which serves to harmonize the six qi and refine the nine virtues. From then on, the musical rules formulated by Jing Fang were adopted, with the tones of Gong and Zhi varying in length sequentially each day. Each of these twelve musical rules governs a specific range, extending to form sixty rules. This can also be inferred from the Eight Trigrams, resulting in sixty-four hexagrams.
Yin and yang generate and transform each other; for example, the Yellow Bell rule produces the Lin Bell rule, with yang energy giving birth to yin energy—this exemplifies transformation. Yin and yang interact and resonate with one another; for example, the Zhong Lu rule corresponds to all things, similar to a mother guiding her children. Therefore, transformation refers to corresponding at different times, while communication refers to continuous correspondence in the same month. If there are timing discrepancies, it indicates that the timing is not in accordance with the correct musical rule but rather reflects a minor rule responding to a major one.
These musical rules were lost during the final years of the Daye era, when Emperor Yang of the Sui Dynasty was assassinated in Jiangdu (Yangzhou).
In the Song Dynasty, Qian Lezhi, after studying Jingfang's music theory, created the 360 musical scales. Shen Zhongzhong, a scholar of the Liang Dynasty, mentioned in his "Discussion on Music Theory": "The Book of Changes employs 360 hexagrams to correspond to the days of the year, which serves as the numerical foundation for music and the calendar. The Huainanzi states: 'One pitch produces five tones, and twelve pitches generate sixty tones, then multiplied by six, that equals 360 tones, corresponding to the days of the year. The numbers of music and the calendar are the laws of the operation of heaven and earth.' Therefore, the method for calculating these 360 musical scales has been established since ancient times." Based on the numbers in the Huainanzi, Shen Zhongzhong applied Jingfang's algorithms to derive the 360 musical scales. He took each month's main pitch as a unit, used the number of the main pitch as the base number, and used the number of days contained in each solar term as the subordinate number, determining the proportion of days governed by each musical scale based on the number of days. Then, he assigned the seven tones to these scales; for example, on the day of the winter solstice, the main pitch is Huangzhong, Huangzhong corresponds to Gong, Taicu corresponds to Shang, Linzhong corresponds to Zhi, Nanlv corresponds to Yu, Guxi corresponds to Jiao, Yingzhong corresponds to Bian Gong, and Ruibin corresponds to Bian Zhi. In this way, the five tones and seven sounds are complete.
In the following days, the various musical scales would operate sequentially. The pitch used that day is the Gong sound, and the Shang and Zhi sounds would be arranged in order. By examining these sounds and their qualities, one could discern the timing, and all things could grow according to the changes of the solar terms. From Huangzhong to Zhuangjin, there are a total of 150 musical scales, all calculated using the method of reducing by one-third; from Yixing to Yizhao, there are a total of 209 musical scales, all calculated using the method of increasing by one-third; only the pitch of Anyun serves as the endpoint and is not subject to further calculation. The lengths of these musical scales are based on the actual length of Huangzhong, which measures 177,147 units, using a ratio of three-ninths to calculate their lengths, precise to the inch, while smaller units are disregarded. These lengths represent the actual lengths of each musical scale. He organized the sequence of these musical scales, which represents the Gong and Zhi order of the upper and lower generations, and will not go into detail here.
Huangzhong:
Baoyu, Hanwei, Dide, Guangyun, Xiaji, Kezhong, Zhishi, Wojian, Chishu, Huangzhong, Tongsheng, Qiansheng.
Yin Pu, Jing Sheng, Zi Meng, Guang Bei, Xian Heng, Nai Wen, Nai Sheng, Wei Yang, Fen Dong, Sheng Qi, Yun Fan Yu Yan
Sheng Yin, Tun Jie, Kai Yuan, Zhi Wei, Xie Mei, Bu Jian, Xuan Zhong, Yu Zhu, Diao Feng
Above is the Yellow Bell, consisting of thirty-four modes. (Each mode corresponds to one thirty-fourth of a day, or thirty-one minutes)
Da Lu:
From the beginning, praise the great Kun Yuan, assist the times, rectify harmony, distinguish right from wrong, both complex and subtle, let go of hope, uphold justice, hold strong, overcome darkness, follow the light, understand depth and brilliance, know when to change, weigh pros and cons, avoid the limelight, work together with others, embrace the light, inherit and carry forward magnificently.
This is the Da Lu, consisting of twenty-seven modes, each corresponding to one day, including three twenty-sevenths of a day.
Next is Tai Cu:
Unaware of one's abilities, but establishing achievements, as upright as a sturdy tree, as swift as the wind, starting smoothly, then calming down, ultimately achieving the goal, like a gourd playing music, the sound of the initial notes, the energy of the minor yang, soft but flexible, supporting the weak, receiving in an orderly manner, flourishing plants and animals, covering mountains and rivers, moderate speed, following the seasons, leaping like a dragon, regulating order with a hooked mane, green branches, buds blooming, then spreading and growing, just punishment, clear hierarchy, spring planting begins, praising the harvest, hidden talents come to light, everything starts to wither.
This is the Tai Cu, consisting of thirty-four modes.
Then comes the Jia Zhong:
Everyone cooperates with each other, Yin energy assists Yang energy, the wind blows from all directions, policies are formulated, all things begin to grow, the virtue of resonance, riding on order, fragrant and overflowing, emitting a beautiful scent, racing like the wind, full of joy, united, blossoming everywhere, all things growing, following one's heart's desire, carefree and at ease, benevolent and dignified, growing towards the south in a rush, the rising sun in the east, morning comes, all things flourishing, each developing on its own, clean and rejuvenated.
This is the first part of Jiazhong, a total of twenty-seven poems.
Next is Guxi:
News comes from the south, remembering ancestors, offering sacrifices to the spirits, only then can they appear, bringing forth the sound of the first notes, washing away the old, changing old customs, overflowing with talent, auspicious energy begins to rise, as beautiful as the morning clouds, charming mountains, clearing the roads, following the seasons, traveling day and night, real and practical, the hot fierce wind, first sprouting, tender branches beginning to bear fruit, punishment begins, all things becoming orderly, flowers and plants flourishing, clearing away weeds, abundant fruits, rising into the light, growing and expanding, following the rules, making fewer choices, following the path, gaining fame, maintaining chastity.
This is the first part of Guxi, a total of thirty-four poems.
Next is Zhonglv:
The fire of the Vermilion Bird brings good luck, the gentle breeze, all things begin to rise up, warmth in the south, spring arrives, guiding farmers in their work, orderly, the star of the south offers light, chasing each other, pure in heart, red plants and trees shining brightly, submitting to the rules, illuminating the fields, the energy of the Hour of the Snake, clear and warm, all things responding, eliminating greed, desolate and lonely, the pure Zhixing star, blessing the Zhou dynasty.
This is the first part of Zhonglv, a total of twenty-seven poems.
Finally, it is Ruibin:
Matters of the South (Jing Fang's Final Principles), peaceful and harmonious, choosing the right timing, flowers blooming, full of vitality, latent power beginning to emerge, grand changes, guests living in peace, longing for distant places, voices echoing everywhere, following the same path, calm sea, averting disasters, staying away from danger, strong and healthy, promoting light, gazing into the future, rising to the center, phoenix soaring, sunrise, seizing the opportunity, good fortune flourishing, shining bright, orderly, flames leaping high, radiating light.
In the second paragraph, it is followed by "Right Lin Zhong, thirty-four musical scales. Yize: ..." which means: The right side of Lin Zhong has thirty-four musical scales. Then thirty-four descriptive words of the Yize musical scale are listed: Ascending Shang Scale, refreshing, ethereal and pure, Yin virtue, White Cang, compliance with laws, strict laws, chaste and resolute, Golden Heaven, Liu Xian (a historical figure), returning to benevolence and righteousness by following the Dao, Yin companions, retreat in the south, gentle and diligent, Yan Yi, and Geng, no weeds, Ti Jin, distribution and savings, Kong Xiu, nine virtues are all present, everyone agrees, for governance. These words also depict the scenes symbolized by the Yize musical scale, possibly focusing on social order and moral norms.
The third paragraph, "Right Yize, twenty-seven musical scales. Nan Lu: ..." means: The right side of Yize has twenty-seven musical scales. Then twenty-seven descriptive words of the Nan Lu musical scale are listed: white Lu tune, abandoning luxury, honest and practical, simple atmosphere, powerful elements, chief's bountiful harvest, unity and dedication, fertile abundance, among the weak, grand Yin energy, upholding integrity, shocking the four directions, severing ties, returning to the deadline, moderate morality, kingly strategy, Yun Sai, Ru Shou, saving reins, falling, unmarked, nature obedient, distributing fullness, Dao Xin, purity and strength, savings stop, returning to preservation, Yihan, average justice, accepting orders, without toil, nine states, glorious and prosperous. The descriptive words of the Nan Lu musical scale appear to emphasize natural laws and social harmony.
In the fourth paragraph, "Nanlu, thirty-four scales. Wusha:..." means: The right side of the Nanlu section contains thirty-four musical scales. Then thirty-four descriptive words for the Wusha scale are listed: thoughtful and balanced, humble and modest, respectful and frugal, rest and recuperation, caring for the people, eliminating disasters, blocking evil, descending, hidden deeply, the sun in its place, spring rotation, cutting and concealment, bright Kui star, harmonious neighborhood, following the masses, large-scale savings, frugal and restrained, helping those in need, resting the burden, boundless, hoping for preservation, longevity and health, deep autumn scenery, dark moon, clear sky. The descriptors of the Wusha melody emphasize social governance and the welfare of the people.
In the fifth paragraph, "Right Wusha section, twenty-seven scales. Yingzhong:..." means: The right side of the Wusha section contains twenty-seven musical scales. Then twenty-seven descriptive words for the Yingzhong scale are listed: clear distribution, tracing the origin, mastering the beginning, achieving success and fame, governance stability, quiet and peaceful, slow and restrained, governing through non-action, Gusheshan, solemn and obscure, stillness and movement, response, not yet born, myriad opportunities, boundless longevity, enduring, recovering cultivation, slow establishment, endless, nine fields, eight wildernesses, billions of generations, peaceful operation. The descriptive words of the Yingzhong scale are more focused on long-term stability and national security.
Finally, "Right Yingzhong section, twenty-eight scales." means: The right side of the Yingzhong section contains twenty-eight musical scales. Specific terms are not included here, and may be documented elsewhere.
In conclusion, this passage describes different scales and their meanings, which are closely tied to ancient political, social, and moral ideas. The descriptors for each scale are quite abstract and require a combination of the social background and cultural connotations of the time to better understand.
The "Records of the Grand Historian" states: "Yu the Great of the Xia Dynasty used his own body as a unit of measurement and used sound to determine musical pitch." The "Book of Rites" states: "The width of a man's outstretched arms is one foot." The "Zhou Official" records: "Use the edge of a bi (a type of jade disc used in ancient China) to determine length." Zheng Xuan explains: "'Xian' means length. This refers to the diameter of the bi being one foot, which is used to determine the unit of measurement." The "Yiwai Tonggua Yan" states: "The width of ten horse tails is one fen." The "Huainanzi" says: "At the autumn equinox, the awns of the grain have taken shape; when the awns take shape, the grain is ripe. The number of musical pitches, where the width of twelve awns equals one grain, and twelve grains equal one cun." Here, "lu" specifically refers to the awns on the grain. The "Shuoyuan" records: "The standard for measurement originated from the grain, with one grain being one fen." The "Sunzi Suanshu" states: "The silk produced by silkworms is called 'hu' (忽), ten hu is a miao, ten miao is a hao, ten hao is a li, ten li is a fen." These are all origins of ancient measurements, but the accounts contradict each other. Only the "Book of Han: Treatise on Law and Calendar" records it more reliably: "Measurement is used to measure length, and its standard was initially determined based on the length of the Huangzhong (a large bell). Selecting an average-sized grain of millet—jiu-shu, the width of one grain of jiu-shu is one fen, and the width of ninety grains of jiu-shu is the length of the Huangzhong. One jiu-shu is one fen, ten fen is one cun, ten cun is one chi, ten chi is one zhang, and ten zhang is one yin, thus establishing five units of measurement." Later authors based their measurement standards on this account and derived various methods based on the size of the jiu-shu, so these ratios became universal. However, the size of the jiu-shu varies, and the quality of the harvest also affects its size, so the calibration of ancient measurements often fluctuated. Additionally, through oral transmission among the populace, inaccuracies inevitably arose, leading to gradual changes in the standards of measurement. I will now briefly list fifteen different measurement scales from various dynasties, along with their differences and accounts, as follows: The "Book of Han: Treatise on Law and Calendar" records the copper weights and measures established by Liu Xin during the Wang Mang period. The copper scale established during the Jianwu period of the Eastern Han Dynasty.
In the tenth year of the Tai Shi period of the Jin Dynasty, Xun Xu established the legal ruler, which was a ruler used prior to the Jin Dynasty. The bronze ruler passed down from the renowned mathematician Zu Chongzhi. It is said that in the ninth year of Emperor Wu of Jin's Tai Shi era, Xun Xu, the supervisor of the Imperial Secretariat, inspected the palace musical instruments and discovered that the eight tones were out of harmony. Upon investigation, it was found that the rulers from the Eastern Han to the Wei Dynasties were over four fen longer than the ancient rulers. Xun Xu instructed the Imperial Clerk Liu Gong to remake the ruler according to the standards of the "Rites of Zhou," which was the genuine ancient ruler! Then, they used this ancient ruler to recast the bronze tuning bells for tuning the musical instruments. When measuring those ancient musical instruments with this ruler, the measurements matched perfectly with those recorded in the inscriptions! What's more, when tomb raiders in Ji County unearthed the tomb of King Wei Xiang, they discovered the jade tuning stones and chime bells of the Zhou Dynasty, which, surprisingly, had tones similar to those of the newly cast tuning bells! At that time, some ancient Han Dynasty bells were also unearthed in several locations, and when tested against the newly made tuning bells, their sounds matched perfectly!
The Liang Wu Emperor also recorded this in the "Zhong Lü Wei," stating that Zu Chongzhi had a bronze ruler in his hand, inscribed with a total of eighty-two characters, which roughly said: In the tenth year of the Tai Shi era of the Jin Wu Emperor, officials from the Central Secretariat examined ancient artifacts and compared them to the current measuring rulers, discovering that they were four and a half inches longer than the ancient ones. They verified a total of seven ancient measurement standards: 1. Gu Xia Jade Ruler; 2. Xiao Lü Jade Ruler; 3. Xi Jing Copper Measuring Instrument; 4. Jin Cuo Copper Measuring Instrument; 5. Copper Dou; 6. Ancient Coins; 7. Jian Wu Copper Ruler. Among them, the Gu Xia Jade Ruler is a bit longer, the Xi Jing Copper Measuring Instrument is a bit shorter, while the others are the same as this bronze ruler. This bronze ruler was the one re-made by Xun Xu in his time. The ruler we use today is the one made by Du Kui. Lei Cizong and He Yinzhi also drew a "Zhong Lü Tu," which recorded the text of Xun Xu correcting the ancient rulers, exactly matching the inscription on this bronze ruler. However, Xiao Ji's music score states that these seven standards were verified by the Liang Dynasty, which is a mistake. We should use this bronze ruler as our standard now. The rulers of the Liang Dynasty are one foot and seven-tenths longer than those of the Jin Dynasty and earlier!
In ancient times, an old farmer dug up a jade ruler from the Zhou Dynasty in the field, which was said to be the standard ruler used throughout the realm. Xun Xu used it to check musical instruments and found that the gold, stone, and silk instruments he made were all one meter shorter than it. Emperor Liang Wu's "Zhong Lu Wei Cheng" also recorded this incident, saying that among the items passed down in the imperial palace, there was a Zhou Dynasty bronze ruler and eight ancient jade musical instruments. Later, it was found that the Zhou Dynasty ruler had been taken by Dong Hunhou as a trust token and could not be found. The remaining seven jade musical instruments, one of which was somewhat damaged, still had inscriptions on them. Emperor Liang Wu then made a new ruler based on these jade musical instruments for cross-checking. He used the fine grains found within the hairs to measure repeatedly, establishing the scale. This was the most precise measurement method of the time, even surpassing Zu Chongzhi's ruler by half a millimeter. Then, he used this new ruler to make four musical instruments known as "Tong." He also made flutes according to the new ruler, then used it to check the ancient bells, setting the pitch for "Yize" based on the scale, and using the flute to determine the pitch of "Yinhe," and found that the pitch of "Yize" was accurate. The lengths of both rulers were nearly identical. Xiao Ji said in his book: "This method comes from the 'Sima Fa.' The Liang Dynasty engraved the scale of the ruler on a shadow table to measure the sun's shadow." This refers to the bronze guibi calculated by Zuxun upon the court's request. Later, after the fall of the Chen Dynasty, this guibi entered the court. During the Sui Dynasty, someone proposed to restore the ancient standards, so this guibi was then used to calibrate the musical scales and create eight types of instruments, including bells and chimes. A person in Shiping County unearthed an ancient bronze ruler.
Xiao Ji's "Score" says: "During the reign of Emperor Zhang of Han, Xi Jing, a literary historian from Lingling County, unearthed a set of jade rulers beneath the Shun Temple and crafted this ruler from them." Fu Chang's "Praise of the Jin Dukes" says: "Ge Xu's bell rulers were regarded as highly accurate at the time, but only Ruan Xian of Chenliu claimed its pitch was too high. Later, an ancient bronze ruler was excavated in Shiping County, which was nearly decayed; when compared to Xun Xu's ruler, it measured a quarter shorter. People at that time all agreed with Ruan Xian." The lengths of these two rulers were also similar. In the fourth year of King Jingyuan of Wei Chenliu, Liu Hui, while annotating the "Nine Chapters on Mathematical Art," noted that the bushel and ruler used by Liu Xin during Wang Mang's reign were four and a half points shorter than those of his time, and compared to the rulers of the Wei Dynasty, the depth of the bushel was nine inches and five and a half points. This aligns with what Xun Xu of the Jin Dynasty stated: "Du Kui's ruler is four and a half points longer than the current ruler." Xiao Ji said that this is the ruler used in the Jiangdong region of the Jin Dynasty. The market ruler of the Later Zhou Dynasty was one foot, nine points, and three tenths shorter than the jade ruler. The official ruler during the Kaihuang period, known as the iron ruler, measured one foot two inches. Prior to this, from the early Wei Dynasty until the division of Eastern and Western Wei, and until the Later Zhou Dynasty ceased using the jade ruler, people mixed these rulers. According to the "Zhenluan Arithmetic," the market ruler of the Zhou Dynasty was equivalent to nine points and two tenths of the jade ruler. Some claim this ruler was crafted by Zhi Gong Dao Ren of the Liang Dynasty, sent to the Zhou Dynasty, and presented to an elderly man with a long beard. Both Emperor Taizu of the Zhou Dynasty and Emperor Gaozu of the Sui Dynasty believed this ruler was made for them, and the common people during the Zhou Dynasty used this ruler. During the Kaihuang period of the Sui Dynasty, it was officially designated as the official ruler, and all departments utilized this ruler until the Renshou period. By the Daye period of the Sui Dynasty, some people still used it privately.
The ruler of the Zhou Dynasty, Wei Dynasty's Lieutenant Yuan Yanming, was constructed using the width of half a grain of millet. The Qi Dynasty continued this practice. Wei Shou wrote in "Weishu·Lu Li Zhi": "Gongsun Chong made a new ruler during the Yongping period, using the length of a millet grain accumulated as an inch standard. Later, Minister of Music Liu Fang was ordered to repair music, using the width of medium-sized millet as a unit. Wei Yuan Kuang used the width of a millet grain plus the space of two millet grains as a unit. The three families had different opinions and argued for a long time without results. It was not until the nineteenth year of Dahe that Gaozu ordered the width of a millet grain as a unit, and used the length of ninety millet grains, equivalent to the length of the Huangzhong, to make a bronze ruler. The relevant authorities reported that the previous edict matched Liu Fang's ruler and the ruler established by Gaozu, so Liu Fang's ruler was officially adopted to make gold and stone tools. Until the Wuding period, no one discussed the law again."
Eleventh, Cai Yong's bronze ruler. The jade ruler from the Later Zhou Dynasty is one foot, one inch, five minutes, and eight tenths longer than the ruler used prior to the Jin Dynasty. From ancient times to the present, there exists a bronze ruler adorned with silver inlay, inscribed with: "Ruler, the palace of the Huangzhong, nine inches long, surrounded by nine minutes, containing 1,200 grains of millet, weighing twelve zhu, with two zhu equaling one he. Three points of loss and gain, turning into twelve tones." Zuxiaosun said: "It is said that this is Cai Yong's bronze ruler."
During the Baoding period of the Later Zhou Dynasty, the emperor ordered Dazongbo Lu Jingxuan, Shangdang Gong Changsun Shaoyuan, and Qiguo Gong Husizheng to make rulers with millet grains, but the dimensions were yet to be finalized. Later, when repairing the warehouse and digging the ground, ancient jade measuring tools were uncovered, and it was believed that this was the standard object. According to the jade measures, laws and measurement standards were established. So this ruler was used, a general amnesty was issued, the era was changed to Tianhe, and all departments used this ruler until the end of the Daixiang period. Its Huangzhong standard is identical to that of Cai Yong's ancient ruler.
Twelfth, the ruler of the Song family. It is six minutes and four tenths longer than the ruler used prior to the Jin Dynasty. Additionally, there is Qian Lezhi's celestial globe ruler. The iron ruler from the Later Zhou Dynasty.
During the Kaihuang period of the Sui Dynasty, adjustments were made to the musical tuning and measurement standards. After pacifying the Chen Dynasty, further adjustments were made to the musical tuning and water measuring standards. This ruler was commonly used by the people during the Song Dynasty, and it later spread to the Qi, Liang, and Chen Dynasties, where they used it to make musical instruments and determine musical scales. Its length is similar to that of the rulers used after the Jin Dynasty, as well as the commonly used rulers in the Liang Dynasty and the rulers on Liu Yao's armillary sphere. This is because the common people used it regularly, and over time it inevitably wore down and changed.
In the sixth year of Zhou's Jiande era, after pacifying the Qi Dynasty, this ruler was adopted as the standard of length and measurement across the country. Later, during the reign of Emperor Xuan, Daxi Zhen and Niu Hong discussed: "Honestly, if we want to get weights and measures right, we need to thoroughly study how it was done in the past and find a reliable standard. I looked into it, and this iron ruler was made by the official Su Chuo on the orders of Emperor Taizu; it is the ruler used in the Former Zhou! We measured it against the Song Dynasty's ruler and found them to be about the same length. It was used at that time to calibrate musical tuning and to measure land."
Now, let's try using the millet produced in Shangdang to measure, following the method in the "Book of Han, Volume on Measures and Calendars." If we use the large millet, when piled up to exactly one foot and put into the Huangzhong tube, it requires a good shake to fill it up. But if we use medium-sized millet, even though it may look a bit sparse, when put into the Huangzhong tube, it can be filled without shaking. The difference between these two situations mainly comes from the varying sizes of millet. We still need to check if this iron ruler is accurate. Moreover, the millet from Shangdang is distinct from that of other regions; it's black, round, and larger. Choosing it for measurements is certainly not arbitrary. After all, harvest quality and soil fertility can vary, and it is normal for millet sizes to differ. "Explaining Simple and Analyzing Compound Characters" also mentioned that the grains of millet are larger compared to ordinary ones. Perhaps these large millet grains are the ancient standards, with one hundred grains piled up exactly one foot, which aligns with ancient standards. Apart from filling the Huangzhong tube, there are still about ten grains left, possibly due to inaccurate measurements of the millet's circumference, or there might have been errors in crafting the tube. However, shaking it to fill it up like we just did is also acceptable.
We checked the ancient coins from the Zhou and Han dynasties again, and their sizes match quite well; the armillary sphere from the Song dynasty is also appropriately scaled; the "Huainanzi" mentions that twelve grains of millet stacked together equal one inch. This indicates that ancient emperors invested considerable effort in establishing laws and conducted careful studies, measuring with standard weights, resulting in similar outcomes. The "Book of Han: Treatise on Food and Money" states: "A piece of gold measuring one inch square weighs one pound." We have also tested gold now and found it to be comparable to this iron ruler. Therefore, from ancient texts and practical situations, many aspects align. Moreover, the use of this iron ruler dates back to the Pingqi period, and continuing to use it now is quite appropriate. Using a jade ruler to measure millet is impractical because the jade ruler is too wide, leaving a lot of space when filled and not filling it completely. After researching both ancient and modern materials, this method appears to be unworkable. The rulers from the Jin and Liang dynasties were too short; using millet with the rulers from the Jin and Liang dynasties simply wouldn't work, and if used to calibrate musical tones, the sound would definitely be too shrill. Harmonious music is a hallmark of wise ancient rulers, and unifying laws and measurement standards has been a governing strategy of enlightened rulers throughout the ages. We carefully studied previous materials and combined them with current situations, concluding that using the iron ruler is more convenient. Before we had the chance to finalize the details, Emperor Gaozu passed. Niu Hong, Xin Yanzhi, Zheng Yi, He Tuo, and a few others discussed for a long time without reaching a conclusion. After pacifying the Chen dynasty, the emperor felt that the music from Jiangdong was better, saying: "This is the ancient music of Huaxia; although it has changed somewhat with the times, it still largely follows the ancient methods." Ancestor Xiaosun said: "After pacifying the Chen dynasty, the jade ruler and the laws of the Zhou dynasty were abolished, and this iron ruler and laws were adopted, stipulating that one ruler equals two inches for the market ruler." In the tenth year of the Kaihuang era, the water ruler for musical pitch made by Wan Baochang is actually one foot, one inch, eight tenths, and six hundredths longer than the rulers used prior to the Jin dynasty. "The current Taiyue warehouse and the copper pitch produced is a work by Wan Baochang, named the water ruler for musical pitch. It is said that its Huangzhong pitch is twice that of the iron ruler's Nanlv. Nanlv is the Huangzhong's feather, hence it is called the water ruler for musical pitch."
Currently, there is a set of bronze tuning pipes stored in both the Tai Le and the palace, manufactured by Wan Bao Chang, called the water尺. The text mentions that its Huangzhong tuning is equivalent to twice that of the Nanlü tuning of the iron ruler. Nanlü corresponds to the feather tone of Huangzhong, hence it is called the water尺.
14. Various types of rulers, such as the earth ruler used on Zhao Liu Yao's armillary sphere, are four fen and three li longer than the Liang legal ruler and are actually one foot and five fen longer than the rulers before the Jin Dynasty. "The earth ruler of Zhao Liu Yao's armillary sphere is four fen and three li longer than the Liang legal ruler and is actually one foot and five fen longer than the rulers before the Jin Dynasty."
15. The commonly used ruler during the Liang Dynasty is six fen and three li longer than the Liang legal ruler, two fen longer than the ruler on Liu Yao's armillary sphere, and is actually one foot and seven fen and one li longer than the rulers before the Jin Dynasty. Emperor Wu of Liang stated in the "Zhong Lü Wei": "After Emperor Wu of Song pacified the Central Plains, he sent a set of armillary spheres and earth rulers, claiming they were made by Zhang Heng. However, based on the inscriptions on the armillary sphere, it was cast in the fourth year of Guangchu, and the earth ruler was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. Liu Yao used it to establish the ruler, which is four fen and three li longer than the newly established standard ruler and two fen shorter than the commonly used ruler." The "new ruler" refers to the Liang legal standard. "The commonly used ruler during the Liang Dynasty is six fen and three li longer than the Liang legal ruler, two fen longer than Liu Yao's armillary sphere ruler, and is actually one foot and seven fen and one li longer than the rulers before the Jin Dynasty. Emperor Wu of Liang stated in the 'Zhong Lü Wei': 'After Emperor Wu pacified the Central Plains, he sent the armillary sphere and earth ruler, claiming they were made by Zhang Heng. Upon examining the inscriptions on the armillary sphere, it was cast in the fourth year of Guangchu, and the earth ruler was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. Liu Yao established the ruler, which is four fen and three li longer than the new ruler and two fen shorter than the commonly used ruler.' The 'new ruler' refers to the Liang legal standard."
Hello everyone, today let's talk about ancient measurements. First, let's discuss the "lǔ" measuring instrument recorded in the "Rites of Zhou." The text states that it is "a measure, one lǔ is one foot in depth, square on the inside and round on the outside; its capacity is one lǔ; its bottom is one inch, which is one dòu; its ears are three inches, which is one shēng. It weighs one jūn and produces a sound like that of the huangzhong. It is a general measure and is not subject to tax. The inscription indicates that through careful design, this standard measuring instrument was created for national use, benefiting future generations.
The "Zuo Zhuan" also mentions four ancient measuring instruments: dòu, qū, lǔ, and zhōng. It states, "The four ancient measures of Qi are dòu, qū, lǔ, and zhōng. Four shēng equals one dòu, each has its four, which can be converted to lǔ." This means that four shēng equals one dòu, and so on, which can be converted to lǔ and zhōng. One lǔ equals six dòu and four shēng, and ten lǔ equals one zhōng, which equals sixty-four dòu. Zheng Xuan had a differing opinion on this calculation method, and his results differed slightly from those in the "Nine Chapters on the Method of Grain." Zu Chongzhi calculated more precisely, finding the volume to be 1562.5 cubic inches in volume. Based on the specifications of being square on the inside, round on the outside, and one foot deep, the diameter is approximately one foot, four inches, one-tenth of an inch, four-tenths of a millimeter, and two microseconds. This is very similar to the specifications of the ancient hǔ.
The "Nine Chapters on the Method of Business" records the volumes of hǔ for different grains, such as millet, rice, legumes, and hemp wheat, etc., with varying volumes due to the different weights of the grains, even though their prices are the same. It uses the rice hǔ measure as a standard, which is similar to what is recorded in the "Book of Han." The "Sunzi Suanshu" also discusses smaller units: six sù equals one guī, ten guī equals one miǎo, ten miǎo equals one cuō, ten cuō equals one shāo, and ten shāo equals one hé. Ying Shao and Meng Kang have slightly different interpretations of "guī," one saying it is the primordial form of yin and yang, and the other stating that sixty-four shǔ equals one guī.
"The Book of Han" offers a detailed account of five ancient measuring instruments: the yuè, hé, shēng, dǒu, and hú, which originated from the Yellow Bell (yuè). It also describes the specific production methods and specifications, made of copper, square inside and round outside, with the hú on top, the dǒu on the bottom, and the shēng, hé, and yuè on the sides. The shape resembles a jue, symbolizing nobility and embodying the concepts of yin, yang, and the five elements, weighing two jin, with a volume of 11,520 cubic inches, and sounding like the Yellow Bell. The inscription on the hú states: "The Lu Jia Liang hú, square inside and round outside, nine lí and five hao beside the táo, 162 cùn in height, one chǐ deep, totaling 1,620 cùn, holding ten dǒu." After Zu Chongzhi calculated a more precise value of pi, he believed the diameter of the hú should be approximately one chǐ, four cùn, three fen, six lí, one hao, and nine seconds, two hù. Liu Xin's calculations differ slightly from this, possibly due to his less precise calculation method.
In the fourth year of the Wei Jingyuan era, Liu Hui wrote in "Nine Chapters on the Mathematical Art": the hú currently used by the Grand Minister of Agriculture has a diameter of one chǐ, three cùn, five fen, five lí, and one hao, with a depth of one chǐ, and a volume of 1,441 cùn and three fen. The copper hú from the time of Wang Mang, measured by modern standards, has a depth of nine cùn, five fen, five lí, and a diameter of one chǐ, three cùn, six fen, eight lí, and seven hao. Using Liu Hui's calculation method, the copper hú from Wang Mang's time, measured by today's standards, is just over nine dǒu, seven shēng, and four hé. Thus, it can be concluded that the hú from the Wei Dynasty is larger and has longer measurements, whereas Wang Mang's hú is smaller and has shorter measurements.
The Liang and Chen Dynasties continued to use the earlier system of measurements. In the Qi Dynasty, five ancient shēng units equaled one dǒu.
In the first year of the Baoding era of the Later Zhou (561 AD), in May, the Jin state built granaries and discovered an ancient jade measuring cup. By October of the fifth year of Baoding (565 AD), Emperor Wu ordered the revision of laws and standards for weights and measures in bronze, ultimately achieving a unified standard for measurements. The inscription reads: "The volume measured by piled millet is consistent with the volume of this jade cup, and with other measuring instruments." This means that the volume measured by piled millet is consistent with the volume of this jade cup, and with other weights and measures. Subsequently, this jade cup was used as the standard to cast bronze sheng (a unit of volume) for distribution across the country. The inscription on the bronze sheng states: "In the first year of the Baoding era of the Great Zhou, in the Chongguang year, in the month of Lüyurui, the officials of the Jin state repaired the granaries and obtained an ancient jade sheng, whose shape and design are correct, like the excellent measures of old. The Grand Minister of the Jin state reported this, and it was decreed to be accepted in the Tianfu. In the fifth year, in the year of Xieqia, the Emperor then commanded to establish the standard, examine the laws, ensuring no loss in the measurements, and no difference in the piled millet. Thus, gold was melted and cast, and it was distributed to the world to establish peaceful standards for weights and measures." This bronze sheng has an inner diameter of 7 inches and 1/10, a depth of 2 inches and 8/10, and weighs 7 jin and 8 taels. On the fifteenth day of the first month of the second year of Tianhe (567 AD), after calibration, the bronze sheng was transferred to the government as a standard measuring instrument. The inscription on the jade sheng also records the process of discovering and casting the bronze sheng.
According to current calculation methods, the volume of this jade sheng is approximately 110 inches and a bit more, while the volume of a hu (another unit of measure) is about 1,185 inches, 7/10, 3/100, and 9/1,000. Zhen Luan in "Arithmetic" states: "One sheng of jade is equal to one sheng and three he and four spoonfuls of the government’s measuring cup." This means that the jade sheng is relatively large, while the government’s measuring cup is relatively small. Based on Zhen Luan's records, the measuring cup used by the Later Zhou government has a volume of about 97 inches and a bit more, and the volume of the hu is about 977 inches and a bit more. The Later Zhou jade measuring cup, along with matching gold-inlaid bronze cups, as well as the gold-inlaid bronze measuring cup from the sixth year of Jiande (577 AD), were all calibrated using millet for volume. When weighed with jade weights, the weight of one sheng consistently measures 6 jin and 13 taels.
During the Kaihuang period, it was stipulated that three ancient sheng were equivalent to one current sheng. By the Daye period, the capacity of the ancient dou was reinstated.
Heng means "balance," while quan means "weight." Heng serves to support quan, used to measure the lightness and heaviness of things. The method of making heng must be corrected according to standards to calibrate its precision and alignment. Rotating left reveals the compass, while bending right shows the square ruler. The role of heng in the heavens is to assist in celestial navigation, to deliberate on construction, and to coordinate the seven celestial bodies; hence it is called the Jade Balance.
Quan refers to weight units like zhu, liang, jin, jun, and shi, which are used to measure things with scales to determine their lightness and heaviness. In ancient times, there were also weight units like shi, zha, chui, ci, huan, gou, yue, and yi, and the standards varied across different dynasties; I am not entirely sure of the specifics. The "Book of Han" states that the origin of quan is based on the weight of the yellow bell. One yue can hold twelve hundred grains of millet, weighing twelve zhu; twenty-four zhu equals one liang, sixteen liang equals one jin, thirty jin equals one jun, and four jun equals one shi. The production of these five kinds of weights is meticulously precise, and their manufacturing standards are established based on principles and calibrated with physical objects. Size differences should be determined according to weight.
Heng is designed in a circular shape, encompassing itself, creating an endless cycle. Only when quan and objects are balanced does heng arise; the functioning of heng creates the compass, the circular shape of the compass gives rise to the square ruler, the square shape of the ruler produces the rope, and the rope's straightness establishes the standard measure. When the standard measure is correct, heng can be balanced, and quan can be accurate. These five principles are embodied in the measuring instruments, which serve as the fundamental standards.
According to the records of the "Zhao Book," in July of the eighteenth year of Shi Le's reign, when the Jiande Palace was built, a round stone shaped like a water mill was obtained. It was inscribed with the words: "Law and Weights Stone, weighing four qin, in accordance with legal standards of measurement. Made by the Xin clan." It was generally thought to be from the Wang Mang era. During the Northern Wei Dynasty, Wang Xianda from Bingzhou presented an ancient bronze weight inscribed with an inscription of eighty-one characters. The inscription read: "Law and Weights Stone, weighing four qin." It also stated: "The Yellow Emperor, the first ancestor, had virtue in the Yu era. Yu, the first ancestor, had virtue in the Xin era. In the year of Daliang, the dragon gathered in Wuchen. Wuchen directly established, heaven's mandate was granted to humanity. Based on the virtue of the land, the rightful title is genuine. Changing and establishing the Chou, longevity and prosperity. In accordance with legal standards of measurement, reflecting on the current society. The dragon in Jisi, the following year was peaceful, initially ruling the world, with all nations forever in obedience. Generation after generation, enjoying an everlasting legacy." This was also made during the time of Wang Mang. At that time, Gong Sun Chong, the Taiyue Ling, based on the "Book of Han," first adjusted the measuring rod, and when he examined this balance, the weight came to one hundred and twenty catties. The new scale and balance matched perfectly. So Gong Sun Chong was put in charge of adjusting the music and laws. During Emperor Xiao Wen of Sui's Kaihuang era, measures and scales were produced based on the standards outlined in the "Book of Han." The Liang and Chen dynasties retained the use of ancient measurement units. During the Qi Dynasty, one ancient catty was equivalent to eight taels today. In the Zhou Dynasty, a catty of jade was four taels, equivalent to four and a half ancient taels. During the reign of Emperor Wen of Sui, it was established that three ancient catties equaled one catty today. By the time of Emperor Yang of Sui in the Daye era, the ancient scales were reinstated.
This discusses the conversion of weight units from different ancient dynasties, which differs from today's standards. Simply put, the standard for "one jin" varied across different dynasties, sometimes heavier and sometimes lighter, making it quite confusing. During the Qi Dynasty, one jin equaled eight taels, which is quite different from today's standard of one jin being sixteen taels. In the Zhou Dynasty, when it came to jade artifacts, one jin was only four taels, which is less than half of today’s one jin! During the Kaihuang period of the Sui Dynasty, the measurement changed again, with three ancient jins equaling one jin. By the Daye period, it reverted back to using the ancient scales. It's clear that ancient measurement units underwent many changes.
