Xin Dufang is exceptionally clever. He can use bamboo tubes to predict the weather; just by looking at the clouds, he can tell when it will snow or rain. One time, he was chatting with someone and pointed to the sky, saying, "Spring has arrived!" The other person quickly went to check his bamboo tube, and hey, the ash in the tube really did fly up! Every month, his weather predictions are spot on. He also made 24 wheel-like fans, buried underground, to track the 24 solar terms. When each solar term arrives, one fan starts moving on its own while the others stay still, perfectly matching the ash flying up in the bamboo tube, as if they had made a prior arrangement.
After Emperor Wen of Sui, Yang Jian, defeated the Chen dynasty, in the ninth year of his reign, he sent Mao Shuang, Cai Ziyuan, and Yu Puming to measure the solar terms. According to the previous method, they had to work in a room sealed with three layers, build a wooden table, and set twelve instruments on it. Each instrument held a bamboo tube tuned to the Lu scale, placed on the table according to the positions of the twelve shichen, then buried in the ground, ensuring the surface was flat, filled with light reed ash, and covered with a thin silk cloth over the mouth of the bamboo tube. When the energy of a certain solar term arrives, matching the musical scale of the bamboo tube, the ash will fly up, break through the silk cloth, and float outside. However, the timing of the energy's manifestation varies, and so does the amount of ash that flies out. Some show results right at the start of the month; some don’t show results until the middle of the month; some ash flies out and disappears in three to five days; and some take the whole month to trickle out gradually.
Emperor Wen of Sui found this situation strange and asked Niu Hong what it meant. Niu Hong replied, "When ashes fly halfway, it suggests a mild climate; when all the ashes fly out, it suggests a violent climate; when ashes do not fly out, it suggests a declining climate. The occurrence of a mild climate suggests that the political situation in the country is stable; the occurrence of a violent climate suggests that the ministers are acting unruly; the occurrence of a declining climate suggests that the emperor is tyrannical." Emperor Wen of Sui disagreed and said, "If the ministers are unruly and the emperor is tyrannical, the country's political situation is definitely unstable. This isn’t something that varies every month! The twelve-month regulations reflect different situations throughout the year. How can one claim that the emperor is tyrannical and the ministers are unruly, and that it will always be this serious?" Niu Hong could not answer. So Emperor Wen had Mao Shuang and the others compile a set of methods. Mao Shuang consulted previous materials and wrote a book called "Lu Pu." The book discusses: According to historical records, Emperor Huang sent Ling Lun to the Xian Valley to cut bamboo, and under the nest of the phoenix, created twelve tones. This reflects the qi of heaven and earth and marks the origin of numbers! The Yang tubes represent tones, while the Yin tubes represent pitches; their qi can predict the four seasons, and the numbers can be used to record all things. Yunli first established the counting method, which serves as the foundation for tones! The numbers one, ten, hundred, thousand, ten thousand, billion, trillion, these numbers are derived from this, and the system of weights and measures also evolved from this. Therefore, during the Xia dynasty, tones were used to harmonize sounds, and later Zou Yan improved it and established the five beginnings. The categorization of the calendar and clothing colors also stems from this. The Xia dynasty focused on people, the Shang dynasty focused on the land, and the Zhou dynasty focused on heaven. Confucius once remarked, "I have grasped the essence of qi."
During the early days of the Han Dynasty, Zhang Cang established legal codes based on the Five Victorious Principles, believing that the virtue of water was paramount. In reality, this was due to the negligence of officials during the Warring States period and the suppression of knowledge during the Qin Dynasty, resulting in a gradual decline in musical knowledge. Zhang Cang merely made some improvements without fully grasping the underlying principles. It was during the reign of Emperor Wu of Han that the Office of Music Regulations was established, appointing Li Yannian as the Commandant. Although Li Yannian could create new musical variations, he did not truly understand the fundamentals of music theory, which led to the lack of a definitive system of musical scales at that time.
During the reign of Emperor Yuan of Han, he had a solid understanding of music theory, and Jing Fang was also knowledgeable in music theory. Emperor Yuan instructed Wei Xuancheng and others to consult Jing Fang. Jing Fang introduced his study of Jiao Yanshou's theory, utilizing the principle of sixty musical scales that interact with each other. He explained, "The upper generates the lower, both are three to two; the lower generates the upper, both are three to four. Yang generates yin below, yin generates yang above, ultimately returning to the proper method of the tonal system." Later, Liu Xin compiled relevant memorials and documents, recording the origins and development of music theory, which became increasingly profound. Ban Gu's "Book of Han: Treatise on Music and Calendars" comprehensively documented Liu Xin's research findings, while Sima Biao's "Records of the Grand Historian" also included Jing Fang's viewpoints.
During the Eastern Han Dynasty, the musical scale was slightly extended. The Wei Dynasty's Du Kui also established musical scales to predict the weather, ensuring that dust would remain settled. Xun Xu, the Grand Minister of Splendor of the Jin Dynasty, obtained ancient bronze pipes and compared them with Du Kui's musical scales, discovering that the ancient bronze pipes were a quarter longer than Du Kui's, revealing the inaccuracies in Du Kui's scales due to a miscalculation. Xun Xu then recreated the ancient ruler following the "Rites of Zhou" to determine the length of the pipes, thereby accurately tuning the musical scales of instruments.
After the fall of the Jin Dynasty, the methods for making the Lu pipes became increasingly unreliable. During the time of Emperor Wu of Liang, although jade Lu pipes were still being excavated from Jizhong, during the Song Dynasty in Cangwu County, some people attempted to replicate the horizontal Lu pipes. However, the length, thickness, and overall dimensions of these pipes remained largely similar to the originals. When my grandfather was young, he studied arithmetic under his ancestors and studied Lu pipes with He Chengtian. After decades of dedicated research, he became quite knowledgeable about the production of Lu pipes. Later, upon becoming the Minister of Music, he took the jade pipes and the ruler used by the court historian of the Song Dynasty to the court. The court ordered the craftsmen to produce the Lu pipes in the original style.
But since then, the production of Lu pipes began to fall into disarray. During the rebellion of Hou Jing, my uncle Xi acquired several Lu pipes from the Tai Le Temple. Later, when Emperor Chen Xuan was taken to Jingzhou as a hostage and encountered the defeat of Emperor Liang Yuan, my uncle perished amidst the chaos of war. He had originally intended to surrender the Lu pipes to the court, but after Emperor Wu of Chen took the throne, he devised a set of theories, claiming that there were rules to follow. During the Taijian period, my uncle, who had risen to the position of Minister of Personnel, wanted to hand over the Lu pipes to the court, but after Emperor Chen Xuan's death, Emperor Chen Houzhu ascended to the throne and demoted my uncle to Yongjia as an official, so the Lu pipes remained in the family and were eventually passed down to his descendants. When the Chen Dynasty fell, these Lu pipes were lost as well.
The twelve tuning pipes remaining in Tai Le Temple are arranged according to the principles of yin and yang. Starting from Huangzhong, the yang energy diminishes, leading to the emergence of yin energy, and ending with the tone Zhonglü, where the yin energy rises, generating yang energy. The changes in climate throughout the four seasons are all reflected here. Above Zhonglü is Zhishi, and below Zhishi is Qumie, ultimately leading to Nanlü. The variations in the sixty musical tones are also reflected here. In the month of mid-winter, the tuning pipe should be played as Huangzhong. Huangzhong is the musical tone that begins at the winter solstice, representing the start of yang energy. According to the cycle of days, its length is nine inches, and in November, the tone of Huangzhong should be played to harmonize the six energies and perfect the nine virtues.
From then on, people began to use the standards of Jingfang's laws. The lengths of the tones Gong and Zhi vary from day to day. Each of these twelve tuning pipes governs a specific range of tones, which can be extrapolated to sixty tones. This is analogous to the eight trigrams, which can be extrapolated to sixty-four hexagrams. The generation and transformation of energies occur, with Linzhong positioned below Huangzhong, where yang energy generates yin energy, hence the transformation. The interconnection and communication, such as with Zhonglü, influence each other like a mother and child. Therefore, the transformed tones should be played at different times, while the interconnected tones are played continuously within the same month. If the tones played differ from morning to evening, they are not the proper tones, but rather the subsidiary tones influenced by the fundamental tone, reflected within the fundamental tone.
Later, during the Daye period, these tuning pipes were lost amidst the turmoil of war in Jiangdu.
During the Song Dynasty, there was a man named Qian Lezhi, who, after studying the music theory of Jing Fang, created three hundred tones of his own. In his "Discussion on Tones," the scholar Shen Zhongzhong of the Liang Dynasty said: "The Book of Changes uses three hundred and sixty hexagrams to correspond to the number of days in a year, which is the number of tones. The Huainanzi says: 'One tone gives birth to five sounds, twelve tones produce sixty sounds, and then multiplied by six, it becomes three hundred and sixty sounds, corresponding to the number of days in a year. The number of tones is the law of the movement of heaven and earth.' Therefore, the algorithm of these three hundred and sixty tones has been like this since ancient times." Based on the numbers in the Huainanzi, Shen Zhongzhong calculated three hundred and sixty tones using Jing Fang's method. Each month designates a primary tone as the mother tone for that month. The number of tones from the mother tone is considered the mother, the number of days when the qi is in that month is used as the child, the mother determines the child, and the number of days and fractions governed by each tone are different. Using this method to allocate seven tones, then on the day of the winter solstice, the base tone is the Gong tone, the Tai Cuo is the Shang tone, the Lin Zhong is the Zhi tone, the Nan Lu is the Yu tone, the Gu Xi is the Jue tone, the Ying Zhong is the Bian Gong tone, and the Rui Bin is the Bian Zhi tone. In this way, the five tones and seven notes are complete. In the following days, the base tone is followed sequentially. The tone corresponding to that day is the Gong tone, and the Shang and Zhi tones follow in order. Using this method to examine sounds and qi, distinguish the timing, and all things should follow the changes of the solar terms.
From Huang Zhong to Zhuang Jin, there are a total of one hundred and fifty tones, all calculated downwards using the method of subtracting one from three parts; from Yi Xing to Yi Zhao, there are a total of two hundred and nine tones, all calculated upwards using the method of adding one to three parts; only An Yun is the last tone, and no other tones are calculated. The calculation of the lengths of these tones is based on the actual length of Huang Zhong, which is 177,147 units, using nine to the power of three (which is 27) as the divisor, calculating their lengths with precision down to inches or even smaller units, and the remaining remainder is discarded. This way, the lengths of each tone are obtained. Revising the tones is to arrange the Gong and Zhi tones in the order of the upper and lower generations. Now, let me now briefly outline their names and sequence:
Huang Zhong:
Bao Yu, Han Wei, Di De, Guang Yun, Xia Ji, Ke Zhong, Zhi Shi, Wo Jian, Chi Shu, Huang Zhong, Tong Sheng Qian Sheng (footnote: names of historical figures or concepts in Chinese philosophy)
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, Yi Mei, Bu Jian, Xuan Zhong, Yu Zhu, Diao Feng
The Right Huang Zhong consists of one section, encompassing thirty-four laws. (Each law corresponds to thirty-one parts of thirty-four days)
Da Lü:
At the beginning of events, there was a sense of great potential, teeming with vitality, much like the earth itself, assisting the situation and correcting deviations. The development of events unfolds rapidly, shifting in various directions, but as long as one persists in justice, difficulties can be overcome. One should be like a strong person, overcoming darkness and moving towards light, recognizing the importance of deep reflection for eventual prosperity and growth, adapting to the times, weighing pros and cons, speaking less and doing more, to work hand in hand with the ruler, upholding the glory of ancestors.
This is the Da Lü palace tune, comprising twenty-seven laws, each corresponding to a day, also including one-third of twenty-seven parts of a day.
Tai Cu Palace Tune:
At the beginning, one is still unclear about their abilities, but the act of justice has already begun, growing like the plant "Ting Du" (a type of plant) with the changing seasons. All things begin to grow, the seasons stabilize, and life flourishes, like the gourd playing the first notes of music, the gentle and compliant energy of the minor sun, the deep, soothing tones of commerce that uplift the weak, all things thrive, the mountains and rivers quiet their clamor, everything follows the seasonal patterns, leaping up like a dragon. Gou Mang (the spring deity) regulates all things, green branches begin to grow, flowers bloom, all things reproduce, the penal system improves, social order is orderly, spring plowing begins, praising the harvest, hidden flaws gradually come to light, and ultimately, all things begin to wither.
This is the Tai Cu palace tune, with a total of thirty-four laws.
Ming Shu Palace Tune:
Everyone helps each other, the yin energy nurtures everything, the wind races from all directions, policies are set, everything thrives, spring arrives, the quaking earth is alive with energy, fragrant and abundant, the sun shines all around, the wind races like lightning, people are joyful and united, planting seeds, all things grow freely, free and easy, benevolence and majesty go hand in hand, spring moves southward, the rising sun brings new life, everyone does their part, everything is renewed.
This is the Jiazhong Palace tune, a total of twenty-seven lines.
Gu Xia Palace tune:
Good news is coming from the south, worshipping the gods and praying for a good harvest, spring arrives, all things are renewed, talents abound, auspicious energy rises, auspicious clouds appear, beautiful mountains, wide roads, perfect timing, people travel, quiet nights and warm breezes, trees bud, branches are soft, laws start to take effect, all things grow, vegetation flourishes, crops mature, light shines all around, vigorous development, following the laws of nature, making few choices, adhering to the way of heaven, dressed in crimson ceremonial robes, showcasing one's talents in the court, maintaining purity.
This is the Gu Xia Palace tune, a total of thirty-four lines.
Zhong Lü Palace tune:
Light appears, everything starts to move, the gentle spring breeze is soft and slow, birds start to take flight, the south enters spring, guiding farmers to plow, following seasonal patterns, auspicious signs appear in the south, everyone lifts each other up, keeping their hearts pure, red plants shine brightly, radiating light, spring arrives, all things grow, abstaining from greed, desolate scenes disappear, pure constellations, the heavens bless the Zhou Dynasty.
This is the Zhong Lü Palace tune, a total of twenty-seven lines.
Rui Bin Palace tune:
Southern matters (Jing Fang's Final Laws), peaceful and harmonious, choosing the right time, flowers in full bloom, all things flourishing, unpredictable changes, guests at ease, longing for the distance, voices passing on, following the same path, calm sea, disasters are averted, leaving oneself, becoming powerful, noble and bright, looking into the distance, rising to the center, phoenix flying, sunrise, seizing the opportunity, auspicious signs, Chunhuo appearing, orderly and organized, flames soaring, shining brightly.
Wow, what does this say? It looks like some ancient song or incantation. Part One: Right Rui Bin, Twenty-Seven Laws, followed by a bunch of words: "Humble Service, Esteem for Virtue, Following the Path, Strong and Resilient, Yin Rising, Eliminate Deception, Avert Disaster, Flourishing Celebration, Cloudy Patterns, Equal Responsibility, Respectfully Achieving, Generous and Calm, Virtue Equal, No Obstacles, Overflowing Ceremony, Profound Wisdom, Respectfully Solemn, Pure and Devoted, Returning to Praise, Beautiful Sound, Gentle Breeze, Seasonal Changes, Vivid Flowers, Embroidered Peaks, Without Things, No Rejection, Scenic Mouth, Bright Well, Daily Transformation, Heavy Wheel, Wealth and Prosperity." I think these twenty-seven words describe some kind of ideal state or life realm; one by one, they sound quite majestic.
Next is Part Two: Right Lin Zhong, Thirty-Four Laws, longer than the previous one: "Rising Commerce, Refreshing, Vital Energy, Yin Virtue, White Concealment, Imperial Narration, Fresh Punishment, Steadfast Restraint, Golden Heaven, Liu Xian, Returning to Kindness, Yin Partner, Leaving South, Yang Dissipating, Soft and Bitter, Extended Yi, Harmonious Geng, No Flowers, Ti Jin, Divided Accumulation, Kong Xiu, Nine Virtues, All Honored, Collective Governance." These thirty-four words seem even more complex than the previous ones; it seems to describe a kind of political ideal or social order; anyway, it's pretty deep.
Then there is "Right Yi Ze, one section, twenty-seven verses." followed by another paragraph, "White Lv Juan Xiu Dun Shi Su Feng Jing Wu Qiu Ren Jie Gong Fei Dun Lei Zhong Sheng Yin Kang Jie Wei Yuan You Jie Gui Qi Zhong De Wang You Yun Sai Ru Shou Zun Pei Yao Luo Wei Yin Zhi Sui Fen Man Dao Xin Zhen Jian Xu Zhi Gui Cang Yi Han Jun Yi Yue Shi Wang Lao Jiu You Guang Ben." These twenty-seven terms seem somewhat similar to the previous two sections, yet also distinct, possibly with a different emphasis.
Next is "Right Nan Lv, one section, thirty-four verses." followed by another long paragraph, "Si Chong Huai Qian Gong Jian Xiu Lao Xu Nong Xiao Xiang Bi Yan Jiang Lou Cang Sui Ri Zai Xuan Chun Yan Cang Ming Kui Lin Qi Gui Zhong Da Xu Se Lian Xia Ji Xi Jian Wu Bian Qi Bao Yan Nian Qiu Shen Ye Se Xuan Yue Cheng Tian." These thirty-four terms appear to emphasize personal cultivation and social harmony more than the previous ones, and they convey a sense of tranquility.
Finally, we have "Right Wu She, one section, twenty-seven verses." "Fen Yan Zu Wei Ju Shi Gong Cheng Yi Ding Jing Mi Chi Nei Wu Wei Er Yi Gu She Ning Hui Dong Ji Ying Zheng Wei Yu Wan Ji Wan Shou Wu Jiang Di Jiu Tian Chang Xiu Fu Chi Shi Fang Zhi Wu Xiu Jiu Ye Ba Huang Yi Zhao An Yun." These twenty-seven terms seem to summarize the content, infused with hopeful aspirations for the future. Lastly, "Right Ying Zhong, one section, twenty-eight verses." There is no content provided, likely due to missing original text or additional notes. Overall, this entire piece appears quite enigmatic, resembling a fragment of ancient scripture, suggesting that in-depth study is necessary to grasp its true meaning.
According to the "Records of the Grand Historian": "Yu of Xia, he used his own body as a measuring tool and his voice to establish laws." The "Book of Rites" also says: "A man's outstretched hand is considered one foot." The "Zhou Guan" writes: "The 'Bi Xian' initiates the measurements." Zheng Sinong clarifies: "'Xian refers to length. The diameter of this bi is a foot, and it is used to establish weights and measures." The "Yi Wei Tong Gua Yan" states that the length of ten horse tails is equivalent to one fen. In the "Huainanzi," it says: "During the autumn equinox, the awns of the grain are set, and when the awns are set, the grain is ripe. In the law of numbers, the length of twelve awns is equal to one grain, and twelve grains are equal to one inch." These awns refer to the bristles on grain heads. "Shuo Yuan" also states: "The standard of weights and measures starts with grains, with one grain being one fen." In "Sunzi Arithmetic," it is written: "The silk spit out by silkworms is called a hulu, ten hulu make a miao, ten miao make a li, ten li make a fen." These are all the origins of weights and measures, but these explanations can be somewhat contradictory.
However, the "Book of Han - Records" explains more clearly: "Measure is used to measure length, and it was originally based on the length of the Huang Zhong bell. Measurements were made using medium-sized grains of millet, known as jushi. The width of a single jushi grain is regarded as one fen, and the length of ninety grains of jushi is the length of the Huang Zhong. One jushi is one fen, ten fen is one inch, ten inches is one foot, ten feet is one zhang, ten zhang is one yin, thus determining five lengths." Later authors based their laws and weights and measures on this explanation and developed various methods depending on the size of jushi, so these proportions can still be interchangeable. The problem is that the size of jushi varies, and the quality of the harvest can also impact yields. Ancient calibration of weights and measures often had discrepancies, and with oral transmission among the people, errors inevitably occurred, resulting in variations over time. I will now briefly outline the fifteen historical scales along with their similarities and differences as follows:
The Liu Xin bronze hu chi from the Wang Mang era, as recorded in the "Book of Han - Records";
The bronze chi from the later Han Jianwu period;
The lu chi established by Xun Xu in the tenth year of the Tai Shi era during the Jin Dynasty, which is the chi used prior to the Jin Dynasty;
The bronze chi that has been passed down from Zu Chongzhi.
In the ninth year of the Tai Shi era of the Jin Dynasty, the Minister of the Imperial Secretariat, Xun Xu, inspected the court music and found that the eight musical instruments were out of tune. Upon investigation, it was discovered that the rulers from the Eastern Han to the Wei Dynasty were more than four inches longer than the ancient rulers. Xun Xu had official Liu Gong to remake a ruler based on the standards outlined in the "Rites of Zhou," which was the authentic ancient ruler! Using this ancient ruler, they recast the bronze tuning instruments to adjust the musical pitch. When this ancient ruler was used to measure the ancient musical instruments, the dimensions matched perfectly with their inscriptions. Interestingly, tomb robbers in Jiyun dug up the old grave of King Xiang of Wei and found jade tuning instruments and bells from the Zhou Dynasty, which sounded nearly identical to the newly cast tuning instruments! At that time, old Han Dynasty bells were also unearthed in various places, and when tested with the newly made tuning instruments, the sounds matched perfectly!
The book "Zhong Lü Wei" records that during the time of Zu Chongzhi, a bronze ruler was circulated, inscribed with the text: "In the tenth year of Tai Shi of Jin, the Minister of the Imperial Secretariat verified ancient artifacts and found that the current ruler is four and a half inches longer than the ancient standard. There are seven ancient standards: first, the Gu Xia jade ruler; second, the Xiao Lü jade ruler; third, the Xi Jing bronze measuring instrument; fourth, the Jin Cuo measuring instrument; fifth, the bronze hu; sixth, ancient coins; seventh, the Jianwu bronze ruler. The Gu Xia jade ruler is slightly longer, the Xi Jing bronze measuring instrument is slightly shorter, while the others are the same as this ruler." This inscription contains eighty-two characters. This is the ruler remade by Xun Xu. The ruler we use today was made by Du Kui. Lei Cizong and He Yinzhi even created a "Zhong Lü Tu," which contains the text of Xun Xu's verification of the ancient ruler, matching this inscription exactly. However, Xiao Ji's music score claims that these seven standards were verified during the Liang Dynasty, which is inaccurate. We will now use this ruler as the standard to verify the rulers from different dynasties.
The ruler from the Liang Dynasty is one foot and seven inches longer than the ruler used before the Jin Dynasty.
Once upon a time, an old farmer found a jade measuring stick from the Zhou Dynasty while digging in the field, reportedly the world's standard measuring stick. Xun Xu used it to check musical instruments and found that the metal and stone instruments he made were a meter shorter than the standard. Emperor Liang Wu's book "Zhonglüweicheng" also records that there has long been a bronze measuring stick from the Zhou Dynasty and eight ancient jade musical pieces in the imperial palace. Later investigation revealed that the Zhou Dynasty ruler was used as a token by the Eastern Hun Marquis but was later lost. Only one of the jade musical pieces was damaged, and the remaining seven were chimes with ancient inscriptions on them. So Emperor Liang Wu made a new ruler based on these jade musical pieces for mutual verification. They used the finest millet grains for precise measurements, repeatedly calibrated, which was the most accurate measurement method at that time, even half a unit more accurate than Zu Chongzhi's measuring stick. Then, Emperor Liang Wu crafted four musical pieces known as "Tong" using this new ruler. He also made flutes according to the new ruler to calibrate the ancient bells, determining the pitch of the "Yize" note according to the scale, and the pitch of "Yize" was also determined. You see, these two rulers are almost the same length.
Xiao Ji writes in his treatise: "This method comes from the 'Sima Fa'. The Liang Dynasty engraved the ruler's scale on the shadow table for measuring the sundial." This refers to the bronze guibiao calculated by Zuxun upon the court's request. After the fall of the Chen Dynasty, this guibiao was presented to the imperial court. During the Sui Dynasty, a proposal was made to restore ancient standards, so this guibiao was employed to calibrate the musical scale and create eight types of musical instruments such as clocks and chimes.
During the Jin Dynasty, a digger in Shiping County unearthed an ancient bronze measuring stick.
Xiao Ji's "Score" mentions: "During the reign of Emperor Zhang of Han, Wen Xing of Lingling discovered a set of jade rules under the Shun Temple in Lingdao County and crafted this ruler based on it." Fu Chang's "Praise of the Jin Dynasty Officials" records: "The bell rules made by Ge Xu were regarded as very precise by people back then, except Ruan Xian from Chenliu who thought the sound was too high. Later, an ancient bronze ruler was discovered in Shiping County, which had deteriorated over time; when compared to Ge Xu's ruler, it was a quarter shorter. Everyone back then agreed with Ruan Xian." The lengths of these two rulers were also similar. In the fourth year of the Wei Dynasty under Prince Jingyuan of Chenliu, Liu Hui commented in the "Annotations of the Nine Chapters on the Mathematical Art" that the bushel and ruler used by Liu Xin during Wang Mang's reign were four and a half fen shorter than the contemporary rulers, and compared to the Wei Dynasty rulers, the depth of the bushel was nine cun, five fen, and five li. This aligns with what Xun Xu from the Jin Dynasty noted: "Du Kui's ruler is four and a half fen longer than the current ruler." Xiao Ji said that this ruler was used in the Jiangdong region of the Jin Dynasty. The market ruler in the Later Zhou Dynasty was one foot, nine fen, and three li shorter than the jade ruler. The official ruler during the Kaihuang period was an iron one, measuring one foot and two inches long. Before this, from the early Wei Dynasty to the division of the Eastern and Western Wei, until the Later Zhou Dynasty ceased using the jade ruler, people used these rulers interchangeably. According to the "Zhen Luan Arithmetic": "The market ruler of the Zhou Dynasty is equivalent to nine fen and two li of the jade ruler." Some claim that this ruler was crafted by Zhi Gong Dao Ren of the Liang Dynasty, and that he sent the ruler to the Zhou Dynasty, even gifting it to an elderly man named Duo Xu. Both Zhou Taizu and Sui Gaozu believed this ruler belonged to them; regardless, the common people of the Zhou Dynasty used this ruler. During the Kaihuang period of the Sui Dynasty, an official decree was issued to adopt this ruler as the standard ruler, and all departments adopted it until the Renshou period. Even during Emperor Yang's reign in the Sui Dynasty, some people still used it privately.
This ruler, crafted using the width of half a grain of millet, was made by Lieutenant Yuan Yanming of the Wei Dynasty. The Qi Dynasty subsequently adopted this ruler. Wei Shou wrote in "Wei Shu · Lu Li Zhi": "Gongsun Chong made a new ruler during the Yongping period, using the length of a single grain of millet as a unit. Later, Taichang Qing Liu Fang was tasked with revising the musical scales, using the width of medium-sized millet as a unit. Lieutenant Yuan Kuang used the width of a grain of millet plus the width of two gaps between grains to define a unit. The three methods differed, leading to prolonged debates without resolution. It wasn't until the nineteenth year of Dahe that Gaozu ordered the width of a grain of millet to be used to determine a unit, and the length of ninety grains of millet equated to the length of the Huangzhong bell, to create the bronze ruler. The relevant authorities reported that Liu Fang's ruler matched the one established by Gaozu, so Liu Fang's ruler was used to revise gold and stone objects. It wasn't until the Wuding period of Northern Wei that legal matters were no longer discussed."
Next, we have Cai Yong's bronze yue ruler. The jade ruler from the Later Zhou was longer by one foot, one inch, five fen, and eight li than the rulers before the Jin Dynasty. A bronze yue has been handed down from ancient times to the present, with silver-inlaid characters on its surface, inscribed with: "Yue, the palace of Huangzhong, nine inches long, nine fen around, capable of holding 1,200 grains of millet, weighing twelve zhu, two of which make one he. Three parts gain or loss, creating twelve scales." Zuxiaosun remarked, "This is traditionally believed to be Cai Yong's bronze yue."
During the Baoding period of Later Zhou Emperor Wu, the emperor commanded Dazongbo Lu Jingxuan, Shangdang Gong Changsun Shaoyuan, and Qiguo Gong Husi Zheng to create a ruler using millet grains, but the exact length could never be agreed upon. Later, when the warehouse was repaired and the ground was dug, an ancient jade container was unearthed and was adopted as the standard measure. Laws and measurements were established based on the jade container. As a result, this ruler was adopted, and a general amnesty was declared, changing the era to Tianhe. All departments used this ruler and continued to be used until the end of Emperor Zhou Xuandi's reign. The Huangzhong scale of this ruler is the same as Cai Yong's ancient yue.
Finally, there is the Song dynasty尺, which is one foot, six inches, and four tenths longer than the尺 used before the Jin dynasty; there is also Qian Lezhi's celestial globe尺; there is the iron尺 of the Later Zhou dynasty; and the尺 used during the reign of Emperor Wen of the Sui dynasty for adjusting timekeeping, as well as the water尺 used for adjusting timekeeping after the Chen dynasty was subdued.
This尺 is the type commonly used by the general public during the Song dynasty and later passed down to the Qi, Liang, and Chen dynasties, employed in crafting musical instruments and establishing musical scales. Compared with the尺 after the Jin dynasty, as well as the尺 used by the general public during the Liang dynasty and on Liu Yao's celestial globe, the lengths are approximately the same. This is likely due to the fact that尺 used by the general public tend to wear down and change over time, leading to slight differences.
In the sixth year of the Jiande era of the Zhou dynasty, after defeating the Qi state, this尺 became the standard measurement tool and was promoted for use across the nation. Later, during Emperor Xuan's reign, Da Xi Zhen and Niu Hong engaged in discussions:
I carefully studied the issue of measurement, governing the country, and establishing laws. It is necessary to carefully examine history to find the most appropriate standards. I consulted the iron ruler currently in use, which is a replica of the ruler made by Su Chao, as ordered by Emperor Taizu. Su Chao used this ruler to inspect it, which was the standard ruler of the former Zhou Dynasty. We measured its length, and it was exactly the same as the ruler of the Song Dynasty. It was used for calibrating musical pitch and measuring land area. Now we use the millet from Yangtou Mountain in Shangdang, following the method recorded in the "Book of Han - Records of Weights and Measures." If a large pile of millet is stacked up and exactly fills a foot by quantity, then according to the Huang Zhong musical pitch standard, it must be shaken vigorously to fill it. If a medium-sized pile of millet is stacked up, although it appears sparse, it can also exactly fill a foot, and it can be filled without shaking. The difference arises from the uneven sizes of the millet, so measuring with an iron ruler is still relatively accurate. Furthermore, the millet in Shangdang is different from other places, very black in color, round and heavy in shape, so using it as a measuring unit is certainly intentional. Because the rainfall, drought, and fertility of land vary in different regions, the size of millet may not necessarily meet the standard. Xu Shen's explanation states that the grains of millet are much larger than ordinary millet. I think these large millets now are the kind of millet at that time, using a hundred of these millets to fill a foot, which is in line with the ancient standard. Apart from filling a foot, there are more than ten millets left. This may be due to errors in measuring the diameter of the circumference, or imprecision in lawmaking at that time. Even if shaking vigorously is required to fill it, this is reasonable in principle. We now examine the ancient coins of the Zhou and Han Dynasties, and the sizes are consistent with each other; the scale of the Song Dynasty's armillary sphere is also accurate. Moreover, the "Huainanzi" also records that twelve grains of millet stacked up are an inch. This indicates that the laws established by ancient emperors, after thorough research and examination, are consistent in their calculations. The "Book of Han - Records of Food and Money" states, "Gold an inch square, weighing a catty." We now cast gold for testing, and the iron ruler is the closest. Based on documentary records and practical calculations, there are many instances that align. Moreover, iron rulers were already in use during the Ping Qi period, and now we have confirmed it, which is more in line with the actual situation. As for the practice of using a jade ruler to measure millet, with width as length, there is still some remaining after being filled, but not completely filled. Considering both ancient and modern contexts, this method may not be suitable. The rulers from the Jin and Liang Dynasties are too short and inadequate; it is impossible to fill a tube with millet, and calibrating the musical pitch with this ruler will make the sound sharp. Harmony of the eight tones is a symbol of a wise ruler and a prosperous era, and a governance strategy of a virtuous ruler is unified laws and weights and measures. We carefully examined previous literature and, based on the actual situation, believe that using an iron ruler is the most convenient.
Before there was time to finalize everything in detail, Emperor Gaozu died. Niu Hong, Xin Yanzhi, Zheng Yi, and He Tuo had a lengthy discussion, but there was no conclusion. After pacifying the Chen Dynasty, the emperor felt that the music of Jiangdong was the best and said, "This is the ancient melody 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 measuring sticks and musical standards of the Zhou Dynasty were abolished, and this iron measuring stick and musical standard were adopted, with one foot and two inches defined as the market foot."
In the tenth year of the Kaihuang era, the musical water measuring stick made by Wan Baochang was actually one foot, one inch, eight tenths, and six hundredths longer than the measuring stick used before the Jin Dynasty. "The current set of copper musical standards retrieved from the Taiyue Library and the palace was made by Wan Baochang and is called the water measuring stick musical standard. It is said to have a Huangzhong pitch that is double that of the iron measuring stick's Nanlü. Nanlü is the secondary tone of Huangzhong, hence it is called the water measuring stick musical standard."
Among various measuring sticks, the earth gage stick of Zhao Liuyao's Huitian Instrument is four inches and three tenths longer than the legal measuring stick of the Liang Dynasty and is actually one foot and five inches longer than the measuring stick used before the Jin Dynasty. "The earth gage stick of Zhao Liuyao's Huitian Instrument is four inches and three tenths longer than the Liang legal measuring stick and is actually one foot and five inches longer than the measuring stick before the Jin Dynasty."
Fifteen, the common ruler used by the people of the Liang Dynasty is six fen and three li longer than the legal ruler of the Liang Dynasty, two fen longer than the ruler of Liu Yao's celestial sphere, and actually one chi, seven fen, and one li longer than the ruler before the Jin Dynasty. Emperor Wu of Liang said in "Zhong Lu Wei": "After Emperor Wu of Song pacified the Central Plains, he sent the celestial sphere and the earth gauge, saying they were made by Zhang Heng. However, according to the inscription on the celestial sphere, it was cast in the fourth year of Guangchu, and the earth gauge was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. He set the ruler of the celestial sphere as the standard, with a length four fen and three li longer than the current standard ruler, and two fen shorter than the commonly used ruler among the people." The "new ruler" here refers to the Liang Dynasty's legal ruler. "The common ruler of the Liang Dynasty is six fen and three li longer than the Liang legal ruler, two fen longer than Liu Yao's celestial sphere ruler, and actually one chi, seven fen, and one li longer than the Jin ruler. Liang Wu's "Zhong Lu Wei" says: "Song Wu pacified the Central Plains, sent the celestial sphere and earth gauge, saying they were made by Zhang Heng. The inscription on the celestial sphere was cast in the fourth year of Guangchu, and the earth gauge was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. Made as a ruler, the current new ruler is four fen and three li longer, and two fen shorter than the commonly used ruler among the people." The new ruler refers to the Liang legal ruler. Hello everyone, today let's talk about ancient measuring instruments; this is quite a technical subject! First of all, the "Zhou Li" records a measuring instrument called "Wu." How big is it? The book says: "Wu is deep, square inside and round outside; its actual capacity is one Wu; its buttocks one inch deep, with a capacity of one bean; its ears three inches deep, with a capacity of one sheng. The total weight of the Wu is one catty (approximately 0.5 kg). Its sound is in the middle of the yellow bell. It is a general-purpose instrument and is exempt from taxation." There is also an inscription on this Wu: "Through careful consideration, one can achieve excellence. Good measure is achieved, to observe the four countries. It will be passed down forever; this instrument will be maintained." This means that after repeated research, this excellent measuring instrument was finally made, so that it could serve as a reference for all countries and benefit future generations.
Next, the "Zuo Zhuan" from the "Spring and Autumn Annals" mentions four types of measuring vessels used in the State of Qi: dou, qu, lu, and zhong. It states: "The four measures of Qi are dou, qu, lu, and zhong. Four sheng equal one dou, four dous equal one qu, and four qus equal one lu." Thus, one lu equals sixty-four sheng. "Ten lu make one zhong," which means ten lu equal one zhong, or sixty-four dous. Zheng Xuan's calculations of this capacity differ slightly from those in the "Nine Chapters on the Art of Rice," while Zu Chongzhi used a more precise method to calculate the volume of lu, which is approximately one thousand five hundred sixty-two and a half cubic inches. According to the description of being "square at the base and round on the outside," considering the value of pi, the diameter is approximately one foot, four inches, one-fifth of an inch, four-tenths of an inch, and two-hundredths of an inch. This lu, with a depth of one foot, represents the prototype of the ancient he.
The "Nine Chapters on Commercial Methods" also records the volume of a he for different grains, such as millet, rice, beans, and hemp, which vary in volume due to their different weights, but their prices are similar. The book states that the volume of the rice he is considered the standard, which is consistent with the account found in the "Han Shu." The "Sunzi Suan Shu" introduces smaller units of measurement as follows: six su make one gui, ten gui make one miao, ten miao make one cuo, ten cuo make one shao, and ten shao make one he. Ying Shao and Meng Kang offer slightly different interpretations of "gui"; Ying Shao believes gui is the natural shape, the beginning of yin and yang, while Meng Kang states that sixty-four sheng equal one gui.
"The Records of the Han Dynasty" summarized the ancient measuring instruments, stating: "The measures are the yue, hé, shēng, dǒu, and hú, used to measure how much." Beginning with the smallest unit, the yue, the sequence continues with hé, shēng, dǒu, and hú; these are all used to measure quantities. It also detailed the manufacturing method of the hú: made of copper, square inside and round outside, with ear-shaped protrusions on its sides, hú on top, dǒu below, shēng on the left ear, and hé and yue on the right ear, shaped like a jue, symbolizing status and reward. The inscription on the hú states: "The hú measures well, square inside and round outside, nine lí and five háo beside, one hundred and sixty-two cù on the bottom, one cù deep, with a total capacity of one thousand six hundred and twenty cù, holding ten dǒu." Based on his calculations of pi, Zu Chongzhi concluded that the diameter of the hú should be one cù, four cù, three fēn, six lí, one háo, nine seconds, and two hú, while Liu Xin's calculations show a slight discrepancy, possibly due to his less precise method of calculation. In conclusion, the manufacture and calculation of ancient measuring instruments were highly precise, reflecting the wisdom and rigor of ancient people.
In the year 227 AD, Liu Hui commented on "Nine Chapters on the Mathematical Art," saying: The hú currently used by the Grand Minister of Agriculture has a diameter of one cù, three fēn, five fēn, five lí, and is one cù deep, with a volume of one thousand four hundred and forty-one cù and three tenths. The copper hú from the time of Wang Mang, calculated by today's standards, is nine cù, five fēn, five lí deep, with a diameter of one cù, three fēn, six fēn, eight lí, and seven háo. According to my calculations, the hú from the time of Wang Mang, calculated by today's hú, is only slightly more than nine dǒu, seven shēng, and four hé. Thus, the hú from the Wei Dynasty is relatively larger, and the measuring units were longer; the hú from the Wang Mang Dynasty is relatively smaller, and the measuring units were also shorter. The Liang and Chen Dynasties maintained the ancient system of weights and measures. The Qi Dynasty established that five ancient shēngs equaled one dǒu.
Later, in the year 561 AD, in the first year of the Baoding era, Emperor Wu of the Zhou discovered an ancient jade dou while the Jin state was constructing granaries in May. By October 565 AD, Emperor Wu of the Zhou issued an edict to re-establish the copper measurement standards, ultimately achieving a state of unity and harmony. Repeated measurements using millet confirmed that the capacity of this jade dou was entirely consistent, with no differences compared to other measuring instruments and tools. A copper sheng was cast based on this standard and distributed for use across the country. The inscription on the copper sheng states: "Inner diameter seven inches one-fen, depth two inches eight-fen, weight seven jin eight liang. On the fifteenth day of the first month in the second year of Tianhe, calibration was completed and handed over to the local government as a standard instrument." The inscription on the jade sheng states: "In the first year of the Baoding era of the Great Zhou, in the year of Chongguang, in the month of Lüruibin, when the Jin state government repaired the granaries, this ancient jade sheng was obtained, with a shape conforming to ancient standard measuring instruments. Grand Tutor Jin Guogong reported to the court, and the emperor ordered it to be stored in Tianfu. Five years later, in the year of Xieqia, the emperor issued an edict to test it with standard ropes and rulers, using millet for repeated measurements, with no errors whatsoever. As a result, copper instruments were cast and replicated, distributed for use across the nation to unify the measurements during the peaceful period."
Now, if calculated numerically, the volume of the jade sheng, according to the jade chi, is a little over one hundred ten inches and eight-fen, and according to the hu, it is one thousand one hundred eighty-five inches and seven-li three-miao nine-hao. Zhen Luan stated in "Arithmetic": "One sheng of jade is equal to one sheng and three he and four shao of the government dou." Therefore, the jade sheng is relatively large, while the government dou is relatively small. Based on numerical calculations, the government dou from the Later Zhou that Zhen Luan referenced has a volume of a little over ninety-seven inches according to the jade chi, and a little over nine hundred seventy-seven inches according to the hu. The jade dou from the Later Zhou also had matching gold-inlaid copper dous and a gold-inlaid copper dou made in the sixth year of Jiande, all of which used millet to determine capacity. When weighed with jade measuring instruments, the weight of one sheng is always six jin thirteen liang.
During the Kaihuang period, it was established that three ancient sheng are equivalent to one current sheng. By the Daye period, the capacity of the ancient dou was reinstated.
The term "heng" means weight scale; "quan" refers to weight. The function of "heng" is to carry "quan," used to measure the weight of objects. The principle of constructing "heng" is similar to that of a compass, ensuring its vertical and horizontal alignment. Turning left reveals a compass, while turning right reveals a ruler. The application of "heng" in the heavens assists the *xuanji* (an ancient astronomical instrument) in adjusting the solar terms, allowing the seven celestial bodies (the sun, moon, and five stars) to move in harmony; thus, it is called "yu heng." "Quan" refers to units of weight including "zhu," "liang," "jin," "jun," and "shi," which are used to measure the weight of items with a scale to determine their weight. In ancient times, there were also weight units like "shu," "zeng," "chui," "ci," "huan," "gou," "zhuo," and "yi," with varying standards across different dynasties, which I am not fully familiar with. The "Book of Han" states that the origin of "quan" is determined by the weight of the yellow bell. One "yue" can hold 1200 grains of millet, weighing 12 "zhu"; 24 "zhu" equal one "liang"; 16 "liang" equal one "jin"; 30 "jin" equal one "jun"; and 4 "jun" equal one "shi." The production of these five weight types is highly precise, and their standards are determined based on principles, calibrated against physical objects. Other size differences are adjusted according to weight. The weights and measures are circular, interlinked, with the good parts doubled, creating an endless cycle. When weight and object reach balance, "heng" is produced; the operation of "heng" produces a compass; the circular shape of the compass produces a ruler; the square shape of the ruler produces a rope; and the straight line of the rope produces a standard measure. If the standard measure is accurate, then "heng" achieves balance, and "quan" is precise. These five principles are embodied in the weighing instruments, serving as a comprehensive standard.
According to the records in the "Zhao Book," in July of the eighteenth year of the reign of Shile, while constructing the Jiande Hall, a round stone shaped like a water pounder was discovered. It was inscribed with the words: "Law Stone, weighing four jun, same law for measurements and weights. Made by the Xin clan." It is believed to be an artifact from the Wang Mang period. During the Jingming years of the Northern Wei, a person named Wang Xianda from Bingzhou presented an ancient bronze weight featuring an inscription of 81 characters. The inscription read: "Law Stone, weighing four jun." It also stated: "The Yellow Emperor, the first ancestor, whose virtue spread in the time of the Yu. The Yu Emperor, the first ancestor, whose virtue spread in the time of the Xin. In the year of Daliang, the dragon gathered on the day of Wuchen. Wuchen was determined, heaven's mandate was given to someone. According to the earth's virtue received, the correct title is the genuine one. Correcting the flawed construction, leading to longevity and prosperity. Same law for measurements and weights, inquiring about the current people. The dragon was in Jisi, the year was indeed Shen, the first class in the world, all nations will forever follow. Generations and descendants will enjoy and pass down for billions of years." This was also produced during the Wang Mang period. At that time, the Grand Music Official Gongsun Chong first adjusted the scales according to the "Book of Han," and when he saw this weight, he weighed it with the new scales, and the weight was one hundred twenty jin. The new scales and weights matched perfectly. Thus, the responsibility of regulating music was assigned to Gongsun Chong. During the reign of Emperor Xiaowen, the dou and chi were made entirely according to the "Book of Han."
It is said that during the Liang and Chen dynasties, they used old scales. In the Qi dynasty, one jin equaled eight liang of today, referred to as the ancient weight of one jin and eight liang. The jade artifacts of the Zhou dynasty, one jin weighed four liang, equivalent to the ancient weight of four and a half liang. During the Kaihuang era of the Sui dynasty, it was stipulated that one jin equaled the ancient weight of three jins. By the Daye era of the Sui dynasty, the old scales were once again restored.
As a result, the standards for weights and measures varied across different dynasties, which can be quite baffling. The Liang and Chen dynasties used the traditional scale, where one Jin was equivalent to eight Liang in the Qi dynasty, and in the Zhou dynasty, jade objects were only four Liang for one Jin, which corresponds to the ancient measurement of four Liang and a half. During the Sui dynasty's Kaihuang period, one Jin was regarded as three Jin from earlier, but during the Daye period, it reverted. "Liang and Chen follow the ancient terms. Qi uses the ancient term of one Jin being eight Liang as one Jin. Zhou jade is weighed as four Liang, which corresponds to the ancient term four Liang and a half. In Kaihuang, the ancient term of three Jin is considered as one Jin, and during Daye, it reverted to the ancient scale." The scales from ancient times are truly mind-boggling.
