It is said that the Yellow Emperor instructed Ling Lun to cut bamboo, which measured three inches and nine-tenths, and then played it, resulting in the Huangzhong scale, called "Hanshao." Then he made twelve bamboo pipes to listen to the phoenix's cry, representing the male and female sounds used to differentiate musical tones. The musical tones are interrelated, beginning with Huangzhong. The "Book of Yu" states: "According to the season, month, and day, unify the pitches, measures, quantities, and weights." Emperor Yu was tasked with using sound to establish the pitches and physical measurements. The "Rites of Zhou" indicates that musical instruments were crafted according to the twelve pitches. Sima Qian in the "Records of Music" notes: "Huangzhong is eight inches and one-seventh long, Taicu is seven inches and two-sevenths long, Linzhong is five inches and three-sevenths long, Yingzhong is four inches, seven-tenths, and just over four fen." These three are the origin of musical pitches and the basis of the twelve pitches. Ban Gu and Sima Biao in the "Record of Music" state: "Huangzhong is nine inches long, producing the richest sound; Taicu is eight inches long; Linzhong is six inches long; Yingzhong is four inches, seven-tenths, and just over four fen, with the clearest sound." Zheng Xuan in the "Book of Rites · Monthly Ordinance Commentary," Cai Yong in the "Monthly Ordinance Chapter and Sentences," as well as Du Kui, Xun Xu, and others' discussions, although the measurements vary slightly, the measurements of the twelve pitches are generally consistent.
"The Book of Han" records that Jing Fang proposed the method of generating every eighth interval, starting from Yellow Bell and ending at Zhong Lu, completing the twelve notes. Zhong Lu generates Yellow Bell upwards, which does not reach nine inches, referred to as 'Grasping the Beginning,' and disappears when generated downwards. The musical notes interact with one another, ultimately reaching Southern Lu, adding forty-eight more notes for a total of sixty. Its operating rules are in the Morning Star, generating everything when going up, and arranged every nine notes after the Winter Solstice. The divisions, delays, and inner components diminish the clarity of the notes. During the Song Yuan Jia period, Tai Shi Qian Lezhi, drawing from the remaining aspects of Jing Fang's Southern Lu, extended it, adding three hundred notes, ultimately reaching An Yun, measuring four inches and four fen. In total, the old and new notes add up to three hundred and sixty. Each day corresponds to a pipe, with Gong, Zhi, Xuan, and Yun arranged in order. He Chengtian said in "The Establishment of Legislation": "The music notes generate each other up and down, with one-third loss or gain, which is the ancient simple method. Just like the ancient calendar set the circumference as three hundred and sixty-five degrees and a quarter, later changes were made by different people. Jing Fang did not understand this principle and mistakenly set it as sixty notes." Chengtian established new music notes, deriving Yellow Bell from Zhong Lu, twelve rotating palaces, without losing the sound and rhythm. Yellow Bell measures nine inches, Tai Cu measures eight inches and two fen, Lin Zhong measures six inches and one fen, and Ying Zhong measures four inches and seven fen and nine fen slightly more. The additional figures from the upward generation of Lu total one hundred seventy-seven thousand one hundred forty-seven, which corresponds to the numbers of the twelve Chen. In the early period of the Liang Dynasty, the system of the Jin, Song, and Qi dynasties was followed with little alteration. Later, Emperor Wu wrote the "Zhong Lu Wei," analyzing the successes and failures of previous dynasties. The essence of his analysis is as follows:
According to the theory of musical tones, Jing, Ma, Zheng, and Cai, all the way to Ruibin, are derived from Dalu; however, Ban Gu, in his "Treatise on Music and Calendar," calculates downwards after reaching Ruibin. The length of the Jiazhong is only a little over three inches and seven tenths. If the pitch pipe is too short, the sound of the Jiazhong will only have one pitch, and the Zhonglü would be a half step off, which would completely disrupt the scale. Early spring and late spring are precisely the times when all things grow, with mild and gentle weather that does not allow for abrupt sounds. Therefore, from the perspective of sound and actual circumstances, Ban Gu's statement is incorrect. Zheng Xuan further explains the order of generation of musical tones using the principles of Yin and Yang. According to Zheng Xuan, if Yin and Yang generate each other, it can only mean that Yang energy rises; but how should we explain the descent of Yin energy? From the mathematical principles of the Eight Trigrams, the Qian trigram corresponds to Jia and Ren, moving left; the Kun trigram corresponds to Yi and Gui, moving right, thus explaining the rise and fall of Yin and Yang. The operation of Yin and Yang is its nature, while the rise and fall of the six positions is a matter of symbolism. Zheng Xuan uses symbolism to explain nature, which renders his argument untenable. He says that nine and six generate each other, but he does not adequately explain how the twelve musical tones are interconnected. It is evident that Zheng Xuan's considerations are incomplete. Jing Fang's sixty musical tones, calculated by his method, yield very accurate results without deviation. However, the results of the musical tone calculations sometimes yield five and other times six, which does not make sense. Moreover, some calculations start by going upwards and then inward, with the results calculated upwards again and then separated for further calculation, which is even more illogical. Jing Fang is very proficient in the principles of Yin and Yang; he must have his reasons. If it’s not because the principles are profound and hard to grasp, then it is that later generations did not study his theories diligently.
I carefully studied these statements but still couldn't grasp them completely. So, I made use of my spare time to try to derive the principles behind them. I referred to previous musical instruments and the ancient jade rules of the clapper clock, and recreated a new ruler, accurate to the millimeter. I made four musical instruments, called "Tong." Each of these four instruments has a string length of nine feet and is one inch and two-tenths tall. The string length of the Huangzhong is nine feet, made from two hundred seventy silk threads, and then I calculated the number of strings and their lengths for the twelve pitches by making successive adjustments of three points. Based on the months represented by the pitch pipes, the relationships of the five elements, and the starting points and sequence of the musical notes, I named them "Tong." I used this "Tong" to play the sanxian, and I calculated the lunar cycles, and the results were quite accurate. When I tested it against the ancient jade rules of the clapper clock, it matched perfectly as well.
I had twelve flutes made to play various tones. These twelve flutes were crafted according to the Jiazhong tuning, perfectly aligned with the standard pitch. Shan Qianzhi wrote in his notes: "These three bells in front of the hall were all cast by King Jing of Zhou as 'Wushè bells'." I had the musicians play using the newly crafted flutes tuned to 'Wushè,' but the pitches were off. However, the flutes tuned to 'Yize' matched perfectly. We also examined the inscription on the bell outside East Gate and confirmed that it was also tuned to 'Yize.' The bell in the West Chamber was moved from elsewhere during the Tianjian period of the Song Dynasty. When played with the current flutes, it was in the 'Nanlü' tuning. Upon closer inspection of its inscription, it turned out to be in 'Taicu' tuning, which is two notes lower than that of the current flutes. I ordered the Grand Music Officer, Sui Xuan, to conduct a thorough inspection, and indeed, there were visible chisel marks on the bell, both inside and out. We consulted with an old expert we knew before and learned that this was caused by Zhang Yong during the Taishi period of the Song Dynasty, as a considerable amount of copper had been removed, resulting in a lower pitch. By studying the pitch of the bells, we could piece together what had happened. After Emperor Wu of the Song Dynasty pacified the Central Plains, he had General Chen Qing transport three bells, one large and one small. The two bells in front of Taiji Hall and the one outside East Gate were transported then. The inscription on the bell to the west reads "Qingmiao Zhuangzhong," and since there was no Qingmiao during the Qin Dynasty, this indicates that it is from the Zhou Dynasty. The inscription on the other bell reads "Taicu Zhongzheng," which is the tuning of the Palace of Linzhong. Jing Fang's calculations of pitch seem to have been based on this. The inscriptions on these bells do not contain characters from the Qin or Han dynasties, only "Yize" and "Taicu," which proves they weren't from the Qin or Han periods. The ancients took great care in their work, even engraving the names of servants; if the inscription states a tuning, it must be accurate, further proving that these bells were not made in recent years. Moreover, ensuring pitch accuracy to adjust political systems is crucial, especially with the five tones and six pitches. Craftsmen ensure pitch accuracy, while Confucian scholars handle textual verification. Over the years, these two fields have become disconnected and don't communicate well. Even if all the instruments are ready, they can't be used. The hymns of the Zhou Dynasty and the musical songs of the Han Dynasty both praise their respective merits; how can they be misused in the names of later emperors? I'm now reporting my findings in detail and have ordered all officials to study them together, in hopes of finding the right answer.
Before the reforms could be implemented, the Hou Jing Rebellion occurred, and the Chen Dynasty's system remained unchanged. In the first year of the Western Wei's Emperor Fei, Emperor Wen of the Zhou acted as regent. He ordered Su Chuo, the Minister of Rites, to conduct a thorough investigation of musical tones. At that time, Su Chuo found the standard ruler from the Song Dynasty to determine the lengths of various pipes. This work began but was interrupted by Emperor Min's abdication and the chief minister's consolidation of power, along with the invasion of the Qi state, and ultimately, this task was not completed. Later, when excavating the Grand Warehouse, ancient jade vessels were unearthed, and the effort to establish musical tones and measurements based on these jade vessels was largely forgotten.
During the early years of the Kaihuang era under Emperor Wen of the Sui, the emperor ordered Doctor of Music Niu Hong to establish musical regulations. Niu Hong brought together scholars knowledgeable in music to discuss methods for formulating musical regulations, but they were unable to reach a consensus. Later, by chance, twelve tuning pipes belonging to the Chen family were found in the Pingjiang area (now Suzhou, Jiangsu), and these pipes were handed over to Niu Hong. The emperor sent experts in musical theory, such as Mao Shuang, the magistrate of Shanyin County, as well as Cai Ziyuan and Yu Puming, to create a "Tuning Score" aligned with the solar terms. At that time, Mao Shuang, being elderly, went to meet the emperor in his everyday clothes. The emperor appointed him governor of Huai Prefecture, but he graciously declined the position. Thus, the emperor sent Xie Lulang Zu Xiaosun to learn from Mao Shuang about the use of the tuning pipes. Niu Hong blew into these pipes and ultimately established the musical tones.
Once the nation was unified, musical instruments from various dynasties were gathered at the Music Bureau, and those well-versed in musical theory examined these instruments to establish the standards for bell tones. Then, new instruments were crafted to perform the fourteen pieces of music known as "Huang Xia." Emperor Wen of the Sui and the ministers listened together, and the emperor remarked, "The sound of this music is grand, harmonious, and elegant, lifting the spirits of all who hear it."
However, all things and human affairs in this world, if they do not have the cycles of the Five Elements, will not be created, will not develop, and will not perish. Therefore, if a fire ruler is used to create the Five Tones, things will lean towards a fiery disposition; if a metal ruler is used, there will be an increase in wars; if a wood ruler is used, there will be an increase in funerals; if an earth ruler is used, the world will descend into chaos; only by using a water ruler can the musical scales be harmonious, and the world be at peace. The Wei Dynasty, Northern Zhou Dynasty, and Northern Qi Dynasty were all greedy for the length of cloth, so they used an earth ruler for measurement. The current musical scales are crafted using a water ruler. The water ruler from the Jiangdong region is shorter than the earth ruler but longer than the jade ruler. The common folk are unaware of this; when they see a ruler made of jade, they simply call it a jade ruler; if it's made of iron, they call it an iron ruler. The emperor ordered the use of the water ruler from Jiangdong to create the musical scales, and all the musical instruments of previous dynasties were melted down to put an end to the ongoing debates.
In the fourth year of Ren Shou, Liu Zhao wrote a memorial to the Crown Prince, discussing Zhang Zhouxuan's calendar and also mentioning music and tuning theory. His main point was that the essence of music lies in its pitch, and the determination of pitch relies on standard tuning tubes. If the pitch is not standardized, harmony cannot be achieved. To achieve harmonious pitch, the length of the tuning tubes must be precisely determined. However, previous methods of calculation were insufficiently accurate, and the length of the Huangzhong was always miscalculated, making it impossible to produce a correct cycle. During the Han Dynasty, Jing Fang arbitrarily devised a system of sixty pitches, and during the Song Dynasty, Qian Lezhi created a system of three hundred sixty pitches. Those who referenced the classics found no basis for these; the customs had remained unchanged, and such practices were likely ineffective. This was not only an issue of the length of the tuning tubes but also a problem with the diameters of the pipes. Moreover, the standards for measurements lacked precise verification, resulting in dissonance in orchestral instruments and errors in weights and measures. Liu Zhao addressed all of these issues, hoping to achieve definitive results. He calculated the actual length of the Huangzhong pipe to be sixty-three fen, then reduced each tuning tube by three fen, with seven fen equating to one cun. Following this calculation, the Huangzhong was nine cun long, the Taicu was eight cun, one fen, and four li, the Linzhong was six cun, and the Yingzhong was four cun, two fen, eight li, and four fen. That year, Emperor Gaozu died, and Emperor Yang took the throne, but there was no time for revisions, and the issue was left unresolved; his article was subsequently lost. In the second year of Daye, Emperor Yang of Sui ordered the adoption of the standard tuning from the Liang Dynasty and the remaking of eight musical instruments such as bells and chimes, which better aligned with ancient standards than their predecessors. However, the relevant systems, documents, and previous laws of Mao Shuang were lost in the turmoil of war in Jiangdu.
The "Book of Han" states: "The diameter of the Huangzhong pipe measures nine fen, the diameter of the Linzhong pipe measures six fen, and the diameter of the Taicu pipe measures eight fen." The "Continuing Book of Han" and Zheng Xuan both say: "The hollow pipes of the twelve pitches of music all have a diameter of three fen and a circumference of nine fen." Wang Anfeng of the Northern Wei, according to Ban Gu's "Book of Han," recorded that the circumference of the Linzhong hollow pipe is six fen, and the circumference of the Taicu hollow pipe is eight fen. When made and played, they do not match the pitches of Huangzhong, Shang, and Zhi. Only by ensuring all of them have a circumference of nine fen can they match the standard bell instruments. After pacifying the Chen dynasty of the Southern Dynasties in the ninth year of Kaihuang, Niu Hong, Xin Yanzhi, Zheng Yi, He Tuo, and others referred to ancient measurements and, based on their respective eras, produced Huangzhong pipes, all with a diameter of three fen and a length of nine inches. Due to variations in measurements, resulting in differences in pitch; the differences in pipe lengths and measurements also result in varying capacities for millet. Now I will list these numbers:
Before the Jin dynasty, the Huangzhong pipe could hold eight hundred and eight grains of millet.
During the Liang dynasty, the official measurement indicated that the Huangzhong pipe could hold eight hundred and twenty-eight grains of millet.
In the Liang dynasty's standard measurement, there were three types of Huangzhong pipes: one could hold nine hundred and twenty-five grains of millet, another could hold nine hundred and ten grains, and the third could hold one thousand and one hundred and twenty grains.
The official measurement used in the Han dynasty indicated that the Huangzhong pipe could hold nine hundred and thirty-nine grains of millet.
On ancient silverware inscribed with "Huangzhong," its volume is one thousand two hundred (unit unspecified).
During the Song dynasty, it was measured with iron rulers, and the volume of Huangzhong was defined by two standards: one was one thousand two hundred, and the other was one thousand forty-seven (unit unspecified).
In the Later Wei period, the early ruler measured the volume of Huangzhong as one thousand one hundred and fifteen (unit unspecified).
In the Later Zhou period, the volume of Huangzhong measured with a jade ruler was one thousand two hundred and sixty-seven (unit unspecified).
In the Later Wei period, during a certain phase, it was measured to be one thousand five hundred and fifty-five (unit unspecified).
In the Later Wei period, the late ruler measured the volume of Huangzhong as one thousand eight hundred and nineteen (unit unspecified).
In the Eastern Wei period, the volume of Huangzhong was measured to be two thousand eight hundred and sixty-nine (unit unspecified).
Wanbao often uses a ruler to measure water. This ruler measures the volume of a yellow bell as one thousand three hundred and twenty grains of shu (an ancient capacity unit). You see, those rulers and iron rulers from the Liang Dynasty, although the length and diameter are the same, there are slight differences in the volume of the yellow bell measured. This is because the makers of these rulers deliberately manipulated the ruler's interior, making the volume appear more or less.
In the Later Qi Dynasty, there was a person named Xindu Fang. He was a Tiancao military officer in the residence of the God of War Emperor, particularly clever. He could observe the weather using a weather observation tube and could tell the weather by looking at the clouds. Once, he pointed to the sky and said to someone, "The season of the beginning of spring has arrived!" Someone went to check his weather observation tube, and sure enough, the ash in the tube had reacted. His weather predictions every month were extremely accurate! He also created a wheel fan with twenty-four sections that was buried underground to measure the twenty-four solar terms. When each solar term came, a fan would move by itself, while the other fans remained still. This was completely consistent with the reaction of the ash in the tube, as if it had been prearranged—it was truly miraculous!
After defeating the Chen Dynasty in the ninth year of the Kaihuang era, the emperor sent Mao Shuang, Cai Ziyuan, and Yu Puming to observe the solar terms. According to the previous method, in a room that was triple-sealed, twelve wooden tables were set up. Each table corresponded to a solar term, with the corresponding musical tube placed on each, buried in soil with a level surface, filled with reed ash inside the table, and covered with a light silk cloth over the mouth of the musical tube. Every month when a solar term arrived, if it matched the musical tube's pitch, the reed ash would fly up, break through the silk, and float outside. However, this reaction sometimes occurred early, sometimes late, and the amount of ash that flew out varied. Some reacted right at the start of the month, while others only started to react in the middle or late of the month; some ash flew out within three to five days, while others only flew out a little bit over the entire month.
The emperor found it very strange and asked Niu Hong. Niu Hong replied, "When half of the ash particles rise, it is an indication of peace; when all the ash particles rise, it is a sign of strength; when no ash particles rise, it is a sign of decline. A peaceful sign indicates political stability, a strong sign indicates the ministers are overstepping their bounds, and a declining sign indicates the monarch is tyrannical." The emperor countered, "If ministers are overstepping their bounds and the monarch is tyrannical, the political situation is surely unstable. This is not something that varies every month. The responses to the twelve months differ; how can we say the situation of a tyrannical monarch and overstepping ministers is that severe?" Niu Hong was at a loss for words. The emperor then instructed Mao Shuang and others to organize a set of methods. Mao Shuang reviewed previous materials and wrote an article called *Lü Pu*. The article roughly states: Minister Mao Shuang verified that the Yellow Emperor sent Ling Lun to collect bamboo in the Xiang Valley and listened to the calls of the phoenix under Feng A, which led to the creation of the twelve pitches. This allowed for the prediction of seasonal changes based on the cosmic energies, marking the origin of numerical techniques. The yang pipe corresponds to the lü (pitches), and the yin pipe corresponds to the yue (notes), using their energies to predict the four seasons and their numbers to record all things. The cloud scribe was the first to create numbers, which likely serves as the foundation of the lü. The numbers one, ten, hundred, thousand, ten thousand, hundred million, and trillion are derived from this, and measurements also originate from it. Thus, the Yu clan utilized lü to harmonize musical tones, and Zou Yan modified it to determine the five beginnings. The official calendar and the colors of clothing are also distinguished in this way. The Xia dynasty used human standards, the Yin dynasty used land as the standard, and the Zhou dynasty used heaven as the standard. Confucius remarked, "I have mastered the Xia dynasty's calendar," meaning he had grasped the key to the energies.
During the early days of the Han Dynasty, Zhang Cang established laws and promoted the theory of "Five Triumphs," believing that the virtues of water should take precedence. This was primarily due to the negligence of officials during the Warring States period, and the Qin Dynasty had eradicated academic studies, resulting in the decline of music theory. Zhang Cang only made some improvements without fully understanding the principles. It was not until the time of Emperor Wu of Han that the position of Chief of Music Laws was established, appointing Li Yannian as a commander. Although Li Yannian understood some new music and modes, he did not truly grasp the fundamental principles of music theory, resulting in uncertainty regarding the dimensions and colors of musical instruments at that time.
During the reign of Emperor Yuan of Han, the emperor himself was knowledgeable about music theory, and the court official Jing Fang was also well-versed in it. Therefore, Emperor Yuan had Wei Xuancheng and others seek advice from Jing Fang. Jing Fang stated his theory, saying: "I have studied Jiao Yanshou's theories and applied the method of sixty modes generating each other. The upper modes generate the lower ones in a three-to-two ratio; the lower modes generate the upper ones in a three-to-four ratio. Yang modes generate Yin modes downwards, and Yin modes generate Yang modes upwards, ultimately returning to the proper mode of the palace." Later, Liu Xin compiled these contents into a memorial, gradually deepening the theory of music. Ban Gu's "Book of Han: Music and Calendar Records" was written based on Liu Xin's work, and Sima Biao's "Continuation of the Book of Han: Music and Calendar Records" mainly referenced Jing Fang's theory.
During the Eastern Han period, the dimensions of musical modes were slightly lengthened. The Wei Dynasty's Du Kui also established music modes for observing the weather, ensuring that ashes would not fly up (indicating the accuracy of the music modes). The Minister of Rites in the Jin Dynasty, Xun Xu, obtained ancient bronze pipes and compared them with Du Kui's music modes, discovering that the ancient bronze pipes were a quarter longer than those established by Du Kui, revealing that Du Kui's music modes were inaccurate due to a dimensional error. Therefore, Xun Xu remade ancient measuring instruments based on the "Rites of Zhou" to determine the dimensions of musical instruments, ultimately achieving accuracy in the tuning of musical instruments.
After the Jin Dynasty, errors gradually emerged in musical theory. During the reign of Emperor Wu of Liang, there was the jade tuning system from Jizhong, and during the Cangwu period of the Song Dynasty, someone adapted it into a horizontal wind instrument, but its general dimensions remained unchanged. I previously studied at Qicheng, where I learned arithmetic from Zuxie and music from He Chengtian. After decades of dedicated study, I have gained a solid understanding of music. Later, I served as the Minister of Ceremonies, overseeing music affairs, and brought the jade pipes and the ruler of the Taishi of the Song Dynasty to the court together. The court commissioned craftsmen to create musical instruments based on the samples. Since then, musical instruments were able to maintain their integrity. During the turmoil of the Hou Jing rebellion, my brother Xi acquired these musical instruments from the Bureau of Music. Later, when Emperor Chen Xuan was taken to Jingzhou as a hostage, my brother died in the Western Wei when Emperor Yuan of Liang was defeated. Just as I was preparing to present to the court, Emperor Wu of Chen ascended the throne, and he expanded the twelve scales into sixty, privately calculating the order of the weather, with corresponding signs and omens. During the Taijian period, my brother became the Minister of Personnel and wanted to present to the court. Just as Emperor Xuan died and the later emperor ascended the throne, my brother was demoted to the position of Interior Minister of Yongjia; thus, the musical instruments remained in the family and were passed down to his descendants. When the Chen Dynasty fell, these musical instruments were ultimately lost.
The twelve pitch pipes currently used in Tai Le Temple represent the transformation of yang into yin energy, starting with Huangzhong, where yin transforms into yang, and concluding with Zhonglü. The changes in climate throughout the four seasons are encapsulated within these twelve pitches. During mid-winter, the pitch pipe used is Huangzhong. Huangzhong begins at the winter solstice, marking the beginning of yang energy. It measures nine inches long, reflecting the number of days, and when the climate reaches the eleventh month, the Huangzhong pitch pipe responds accordingly, regulating the six energies and harmonizing the nine virtues. After this, the pitch pipe standards were set according to Jingfang, with the lengths of the Gong and Zhi pitches used in sequence every day. Each of these twelve pitch pipes governs specific solar terms, extending to a total of sixty. They evolve in layers like the Eight Trigrams and evolve into sixty-four hexagrams. The pitch pipes that produce one another change in relation. For example, the Huangzhong pipe produces the Linzhong pipe, as yang energy gives rise to yin energy, resulting in change. The pitch pipes that intersect connect with each other; for instance, the Zhonglü pipe corresponds to material responses, similar to a mother overseeing her children. Therefore, the pitch pipes that undergo change correspond at different times, but each has its own relevance; the interconnected pitch pipes correspond in sequence within the same month. Some solar terms may respond early or late, which does not align with the proper pitch pipe's climate but rather the mutual responses of the subordinate pitch pipes, which rely on the mother pitch pipe for correspondence. These pitch pipes were ultimately lost during the final years of the Daye era in Jiangdu.
During the Song Dynasty, Qian Lezhi, after studying the music theory of Jing Fang, created three hundred musical scales. Shen Zhongzhong, a doctor from the Liang Dynasty, said in his "Discussion on Scales": "The Book of Changes uses three hundred and sixty strategies to correspond to the number of days in a year, which is the number of musical scales. The Huainanzi says: 'One scale produces five sounds, twelve scales produce sixty sounds, multiplied by six, is three hundred and sixty sounds, corresponding to the number of days in a year. The number of scales is the law of the movement of heaven and earth.' Therefore, these three hundred and sixty scales have been calculated in this way since ancient times." Shen Zhongzhong, based on the numbers of the Huainanzi, calculated three hundred and sixty scales using Jing Fang's method. Every month, a portion of the scales is calculated based on the scales of that month. Using the number of a portion of scales as the dividend, using the number of days contained in a midday as the divisor, and using the dividend to determine the divisor, depending on the number of days, the days and fractions governed by each scale are different. Using this method to distribute seven sounds, on the day of the winter solstice, the scales used are: Huangzhong as the tonic, Taicu as the subdominant, Linzhong as the mediant, Nanlu as the dominant, Guxi as the submediant, Yingzhong as the leading tone, and Ruibin as the subtonic. With five sounds and seven tones, everything is complete. The scales used in the following days are all deduced in sequence. The scale used on a given day is the tonic, and the subdominant, mediant, etc., sounds are deduced in sequence. Using this method to investigate sound and qi, distinguish time, all things should follow the solar terms. From Huangzhong to Zhuangjin, a total of one hundred and fifty scales were calculated using the method of reducing three parts to one; from Yixing to Yizhao, a total of two hundred and nine scales were calculated using the method of increasing three parts to one; only the Anyun scale is the final one and is not continued to be calculated. These numbers are all based on the actual value of Huangzhong, 177,147, using nine cubed (729) as the divisor, respectively divided, to obtain inches, minutes, and seconds, the rest are discarded. This way, the length of each scale is determined. The revision of the scales involves arranging the tonic and other sounds in the order of the upper and lower generations. Now, I will briefly explain their sequence...
Huangzhong:
Baoyu, Hanwei, Dide, Guangyun, Xiaji, Kezhong, Zhish, Wojuan, 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 E Mei Bu Jian Xuan Zhong Yu Zhu Diao Feng
The above is the Yellow Bell part, a total of thirty-four tonalities. (Each tonality governs thirty-one minutes of a thirty-fourth of a day)
Da Lu:
It is said that the operation of the heavens and the earth has its own rules, just like a musical composition, performing the symphony of the universe. Let's talk about this "Da Lu" first. It has a total of twenty-seven tonalities, each corresponding to one day, plus one-third of a day, with a compact rhythm and magnificent momentum, just like the scene of the universe's creation and the flourishing of all living things.
Next is "Tai Cu"; it has thirty-four tonalities! These thirty-four tonalities, from the ignorance of "not knowing oneself" to the determination of "Yi Jian Ting Du," and then to the growth of all things, paint a vibrant and hopeful picture. "Tiao Feng Cuo Shi, Shi Xi Da Sheng," as the spring wind blows, everything begins to grow endlessly—how beautiful!
Then there is "Jia Zhong," which also has twenty-seven tonalities like "Da Lu." These twenty-seven tonalities, from the harmony of "Xie Lu Yin Zan" to the prosperity of "Wan Hua Kai Shi," and then to the vigorous development of "Ren Wei Zheng Nan," depict the scene of prosperity and flourishing of all things in harmony. "Feng Cong Bu Zheng, Wan Hua Kai Shi," the wind across the heavens and earth seems to herald a new beginning, and all things are thriving in this season of spring.
Look at "Gu Xi"; it also has thirty-four tonalities. From "Nan Shou Huai Lai, Kao Shen Fang Xian," to "Wu Hua Ge Ti, Mao Shi Deng Ming," it depicts the whole process from incubation to maturity of all things. "Xie Jiao Xi Chen, Bian Yu Zhuo Ying," new things continue to emerge while old ones are gradually phased out; this is a vibrant and hopeful time.
"Zhong Lu" has twenty-seven tonalities, from "Zhu Ming Qi Yun, Jing Feng Chu Huan," to "Wu Ying Jie Mu, Huang Luo Zhen Zhen," illustrating the changes of all living things across the seasons. "Nan Zhong Li Chun, Lv Nong You Cheng," as spring arrives, people begin to cultivate the land, and everything proceeds in an orderly fashion.
Lastly, we have "Rui Bin," which is also a grand movement, full of vitality and hope. "When things in the south are quiet, choose fabric petals," everything is happening quietly, nurturing new developments. "With prosperity comes change and peace, resonating with distant sounds," change is eternal, but harmony and peace are always what people pursue. "As the phoenix spreads its wings and the sun rises," it heralds a bright future.
These six movements together play the symphony of the universe, depicting the laws of the movement of heaven and earth, and the scenes of all things growing; it's truly beyond words!
I have a book titled "You Rui Bin" that contains twenty-seven melodies; the melodies are named: Humble Service, Esteem for Virtue, Follow the Path, Square Strong, Yin Rise, Mi Te, Go Extinct, Hua Xiao, Friend Celebration, Cloud Cloth, Equal Responsibility, Wide Middle, Peaceful Degree, Virtuous Balance, No Obstacles, Overflowing Ritual, Deep Wisdom, Any Solemn, Pure Respectful, Return Good, Beautiful Sound, Warm Wind Season, Mi Hua, Embroidered Ridge, Nothingness, Denial, Scenic Mouth, Bright Well, Sun Shining, Heavy Wheel, Wealth and Splendor.
Next up is "You Lin Zhong," which features thirty-four melodies, including: Ascending Commercial, Refreshing, Refined Air, Yin Virtue, White Storage, Imperial Narrative, Fresh Punishment, Loyal Restraint, Golden Sky, Liu Xian, Meeting the Way of Benevolence, Yin Couple, Going South, Sun Dissipation, Soft Bitterness, Extending Yi, Harmonious Geng, Mi Hui, Ti Jin, Dividing Accumulation, Kong Xiu, Nine Virtues, Qian Wei, Let Yi.
Finally, we have "You Yi Ze," which also includes twenty-seven melodies: White Lü, Donate Talent, Honest and Solid, Simple Wind, Robust Essence, Chief Fertile, Structured Devotion, Fat Retreat, Slender Center, Sheng Yin, Resistant to Festivals, Cutting Off, Returning to Storage, Middle Virtue, King's Plan, Permission to Block, Ruxiao, Zunjie, Shaking Off, Not Printed, Quality Follows, Dividing Fullness of Heart, Loyal and Firm, Accumulating Stop, Yi Han, Equal Righteousness, Pleasing Service, Without Toil, Nine Existences, Bright Splendor.
Taking another look at "Ruyou Nanlv," there are thirty-four musical modes: the names of these musical modes are as follows: *Bai Lu*, *Juan Xiu*, *Dun Shi*, *Su Feng*, *Jin Wu*, *Qiu Ren*, *Jie Gong*, *Fei Dun*, *Lei Zhong*, *Cheng 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*.
Finally, "Ruyou Wusha" has a total of twenty-seven musical modes as follows: *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*.
The final book is "Ruyou Ying Zhong," which has twenty-eight musical modes: *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* (Boundless), *Di Jiu*, *Tian Chang*, *Xiu Fu*, *Chi Shi*, *Fang Zhi*, *Wu Xiu*, *Jiu Ye*, *Ba Huang*, *Yi Zhao*, *An Yun*.
It is said that in the "Records of the Grand Historian," it is recorded: "Yu the Great used his body as a unit of measurement and used sound to determine musical pitch." The "Book of Rites" also states: "A man's outstretched palm measures one foot." The "Book of Zhou" records: "The edge of a jade disc serves as a measure of length." Zheng Xuan notes that "'Xian' means long. This refers to the diameter of the jade disc being one foot, which is used to establish the standard of length." The "Book of Changes: Interpretation of the Hexagrams" states: "The length of ten horse tails is one part." The "Huainanzi" states: "At the autumn equinox, the awns of the rice heads take shape; when the awns take shape, the rice is ripe. Twelve musical units are equivalent to one grain of millet, and twelve grains of millet correspond to one inch." The "li" mentioned here refers to the awns on the rice heads. The "Shuoyuan" also states: "The standards of measurement are based on millet, with one grain of millet equaling one part." The "Suanzi Arithmetic" records: "The silk from silkworms is known as 'hu' in Chinese; ten 'hu' equal one 'miao,' ten 'miao' equal one 'hao,' ten 'hao' equal one 'li,' and ten 'li' equal one 'fen.'" These represent the origins of ancient measurement systems, but the explanations are somewhat contradictory. Only the "Book of Han: Treatise on Arts" records more reliably: "Measurement is a tool used to measure length, and its origin is the length of the yellow bell. The width of an average-sized millet grain is measured, and the length of ninety millet grains is the length of the yellow bell. The width of one millet grain is one part, ten parts equal one inch, ten inches equal one foot, ten feet equal one zhang, and ten zhang equal one yin, thus establishing five basic units of measurement." Later authors formulated standards of measurement based on this explanation, and due to the varying sizes of millet, different methods emerged. However, the proportional relationships of these methods can still be derived from one another. The problem is that the size of millet varies, and years of good or poor harvests also affect the size of the grains, so the standards of ancient measurements often varied. Additionally, mistakes from oral transmission caused gradual changes in measurement standards.
Now, let's take a look at fifteen different measurements from various dynasties, along with their similarities and differences, as follows: The "Han Treatise" mentions a copper measuring stick created by Liu Xin during Wang Mang's reign. A copper measuring stick from the Jianwu period of the Eastern Han dynasty.
In the tenth year of the Taiyi era of the Jin Dynasty, Xun Xu created a ruler; this ruler is identical to those used prior to the Jin Dynasty. This refers to the copper ruler that has been handed down from Zu Chongzhi. It is said that in the ninth year of the Taiyi era of Emperor Wu of Jin, the "Book of Jin" records that the Minister of the Imperial Secretariat, Xun Xu, inspected the eight tones of the court and found them to be discordant. Upon investigation, it was found that the rulers from the Eastern Han through the Wei Dynasty were more than four inches longer than the ancient rulers. Xun Xu then instructed official Liu Gong to remake the ruler according to the standards of the "Rites of Zhou," which was the ancient ruler. They then used this ancient ruler to recast the copper律吕 (lu: pitch pipes), which was used to tune musical pitches. When measuring ancient musical instruments with this ancient ruler, the sizes matched exactly with those recorded in inscriptions. Coincidentally, someone in Jijun excavated the tomb of King Xiang of Wei and unearthed jade律管 (lu: musical pipes) and bells from the Zhou Dynasty, whose musical tones surprisingly matched the newly cast律吕. At that time, old Han bells were also found in different locations, and when tested with the newly made律吕, their tones also matched. Emperor Wu of Liang noted in the "Bell and Pitch Weaving": "The copper ruler passed down by Zu Chongzhi is engraved with the following inscription: 'In the tenth year of Taiyi of Jin, the Minister of the Imperial Secretariat examined ancient artifacts, measuring and comparing them with the current rulers, finding them to be four and a half inches longer. The ancient standards examined include seven types: first, the Gu Xie jade ruler; second, the Xiao Lü jade ruler; third, the Western Capital bronze望臬; fourth, the gold错望臬; fifth, the bronze斛; sixth, the ancient coins; seventh, the Jianwu copper ruler. The Gu Xie jade ruler is slightly higher, the Western Capital bronze望臬 is slightly lower, and the rest are consistent with this ruler.' (The inscription has a total of eighty-two characters)." This ruler is the one newly made by Xun Xu, while the ruler currently in use is the one made by Du Kui. The text recorded in the "Bell and Pitch Diagram" drawn by Lei Cizong and He Yinzhi, which documents Xun Xu's verification of the ancient ruler, is exactly the same as this inscription. Xiao Ji’s musical score claims these seven standards were established during the Liang Dynasty, which is incorrect. We should now use this ruler as the standard to verify the rulers of all dynasties. The ruler from the Liang Dynasty is actually one foot and seven tenths longer than those used before the Jin Dynasty.
It is said that an old farmer found a jade ruler from the Zhou Dynasty in the field, which was considered the national standard ruler. Xun Xu used it to calibrate musical instruments and discovered that the instruments he created were one meter shorter than the standard. Emperor Wu of Liang also mentioned this in the "Zhong Lu Wei Cheng," saying that among the imperial family's ancestral belongings, there was a Zhou Dynasty bronze ruler and eight ancient jade pieces. Upon investigation, it was revealed that the Zhou Dynasty ruler had been used as a token by the Dong Hun Hou, but it has since been lost. Only one of those jade pieces is damaged, while the remaining seven are paired with the laws of the bells, featuring earlier inscriptions. Emperor Wu of Liang commissioned a new ruler to be made based on these jade pieces for cross-verification. They used the finest grains of millet for precise measurements, repeatedly correcting it, which was the most accurate method available at the time, only half a fen shorter than Zu Chongzhi's ruler. They then crafted four instruments known as "Tong" using this new ruler. They also made a flute according to the new ruler, used it to calibrate ancient bells, adjusting the Yi Ze music scale accordingly, and found that the Yi Ze music was just right. The lengths of these two rulers were almost the same. Xiao Ji noted that this method originates from the "Sima Fa." During the Liang Dynasty, the ruler's scale was engraved on a sundial to measure the shadow of the sun. This refers to the bronze sundial devised by Zuxun at the court's request. After the downfall of the Chen Dynasty, this item was sent to the court. During the Sui Dynasty, someone proposed restoring the ancient standards, leading to its use for calibrating music and crafting eight types of instruments, including bells and chimes. In the Jin Dynasty, someone in Shiping County unearthed an ancient bronze ruler.
Xiao Ji's "Music Score" says: "During the reign of Emperor Zhang of Han, the literary historian Xie Jing from Lingdao County in Lingling dug up a set of jade pitch instruments under the Shun Temple and crafted this ruler from it." Fu Chang's "Praise of the Jin Lords" states: "The bell pitch instruments made by Ge Xu were said to be very accurate by people at that time, except for Ruan Xian from Chenliu who claimed that its tones were too high. Later, in Shiping County, an ancient bronze ruler was excavated, which had significantly deteriorated over time, and in comparison to Ge Xu's ruler, it was a quarter shorter. People at that time largely agreed with Ruan Xian." The lengths of these two rulers were also similar.
In the fourth year of Prince Jingyuan's reign in the Chenliu state of the Wei Kingdom, Liu Hui commented in "Nine Chapters on the Mathematical Art" that during the time of Wang Mang, Liu Xin's hu and ruler were four fen and five li shorter than the rulers at that time, and compared to the rulers of the Wei Dynasty, the depth of the hu was measuring nine cun, five fen, and five li. This is the same as Xun Xu of the Jin Dynasty noted, "Du Kui's ruler is four and a half fen longer than the current ruler."
Xiao Ji said that this was the ruler used in the Jiangdong region of the Jin Dynasty.
The market ruler of the Later Zhou Dynasty was shorter than the jade ruler by one chi, nine fen, and three li.
The official ruler during the Kaihuang period was an iron ruler, one chi and two cun in length.
Before this period, from the early Wei Dynasty to the division of the Eastern and Western Wei, and until the Later Zhou ceased using the jade ruler, people used these rulers interchangeably.
Zhen Luan's "Arithmetic" states: "The market ruler of the Zhou Dynasty is equivalent to nine fen and two li of the jade ruler." It is said that this ruler was made by Zhi Gong Dao Ren of the Liang Dynasty and was sent to the Zhou Dynasty, given to an elderly man. Emperor Taizu of the Zhou Dynasty and Emperor Gaozu of the Sui Dynasty both believed that this ruler was made for them, and the common people of the Zhou Dynasty used this ruler. During the Kaihuang period, it was officially designated as the standard ruler, used by all departments, and continued to be used until the Renshou period. By the time of the Daye period, some common people also began using it privately.
Next is another account, stating that Yuan Yanming, a lieutenant of the Wei Dynasty, established a foot based on the width of half a grain of millet, and the Qi Dynasty continued to use this standard. Wei Shou recorded in the "Book of Wei · Treatise on Law and Calendar": "Gongsun Chong during the Yongping years made a new ruler, using the length of a grain of millet accumulated to set the standard for an inch. Later, the Minister of Rites Liu Fang was ordered to revise the music, and he used the width of a medium-sized grain of millet as a unit. Meanwhile, Lieutenant Yuan Kuang used the width of a grain of millet plus the width of the gaps of two grains of millet as a unit. These three accounts differed, leading to a prolonged debate without resolution. Until the 19th year of the Dahe era, Emperor Gaozu ordered that the width of a grain of millet be used as a unit, and the length of ninety grains of millet was established as the length of the Huangzhong, thereby determining the standard for the bronze ruler. The relevant authorities reported that Liu Fang's ruler matched Emperor Gaozu's standard, so the standard for metal and stone objects was revised according to Liu Fang's ruler. Until the Wuding era, no one discussed the issues of legal measurements again."
The jade ruler of the Later Zhou was actually longer by one foot, one inch, and five lines compared to rulers before the Jin Dynasty. From ancient times to the present, a bronze yue has been passed down, with silver inlaid inscriptions stating: "Yue, the palace of Huangzhong, nine inches long, nine-tenths in circumference, holds one thousand two hundred grains of glutinous millet, weighs twelve zhu, two of which make one he. Three-tenths of increase and decrease, transforming into twelve pitches." Ancestor Xiaosun said: "It is said that this bronze yue was made by Cai Yong."
During the Baoding years of the Later Zhou's Wu Emperor, the emperor ordered Grand Minister Lu Jingxuan, Duke of Shangdang Changsun Shaoyuan, and Duke of Qi Husi Zheng among others to create rulers using accumulated grains of millet, but the horizontal and vertical lengths could not be determined. Later, during the construction of granaries, when they dug into the ground, they unearthed a set of ancient jade measures, which they adopted as standard measures and based laws, measurements, and weights on these jade measures. Thus, this ruler was adopted, and the emperor ordered a general amnesty, changing the era to Tianhe, and all departments began to use this ruler, continuing until the end of the Daxiang era. The musical pitches of this set of laws corresponded with those of Cai Yong's ancient yue.
The Song dynasty ruler is actually longer by one foot, six inches, and four-tenths of an inch than the rulers used before the Jin Dynasty. There are also the celestial sphere ruler created by Qian Lezhi, the iron ruler from the Later Zhou, the ruler used for adjusting musical measures during the early Kaihuang period, and the water ruler used to adjust musical measures after the pacification of the Chen Dynasty.
This ruler is the type commonly used by ordinary people in the Song Dynasty, which later spread to the Qi, Liang, and Chen Dynasties, where they used it to establish musical scales. This ruler's length is comparable to those from the Jin Dynasty onward, as well as to the commonly used rulers from the Liang Dynasty and the ruler on Liu Yao's celestial sphere. This is likely because rulers used by ordinary people inevitably wear down and change over time, resulting in slight differences.
In the sixth year of Jiande during the Zhou Dynasty, after defeating the Qi Dynasty, this ruler was adopted to unify the national standards for weights and measures, and it was issued nationwide. Later, during the reign of Emperor Xuan of the Northern Zhou, Daxi Zhen and Niu Hong held discussions about:
I carefully pondered the issue of measurements and standards; governing a country requires a standard, and it's crucial to thoroughly investigate how it was done in the past to find a reliable method. I checked, and the iron ruler currently in use was made by order of Emperor Taizu, based on the ruler created by Su Chuo from the Book of Documents, which served as the standard ruler during the early Zhou Dynasty. I did a close comparison, and the length of this iron ruler is approximately the same as that of the ruler from the Song Dynasty; it was used to calibrate musical pitches and measure land at that time. Now, I'm testing it with millet grown in Yangtoushan, Shangdang, following the method described in the "Book of Han: Treatise on Law and Calendar." If I use those large millet grains, stacking them will just fill one foot, and I have to shake them vigorously to fit them into the Huangzhong pipe. However, if I use medium-sized millet grains, although they are a bit sparse, they can fill the Huangzhong pipe without any shaking. The two situations differ mainly due to the varying sizes of the millet grains; whether this iron ruler is accurate still needs further examination. Moreover, the millet from Shangdang is different from that of other places; it is particularly dark in color, round, and heavy, indicating that it was not randomly selected for measurement. Because rainfall and drought vary by region, and the fertility of the land is also different, the size of the millet will certainly vary and might not fit exactly in the middle. Xu Shen noted that jujube millet is quite large and differs from ordinary millet. I believe these large millet grains must be jujube millet; a hundred of them stacked would just measure one foot, which aligns with ancient practices. Besides the millet that fills the pitch pipe, there are still about ten left, likely due to the uneven sizes of the millet or imprecision in the measurement process. However, it’s reasonable to say that shaking them to fill it up, as I just did, makes sense.
I checked the ancient coins of the Zhou and Han dynasties, and the sizes are quite consistent; the armillary sphere from the Song dynasty is also accurate. The "Huainanzi" states that twelve grains of millet stacked up make one inch. It can be seen that ancient emperors were very meticulous in setting standards, using laws and regulations to calculate, with the same importance. The "Book of Han - Records of Food and Goods" states: "A square inch of gold weighs one jin." When we mint gold today for verification, the iron ruler is the most accurate. From literature and actual situations, there are many areas that match. Furthermore, this standard has been used since the Ping Qi period, and it makes sense to continue using it today. As for measuring foxtail millet with a jade ruler, using the width as the length, stacking it full and having some left, not filling it up, consulting both ancient and modern texts, this approach may not be viable. The rulers of the Jin and Liang dynasties were too short; trying to stuff foxtail millet into the tube, it simply wouldn't fill up. Tuning according to this standard would definitely result in a pitch that is too high and sharp. Harmonizing the eight tones is the model of the ancient sage kings; unifying laws and weights and measures is a rule that wise rulers of all generations have adhered to. After thoroughly reviewing the existing literature and considering the current situation, we believe that using an iron ruler is the most convenient. Before we could finalize the details, the founding emperor passed away. Niu Hong, Xin Yanzhi, Zheng Yi, and He Tuoya discussed for a long time without reaching a conclusion. After the Chen dynasty was pacified, the emperor felt that the music of Jiangdong was the best, saying, "This is the ancient music of Huaxia; although it has changed with the times, it still largely follows the ancient methods." Zuxiaosun said, "After pacifying the Chen dynasty, the jade ruler and laws from the Zhou dynasty were abolished, and this iron ruler and laws were used instead, stipulating that one chi and two cun is the market ruler."
13. In the tenth year of the Kaihuang era, the water ruler crafted by Wan Baochang is actually one foot, one inch, and eight-tenths longer than the rulers used before the Jin Dynasty. "The current set of bronze rulers from the Taiyue Bureau and the inner court is made by Wan Baochang, known as the water ruler. It is said that its Huangzhong ruler corresponds to double the pitch of the iron ruler's Nanlv. Nanlv is the feather sound of Huangzhong, hence it is called the water ruler." Currently, a set of bronze tuning pipes crafted by Wan Baochang is housed in both the Taiyue Bureau and the palace, called the water ruler. The text states that its Huangzhong ruler is equivalent to double the pitch of the iron ruler's Nanlv. Nanlv is the feather sound of Huangzhong, thus it is named the water ruler.
14. Among various rulers, the earth gnomon ruler of Zhao Liuyao's armillary sphere is four and three-tenths longer than the official ruler of the Liang Dynasty and is actually one foot and five-tenths longer than the rulers used prior to the Jin Dynasty. "The earth gnomon ruler of Zhao Liuyao's armillary sphere is four and three-tenths longer than the Liang official ruler and is actually one foot and five-tenths longer than the pre-Jin rulers."
Fifteen, the commonly used ruler during the Liang Dynasty was six fen and three li longer than the official ruler of the Liang Dynasty, two fen longer than Liu Yao's armillary sphere ruler, and actually one foot, seven inches, and one tenth longer than the rulers before the Jin Dynasty. Emperor Wu of Liang said in the "Zhonglv Wei": "After Emperor Wu of Song pacified the Central Plains, he sent a set of armillary sphere and soil gnomon, claiming it was made by Zhang Heng. However, according to the inscription on the armillary sphere, it was cast in the fourth year of Guangchu, and the soil gnomon was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. He used the soil gnomon of the armillary sphere as a ruler, which is four inches and three tenths longer than the current standard ruler and two inches shorter than the commonly used ruler." The "new ruler" mentioned here refers to the official ruler of the Liang Dynasty.
Hello everyone, today let's talk about the ancient units of measurement. First, let's mention the "Lü" recorded in the "Rites of Zhou." This item is one foot deep, with a square base of one foot on each side, and a circular exterior, with a capacity of one "Lü"; its bottom diameter is one inch, with a capacity of one "Dou"; its ears (or handles) are three inches long, with a capacity of one "Sheng"; the entire "Lü" weighs one jun and produces a sound similar to that of a "huangzhong." It is not subject to taxation, and the inscription reads: "Through careful consideration, this instrument has finally achieved perfection. The excellent measurement has been established for the observation of the four nations and may inspire future generations as a standard." The meaning of this inscription is that after repeated contemplation, a perfect measuring instrument has finally been made, for the four nations to observe and serving as a standard for posterity.
"Zuo's Commentary on the Spring and Autumn Annals" also mentions four types of measuring vessels in the state of Qi: dou, qu, fu, and zhong. One dou equals four sheng, four dou make one qu, four qu make one fu, and ten fu make one zhong. This means that one fu equals six dou and four sheng, and one zhong is equivalent to sixty-four dou. Zheng Xuan believed that based on the calculation of a square with a side length of one chi, the capacity of a fu should be one thousand cun, which is two sheng and eighty-one fen less than the calculation in "The Nine Chapters on the Mathematical Art" by one twenty-second. Zu Chongzhi recalculated using mathematics, and the result was a capacity of one thousand five hundred sixty-two and a half cun. If calculated based on a side length of one chi, with the outer perimeter circular, and slightly reducing the edge, the diameter is approximately one chi four fen one li four hao seven seconds two hou, with a depth of one chi; this defines the standard for the ancient hu.
In "The Nine Chapters on the Mathematical Art - Commercial Arithmetic," it states that the volume of one hu of grain is two thousand seven hundred cun, one hu of rice is one thousand six hundred twenty cun, and one hu of beans, rapeseed, hemp, and wheat is two thousand four hundred thirty cun. This illustrates that while the volume varies by grain type, the price remains constant, which reflects the ancient principle of fair trade. Among them, the volume of a hu of rice matches that recorded in the "Book of Han." In "The Mathematical Classic of Sunzi," it states that six grains of millet equal 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 noted that the gui has a natural shape, symbolizing the beginning of yin and yang; four gui equal one cuo. Meng Kang said that sixty-four grains of millet make one gui.
"The Book of Han" states that there are five measuring instruments: the yue, he, sheng, dou, and hu, used to measure quantity. The yue was originally made according to the musical scale of the Huangzhong. Precise measuring instruments were used to determine volume, with the yue being filled with one thousand two hundred grains of cereal and calibrated with well water. One yue equals one he, ten he make up one sheng, ten sheng make up one dou, and ten dou make up one hu, completing the set of five measuring instruments. The method of making it is to use copper to create a square with sides measuring one chi, with a circular perimeter and handles on the sides. The top represents the hu, the bottom the dou, the left side the sheng, and the right side the he and yue. Its shape resembles a jue, symbolizing nobility. The top three parts and the bottom two parts symbolize the three heavens and two earths; the circle contains the square, with one part on the left and two parts on the right symbolizing yin and yang. The circle resembles a ruler, weighing two jin, containing quantities of various gases, each being eleven thousand five hundred and twenty. The sound is the same as the Huangzhong, starting from the Huangzhong and repeating. The hu is inscribed with the inscription: "The law of good measure for the hu, square with a foot and round on the outside, with a side of nine li and five hao, a power of one hundred and sixty-two inches, a depth of one foot, a volume of one thousand six hundred and twenty inches, holding ten dou."
Zu Chongzhi calculated using the value of pi; the diameter of this hu should be one chi, four cun, three fen, six li, one hao, nine seconds, and two hou, and the width of the handle is around one fen, nine hao. Liu Xin calculated that the width of the handle was less by around one li, four hao, due to his inaccurate arithmetic.
In the fourth year of Wei Jingyuan, Liu Hui wrote in "The Nine Chapters on the Mathematical Art": the hu used by the Grand Minister of Agriculture now has a diameter of one chi, three cun, five fen, five li, a depth of one chi, and a volume of one thousand four hundred and forty-one inches plus three tenths. The copper hu from the time of Wang Mang, calculated by today's standard, has a depth of nine cun, five fen, five li, and a diameter of one chi, three cun, six fen, eight li, seven hao. Using Liu Hui's calculation method, Wang Mang's hu is only slightly more than nine dou, seven sheng, four he of the current hu. Therefore, the hu from the Wei Dynasty is larger and the ruler is longer, while Wang Mang's hu is smaller and the ruler is shorter.
The Liang and Chen Dynasties continued to use the ancient system of weights and measures. The Qi Dynasty used the ancient standard of five sheng equaling one dou.
In the first year of the Baoding era of the Later Zhou, which is the fifth month of the Xin Si year, while the Jin state was constructing granaries, an ancient jade measure was discovered. By the fifth year of Baoding, which is the year of Yi You in October, the emperor ordered the re-establishment of laws and standards for copper and measurements, ultimately to achieve a unified standard. The inscription records that the measurement of piled millet exactly matches the capacity of this jade measure, and there is no difference with other weighing instruments. Subsequently, this jade measure was used as a standard to cast copper measures, which were then distributed throughout the country. The inner diameter of the copper measure is seven and one-tenth inches, with a depth of two inches and eight-tenths, weighing seven catties and eight taels. On the fifteenth day of the first month in the second year of the Tianhe era, after calibration, the copper measure was handed over to the government as a standard object. The inscription on the jade measure reads: "In the first year of the Baoding era of the Great Zhou, in the year of Chongguang, in the month of Ruibin, while the Jin state government was repairing the granaries, this ancient jade measure was discovered, and its shape and standards were very precise, just like the good measuring instruments of ancient times. The Grand Minister of the Jin state presented it to the emperor, who ordered it to be kept in the Tianfu. By the fifth year of Baoding, in the year of Xieqia, the emperor ordered a careful inspection of the measuring ropes and weights, ensuring that everything was accurate, and then a replica of this jade measure was cast in gold and distributed for use throughout the country in order to establish a unified and prosperous system of weights and measures." Now, let’s take a look at the numbers: the volume of the jade measure is approximately one hundred ten and eight-tenths inches, and the volume of a hu is about one thousand one hundred eighty-five inches, seven-tenths, three hundredths, and nine thousandths. Zhen Luan notes in "Arithmetic" that one jade measure is equivalent to one and three-tenths government dou and four shao. Thus, the jade measure is larger compared to the government dou. According to the numerical calculations, the dou of the Later Zhou government, as stated by Zhen Luan, has a volume of about ninety-seven inches, and the volume of a hu is about nine hundred seventy-seven inches. The jade measure from the Later Zhou, along with its corresponding gold-inlaid copper dou and the gold-inlaid copper dou cast in the sixth year of Jiande, were all measured using millet. The weight of one measure using a jade weight is consistently six catties and thirteen taels.
During the Kaihuang period, it was stipulated that three ancient sheng were equal to one modern sheng. By the time of the Daye period, the capacity of the ancient dou was reinstated. Heng means balance; Quan means weight. The purpose of Heng is to weigh objects, achieving a state of balance. The method of making Heng is as follows: to ensure that its base is level and the vertical line is straight. If you turn left, you will see the compass; if you turn right, you will see the square. Heng's application in astronomy is to assist the Xuanji (ancient astronomical instrument), accurately determining the solar terms and coordinating the movements of the seven planets (sun, moon, and five stars), so it is called Yuheng. Quan refers to weight units such as zhu, liang, jin, jun, and dan. By using it to weigh objects, you can determine their weight. In ancient times, there were also weight units such as shu, lei, chui, zi, huan, gou, lue, and yi, but their definitions have varied across dynasties, and I am not well-versed in the specifics. "History of the Former Han" states that the origin of Quan is based on the weight of the Huangzhong bell. One yue (ancient capacity unit) can hold 1,200 grains of shu, weighing twelve zhu. Twenty-four zhu equals one liang, sixteen liang equals one jin, thirty jin equals one jun, and four jun equals one dan. The craftsmanship of these five types of scales is intricate, and their production is determined based on reason, ensuring that the weights are balanced. The remaining differences in size should be determined based on weight. Quan is crafted into a round shape and encircled, effectively doubling its thickness, so it goes on endlessly. When Quan and objects achieve balance, Heng is created; the function of Heng produces the compass, the circular shape of the compass leads to the square, the square shape of the square produces the rope, and the straightness of the rope produces the standard. If the standard is correct, Heng is balanced, and Quan is precise. These are the five rules, all contained in the weighing instrument, as important guidelines.
According to the records in the "Zhao Shu," in July of the eighteenth year of Shi Le's reign, when the Jian De Dian was built, a round stone was found that was shaped like a water grinding stone. The stone was engraved with an inscription: "Law Stone, weighing four jun, standardized for measurement and weighing. Made by the Xin clan." The continuation of this discussion dates back to the Wang Mang period. During the Jingming years of the Northern Wei, a person from Bing Prefecture named Wang Xianda presented an ancient bronze weight inscribed with an eighty-one-character inscription. The inscription stated: "Law Stone, weighing four jun." It also mentioned: "The Yellow Emperor, the first ancestor, had virtue extended to Yu. The Yu Emperor, the first ancestor, had virtue extended to Xin. In the year of Daliang, the dragon gathered on Wu Chen. Wu Chen was determined, and heaven's mandate was given to someone. Based on the virtue of the land received, the correct title is indeed accurate. Rectifying the flawed construction, longevity and prosperity are exalted. Following the same law of measurement and weighing, it is in accordance with the present people. The dragon is in the year of Ji Si, which is truly Shen, initially classifying the world, ensuring all nations will comply for eternity. Generations of descendants will enjoy the inheritance for billions of years." This was also produced during the Wang Mang era. At that time, the Grand Music Official Gongsun Chong first adjusted the weights and measures according to the "Book of Han," and when he saw this weight, he used the new scale to weigh it, and the weight was one hundred and twenty jin. The new scale and weight matched perfectly. Thus, it was handed over to Gongsun Chong for adjusting the musical pitch. During the reign of Emperor Xiaowen, the dou and chi were produced entirely according to the records in the "Book of Han."
It is said that during the Liang and Chen dynasties, the traditional scales were in use. At that time, in the state of Qi, one jin was eight liang. The jade scales of the Zhou dynasty, for an item that weighed four liang, were equivalent to four and a half liang of the old scales. By the Kaihuang period of the Sui dynasty, it was mandated that three jin on the traditional scales equaled one jin. By the Daye period of the Sui dynasty, the ancient scales were reinstated.
This indicates that the standards of measurement and weighing in ancient times were inconsistent across different dynasties, different regions, and even during different periods within the same dynasty, leading to significant confusion. "Liang and Chen used the ancient scale. Qi used the ancient scale of one jin being eight liang. Zhou's jade scale measured four liang, equivalent to four and a half liang of the ancient scale. Kaihuang counted three jin of the ancient scale as one jin, and during Daye, the ancient scale was restored." Indeed, there were numerous changes in the weighing methods across these dynasties!
