The Book of Changes says: "That which is above form is called the Dao, that which is below form is called the vessel." This means that the higher realm above the material is the "Dao," while the material itself belongs to the "vessel." You see, the mystery of the operation of heaven and earth lies in the interaction of yin and yang; the intricacy of various objects lies in adhering to the principles of music. The sages of ancient times observed the changes of the four seasons, using jade artifacts to mark the passage of time; they carefully studied the sounds of the five elements, using metal to achieve clarity in sound, ultimately achieving the goal of governing the world and establishing great order. However, the properties of metal can change, and the size of the objects made varies, making it difficult to standardize; the shape of bamboo is round, and the length and thickness vary, complicating standardization. Therefore, the wise established musical rules to capture the pitch of bells. They used three notes as the foundation, then used six notes to adjust, eventually forming twelve scales, which reflects the laws of heaven and earth! They also determined time based on the movement of the sun, adjusting musical instruments according to changes in the earth's energy, so when yin and yang are in harmony, sunlight is abundant; when music and earth's energy are in harmony, ashes will rise. With ashes rising and music flowing smoothly, playing musical instruments will produce the central sound of heaven and earth. With this central sound, various matters can be regulated and transformed, as stated in the "Book of Yu," "Leaves, time, moon, sun, same rules for measuring weight and length." When the rhythm of music is harmonious, and the moral tone is beautiful and complete, it can move heaven and earth, influence ghosts and gods, guide human nature, and change social customs. Express aspirations through song, reflect the rise and fall of society through music. Therefore, a noble person understands music through examining sound, understands politics through understanding music, all from this principle. The Grand Historian Sima Qian said in the "Book of Music": "Emperors must adhere to specific laws and principles when establishing various systems and objects, all of which come from the six tones. The six tones are the basis of all things, especially important in military matters. Therefore, observing the enemy's situation can determine good and bad outcomes; hearing sounds can judge victory or defeat. This is the unchanging principle of emperors throughout history."
After the fall of the Qin Dynasty, the study of music theory gradually declined. When the Han Dynasty was first established, Chancellor Zhang was the first to mention music theory, but he did not address it comprehensively. It was not until Emperor Wu of Han that a dedicated official role for music theory was formally established, and Sima Qian provided a detailed explanation of the order of musical scales. During the Wang Mang period, people began to study music theory again, and Liu Xin submitted a memorial to the court summarizing five aspects of music theory: firstly, the preparation of numbers, namely one, ten, hundred, thousand, and ten thousand; secondly, harmony, which includes gong, shang, jiao, zhi, and yu; thirdly, measurement, which includes fen, cun, chi, zhang, and yin; fourthly, preferred measurements, which include yue, he, sheng, dou, and hu; fifthly, weights and measures, which include zhu, liang, jin, jun, and shi. Ban Gu later recorded all of these. Cai Yong also documented discussions about musical notes after the Jianwu period, until Sima Shao compiled and organized these materials.
In the late Han Dynasty, the realm was in turmoil, and musicians fled and dispersed, causing the standards for musical instruments and notes to be lost. It was not until the time of Emperor Wu of Wei that Du Kui was found to establish the tuning standards for musical instruments. Du Kui organized and improved the statutes based on the measurements of the time. After Emperor Wu of Wei ascended the throne, he continued to use the musical rules established by Du Kui unchanged. By the tenth year of the Taishi era, the Grand Minister of Ceremonies Xun Xu petitioned to create new musical standards and to recast the tuning pipes. During the Yuan Kang period, Xun Xu's son Xun Fan inherited his father's work, but before he could complete it, the Yongjia Rebellion occurred, and the court's statutes were destroyed by Shi Le.
When Emperor Yuan moved south and the court was just established, the system of rituals and musical instruments had entirely vanished. Although some were later collected, most had been lost to time, and by the time of Emperors Gong and An, the music system had yet to be fully restored. Now, based on historical materials, I have organized the order of ancient musical scales' development and the records of musical measurements after Emperor Wu of Wei, and compiled this document.
It is said that in "Records of the Grand Historian," the twelve musical tones were said to be invented by the Yellow Emperor. He sent a person named Ling Lun to the foot of Mount Kunlun, west of Da Xia, to a place called Xiang Valley, to find a kind of bamboo with thick and uniform joints. He cut a segment that measured three inches and nine tenths long from the middle of two joints, blew into it, producing the Huangzhong tone known as "Hanshao." Then, he made twelve bamboo pipes, imitating the call of the phoenix. The male phoenix has six distinct calls, and the female phoenix has six as well, all corresponding to the Huangzhong tone, thus establishing a system of musical tones. Therefore, the earliest musical tones were created using bamboo pipes, as bamboo is naturally round and hollow.
The book also states that the Yellow Emperor crafted musical pipes from jade, one foot in length with six holes, representing the tones of twelve months. During the reign of Emperor Shun, the Queen Mother of the West sent a set of jade pipes called "Zhaohua." During the reign of Emperor Zhang of the Han Dynasty, a scholar named Xi Jing in Lingling discovered a white jade pipe in Emperor Shun's temple. In the first year of Emperor Wu's Taikang reign, someone in Ji County looted a tomb and unearthed the jade musical tones from the tomb of King Wei Xiang of the Warring States period. Therefore, in ancient times, jade was often used to make musical pipes due to its gentle and noble qualities. During the reign of Emperor Ping of the Han Dynasty, Wang Mang began using bronze to craft musical pipes. Bronze was chosen for its symbolism of unity, capable of harmonizing customs across the realm. Bronze is exceptionally durable, resistant to moisture, cold, and heat, remaining consistent like a true gentleman.
The "Rites of Zhou" states that the Grand Master position is responsible for overseeing the six musical tones and six yin pitches, used to coordinate the sounds of yin and yang. The six musical tones are yang sounds, namely Huangzhong, Taicuo, Guxi, Ruibin, Yize, and Wushe; the six yin pitches are Dalu, Yingzhong, Nanlu, Linzhong, Zhonglu, and Jiazhong. The Grand Master also uses the same tones to interpret military commands and then assesses good or bad fortune based on the sounds. In summary, the Grand Master is primarily responsible for managing the harmony of the six musical tones and six yin pitches, discerning the sounds of yin and yang in all directions, and crafting musical instruments, all of which are tuned and set to the twelve tones.
King Jing of Zhou wished to cast the "Wushe" bell and asked the expert Lingzhou Jiu what this bell truly represented. Lingzhou Jiu explained: "'Huangzhong' is the middle tone among the six pitches, its color is yellow, which is why it is called Huangzhong. It can harmonize six types of qi and embodies nine virtues. Following that are: 'Taicuo', used to praise yang qi and dispel gloom; 'Guxi', used to purify all things and welcome guests; 'Ruibin', used to promote harmony and facilitate interactions; 'Yize', used to celebrate the nine virtues, ensuring that people remain united in purpose; 'Wushe', used to promote the virtues of sages and set an example for people. These six tones harmonize various sounds through their fluctuations, achieving harmony. Of these, 'Huangzhong' serves as the primary tone, 'Dalu' assists it; 'Jiazhong' is on both sides of 'Huangzhong', expressing subtle variations; 'Zhonglu' is the middle tone, harmonizing the central qi; 'Linzhong' coordinates various affairs to keep everything orderly; 'Nanlu' praises the vibrant scenes of yang qi; 'Yingzhong' enables various instruments to work together effectively." In short, these tones are used to reflect seasonal changes and the growth of all things.
Emperor Qin Shi Huang burned books and buried alive scholars, destroying many texts and causing a lot of knowledge to be lost. However, some fragmentary records have survived. Lü Buwei recorded the sequence of musical pitch generation in his work "Spring and Autumn":
- Huangzhong (the yellow bell) is the fundamental tone,
- followed by Linzhong,
- which generates Taicuo,
- Taicuo generates Nanlü,
- Nanlü generates Guxi,
- Guxi generates Yingzhong,
- Yingzhong generates Ruibin,
- Ruibin generates Dalu,
- Dalu generates Yize,
- Yize generates Jiazong,
- Jiazong generates Wushè,
- and Wushè generates Zhonglü.
Specifically, when ascending in the three-part pitch system, one must add one part; when moving down, one must subtract one part. Most later music theorists followed this explanation. After the Han Dynasty was established, it inherited the shortcomings of the Qin Dynasty. Although Zhang Cang also organized the musical calendar, his efforts were not particularly effective. Therefore, Emperor Wu of Han reestablished the musical system and established dedicated officials for music regulation. Although the pitch of music and the pitch of metal and stone instruments were standardized, it was essentially a makeshift compilation of surviving materials, resulting in a temporary solution, and at that time, the five-tone system remained the primary method used.
King An of Huainan was a knowledgeable Confucian scholar who was also well-versed in music theory, particularly regarding the twelve pitches. He said that the sound of the Yellow Bell has a pitch pipe that is nine inches long, which serves as the fundamental tone of the 'gong' (宫) scale. Nine multiplied by nine equals eighty-one, so the Yellow Bell is assigned the number eighty-one, corresponding to the 'zi' (子) position. The Lin Bell corresponds to the 'wei' (未) position, with a number of fifty-four; the Great Cang (太蔟) is seventy-two; the Southern Bell is forty-eight; the Gu Bell is sixty-four; the Ying Bell is forty-two; the Rui Bin is fifty-seven; the Great Bell is seventy-six; the Yi Ze is fifty-one; the Jia Bell is sixty-eight; the Wu She is forty-five; and the Central Bell is sixty. These twelve pitches, except for the Central Bell, each produce other sounds. The Yellow Bell is the palace, the Great Cang is the business, the Gu Bell is the angle, the Lin Bell is the 'zhi' (徵), and the Southern Bell is the 'yu' (羽). The palace produces 'zhi', 'zhi' produces business, business produces 'yu', 'yu' produces angle, and angle produces the Ying Bell, which differs from the standard pitch, thus creating harmony; the Ying Bell produces the Rui Bin, which is also different, so it is modulation. In winter solstice, the sound resembles that of the Lin Bell, which is more muffled; in summer solstice, the sound resembles that of the Yellow Bell, which is clearer. The twelve pitches correspond to the changes of the twenty-four solar terms. Jia Zi is the 'zhi' (徵) sound of the Central Bell, Bing Zi is the 'yu' (羽) sound of the Jia Bell, Wu Zi is the palace sound of the Yellow Bell, Geng Zi is the business sound of the Wu She, and Ren Zi is the angle sound of the Yi Ze. One pitch pipe can produce five sounds, so twelve pitch pipes can produce sixty sounds. Sixty multiplied by six equals three hundred sixty, so three hundred sixty sounds correspond to three hundred sixty days in a year. Therefore, the numbers associated with the pitch pipes reflect the principles governing the movement of heaven and earth.
Sima Qian also wrote about musical theory in "Records of the Grand Historian," outlining the main theories. He said that the primordial energy of Taiji, the combination of three into one, begins its movement in the Zi position, which leads to the creation of the twelve musical tones. Then, by adding one to the Zi position to arrive at San, and multiplying San by Jiu to combine the original position with the ten celestial stems, we arrive at 19,683, referred to as the "cheng number," which is the Huangzhong calculation method. Multiplying this number by the twelve earthly branches, we get 177,147, known as the "gai number," which is the actual value of Huangzhong. Dividing the actual value by the calculation method, we find that Huangzhong's musical pipe is nine inches long, corresponding to the climate of the winter solstice in the eleventh month. The combination of Yin and Yang, with energy gathering in the Zi position, leads to the birth of all things, which is why all things contain the number three. Therefore, the diameters of the twelve musical tones are all fractions of three, with both upward and downward generation involving the addition or subtraction of three. The specific method is to start from Huangzhong's nine inches, multiply the actual value by two for downward generation, then divide by three; for upward generation, multiply the actual value by four, then divide by three. This explains how Yang energy generates Yin energy downwards, and Yin energy generates Yang energy upwards.
Starting from the Zi position, Huangzhong is denoted as one;
The Chou position corresponds to two-thirds;
The Yin position corresponds to eight-ninths;
During the Mao hour, it is 17/16. During the Chen hour, it is 81/64. During the Si hour, it is 243/128. During the Wu hour, it is 729/512. During the Wei hour, it is 1,187/1,024. During the Shen hour, it is 6,561/4,096. During the You hour, it is 19,682/8,192. During the Xu hour, it is 59,049/32,768. During the Hai hour, it is 147,147/65,536. These are the proportions of the twelve hours. If it is yang in the six lü, it naturally generates yin downwards; if it is yin in the six lü, it obtains its proper position and then generates yang upwards. There are no repeated steps in the calculation of the generation. This is like "lü takes a wife, lü gives birth to a son," the rise and fall of yin and yang, which is the fundamental principle of lü. Some say that the longest of the twelve lü is Rui Bin, as calculated based on the number nine from the "Huainanzi." Some say that the five sounds generate each other: the palace generates the angle, the angle generates the commercial, the commercial generates the zhi, the zhi generates the feather, and the feather generates the palace. However, a clear explanation of these principles and their applications remains elusive.
In the second paragraph:
During Wang Mang's regency, he extensively recruited people who were proficient in the Zhong lü, carefully studied the significance of musical scales, and had Xihe and Liu Xin responsible for formulating and playing the music. Ban Gu documented this event in the "Book of Han." Although Ban Gu's discussion is comprehensive, regarding the order of the twelve lü's gains and losses, he said: the length of the Yellow Bell is nine inches; losing one third of its length, it generates the Lin Bell, which is six inches long; with a gain of one third, it generates the Tai Bell, which rotates leftward, occupying eighty-eight positions. This process of going up and down ultimately leads to Wu She, and then generates the Zhong lü downwards. His calculations of the generative relationships align perfectly with Sima Qian's records. Ban Gu documented all of this in the "Book of Han."
In the time of Emperor Yuan, there was a man named Jing Fang, who was particularly knowledgeable about the five tones and sixty pitches system. The Emperor sent the Crown Prince's tutor, Xuan Cheng, and Grand Counselor Zhang Za to the Bureau of Music to assess him. Jing Fang launched into an explanation: "I learned from the former Xiaohuangling, Jiao Yanshou. The way the sixty pitches generate is as follows: the upper tone creates the lower tone in a ratio of three to two; the lower tone creates the upper tone in a ratio of three to four. Yang tones produce Yin tones below, while Yin tones produce Yang tones above, eventually reaching the Zhonglu, completing the twelve pitches. The transformation of twelve pitches into sixty is akin to the evolution of the Bagua into sixty-four hexagrams. Fu Xi authored the 'Book of Changes,' using a method to record the initial Yang Qi to set the laws of pitches. Using the sound of the Winter Solstice as a benchmark, Huangzhong is set as the palace, Taicu as the shang, Guxi as the jue, Linzhong as the zhi, Nanlu as the yu, Yingzhong as the bian gong, and Ruibin as the bian zhi; this forms the foundation of sound, the standard for the five tones. Therefore, the pitch for that day is the palace tone, and the others follow in the order of shang, jue, zhi, and yu. The 'Book of Rites: The Rites of Music' states that 'the five sounds, six pitches, and twelve tubes are all connected as the palace,' this is what it means. Using the sixty pitches to divide each day, Huangzhong begins at the Winter Solstice and returns to Huangzhong again at the Winter Solstice; divination concerning yin and yang, cold and heat, and wind and rain all originate from this. This can be used to test various sounds, investigate their pitch, as long as it’s a sound that conforms to music, the corresponding pitch can be identified. The 'Book of Documents: The Book of Yu' states, 'pitch and sound, this is what it means.'"
Jing Fang continued, "The sound of bamboo pipes is not ideal for determining pitch, so a tuning fork was created to establish the numerical values of the pitches. This tuning fork is shaped like a se, measuring one zhang in length, with thirteen strings, and the distance between the strings is nine chi apart, corresponding to the nine cun of the Huangzhong pitch. The middle string is marked with fractions below, used to indicate the clarity and murkiness of the sixty pitches." Jing Fang's explanation of the pitch system was more detailed than Xun's performance, and his method was adopted by historians and also used by the imperial music department, although the specific details weren't thoroughly documented. Crafting pitch pipes from bamboo, playing to explore sound, and arranging to verify breath - this is the foundation of the pitch system. The diviners found the sound weak and hard to grasp; the fractions were also a bit rough, so they used the tuning fork as a substitute. The sound of the tuning fork is clear and distinct, easy to distinguish, but the tension of the strings determines the clarity and murkiness of the sound, and it can't be corrected without adjusting the strings. By tuning the middle string to match the Huangzhong pitch and using the scale to find other pitches, all pitches can be accurately matched. The "History of the Later Han Dynasty: Treatise on Pitch and Tuning" details the accuracy and measurements of the sixty pitches; their order of succession aligns with the "Lv Luan" and "Huainanzi."
In the first year of Emperor Zhang of Han, an official named Yin Yong submitted a memorial to the emperor, saying, "Currently, there is no one in the court who is proficient in the sixty musical tones, and therefore, they are unable to calibrate the musical instruments. Therefore, I hope the emperor will summon Yan Xuan, the son of Yan Chong, to serve as a music official and be responsible for calibrating the instruments." The emperor said, "If Yan Chong's son is truly proficient in musical theory, able to distinguish the tones of various instruments, then let him try. We cannot assume he will be a musician just because his father was, nor can we mistake someone who does not understand music for someone who does. Music is very subtle; only those who truly understand it can comprehend its nuances, while those who do not cannot. If he can play all twelve musical tones flawlessly on the xiao, then it will prove that he has inherited his father's knowledge." As a result, Yan Xuan played the twelve tones, only getting two right, four wrong, and not even recognizing the other six, so he was eliminated. Since then, no one has been able to accurately calibrate the musical tones.
In the sixth year of Emperor Ling of Han, the Eastern Court summoned officials responsible for the classics, including the Crown Prince's Attendant Zhang Guang, to inquire about the standards of musical tones. Zhang Guang and the others were unsure, so they went back to search through the old classics, only then finding information about the instruments. The shape of these instruments was recorded in the books as being house-shaped, but they still couldn't ascertain the tension of the strings. Musical scales cannot be adequately explained in words; those who understand music cannot find a way to teach others, and those who truly grasp it can understand independently, without needing a teacher. Therefore, the historians who could discern the nuances of musical scales have also vanished. The only knowledge that remains is the ability to judge musical scales by intuition.
At the end of the Han Dynasty, the world was in great turmoil, and the art of music was lost. During the reign of Emperor Wu of Wei, a man from Henan named Du Kui was well-versed in music theory and served as an official in charge of court music. He had a bronze craftsman named Chai Yu cast bells, but the bells produced uneven sounds that did not meet the standards. After several attempts at recasting and modifying, Chai Yu became very frustrated and complained that Du Kui was carelessly altering the musical standards. Emperor Wu of Wei then tested the bells made by Chai Yu and recognized that Du Kui truly understood music theory, so he punished Chai Yu.
In the tenth year of the Taishi era, the Grand Librarian Xun Xu and the Prefect of the Palace Library Zhang Hua produced twenty-five sets of bronze bamboo pipes from the palace for the musicians to review. Three of the sets matched the musical theory of Du Kui and Zuo Yannian, while the other twenty-two sets, based on their inscriptions and measurements, were designated for flute music. They asked the Deputy Director of Music Li He about these sets, and he replied, "During the reign of Emperor Ming of Wei, I developed these musical principles based on the flute's sound. I wanted people learning music theory to live in the same neighborhood, sing, play music, and learn together, tuning their instruments according to these principles. When it comes to ensemble playing, as long as you are familiar with the dimensions and names of these flutes, string instruments and songs can be brought into harmony. For deep, rich tones, use long flutes and their corresponding scales; for clear and bright singing, use short flutes and their corresponding scales. In short, if the clarity, richness, pitch, and depth of string instruments and vocals are not determined according to the dimensions and names of the flutes, they won't be able to harmonize."
The nobles reported: "In the past, the former kings created music to promote social harmony, worship the deities, and honor the virtuous, and they certainly adjusted the tones of the eight tones according to the harmony of the musical scales. Therefore, the music for sacrifices, court meetings, and banquets all had prescribed systems, with singing and playing each having their own narratives, and the purity and muddiness of the sounds were also taken into account. Ancient texts state that 'the five tones and twelve pitches mutually serve as the palace tone,' and these records can be found in the classics, transmitted texts, and historical writings. However, nowadays, the lyrics for ensemble music and the lengths of flutes do not adhere to standards and are all created arbitrarily, not following musical laws at all. When we measure them against proper regulations, they do not conform; even if the sounds produced seem similar, most are not harmonious. Some say, 'The flutes passed down by the teachers only concern the clarity and muddiness of the sounds, and only look at their lengths. The craftsmen never follow musical laws in their production.' This means that the current flute-making lacks any standards. Yet, He has written the method for making flutes and has integrated it with string instruments and singing, using this as a standard; does this not follow the rules of ancient sages and leave a framework for future generations? We have carefully consulted various musical laws and inquired about He’s method of production, and the situation is as follows: We will produce flutes according to the regulations, using the twelve pitches, one for each pitch, ensuring uniform and harmonious sounds that are easy to play. Regular practice of playing must conform to the musical laws, especially when performing for foreign guests in the temple! Even the ancient musicians Ling Lun, Kui, and Kuang Yuan, even the most exquisite musical tones are challenging to master, but we should still emulate the ancient methods, pursue their essence, and comply with the classics and rituals, ensuring thoroughness in the system. If this can be adopted, please reselect flute craftsmen, choose bamboo for production, and assign it to the Taiyue Bureau for execution. The musical laws of Du Kui, Zuo Yan Nian, and others can be retained, and one flute of Zhengsheng and one of Xiazheng should be kept in the royal court, each flute engraved with the author's name, while the remaining flutes should be returned to the royal court for disposal." The emperor approved.
Next, the memorial continued: We believe that the establishment of musical regulations is to standardize music, to ensure it aligns with the ritual music system, rather than for random creation that undermines traditional music norms. The current production of flutes has strayed from established practices, and it is necessary for us to restore the standards of ancient musical regulations in order to inherit the cultural heritage of the nation. This not only concerns the norms of court music but also relates to the cultural inheritance of the entire country. We suggest selecting skilled artisans anew to make flutes according to the standards of the twelve pitches, ensuring that their pitch and tone quality meet the standards. At the same time, we also suggest preserving some ancient masters' musical regulations as reference and research materials in order to better inherit and develop our country's traditional music culture. We hope that Your Majesty can approve our memorial so that court music can return to a standard that conforms to the ritual music system.
Xu then asked: "Can we make a flute based on the twelve pitches, make twelve flutes, with each hole corresponding to a pitch, and then use it to play music?"
He replied: "The flute in the east wing of the Bureau of Music, which produces the correct pitch, is already four feet two inches long. Now we need to make another one to get its lower note. According to the rules, a flute with a low pitch should be longer, which means it should be over five feet long. I’ve made one before, and it was unplayable. Also, even if the holes on the flute are not calibrated, it does not mean that each hole will correspond exactly to a pitch."
The flute in the Bureau of Music that is four feet two inches long should have the correct pitch of Rui Bin, and the twelve pitches should correspond as court tones. Calculating, the hole for the lower note should correspond to the Da Lu pitch. A Da Lu tone flute typically measures just over two feet six inches; it is impossible for it to be over five feet long. So the musicians in the Bureau of Music, Liu Xiu and Deng Hao, crafted a Da Lu tone flute according to regulations for He to inspect. They played seven pitches, each hole was calibrated, and the sounds matched perfectly. Then they had Hao Sheng play the zither, and Song Tong play the flute, and they performed pieces like "Mixed Attraction" and "Harmony."
He said, "Our family has been making flutes since the time of the Han Dynasty, and it has always been passed down like this. I never knew about this approach. Being able to make the tones match the musical notes Gong, Shang, Jue, and Yu is something I cannot achieve." Hao Sheng, Lu Ji, Zhong Zheng, and Zhu Xia all held the same view.
I asked Mr. He, "The flute has six holes, plus the internal space of the flute body counts as seven. Can you tell me which of these seven holes correspond to the musical notes Gong, Shang, Jue, and Yu? How do you check if the holes of the flute are properly tuned?"
Mr. He replied, "The method passed down by our teacher is to focus on composing music when playing the flute, and agree on which fingering to use for a certain piece, without knowing which of the seven holes correspond to which note. If you want to make a flute, you have to ask a professional flute maker to make it according to the old ways. As long as the flute produces sound, that's sufficient; there's no concern about whether the holes are properly tuned."
According to the records of the Zhou Li, adjusting the musical instruments of metal and stone has strict standards for pitch. Therefore, those who make bells and chimes must first tune the pitch according to the musical scale, and then hang them up. During performances, all musical instruments use the pitch of the bells and chimes as the standard, ensuring that all musical instruments are in tune with the musical scale. However, in the palace banquet hall, there are no bells and chimes to calibrate the pitch, so the flute takes on this role. Other string instruments and songs are based on the flute, so the flute acts as the standard and must also adhere to the musical scale. Mr. He's method relies on intuition and involves arbitrary lengths, and although the sounds produced by the seven holes are consistent, it is unknown which notes they correspond to. The tuning cannot be checked, so only bamboo that can produce sound is chosen for making flutes, which lacks any systematic approach. Therefore, officials from our department, such as Liu Xiu, Deng Hao, Wang Yan, and Wei Shao, collaborated with flute makers to craft flutes. The craftsmen focused on shaping the flutes, while those knowledgeable in musical scales ensured the correct pitch. This collaboration resulted in flutes with standardized shapes and pitches, producing a harmonious and unified sound.
I continued to ask Mr. He, "If one doesn't understand musical theory and only crafts instruments based on intuition, knowing only that there are high and low pitches and a distinction between pure and muddy timbres, how should these pitches be named?" Mr. He replied, "Each time we perform together, we choose different lengths of flutes based on the quality of the singer's voice. For example, if the singing is rather low, we use a three-foot-two flute, which we call 'three-foot-two tune'; if the singing is relatively high, we use a two-foot-nine flute, which we call 'two-foot-nine tune.' This was done during the Han and Wei dynasties and has continued to this day." According to the records in the "Rites of Zhou," when playing six types of instruments, singing in the Da Lü tune corresponds to playing the Huang Zhong pitch; when playing the Tai Cu pitch, it corresponds to singing the Ying Zhong tune, all determined according to musical pitch. However, the method Mr. He mentioned of naming pitches by their lengths, although used during the Han and Wei dynasties, is rather crude and not in line with standards. In our department, people like Liu Xiu and Deng Hao make flutes according to musical pitch; the flute that is three feet two inches long corresponds to the Wu She pitch, and when performing, the musician will say, "Please play Wu She"; the flute that is two feet eight inches and four-tenths long corresponds to the Huang Zhong pitch, and the musician will say, "Please play Huang Zhong." This ensures that the songs and instrument performances adhere to the standards outlined in classical texts, investigating classical musical pitch, making the production appear elegant. The text states, "I want to understand the six pitches, five tones, and eight sounds; these are essential knowledge for statecraft." The "Rites of Zhou" and "National Language" both record the six pitches and six harmonies, while the "Book of Rites" states, "The five tones and twelve pitches mutually serve as the palace tunes." Liu Xin and Ban Gu's "Record of Music and Calendar" also documents the twelve pitches, but only Jing Fang created the sixty pitches. By the time of Emperor Zhang of Han, the method for calculating the sixty pitches had been lost to history. Although Cai Yong recorded Jing Fang's theories, he also said that no one can produce them now. According to ancient texts and the practices of contemporary musicians, the sixty pitches are not practically applicable in music today.
I carefully consulted ancient classics and, following the method of "five tones and twelve pitches working together as the tonal center," crafted twelve flutes, complete with detailed annotations beside the blueprints. Originally, I wanted to simplify the blueprints, but later found it more convenient to directly look at the hole positions on the flutes, so I crafted another flute with holes positioned for Ruibin and Fukong. The method of making this flute is as follows: the Huangzhong flute, its main note corresponds to Huangzhong, the lower tonic corresponds to Linzhong, and the length of the flute is two feet, eight inches, and just over four fen. (The main note is determined by taking Huangzhong as the tonal center, with Guxi as the subtonic. The length of the Huangzhong flute is based on the pitch of Guxi, ensuring its tonal center is precise and balanced, hence the term "correct tone.")
First, let's discuss the tones of the flute. Huangzhong is the tonal center, which is the first hole on the flute. Yingzhong is the lower tonic, in the second hole. Nanlu is the supertonic, in the third hole. Linzhong is the mediant, in the fourth hole. Ruibin is the submediant, in the fifth auxiliary hole. Guxi is the leading tone, in the middle position of the flute. Taicuo is the subdominant note, in the holes towards the back of the flute. The subdominant note is slightly lower than the leading tone and theoretically should be below the leading tone, but because the leading tone is in the middle of the flute, the hole for the subdominant is located above the tonal center, making it sound clearer than the tonal center. In conclusion, the tonal center and subdominant are the main tones, and the other tones are multiples of them; so starting from the tonal center downwards, the lower the hole position, the deeper the sound. This section primarily addresses the positions of the flute holes and their corresponding names. Next, we will talk about how the flute is made and the relationships between the tones.
Next, let's continue talking about the making of the flute. Huangzhong remains the tonic. To make a flute with the Huangzhong tone, first find the position of the tonic note hole. Measure the lengths of the Gu Xi and Huangzhong tones from the top of the flute downwards, add up the lengths of these two tones, then open a hole at this position to get the tonic. The tonic produces the Zhi tone, which means Huangzhong produces Linzhong. Measure the length of the Linzhong tone from the tonic note hole downwards, then open a hole at this position to get the Zhi tone. The Zhi tone produces the Shang tone, which means Linzhong produces Taicu. Measure the length of the Taicu tone from the Zhi hole upwards, then open a hole at this position to get the Shang tone. The Shang tone produces the Yu tone, which means Taicu produces Nanlu. Measure the length of the Nanlu tone from the Shang hole downwards, then open a hole at this position to get the Yu tone. The Yu tone produces the Jiao tone, which means Nanlu produces Gu Xi. Measure the length of the Gu Xi tone from the Yu hole upwards, then open a hole at this position to get the Jiao tone. However, if the hole for the Jiao tone is measured from the Shang hole upwards, the flutist cannot reach it with their left hand; if it is measured from the Yu hole downwards, the flutist cannot reach it with their right hand, so the Jiao tone hole is not opened separately. In ancient times, flute-making methods determined hole positions based on the relationships of tone multiples, ensuring harmony and unity of the tones. The "Guoyu" states: "Using gourd bamboo is beneficial, focusing on convenience of use." Then, we continue. The Jiao tone produces the Bian Gong, which means Gu Xi produces Yingzhong. The Jiao tone hole measured from the Shang tone hole upwards earlier is marked with ink dots, then measure the length of the Yingzhong tone from the ink dots downwards, open a hole at this position to get the Bian Gong tone. The Bian Gong produces the Bian Zhi, which means Yingzhong produces Ruibin. Measure the length of the Ruibin tone from the Bian Gong hole downwards, then open a hole at this position to get the Bian Zhi tone. The twelve-hole flute-making method is based on the tonic, determining the positions of other tone holes based on the multiple or ratio relationships between tones, making it convenient to use, and the methods are all the same.
Let's talk about the modes of the flute. First is the "Xiazheng tuning." Linzhong refers to the fourth hole of the flute. Originally, the Zheng sound of Huangzhong is typically clear, and should be above the Gong sound, but playing the flute often produces a muddy sound, so it is called "Xiazheng." The "Yue Ji" states, "Five sounds, twelve tones are still relative to the Gong," meaning that Xiazheng serves as Gong. Therefore, the Zheng sound in the Zheng tuning is clear, while the Gong sound in the Xiazheng tuning tends to be muddier. Nanlu corresponds to the Shang note, the third hole, which originally was the feather sound of Huangzhong, but now has become the Shang sound of Xiazheng. Yingzhong is Jiao, the second hole, which originally was the Bian Gong of Huangzhong, but now has become the Jiao sound of Xiazheng. Huangzhong represents the Bian Zheng note; in the Xiazheng tuning, Linzhong is Gong. Daliu should be Bian Zheng, but the Huangzhong flute originally does not have the sound of Daliu, so Huangzhong is used instead of Daliu as Bian Zheng. So how do we achieve this? You need to produce the sound of the three holes of Huangzhong, Taicu, and Yingzhong. Huangzhong is relatively muddy, Taicu is relatively clear, and the pitch of Daliu is between the two. Blow these three holes together, with a slight adjustment, and you can get the sound of Daliu Bian Zheng. The method for achieving the Bian Zheng sound in other flutes tuned to Xiazheng is the same. Taicu corresponds to the Zheng note; it is the hole at the back of the flute, which originally was the Shang sound of Zheng tuning, but now has become the Zheng sound of Xiazheng. Guxi is Yu, located at the sound-producing area in the middle of the flute, which originally was the Jiao sound of Zheng tuning, but now has become the Yu sound of Xiazheng. Ruibin is Bian Gong, the additional hole next to the flute, which originally was the Bian Zheng of Zheng tuning, but now has become the Bian Gong of Xiazheng. Thus, in the Zheng tuning, lower hole positions produce muddier sounds, while higher positions in the Xiazheng tuning yield clearer sounds.
Next is the "Qing Jiao Diao." The "Gong" refers to the middle note on the dizi (Chinese bamboo flute), where the sound is produced; in the Zheng Sheng (standard pitch), it corresponds to the Jiao sound, while in the Xia Zheng, it corresponds to the Yu sound. Qing Jiao Diao treats this note as the Gong sound and plays it clearly, which is why it’s called "Qing Jiao." This mode is better suited for playing popular tunes rather than formal, elegant music. Rui Bin corresponds to Shang, which is correct. Lin Zhong corresponds to Jiao, which is incorrect. Nan Lü corresponds to Bian Zheng, which is also incorrect. Ying Zhong corresponds to Zheng, which is correct. Huang Zhong corresponds to Yu, which is incorrect. Tai Cu corresponds to Bian Gong, which is also incorrect. Qing Jiao Diao only has Gong, Shang, and Zheng that correspond to the standard tuning; the other four notes do not correspond correctly and produce relatively muddier sounds. However, through various playing techniques, these notes can be made to sound clear, which is why they are utilized, and the methods remain consistent.
The length of the flute is determined by its tuning. A long flute is eight times the standard length, such as the Rui Bin and Lin Zhong flutes; a short flute is four times the standard length. (The other ten flutes are all four times the standard length.) In reality, the length that can be accommodated in the air is sixteen times for the long flute. (Short flutes are made of bamboo and are suitable for measuring as eight times the millet. If the length does not meet this standard, or if the instrument is not easy to make, the sound may not achieve the desired uniformity and clarity. However, the flute is typically wider at the top and narrower at the bottom, so it cannot be completely uniform, and the sound can only be made as even as possible.) The flute has three tonal modes (one is called Zheng Sheng, one is called Xia Zhi, and one is called Qing Jiao). There are a total of twenty-one variations. (Each tonal mode has seven notes, which are used in combination with each other, resulting in twenty-one variations. Other flutes are also like this.) There are four hidden holes on the flute to facilitate playing. (These four holes are: Zheng Jiao, which is derived from the Shang mode; Bei Jiao, which is near the lower end of the flute; Bian Gong, which is positioned near the tonal center and moves down an octave; Bian Zhi, which is far from the Zhi tonal center and moves up an octave. Some of these holes have a multiple relationship, and some are halves or quarters, all based on the position of the frets on the strings. These four holes are not physically drilled, but their pitch is calculated to determine their position, in order to match the rules of the upper and lower notes, making the sound harmonious and even, and easy to play. Because these holes are hidden, they are called hidden holes.)
Da Lu flute, Zheng Sheng corresponds to Da Lu, Xia Zhi corresponds to Yi Ze, and its length is two feet six inches and six-tenths of a ma.
Tai Su flute, Zheng Sheng corresponds to Tai Su, Xia Zhi corresponds to Nan Lu, and its length is two feet five inches and three-tenths of a ma.
Jia Zhong flute, Zheng Sheng corresponds to Jia Zhong, Xia Zhi corresponds to Wu She, and it is two feet four inches long.
Gu Xi flute, Zheng Sheng corresponds to Gu Xi, Xia Zhi corresponds to Ying Zhong, and its length is two feet two inches and three-tenths of a ma.
Rui Bin flute, Zheng Sheng corresponds to Rui Bin, Xia Zhi corresponds to Da Lu, and its length is three feet nine inches and nine-tenths of a ma. The Bian Gong hole is positioned near the tonal center, so it moves down an octave and a half for easy playing. The Lin Zhong flute is the same.
Lin Zhongdi, Zhengsheng corresponds to Lin Zhong, Xiazheng corresponds to Taicu, with a length of three chi, seven cun, nine fen, and seven mao, making it unique.
Yize flute, Zhengsheng corresponds to Yize, Xiazheng corresponds to Jiazhong, with a length of three chi and six cun. The method for changing the scale is the same as that of the Rui Bin flute, which involves adding one quarter to one quarter.
Nanlv flute, Zhengsheng corresponds to Nanlv, Xiazheng corresponds to Guxi, with a length of three chi and three cun, seven fen, making it unique.
Wusha flute, Zhengsheng corresponds to Wusha, Xiazheng corresponds to Zhonglv, with a length of three chi and two cun.
This flute has exceptional pitch, Zhengsheng corresponds to Huangzhong, Xiazheng corresponds to Ruibin, with a length of two chi, nine cun, nine fen, and six mao plus a little bit.
Huangzhong is the Earth tone scale, represented by the number eighty-one, which is the beginning of the sound. Earth corresponds to Huangzhong because the earth is the most grounded, representing the monarch. When the weather is mild at the end of summer, the gong sound is harmonious. If the gong sound becomes chaotic, it signifies that the country is in turmoil and the monarch is overbearing. The gong sound of Huangzhong is the longest among all the musical scales.
Zheng sound is Fire, calculated by subtracting one third from the gong sound, resulting in the number fifty-four. Fire corresponds to Zheng sound because Zheng sound is clear and bright, representing matters. When the weather is mild in summer, the Zheng sound is harmonious. If the Zheng sound is chaotic, it indicates that matters are deteriorating, leading to suffering for the populace and financial waste.
Shang sound is Metal, obtained by adding one third of the Zheng sound to one third, resulting in the number seventy-two. Metal corresponds to Shang sound because its turbidity is less than that of the gong sound, representing the officials. When the weather is mild in autumn, the Shang sound is harmonious. If the Shang sound is chaotic, it means that the officialdom is corrupt.
Yu sound is Water, calculated by subtracting one third from the Shang sound, resulting in the number forty-eight. Water corresponds to Yu sound because it is the clearest and represents all things. When the weather is mild in winter, the Yu sound is harmonious. If the Yu sound is chaotic, it indicates an economic crisis and a shortage of resources.
The note "角音" corresponds to wood, with one third of the feather note combined with another third, resulting in a numerical value of sixty-four. Wood corresponds to the note "角音" because its clarity and turbidity are balanced, representing the common people. When the weather is mild in spring, the note "角音" is harmonious. If the note "角音" is disordered, it signifies unrest and dissatisfaction among the people. In short, the pitch of various notes corresponds to the five elements, with higher-numbered notes being turbid and lower-numbered notes being clear and bright; the highest note is capped at "宫" and the lowest note is capped at "羽".
In the eleventh month, the musical note corresponds to "黄钟", which marks the beginning of the musical note and has a length of nine inches. In midwinter, as the weather shifts, the musical note adapts accordingly to regulate the six qi and nine virtues. Ban Gu's method is to divide by three and subtract one, deriving "林钟" downwards.
In the twelfth month, the musical note corresponds to "大吕", which Sima Qian did not derive its lower-born musical scale. Its length is four inches and two hundred forty-three fifths of an inch, and its double is eight inches and two hundred forty-three fifths of an inch. In late winter, as the weather shifts, the musical note adapts to support the growth of all living things. By dividing by three and adding one, the "夷则" is derived upwards; Jing Fang's method is to divide by three and subtract one, deriving the "夷则" downwards.
In the first month, the musical note corresponds to "太蔟", with its upper-born musical scale not derived. Its length is eight inches. In early spring, as the weather changes, the musical note adjusts accordingly to aid in the expansion of yang qi and the removal of blockages. By dividing by three and subtracting one, the "南吕" is derived downwards.
In the second month, the musical note corresponds to "夹钟", which is derived from the note "酉音", with a length of three inches and two thousand one hundred eighty-seven fifths of an inch, and its double is seven inches and two thousand one hundred eighty-seven fifths of an inch. In mid-spring, as the weather changes, the musical note adjusts to regulate subtle shifts in climate. By dividing by three and adding one, the "无射" is derived upwards; Jing Fang's method is to divide by three and subtract one, deriving the "无射" downwards.
In the third month, the central note in the musical note is "姑洗", which is the upper-born note of "酉", with a length of seven inches and nine fifths of an inch. By the end of spring, this note will come to fruition, so everything should be kept clean and tidy, gods should be honored, and guests should be welcomed. By dividing by three and subtracting one, the "应钟" is derived downwards.
Simply put, in March, there is a musical scale called "Gu Xi" that is seven and one-ninth inches long. As spring comes to an end, this musical scale takes effect, so people clean up, offer sacrifices to the gods, and entertain guests. Two-thirds of the length of this musical scale can obtain the length of the next musical scale called "Ying Zhong."
In April, the musical scale called Zhong Lu, which is associated with the Hai, has a length of three inches and 6,487/19,683 of an inch. Twice this length is six inches and 12,974/19,683 of an inch. As the summer begins, this musical scale will come into play, so the righteousness should be promoted.
In May, the musical scale is Rui Bin, which is a scale born above Hai, with a length of six inches and twenty-six parts of one inch. By the middle of summer, this musical scale will come into play, so people should remain calm and engage in offerings and exchanges. For every three parts, subtract one to yield Da Lu; for every three parts, add one according to Jing Fang to yield Da Lu.
In June, the musical scale is Lin Zhong, which is a scale born under Chou, with a length of six inches. By the end of summer, this musical scale will take effect, so all things should develop in accordance with rules and regulations, and everything should follow the principles carefully. Add one part for every three parts to give rise to Tai Cu.
In June, the musical note is "Lin Zhong," which is six inches in length. At the end of summer and the beginning of autumn, this musical note takes effect, so everyone should abide by the rules and regulations and be responsible. Three-quarters of it can be used to obtain "Tai Cu."
In July, the musical note is "Yi Ze," which is derived from "Chou Shang," measuring five inches and seven hundred twenty-nine parts of a unit, totaling four hundred fifty-one parts. At the beginning of autumn, this musical note will be realized, so nine poems should be sung to ensure the people live in peace and prosperity, without any worries. Three parts loss one, giving rise to "Jia Zhong"; Jing Fang three parts gain one, giving rise to "Jia Zhong." Two-thirds or three-quarters can be used to obtain "Jia Zhong."
In August, the musical note is "Nan Lu," which is derived from "Mao Xia," measuring five inches and a third. In the middle of autumn, this musical note will be realized, so the beauty of autumn should be celebrated. Three parts gain one, giving rise to "Gu Xi." Three-quarters of it can be used to obtain "Gu Xi."
In September, the musical note is "Wu She," which is derived from "Mao Shang," measuring four inches and six thousand five hundred twenty-four parts, with a total of sixteen thousand five hundred sixty-one parts. At the end of autumn, this musical note will be realized, so the virtues of the sages should be promoted as a model for others. Three parts loss one, giving rise to "Zhong Lu"; Jing Fang three parts gain one, giving rise to "Zhong Lu." Two-thirds or three-quarters can be used to obtain "Zhong Lu."
In October, the pitch "Yingzhong" is measured as four inches and twenty-seven and a half minutes (or 20 minutes). At the beginning of winter, this pitch will take effect, so various tools must be used reasonably to restore vitality to all things. Three parts yield one, resulting in Ruibin above.
October is "Yingzhong," measuring four inches and one hundred and twenty-seven and a half minutes (or 20 minutes). When early winter comes, this musical pitch comes into effect, so various tools must be used reasonably to restore vitality to all things. Three-quarters of it can produce "Ruibin."
Confucian scholars such as Huainanzi, Jing Fang, and Zheng Xuan studied music and calendars, all believing in the relationship of mutual generation among pitches. For example, Ruibin produces the Great Lu above, measuring eight inches plus two hundred and forty-three and a half minutes by one hundred and four; Yi leads to Jiazhong above, measuring seven inches plus one thousand one hundred and eighty-seven and a half minutes by one thousand seventy-five; Wu She produces Zhong Lu above, measuring six inches plus nineteen thousand six hundred and eighty-three and a half minutes by twelve thousand nine hundred and seventy-four. The lengths of these three pitches are all doubled compared to the measurements calculated by Sima Qian and Ban Gu, while others remain the same. This concept is referred to as the "six ways" by Lingzhou Jiu, which are used flexibly according to needs: Yang, Shen, Fu, Chu, San, and Yue. Adjusting according to actual circumstances is the method of assistance.
The fundamental principle of sound is harmony and balance. Increase means doubling, decrease means halving, in order to maintain the original sound. Therefore, the principle of mutual generation between high and low pitches is true, and the application of heavy pitches aligns with seasonal changes. Ruibin's heavy pitch generation is exactly in line with the actual quantity used, so the music and calendar are derived in this way; however, this does not represent the fundamental principle of mutual generation.
Yang Ziyun said, "Sound originates from the sun (with Jia (角) as the angle, Yi (乙) as the second note, Bing (丙) as the Zhi (徵), Ding (丁) as the feather, and Wu (戊) as the palace). Music theory is derived from the stars (with Zi (子) as the yellow bell, Chou (丑) as the big Lu and so on). Sound is based on its nature, while music theory is based on harmonious sound, which should be calibrated using musical tubes and bells to ensure sound clarity. When sound and music theory are coordinated, the eight sounds are produced." Gong (宫), Shang (商), Jue (角), Zhi (徵), Yu (羽) are called the five sounds; Jin (金), Shi (石), Pao (匏), Ge (革), Si (丝), Zhu (竹), Tu (土), Mu (木) are called the eight sounds; harmonious sound is called the five melodies. When Yin and Yang are harmonious, favorable conditions will arise; when musical harmony aligns with cosmic energy, bad omens will be eliminated. Therefore, on the winter solstice and summer solstice, the emperor will convene eight esteemed scholars in the court, set up the eight sounds, listen to whether the musical instruments are harmonious, measure the length of the sun's shadow, observe the timing of the musical instruments, weigh the soil residue and charcoal, to observe the changes of Yin and Yang. During the winter solstice, if the Yang energy is verified, bad omens will be eliminated, so the music sounds very clear, the sun's shadow is longest, the yellow bell's rhythm is smooth, the soil residue is light, and the balance tilts upward. During the summer solstice, if the Yin energy is verified, the music sounds muddier, the sun's shadow is shortest, the rhythm of the Rui Bin is smooth, the soil residue is heavy, and the balance tilts downward. Within these five days, the eight esteemed scholars will report according to the observed situation, and the Grand Historian will document and submit the findings. If the results align with expectations, it indicates harmony; if not, divination will be conducted.
The ancient method of measuring qi is as follows: first, build a three-tiered structure, close the doors and windows tightly, seal the walls and crevices with mud, and then hang thick curtains. Inside the structure, place wooden cases, with each solar term corresponding to a case, the cases being higher on the outside and lower on the inside, arranged according to the direction of the solar term, and place a qi tube on the case. Fill the qi tube with reed ash at the inner end, then observe the ash on the qi tube: if the ash is blown away, it means the qi has arrived; if the ash is scattered, the qi is in motion; if the ash does not move, it may be due to a person or wind blowing. In the palace, a jade qi tube is used, and measurements are taken only during the winter and summer solstices. Lingtai employs bamboo qi tubes. According to Yang Quan's notes: "Use bamboo from Jinmen Mountain in Yiyang County, Hongnong, and reed ash from Henan." There are also accounts of placing the qi tube in the house, burying it underground according to the twelve shichen, with the opening of the tube flush with the ground, filling the qi tube with reed ash, covering it with silk; the ash shifts when the qi arrives, causing the silk to move as well. Slight movement represents harmony, violent movement represents a weak ruler and strong ministers; no movement represents a harsh and cruel ruler.
Regarding the correction of length standards, the "Book of Han" records it in great detail. In the ninth year of the Tai Shi era of Emperor Wu of Han, the Minister of the Imperial Secretariat, Xun Xu, corrected the instruments of the grand music and discovered that the eight tones were not harmonious. This led to the realization that from the Eastern Han to the Wei Dynasty, the length of the尺 (chi) had increased by more than four parts compared to its ancient standard. Xun Xu then instructed the official Liu Gong to create an ancient尺 according to the records in the "Rites of Zhou." With this ancient尺, he recast the bronze pitch pipes to adjust the pitch of the instruments. Measuring ancient artifacts with this尺, the dimensions perfectly matched those recorded in the inscriptions. Additionally, tomb robbers in Ji County unearthed the tomb of King Xiang of Wei from the Warring States period and discovered jade pitch pipes and bells from the Zhou Dynasty, whose pitches were almost identical to the newly cast pitch pipes. At that time, some old bells from the Han Dynasty were also found in various places, and they were corrected using the new pitch pipes, resulting in perfectly matching pitches. Xun Xu inscribed a total of 82 characters on the尺, which read: "In the tenth year of the Tai Shi era of Jin, the Imperial Secretariat examined ancient instruments and calibrated the current尺, which is four and a half parts long. The ancient methods calibrated have seven categories: first is the Gu Xie jade律, second is the Xiao Lü jade律, third is the Xi Jing bronze望臬, fourth is the Jin Cuo望臬, fifth is the bronze dǒu, sixth is the ancient coins, and seventh is the Jian Wu bronze尺. Gu Xie is slightly strong, Xi Jing望臬 is slightly weak, the rest are the same as this尺." This尺 was newly made by Xun Xu, while the尺 in common use today was made by Du Kui.
Xun Xu made a new bell, and its pitch was very harmonious with the sounds of ancient instruments; people at the time said it was very precise. Only the Cavalry Attendant Ruan Xian felt that the sound was too high and felt desolate, not a music of a prosperous nation, but rather music of a fallen nation. The sound of a fallen nation is mournful and evokes deep reflection, and its people are troubled. Ruan Xian felt that this pitch did not meet the standards of refined music and worried that it was not the kind of upright, harmonious, and beautiful music, possibly due to the differences in尺 lengths between ancient and modern standards. Later, Ruan Xian passed away, and Emperor Wu felt that Xun Xu's pitch aligned with those of the Zhou and Han Dynasty instruments, leading to its adoption.
Later, while excavating at Shiping, an ancient bronze measuring stick was uncovered, which had nearly corroded away over time, and its dynasty remains unknown. It turned out that this bronze measuring stick was four inches longer than that of Xun Xu. Contemporaries admired Ruan Xian's keen insight, yet no one could grasp his thoughts.
The historical records state: Xun Xu, a figure who spanned a millennium and upheld the systems of countless generations. His measurements were precise, and his music theory was harmonious. It can be said that it was very precise, and there is evidence to support this. However, the people of that time had limited knowledge and only focused on Ruan Xian's statement about a certain measuring stick, ignoring the musical instruments of the Zhou and Han dynasties. They blindly followed Ruan Xian's viewpoint, which is quite absurd! In "Shishuo Xinyu," it is said: "A farmer discovered a jade measuring stick from the Zhou dynasty in the fields, claiming it to be the standard measuring stick of the world. Xun Xu compared it to his own musical instruments, which were all found to be one meter shorter." Additionally, during the reign of Emperor Zhang of Han, the literary historian Xi Jing discovered a jade ruler at Lingdao Shun Ci, which came to be known as the Han official ruler. When compared to Xun Xu's measuring stick, it was four fen shorter than Xun Xu's measuring stick; the Han official ruler and the measuring stick discovered by Shiping were of similar lengths. Furthermore, Du Kui's tuning measuring stick was one chi, four fen, and seven mao longer than Xun Xu's new measuring stick. In the fourth year of the Wei Jingyuan era, when Liu Hui annotated the "Nine Chapters on the Mathematical Art," he stated that during Wang Mang's time, Liu Xin's hu and measuring stick were four fen and five mao shorter than the current measuring stick; compared to the Wei dynasty's measuring stick, the depth of the hu was nine cun, five fen, and five mao, which was the same as Xun Xu's statement that the current measuring stick was four fen and a half longer. After the Yuan Emperor, the measuring stick used in Jiangdong was one chi, six fen, and two mao longer than Xun Xu's measuring stick. In the fourth year of Guangchu, Zhao's Liu Yao cast the Hunyi, and in the eighth year, the Tugui. The measuring stick he used was one chi and five fen longer than Xun Xu's measuring stick. Xun Xu's new measuring stick was primarily for tuning music and didn't see widespread use among the common folk. Therefore, the instruments used in Jiangzuo and by Liu Yao were comparable to those of the Wei dynasty.
In the "Book of Rites", it is recorded that the Li clan was responsible for establishing the standard measuring instruments. This instrument, called *Wu*, has a depth of one foot, with a square inner section, each side measuring one foot, and a circular outer section, with a total volume of one *Wu*. Its "tun" (small opening) has a diameter of one inch, with a volume of one dou; its "er" (large opening) has a diameter of three inches, with a volume of one sheng; it weighs one jun, and it produces a sound that matches the tone of the Huang Zhong. This type of measuring instrument is exempt from taxes. Engraved on top is the inscription: "Carefully designed with a focus on perfection; the standard measuring instrument is complete, available for reference by all countries; to be followed by generations to come, this instrument is the standard." The "Zuo Zhuan" also mentions that before the Qi State, there were four types of measuring instruments: dou, qu, *wu*, and zhong. Four sheng equal one dou, and so on, with four dou making one qu, and sixty-four dou making one zhong.
In simple terms, the ancient system of measuring instruments was quite complex, with sheng, dou, qu, and zhong, progressing step by step. Zheng Xuan calculated the volume of ancient pots (a type of measuring instrument) and found slight discrepancies when compared to the data in the "Nine Chapters on the Mathematical Art". Through calculations, he estimated that the volume of ancient *hu* (a type of measuring instrument) was approximately 1562.5 cubic inches in volume, with a square bottom and cylindrical body, a depth of one foot, and a diameter of about one foot four inches one fen four hao seven miao two hui.
In the "Nine Chapters on the Mathematical Art: Commercial Arithmetic", it is recorded that the volume of a *hu* of millet is 2700 cubic inches, a *hu* of rice is 1627 cubic inches, and a *hu* of beans, peas, hemp, and wheat is 2430 cubic inches. This indicates that in ancient times, when calculating volume, adjustments were made based on the type of grain (fine or coarse) to ensure consistent prices, rather than rigidly using the same volume. Using the *hu* of rice as a standard, this is consistent with the records found in the "Book of Han".
In the fourth year of the reign of Wei Jingyuan, Liu Hui stated while annotating "Nine Chapters on the Mathematical Art: Commercial Calculation" that the standard measure of a "hu" (a unit of volume) at that time had a circular diameter of one foot, three inches, five decimal points, and five hundredths, a depth of one foot, and a volume of one thousand four hundred forty-one point three three cubic inches. During the Wang Mang period, the bronze "hu" as measured by the standards of that time had a depth of nine inches, five-tenths, and five-hundredths, and a diameter of one foot, three inches, six-tenths, eight-hundredths, and seven-thousandths. After applying his own calculation method, Liu Hui found that the volume of the bronze "hu" from the Wang Mang period was approximately nine dou, seven sheng, and a little over four he. Therefore, the "hu" of the Wei Dynasty was relatively larger, and the measuring units were longer; the "hu" of the Wang Mang period was relatively smaller, and the measuring units were shorter.
Speaking of "measuring and weighing," the term "measuring" refers to balance, while "weighing" refers to weight itself. The purpose of measurement is to support weight, achieving a balance between light and heavy. Ancient weighing instruments were known by many names, such as "shu," "du," "chui," "zi," "huan," "jun," "zhuo," "yi," and so on, with different standards in each dynasty. The "Book of Han" states that the naming and system of measurements in the Han Dynasty were very well established, but later underwent numerous modifications, and I don’t know the specifics of those changes. During the Yuan Kang period, Pei Wei believed that medical prescriptions were related to human life, but the weight units at that time were different from those in ancient times, which posed serious risks, so he suggested that the weighing system should be modified, but no one paid him any mind. During Shi Le's eighteen years and seven months in power, while building the Jiande Hall, he discovered a round stone shaped like a water mill, inscribed with the words: “Law Weight Stone, weighing four jun, consistent with the laws of measurement and weighing. Made by the Xin family.” Later, a discussion ensued among everyone, and they concluded that this was an item from the Wang Mang era.
This first paragraph discusses the evolution of ancient weighing instruments and the measurement system, from the various names of weighing instruments to the perfected system in the Han Dynasty, then to later changes and Pei Wei's suggestions, ultimately concluding with the discovery of the Law Weight Stone from the Wang Mang period, leading into the next section. This stone illustrates the significance of measurement and weighing practices in ancient times, as well as the inheritance and changes of the system.
