Ancient people believed that the Gong tone is the foundation of sound, represented by the number 81, belonging to earth because earth is the most opaque, symbolizing the monarch. When the climate is suitable in summer, the Gong tone is harmonious; if the Gong tone is chaotic, it means the country is in chaos and the monarch's arrogance prevails. The Yellow Bell is the Gong tone and also the longest among all the musical notes.
Fire corresponds to the note of Zhi, represented by the number 54, which is two-thirds of the Gong tone. Fire corresponds to Zhi because Zhi is brighter, symbolizing major national events. When the climate is suitable in summer, the Zhi tone is harmonious; if the Zhi tone is chaotic, it means the country's affairs are busy and exhausting.
Metal corresponds to the Shang note, represented by the number 72, which is two-thirds of the Zhi tone plus one-third. Metal corresponds to Shang because Shang is less turbid than the Gong tone, representing the officials. When the climate is suitable in autumn, the Shang tone is harmonious; if the Shang tone is chaotic, it means corruption in the officialdom.
Water corresponds to the note of Yu, represented by the number 48, which is two-thirds of the Shang note. Water corresponds to Yu because Yu is the brightest, representing all things. When the climate is suitable in winter, the Yu tone is harmonious; if the Yu tone is chaotic, it means the country is economically poor.
Wood corresponds to the Jiao note, represented by the number 64, which is two-thirds of the Yu tone plus one-third. Wood corresponds to Jiao because Jiao is moderately clear and turbid, representing the common people. When the climate is suitable in spring, the Jiao note is harmonious; if the Jiao note is chaotic, it means the people voice their grievances.
In summary, the hierarchy of musical notes aligns with the five elements, with higher-numbered notes being more turbid and lower-numbered notes being brighter; the highest note does not surpass the Gong tone, and the lowest note will not be lower than Yu.
In the eleventh month, the musical note is the Yellow Bell, signifying the start of the musical scale, with a length of nine inches. During midwinter, the climate changes in accordance with the Yellow Bell musical note, in order to regulate the yin and yang, the six energies, and the nine virtues. Ban Gu believed that by subtracting a third, one can derive the Lin Bell.
In December, the tone corresponds to the Great Lu; however, Sima Qian did not document the pitches that fall below the Great Lu. Its length measures four inches and two hundred forty-three and five hundred fifty-two parts of an inch. Twice that is eight inches and two hundred forty-three and one hundred four parts of an inch. In late winter, the climatic changes align with the Great Lu, facilitating the growth of all living things. Adding three parts to one can yield the Yi Ze; Jing Fang believed that subtracting three parts from one can also derive the Yi Ze.
In January, the tone corresponds to the Great Cang, but there are no records of pitches above the Great Cang, measuring eight inches. In early spring, the climatic changes correspond to the Great Cang, assisting the emergence of Yang energy and eliminating stagnation. Subtracting three parts from one can derive the South Lu.
In February, the tone corresponds to the Jia Zhong, which is the tone derived from the You position below, measuring three inches and two thousand one hundred eighty-seven and one thousand six hundred thirty-one parts of an inch. Twice that is seven inches and two hundred eighty-seven and one thousand seventy-five parts of an inch. In mid-spring, the climatic changes correspond to the Jia Zhong, which helps regulate subtle climate changes. Adding three parts to one can derive the Wu She; Jing Fang believed that subtracting three parts from one can also derive the Wu She.
In March, the tone used is Gu Xia, which is the tone born from the You position above, measuring seven inches and nine-tenths of an inch. By late spring, this tone will manifest, so it is essential to organize everything, honor the deities, and welcome guests. By applying the method of subtracting three parts from one, we can derive the next pitch, Ying Zhong.
In simple terms, in March, we need to use the Gu Xia tone. It measures seven inches and nine-tenths of an inch long, a tone born from the You position. As spring is coming to an end, this tone will be appropriate, so we must properly organize various items, worship the gods, and entertain guests. Then, using the "three parts subtracted from one" method, we can calculate the next tone, "Ying Zhong."
In April, the tone used is the Zhong Lu, which is the tone born from the Hai position below, measuring three inches and ten thousand nine hundred sixty-three parts of six thousand four hundred eighty-seven. Its double is six inches and ten thousand nine hundred sixty-three parts of ten thousand two hundred ninety-four. By the start of summer, this tone will become relevant, so it is necessary to promote the energy of harmony.
In April, the tuning Zhonglü is used, originating from the Hai position, with a length of 19683/6487 inches, doubling to 19683/2974 inches. With the arrival of early summer, this scale becomes relevant, spreading harmony throughout heaven and earth. In May, the tuning Ruíbīn is used, which originates from the Hai position and has a length of 6.81/26 inches. As midsummer arrives, this scale will be realized, bringing tranquility to people's spirits and prompting banquets where toasts are exchanged. Using the method of reducing three parts to one, one can derive the Da Lü scale; similarly, Jing Fang's method of increasing three parts to one can also yield the Da Lü scale. In June, the tuning Línzhōng is used, originating from the Chou position and having a length of 6 inches. As late summer approaches, this scale will come into its own, encouraging harmony in all things and ensuring everything is upright and pure. By using the method of increasing three parts to one, the Tài Cù scale can be derived. In July, the tuning Yízé is used, originating from the Chou position and having a length of 5729/451 inches. As early autumn arrives, this scale will come into its own, so it is necessary to recite the Nine Songs to bring peace to the people without any deficiencies. Using the method of reducing three parts to one, one can derive the Jiāzhōng scale; similarly, Jing Fang's method of increasing three parts to one can also yield the Jiāzhōng scale.
In July, the scale used is Yi Ze, which comes from the Chou position, with a length of four hundred fifty-one over seven hundred twenty-nine inches. Early autumn has arrived, and this musical scale is in season, so we should recite the "Nine Songs" to ensure that the people live and work in harmony and without burdens. Using the method of "three parts loss one" or Jingfang's "three parts gain one," we can calculate the Jiazhong scale.
In August, the scale used is Nan Lü, which is the scale derived from the Mao position, with a length of five and one-third inches. Mid-autumn has arrived, and this scale will come to fruition, so we should praise the beautiful scenery of autumn. Using the method of "three parts gain one," we can deduce Gu Xia.
In September, the scale used is Wu She, which is the scale derived from the upper Mao position, with a length of four inches and six thousand five hundred sixty-one out of six thousand five hundred twenty-four. Late autumn is upon us, and this scale will come to fruition, so we should promote the virtues of the sages and set a good example for the people. Using the method of "three parts loss one," we can deduce Zhong Lü; Jingfang using the "three parts gain one" method can also deduce Zhong Lü.
In October, the scale used is Ying Zhong, which is the scale born from the lower Si position, with a length of four and twenty-seven-twentieths inches. Early winter has arrived, and this scale will come to fruition, so we should ensure that instruments are equally applicable, to let everything come back to life. Using the method of "three parts gain one," we can deduce Rui Bin.
The Huainanzi, Jing Fang, and Zheng Xuan, these Confucian scholars who studied music and calendars, all believed that musical tones are in a relationship of mutual generation. For example, Rui Bin generates Dalu from above, with a length of eight inches plus one two-hundred forty-third of one hundred four; Yize generates Jiazong from above, with a length of seven inches plus one thousand one hundred eighty-seventh of one thousand seventy-five; Wushe generates Zhonglu from above, with a length of six inches plus nineteen thousand six hundred eighty-three ten-thousandths of twelve thousand nine hundred seventy-four. The lengths of these three musical tones, compared to those calculated by Sima Qian and Ban Gu, are all twice as long, and the others are the same. This is what Lingzhou Jiu refers to as the "Six Ways of Interval," where Yang, Shen, Fu, Chu, San, and Yue are applied flexibly as needed. Adaptability and balance, adjusting according to actual conditions, is this method of guidance. The essence of all sounds is rooted in harmony and balance; increasing doubles the sound, while decreasing halves it, thus ensuring consistency with the fundamental tone. Therefore, the principle of mutual generation is one of rising and falling; the idea of "heavy rising" is applied based on seasonal changes. Rui Bin's heavy rising precisely fits the actual quantity used, so this explains the origin of music, but it is not the fundamental principle of mutual generation.
Yang Ziyun said: "Sound arises from the sun (referring to Jia and Ji as Jiao, Yi and Geng as Shang, Bing and Xin as Zhi, Ding and Ren as Yu, Wu and Gui as Gong), while music arises from the stars (referring to Zi as Huangzhong, Chou as Dalu, etc.). Sound is based on its nature, and music is based on harmonious sound (it should utilize instruments like bells to regulate the clarity and quality of the sound). When sound and music are harmonious, the eight tones are produced." Gong, Shang, Jiao, Zhi, Yu, these are called the five tones; Jin, Shi, Pao, Ge, Si, Zhu, Tu, Mu, these are called the eight tones; when sound is harmonious and pitches are well-coordinated, this is called the five forms of music.
Harmony of yin and yang brings beauty to the scene; when the natural laws align, the ashes vanish. Therefore, on the winter and summer solstices each year, the emperor would summon eight capable individuals to the palace, set up eight types of musical instruments, listen to whether the music resonates clearly, measure the length of the shadow cast by the sun, observe the rhythms of the clock, weigh the soil and charcoal, and observe the changes in yin and yang. During the winter solstice, when the yang energy manifests, the ashes disappear, so the music resonates clearly, the shadow is longest, the pitch of the yellow bell flows smoothly, the soil ash is light, and the balance beam rises. During the summer solstice, when the yin energy manifests, the music turns muddled, the shadow is shortest, the rui bin's pitch flows smoothly, the soil ash is heavy, and the balance beam droops downward. Over the five days before and after, the eight experts report their findings, and the Grand Historian presents the findings to the emperor. If the results meet expectations, it indicates harmony; otherwise, divination is needed to assess fortune or misfortune.
In ancient times, the method for gauging qi was as follows: first, build a three-story house with tightly shut doors and windows, apply a layer of mud to both the inside and outside, and then hang thick curtains. Inside the house, place a wooden table with wooden rulers representing the twelve pitches, arranged with the inner side lower than the outer side according to the directions, and place some reed ash at the inner end of each wooden ruler. Then observe: if qi arrives, the reed ash gets blown away; if qi disperses the ash, it signals movement; if it is moved by a person or wind, the ash will accumulate together. In the palace, jade instruments representing the twelve pitches are used to measure qi, and measurements are only taken during the winter and summer solstices. The spiritual platform employs bamboo pitch pipes. Yang Quan's notes record: "Use bamboo from Jinmen Mountain in Yiyang County, Hongnong, for the pitch pipes, and reed ash from He Nei." Some also say to place the pitch pipes inside the house, bury them according to the twelve hours, with the mouth of the pipe level with the ground, fill the pipes with reed ash, and cover them with silk; when qi arrives, it will blow the ash and silk. A gentle vibration signifies harmony, a strong vibration suggests a weak ruler and strong subjects; if there is no movement at all, it signals the ruler's oppressive tyranny.
Regarding the correction of length units, the "Book of Han" records it in great detail. In the ninth year of the Tai Shi era during the reign of Emperor Wu of Han, Xun Xu, the supervisor of the Central Secretariat, corrected the musical 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 foot had increased by more than four fen compared to ancient times. Xun Xu then instructed Liu Gong, the official in charge of writings, to remake the foot according to the standards of the "Rites of Zhou," which is the ancient foot. Following this, he had the bronze tuning pipes recast according to the standards of the ancient foot to adjust the tuning of the instruments. When this foot was used to measure ancient artifacts, the dimensions matched perfectly with those recorded in inscriptions. Additionally, tomb robbers in Jiyun County unearthed the tomb of King Xiang of Wei from the Warring States period and discovered ancient jade tuning pipes, bells, and chimes from the Zhou Dynasty, whose tones were very similar to the newly cast tuning pipes. At that time, various counties also found some old bells from the Han Dynasty, which were corrected using the newly cast tuning pipes, and their tones matched. Xun Xu inscribed a total of eighty-two characters on the foot, which read: "In the tenth year of the Tai Shi era of Jin, the supervisor of the Central Secretariat verified ancient artifacts and corrected the current foot, which is four and a half fen longer. The corrected ancient standards include seven types: 1. Gu Xia jade tuning pipe; 2. Xiao Lü jade tuning pipe; 3. Xi Jing bronze望臬; 4. Jin Cuo望臬; 5. bronze斛; 6. ancient coins; 7. Jianwu bronze foot. The Gu Xia jade tuning pipe is slightly higher, the Xi Jing bronze望臬 is slightly lower, while the rest are the same as this foot." This foot was newly made by Xun Xu, while the foot currently in use was made by Du Kui.
Xun Xu invented a new concept and created a new set of musical scales, which harmonized well with the sounds of ancient instruments. People at that time praised him for his meticulous work. However, a cavalry officer named Ruan Xian was critical of it. He said high-pitched sounds evoke sadness and desolation, not the music of a thriving nation, but rather a harbinger of a fallen one. He remarked that the music of a fallen nation is always mournful and brings tears to people's eyes because the country is in trouble and the people are suffering! The sound now does not meet the standards of orthodox court music. I fear it lacks the noble character and harmonious quality expected, probably due to the discrepancies between ancient and modern measurement standards. Later, Ruan Xian passed away. Emperor Wu thought that Xun Xu's new musical scales matched those of the Zhou and Han dynasties, so he officially adopted them. Later, when digging in Shiping, an ancient bronze ruler was unearthed, nearly decayed, and it was unknown from which dynasty it belonged. Upon measurement, it was found to be four inches longer than Xun Xu's ruler! This revelation finally led everyone to acknowledge Ruan Xian's foresight, but sadly, he was not there to witness it.
The historical records say: "Xun Xu, he transcended a thousand years, inherited the methods of the past dynasties, the lengths are suitable, and the musical theory is accurate, truly meticulous and trustworthy! However, people back then had a limited perspective, just using a ruler of unknown origin, overlooked the musical instruments from both the Zhou and Han Dynasties, and made arbitrary judgments, which is utterly ridiculous!" In "Shishuo Xin Yu," it is also mentioned that a farmer dug up a jade ruler from the Zhou Dynasty in the field, claiming it to be the most standard ruler in the world. Xun Xu compared it with the musical instruments he made and found that they were all one meter short! Also, during the reign of Emperor Zhang of Han, the literary historian Xi Jing from Lingdao Shun Ci found a jade tuning ruler, used it as a ruler, and it has long been said to be the official ruler of the Han Dynasty. Compared to Xun Xu's ruler, it was four fen shorter; the Han Dynasty's official ruler and the one excavated in Shiping were of similar lengths. In addition, Du Kui's tuning ruler was one chi, four fen, and seven mao longer than Xun Xu's new ruler. In the fourth year of Wei Jingyuan, when Liu Hui annotated "Nine Chapters on the Mathematical Art," he said: during the time of Wang Mang, the ruler used by Liu Xin was four fen and five mao shorter than the current ruler; compared with the ruler of the Wei Dynasty, the depth of the ruler was nine cun, five fen, and five mao shorter; this aligns with what Xun Xu stated, "the current ruler is four fen and a half longer." After the Yuan Emperor, the ruler used in the Jiangdong region was one chi, six fen, and two mao longer than his. In the fourth year of Guangchu of Zhao Guo, Liu Yao cast the Hunyi, and in the eighth year cast the Tugui; his ruler was one chi and five fen longer than Xun Xu's ruler. Xun Xu's new ruler was primarily used for tuning, and it wasn't widely adopted among the general populace, so the instruments used in Jiangdong and by Liu Yao were similar to those of the Wei Dynasty.
The "Rites of Zhou" states: "The Li clan is responsible for making the measuring vessel called 'Lu'. It is one foot deep, with an interior shaped like a square with a side length of one foot, and an exterior that is circular, with a volume equivalent to one Lu. Its 'tui' (small mouth) has a diameter of one inch, with a volume equivalent to one Dou; its 'er' (large opening) has a diameter of three inches, with a volume equivalent to one Sheng. A Lu weighing one Jun (a weight unit) produces a sound resembling Huangzhong (a musical tone). This measuring vessel is tax-exempt. It is inscribed with the following: 'In due time, through careful thought, to achieve its utmost. The fine measure having been established, to observe the four nations. To eternally initiate what follows, this vessel maintains the standard.'" This passage primarily discusses the production standards and inscriptions of an ancient measuring vessel—Lu.
The "Zuo Zhuan" of the "Spring and Autumn Annals" records: "In the past, the state of Qi had four types of measuring vessels: Dou, Qu, Lu, and Zhong. Four Sheng make one Dou, four Dou make one Qu, four Qu make one Fu, and ten Fu make one Zhong." This indicates that the ancient capacity units were hierarchical, progressing from Dou to Qu, then to Fu, and finally to Zhong, with increasing capacity. The text also mentions that four Dou equal one Qu, which is six Sheng; four Qu equal one Fu, which is sixty-four Sheng; and ten Fu equal one Zhong, which is six hundred forty Sheng. Zheng Xuan believes that the side length of the Fu is one foot, with a volume of one thousand cubic inches, which slightly differs from the calculations in "Nine Chapters on the Mathematical Art: Grain," falling short by two Sheng, eighty-one Fen, and twenty-two Li units. Through calculations, we can estimate that the volume of the ancient Hu is approximately one thousand five hundred sixty-two point five cubic inches, with a side length of one foot, an external circular shape, and a diameter of approximately one foot, four inches, one-tenth, four hao, seven miao, and two hu.
In the "Nine Chapters on the Mathematical Art - Commerce," it is recorded that a hu of millet has a volume of 2,700 cubic cun; the volume of a hu of rice is 1,627 cubic cun; and the volume of a hu of beans, peas, hemp, and wheat is 2,430 cubic cun. This indicates that the methods for calculating the volume of different grains vary due to their differing densities, which is calculated for the convenience of trade. Using the hu of rice as a standard, it is consistent with the records in the "Book of Han." In the fourth year of Wei Jingyuan, when Liu Hui annotated the "Nine Chapters on the Mathematical Art - Commerce," he stated: "The current official hu for agriculture has a diameter of 1 chi, 3 cun, 5 fen, and 5 hao, a depth of 1 chi, and a volume of 1,441 cun and one-tenth of a third. The copper hu from the time of Wang Mang, according to today's measurements, has a depth of 9 cun, 5 fen, and 5 hao, and a diameter of 1 chi, 3 cun, 6 fen, 8 hao, and 7 huo. According to my calculation method, the volume of the hu from the time of Wang Mang is approximately 9 dou, 7 sheng, and 4 he." It can be seen that the hu of the Wei Dynasty is relatively large, and the ruler is also relatively long; the hu of the time of Wang Mang is relatively small, and the ruler is also relatively short.
Here, "heng" refers to balance, while "quan" denotes weight. The purpose of the balance is to support weight and achieve equilibrium for items. Ancient balances had many names, including shu, lei, chui, zi, huan, jun, lv, and yi, and the standards of each dynasty differed. The "Book of Han" records that the names and methods of using balances during the Han Dynasty were quite comprehensive, but these were modified later, and I am unclear on the specifics of those changes. During the Yuan Kang period, Pei Wei believed that medicinal formulas were related to people's lives, but at that time, the measurement units differed from those used in ancient times, causing great harm. Therefore, he suggested that the weights and measures system be standardized, but this suggestion was not adopted.
Shi Le was in power for eighteen years; in July of 332 AD, while constructing Jiande Palace, he discovered a round stone resembling a water millstone, bearing the inscription: "Lu Quan Stone, weighing four jun, in accordance with the law of measurement." After some discussion, it was concluded that this artifact originated from the time of Wang Mang.
