The "Book of Documents" says: "Thus unified weights and measures were achieved, so that people near and far could all follow the rules and establish trust among the people." From the time when Fuxi drew the Bagua, the concept of numbers emerged, and by the time of the Yellow Emperor, Yao, and Shun, it was already quite perfected. The Xia, Shang, and Zhou dynasties all followed ancient systems, with very clear laws and regulations. After the decline of the Zhou dynasty and the confusion of the official system, Confucius presented methods of governing the country to later monarchs, saying: "Carefully calibrate the balance, meticulously inspect the laws and regulations, rectify the lax official positions, and appoint talented individuals who have been neglected, so that governance in all directions can proceed smoothly." After the establishment of the Han dynasty, Zhang Cang, the Marquis of Beiping, initially handled legal matters, and during the reign of Emperor Wu of Han, the music officials conducted a study of laws and calendars. During the reign of Wang Mang, who held power during the Yuan Shi period, wanting to show off his reputation, he gathered more than a hundred people from all over the country who understood timekeeping, and assigned Xihe, Liu Xin, and others to organize memorials in great detail. Therefore, we have removed the false rhetoric and retained only the correct principles, writing this text. This article mainly discusses five points: first is number systems, second is musical harmony, third is accurate measurement, fourth is calibrated measures, and fifth is calibration. These five aspects interact and change with each other, using numbers in a complex manner, comparing past and present, emulating the laws of the natural world, designed to be intuitive and harmonious, and using classics for verification, all of which have been rigorously tested and proven consistent.
Numbers, from one to ten thousand, are used to calculate things and conform to the natural order. The "Book of Documents" states, "You must calculate first." It originated from the musical scale of the Yellow Bell, starting from one, multiplied by three, and then accumulating the results of three multiplications, all the way to the twelve earthly branches, totaling 177,147, thus completing the five-element system. The calculation tool at that time was a bundle of 271 bamboo sticks, with a diameter of one fen and a length of six inches, arranged in a hexagonal shape, called a "grip." The diameter symbolizes the Qian hexagram, representing the Yellow Bell's pitch, while the length symbolizes the Kun hexagram and the length of the Lin Bell. The calculation method uses the number fifty, central to the cosmology of the *Yijing*, taking forty-nine of it to form six yang lines, thus illustrating the cyclical nature of the hexagrams. Calculating calendars, generating musical scales, making instruments, drawing circles and squares, weighing light and heavy, calibrating measuring tools and instruments, exploring profound principles, tracing distant origins—nothing is done without numbers. Measuring lengths will not be off even a tiny bit, measuring quantities will not be off by a small margin, weighing light and heavy will not be inaccurate. Starting from one, coordinating with ten, extending to a hundred, greater than a thousand, deriving to ten thousand—all methods are found within arithmetic. This should be taught in schools nationwide, with the responsibility resting on the Grand Historian, while Xihe oversees it.
Sounds are composed of the five tones: Gong, Shang, Jiao, Zhi, and Yu. The purpose of making music is to coordinate the sounds of these eight musical instruments, purify the spirit, maintain righteousness, and thus change customs and habits. The eight musical instruments are: the xun made of clay; the sheng made of gourd; the drum made of leather; the wind instrument made of bamboo; the string instrument made of silk; the chime made of stone; the bell made of gold; and the zhu made of wood. When the five tones are harmonious and the sounds of the eight musical instruments are coordinated, music is complete.
The meaning of "商" is "standard," indicating that once things are successful and mature, rules and regulations can be established. The meaning of "角" is "budding," suggesting that all things sprout from touching the ground, much like the antlers of a deer. The meaning of "宫" is "central tone," as it resides at the center and spreads sound in all directions; it is the beginning of music and the foundation of the other four tones. The meaning of "徵" is "auspicious," signifying that all things flourish and prosper. The meaning of "羽" is "enveloping," representing the gathering of all things and the covering of the heavens and the earth.
Sound is generated with 宫 as its central tone, 角 as its budding force, 徵 as its flourishing aspect, 商 as its established order, and 羽 as its all-encompassing presence. Let's match up these five tones with the five elements, five virtues, and five matters: 角 corresponds to wood, benevolence, and appearance; 商 corresponds to metal, righteousness, and speech; 徵 corresponds to fire, propriety, and sight; 羽 corresponds to water, wisdom, and hearing; and 宫 corresponds to earth, trust, and thought.
From the perspectives of ruler, minister, people, matters, and things, 宫 corresponds to the ruler, 商 corresponds to the minister, 角 corresponds to the people, 徵 corresponds to matters, and 羽 corresponds to things. The interplay of these tones symbolically represents the order of ruler, minister, people, affairs, and the cosmos.
Five tones are the foundation of music, all stemming from the Yellow Bell. A nine-inch length determines the Gong tone; the Shang, Jiao, Zhi, and Yu tones are derived by adjusting this length. Nine and six are intertwined, reflecting the yin and yang balance. These tones govern the energies of heaven, earth, and everything. There are twelve tones, with six representing the yang and six representing the yin. The tones used to govern the energies are known as the Yellow Bell, Da Lu, Gu Xi, Rui Bin, Yi Ze, and Wu She. The Lu tones complement the yang energy and promote the energy of all things, known as Lin Zhong, Nan Lu, Ying Zhong, Da Lu, Jia Zhong, and Zhong Lu. This reflects the principle of the "Three Harmonies," which is said to have been invented by the Yellow Emperor.
The Yellow Emperor sent Ling Lun to the western side of the Kunlun Mountains in Daxia, where he found bamboo in Jiegu with uniform joints and hole sizes. He cut and played the section between two joints, establishing the Yellow Bell Gong tone. He crafted twelve bamboo pipes to discern the phoenix's calls. The male phoenix produced six tones, and the female phoenix also had six tones, all of which could be derived from the Yellow Bell Gong tone, forming the basis of the pitch system. Only in times of peace and harmony, when heaven and earth's energies aligned to create a harmonious wind, could the twelve pitches be accurately determined.
Yellow, the color of the emperor's robes, represents the center; Bell refers to seeds. The center of the celestial number is five, symbolizing sound, with the fundamental tone being Gong. There is nothing greater than Gong in the five tones. The center of the terrestrial number is six, representing tones that have shapes and colors, with yellow being the most prominent of the five colors. Therefore, the yang energy sows in the yellow spring, nurturing all things, and is the foundation of the six energies. Yellow is used to name the original energy and tones because it represents the Gong tone. The Gong tone uses nine as its base, but six governs its variations, constantly shifting and cycling through six positions. It starts in November (the Zi month).
These terms refer to the twelve lü, or pitch pipes, used in ancient Chinese music theory to represent the cyclical interplay of Yin and Yang throughout the year.
Da Lu represents the culmination of receptive energy, its gathering strength supporting the active energy of Huang Zhong and fostering the first stirrings of spring. It corresponds to December.
Tai Zu signifies the flourishing of active energy, resonating with the earth to promote growth and vitality. It corresponds to January.
Jia Zhong embodies the mingling of receptive energy with the support of Tai Zu, spreading energy in all directions and nurturing development. It corresponds to February.
Gu Xi symbolizes the cleansing power of active energy, revitalizing all things and encouraging robust growth. It corresponds to March.
Zhong Lu reflects the emergence of subtle receptive energy, still nascent, positioned centrally to assist Gu Xi in promoting active energy and ensuring harmonious growth. It corresponds to April.
Rui Bin conveys the notion of continuity and guidance, where active energy begins to lead receptive energy, providing ongoing nourishment to all forms of life. It corresponds to May.
Lin Zhong denotes the role of the monarch, where receptive energy takes on significant responsibilities, aiding Rui Bin (active energy) in guiding the flourishing of all things. It corresponds to June.
Yi Ze represents the adherence to natural laws, where active energy calms receptive energy to protect vulnerable life forms. It corresponds to July.
Nan Lu indicates the gathering of receptive energy to support Yi Ze, taking on the vital task of ripening all life. It corresponds to August.
Wang She expresses a sense of completion, where active energy fulfills its mission, allowing receptive energy to gently recede, completing the cycle and preparing for renewal. It corresponds to September.
Ying Zhong signifies the response of receptive energy to Wang She, preserving all forms and blending with active energy, setting the stage for the coming year's planting. It corresponds to October.
Speaking of the "Three Harmonies," it refers to the three operating principles of Tian Dao, Di Dao, and Ren Dao. In November, it corresponds to the initial nine of the "Qian" hexagram in the *I Ching*, with the yang energy dormant beneath the earth, all of nature stirring to life, nourished by the moon's energy. Thus, the Huang Zhong musical pipe represents Tian Dao, measuring nine inches in length. The number nine signifies perfect balance, the foundation of all creation. The *I Ching* states, "The way of Heaven is Yin and Yang."
In June, it aligns with the initial six of the "Kun" hexagram in the *I Ching*, where yin energy is nourished by the sun, allowing nature to flourish and grow strong. Hence, the Lin Zhong musical pipe represents Di Dao, measuring six inches. The number six reflects the distribution of yang energy, spreading throughout heaven and earth, balancing strength and flexibility. The *I Ching* further states, "The way of Earth is gentle and firm." "'Qian' knows the beginning, while 'Kun' brings things into being."
In the first month, corresponding to the initial three of the "Qian" hexagram in the *I Ching*, all of creation begins to grow. Starting from the Yin month (the first month), people participate by nurturing nature with a heart of benevolence and guiding it through righteous actions, ensuring that everything finds its rightful place. Yin is associated with wood, representing benevolence; the musical tone of the Yin month is Shang, symbolizing righteousness.
Therefore, the Tai Zu pipe, eight inches long, represents Ren Dao. It symbolizes the eight trigrams and Fuxi's method of understanding the world through communion with Heaven and its energies. The *I Ching* states, "The way of man is founded on benevolence and righteousness." "Form the image in heaven, shape it on earth." "Then, to carve and shape the way of Heaven and Earth, to assist in harmony with nature, and to guide the people." These three pipes represent the Three Harmonies.
These three types of musical notes correspond to three seasonal markers: Huangzhong corresponds to the eleventh month (Zi month), which is Tianzheng; Linzhong corresponds to the fifth month (midsummer), the counterpart to the eleventh month, which is Dizheng; Taizu corresponds to the first month (Yin month), which is Renzheng. Among these three seasonal markers, Dizheng (May) is taken as the starting point because it is located exactly in the northeast direction of the Earthly Branches. The Book of Changes states, "The northeast loses friends, but ultimately finds joy." This indicates that the starting point of Dizheng aligns with the laws of the heavens. When Huangzhong is the main tone, Taizu, Guxi, Linzhong, Nanlu, and other tones will all harmonize perfectly without any deviation, unaffected by other tones, reflecting the essence of unity and concord. However, if other tones are used as the main tone instead of Huangzhong, even in their respective months, deviations in harmony with other tones will occur, making it impossible to achieve a state of unity and balance. Therefore, Huangzhong reigns supreme, unmatched by others.
The Book of Changes says, "Heaven and earth are governed by numbers." This means that there are certain rules for the numbers of heaven and earth. The number of heaven starts from one and ends at twenty-five. The rule is to use three to count, so one multiplied by three, plus twenty-five divided by six, calculated twenty-five times, ultimately gives us the total number of days: eighty-one. Multiplying this by the sum of the five positions of heaven and earth (which is ten), we arrive at eight hundred and ten, corresponding to a cycle of one thousand five hundred and thirty-nine years in the calendar, representing the actual length of the Huangzhong musical note. From this rule, we can derive the frequencies of the twelve musical notes.
The earth number ranges from two to thirty. It's based on doubling, so one multiplied by two is repeatedly doubled thirty times, eventually yielding the total number of Earth: sixty. Then, multiplied by the midpoint of Earth (which is six), it results in 360 units, corresponding to the number of days in a year, representing the actual length of the Lin Zhong rhythm. Humans, inheriting heaven and earth, follow the laws of nature, nurturing all things according to the changes of solar terms, embodying the principles of Heaven and Earth to govern and harmonize all aspects of creation. Therefore, it is eight multiplied by eight, equaling sixty-four. This number represents the ultimate expression of cosmic change, then multiplied by the sum of the five elements of heaven and earth (ten), resulting in 640 units, corresponding to the sixty-four hexagrams, representing the actual length of the Tai Zu rhythm. The *Shangshu* states, "Heaven works, and man inherits it." This means that humans must inherit and complete the work of heaven and earth. Since Heaven encompasses Earth, and humanity mirrors Heaven, both are multiplied by ten (the sum of the five elements). The earth number is multiplied by six (its midpoint), reflecting the inward nature of Yin Qi's circulation. The lengths of these three rhythms (Huang Zhong, Lin Zhong, Tai Zu) are all whole units, interconnected without any remainder. Consider this: heaven comprises five elements, Earth six; their interaction is fundamental to this system. Six represents the void, the potential; five, the active elements cycling through this void. This void embodies the interplay of Yin and Yang, their rise and fall generating the twelve harmonious pitches.
Tai Chi is the original energy of the universe, embodying the harmony of Heaven, Earth, and Humanity. ‘Ji’ represents the central point, while ‘Yuan’ signifies the beginning. It operates on the twelve earthly branches, starting at midnight (Zi). The energy increases as follows: 1 at Zi, 3 at Chou (1-3 am), 9 at Yin (3-5 am), 27 at Mao (5-7 am), 81 at Chen (7-9 am), 243 at Si (9-11 am), 729 at Wu (11 am-1 pm), 2187 at Wei (1-3 pm), 6561 at Shen (3-5 pm), 19683 at You (5-7 pm), 59049 at Xu (7-9 pm), and finally 177147 at Hai (9-11 pm). This shows how the combination of Yin and Yang gathers energy at Zi, giving birth to all things.
Life begins to stir at midnight (Zi), with tender shoots emerging by 1 am (Chou), branches and leaves extending by 3 am (Yin), new branches sprouting by 5 am (Mao), flourishing with dense foliage by 7 am (Chen), reaching their peak by 9 am (Si), bearing fruit by 11 am (Wu), gradually fading by 1 pm (Wei), becoming hard by 3 pm (Shen), maturing and harvesting by 5 pm (You), returning to their origins by 7 pm (Xu), and resting and recuperating by 9 pm (Hai).
Then, starting with Jia wood, the cycle continues with Yi wood's upward growth, the bright radiance of Bing fire, the intensity of Ding fire, the abundance of Wu earth, the order of Ji earth, the contraction of Geng metal, the renewal of Xin metal, the inclusiveness of Ren water, and the quiet stillness of Gui water.
So, the ebb and flow of Yin and Yang, the cycle of life and death, all align perfectly with the rhythms of the twelve musical notes and the twelve earthly branches – isn't it remarkably clear?
It is said that the celestial phenomena in the sky, with the handle of the Jade Heng pointing, is the framework of the heavens, the trajectory of the sun and moon's movement, and the record of the stars. Where this framework and record meet, you find the universe's original blueprint, expressed through music. These musical tones harmonize with each other, nurturing the growth and changes of all things, celebrated through music. By observing celestial phenomena and deducing all things, the harmony and order of yin and yang are achieved. Therefore, based on this harmonious mathematical relationship, the accumulation of this harmony is calculated as an inch according to a certain proportion, which is the length of the Yellow Bell. To get the length of the Lin Bell, take one-third less than the Huang Zhong; for the Tai Zhu, add one-third of the Lin Bell's length. Following this pattern, continuously adding and subtracting by thirds, the eight musical notes of Nan Lu, Gu Xi, Ying Zhong, Rui Bin, Da Lu, Yi Ze, Jia Zhong, Wang She, and Zhong Lu can be obtained. Yin and yang generate and control each other, starting from the Yellow Bell and going left, the eight musical notes cycle back and forth, totaling sixty-four. The standard instruments for these musical notes are all made of copper, managed by the Imperial Music Bureau under the supervision of the Ministry of Rituals.
Now, let's talk about "measure." "Measure" refers to fen, cun, chi, zhang, and yin, used to measure lengths. Its basis is the length of the Yellow Bell. Selecting an average-sized grain of millet, the width of one grain of millet multiplied by ninety fen equals the length of the Yellow Bell. One is fen, ten fen is cun, ten cun is chi, ten chi is zhang, and ten zhang is yin, thus determining the five length units. Their standard instruments are made of copper, a copper bar, one cun high and two cun wide, stretching a full zhang in length, marked with fen, cun, chi, and zhang. The standard instrument for "yin" is made of bamboo, one fen high, six fen wide, and ten zhang long. The proportions of these standard instruments all reflect the corresponding relationship of yin and yang. Fen is the accumulation of tiny things to a certain extent that can be distinguished; cun is estimation and measurement; chi is measurement; zhang is extension; yin is the ultimate measure. Therefore, the concept of "measure" is embodied in the five units of fen, cun, chi, zhang, and yin. "Yin" represents the standard length of the world. The standard instruments of this system of weights and measures are kept by the internal officials and managed by the Imperial Court of Justice.
Whoa, this is talking about ancient weights and measures! First of all, there are measuring gizmos like the "yuè" (a type of vessel), "hé" (1/10 of a "yuè"), "shēng" (10 "hé"), "dǒu" (10 "shēng"), and "hú" (10 "dǒu"), used to measure the quantity of things. These instruments were originally based on the volume of the "huángzhōnglǜ" (Yellow Bell Law), carefully measuring its volume, filling a "yuè" with 1,200 medium-sized grains of millet, and calibrating its water level with well water. One "yuè" equals one "hé," ten "hé" equals one "shēng," ten "shēng" equals one "dǒu," ten "dǒu" equals one "hú," and there you have it.
These measuring instruments are made of copper, square but with rounded edges, and a small handle on the side. On top is the "hú," below is the "dǒu," on the left is the "shēng," and on the right are the "hé" and "yuè." This instrument looks like a wine goblet, representing rank and privilege. It has three squares on top and two below, symbolizing heaven (3) and earth (2). Inside, there’s a circle within a square, representing yin and yang (one on the left, two on the right). The circle represents a compass, weighing two "jūn," encompassing all quantities of heaven, earth, and all things, totaling 11,520. Its pitch is based on the Yellow Bell Law, starting from the Yellow Bell Law and repeating, symbolizing the rule of monarchs in making objects. The "yuè" embodies the Yellow Bell Law; its subtle vibrations were believed to create all things. The "hé" was a tenth of a "yuè," the "shēng" ten "hé," the "dǒu" ten "shēng," and the "hú" ten "dǒu." Therefore, with measuring instruments, starting from the "yuè," to "hé," to "shēng," to "dǒu," and finally to "hú," progressing step by step. The Tai Cang warehouse, run by the Grand Minister of Agriculture, kept tabs on all this.
Next, let's talk about the scales. "Héng" is balance; "quán" is weight; the "héng" is used to weigh things, balancing light and heavy. This "héng" had to have a perfectly level base, the plumb line straight, and when you swung it, you'd see a compass on one side and a square on the other. The "héng" is in the sky, assisting in the movement of celestial bodies, considering the solar terms, ensuring the harmonious operation of the seven celestial bodies (sun, moon, five stars), hence it is called the "yùhéng" (Jade Balance). The Analects say you could see it from anywhere—standing up, sitting in a cart—always in front, leaning against the scales. And it needed to be kept in order with proper ritual. So, the "héng" was always in front, representing the south.
Ancient Chinese weights and measures included the zhu, liang, jin, jun, and shi, used to weigh things. This system's origins are rooted in the weight of the Huangzhong (a musical pitch pipe). A yue (a unit of volume) held 1200 grains of millet, weighing 12 zhu; 24 zhu made up one liang. The character 'cun' (忖) means eighteen, reflecting the 18 changes symbolized in the *I Ching*.
This five-weight system, grounded in philosophical principles, used physical objects as its basis, with size differences defined by weight. It's a cyclical system, endlessly repeating. The zhu represents the smallest increment, symbolizing growth from humble beginnings. A liang, equivalent to 24 zhu, was roughly the weight of two Huangzhong pipes and symbolized the 24 solar terms.
The jin, equal to 384 zhu, represented brightness and symbolized the yin and yang transformations described in the *I Ching*. A jin (16 liang) symbolized the four seasons multiplied by the four cardinal directions. The jun represented balance, the point where the energy of yang and the generative force of yin achieve equilibrium. A jun (11,520 zhu) symbolized the totality of things. 480 liang represented the 60-day cycle encompassing eight solar terms. A jun (30 jin) symbolized a month.
The shi was the largest unit of weight. From the smallest zhu to the largest shi, the system encompassed all scales of measurement. A shi (4 jun) symbolized the four seasons; 120 jin represented 12 months; 1920 liang symbolized the interplay of yin and yang; 384 hexagrams represented the five elements; and 46,080 zhu represented 11,520 objects undergoing seasonal change. The entire system thus reflected the yearly cycle.
Power and material things are produced simultaneously, balancing each other. This interplay of power and materials led to the invention of the compass, which in turn led to the carpenter's square, the square led to the development of ropes, the ropes gave rise to the plumb bob, and the plumb bob ensures balance and harmony. This is what is known as the "five tools." The compass is used to draw circles and create circular tools that meet specifications. The carpenter's square is used to draw squares and create square tools that maintain their shape. The compass and carpenter's square work together in harmony to create circular and square objects. The plumb bob is used to measure flatness and correct direction. The rope, with its straight ends and crosswise threads, is used to determine direction and position. With the help of the plumb bob and careful balancing, craftsmen rely on these tools to establish standards and advise the emperor in governance, aiming for peace in the world. The Classic of Poetry says: "The great master of the Yin clan, holding the state's balance, maintaining the four corners of the realm, supporting the Son of Heaven, keeping the people from going astray." These five tools all embody the same principle.
From the perspective of yin and yang, the greatest yin energy is in the north. The north, with its hidden yang energy, represents the stillness of winter. Winter signifies endings, as all things come to an end and are stored away. Water flows downwards. Wise individuals plan ahead, and planners value balance, hence balance represents wisdom and strategy. The greatest yang energy is in the south. The south, brimming with yang energy, embodies the vibrant growth of summer. Summer signifies growth and prosperity, as all things grow abundantly, appearing flat and expansive. Fire rises upwards. Etiquette emphasizes orderliness, and orderliness is synonymous with harmony, thus harmony represents etiquette and proportion.
Lesser Yin energy is in the west. West represents movement and change, with yin energy causing all things to wither and decay, corresponding to autumn. Autumn brings the harvest and the maturation of all things. Metal can be cast and transformed, representing change. Justice leads to order and structure, symbolized by the square. Lesser Yang energy is in the east. East signifies movement, with yang energy causing all things to move and grow, corresponding to spring. In spring, all things sprout, grow, and begin to develop. Even crooked trees grow straight. Benevolence fosters growth, which is round, so the compass represents benevolence and roundness. The center represents the balance of yin and yang, and the harmony of the four directions. The land nurtures all things. Sincerity ensures uprightness, so the plumb line represents sincerity and uprightness. These five tools represent the principles of measurement, encompassing weight, shape, and the balance of yin and yang. These tools embody the principles of the four directions, four seasons, and the five elements. Each tool has its own function and operates according to its nature. This system was of critical importance, overseen by the Ministry of Rites.
In the Book of Documents, it says: "I want to listen to the chanting of the Six Laws, Five Sounds, Eight Tones, and Seven Beginnings (referring to Heaven, Earth, the four seasons, and humanity), to express the inner five-character poem, and see what you think." This "I" refers to Emperor Shun. This refers to using the principles of the Six Laws and Five Sounds within the framework of the Eight Tones to create music. By applying these principles to the Five Constants in song, one can align with heaven and earth, harmonize with the four seasons, resonate with human relationships, conform to yin and yang, and reflect human nature. One should guide with virtue and inspire through music, all leading to the same goal by different paths. Only a sage can unify the thoughts of the world; that's why Emperor Shun wanted to listen to these.
Now, they were actively recruiting scholars and encouraging open dialogue, refining old classics, unifying laws and measures, balancing and standardizing them, using a straight ruler for correction, establishing five principles, and perfecting mathematics and music to benefit the people, unify the world, and bring the hearts of the people together. Each standard weight and measure was made of copper and given its own name to ensure consistency and uniformity throughout the land. Copper was seen as the purest substance; it does not change its nature due to dryness, humidity, cold, or heat, nor does it change its shape due to wind, rain, or exposure. It remains constant, just like the character of a noble person, which is why copper is used for making them. Bamboo was used for the scales, a practical necessity.
The origin of the calendar goes way back. Legend has it that Emperor Zhuanxu appointed Nan Zhengzhong for astronomy and Huo Zhongli for geography. Later, the Sanmiao rebellion disrupted the established order, and both of these official positions were abolished. Intercalary month calculations went haywire, the Mengzhi month disappeared, and the She-ti star's position was off. Yao reinstated the descendants of Zheng and Li, letting them take over. Therefore, the "Book of Documents" says: "So he appointed Xihe, revered the heavens, observed the sun, moon, and stars, and told the people about the seasons." A year had 366 days. Intercalary months kept the seasons on track. Everything ran smoothly, and things got done. Later, it was passed on to Shun, saying: "Shun, it's your job to keep the calendar right now." Shun passed it on to Yu. When King Wu of Zhou came along, he visited Ji Zi, who explained the nine chapters of the Great Law, including a section on the calendar. Therefore, from the Shang Dynasty to the Zhou Dynasty, whenever there was a regime change, they'd adjust the calendar and clothing to match the seasons and please Heaven.
After the Three Dynasties, during the era of the Five Hegemons in the Spring and Autumn period, historians got slack, and astronomy and calendar experts were scattered far and wide, some even among the barbarians. This resulted in the preservation of records such as the "Yellow Emperor's Calendar," "Zhuanxu's Calendar," "Xia Calendar," "Yin Calendar," "Zhou Calendar," and "Lu Calendar." During the Warring States period of constant warfare, after the unification of the Qin Dynasty, there was no time to organize these records, so they mostly followed the Five Virtues theory, believing they had acquired the virtue of water, and thus made October the first month, and black the main color for clothes.
In the early days of the Han Dynasty, the country was still finding its feet, and lots of things were still being worked out. They followed the calendar and system of the Qin Dynasty. Beiping Marquis Zhang Cang suggested using the Zhuanxu Calendar. It was the most accurate of the seven calendars. However, we don't have clear records of details like clothing colors, and lots of the records about moon phases are wrong.
So, at the beginning of the Han Dynasty, many systems were still figuring things out, especially regarding the calendar. They used the 'Zhuanxu Calendar', which was pretty solid, even if there were still lots of kinks to work out and many records weren't accurate enough. This is like a newly established company, needing continuous improvement.
In the seventh year of Emperor Wu of Han, the Han Dynasty had been around for 120 years. At that time, top officials like Gongsun Qing, Hu Sui, and the Chief Historian Sima Qian all said the calendar was all messed up and needed fixing.
Er Kuan, the Imperial Historian, was a classics scholar, so the emperor issued a decree: "I need you and the scholars to figure out what standard to use for the calendar, and what colors our clothes should be." Er Kuan discussed this with the scholars, and everyone said, "Changing the calendar and clothes shows he's got a mandate from Heaven. It should change at the founding of the country, but then it shouldn’t need to change again. According to historical order, it should be the calendar of the Xia Dynasty now. We’re not knowledgeable enough to explain this clearly. Your Majesty's wisdom and power will proclaim this to Heaven and Earth. The system of the three generations, with later saintly kings inheriting from the previous ones, is two generations ahead. Now the systems of two generations have been broken, and there is no order. Only Your Majesty can demonstrate saintly virtues, promote the laws of Heaven and Earth, to conform to Yin and Yang, and create a great system for ages to come."
So the emperor ordered the Imperial Historian to say, "Officials have been complaining the calendar's still a mess, and all this research into the stars hasn't helped much. I hear the Yellow Emperor sorted out the calendar ages ago – what a guy! But the old texts are patchy, so I've been struggling to get this right. Let's just call this year one, then!"
Then the emperor ordered Gong Sunqing, Hu Sui, Sima Qian, Zun, Xingshe Xing, and others to discuss and establish the calendar of the Han Dynasty. They figured out the rules governing new moons, full moons, solar terms, and the movements of the constellations. Using the previous calendar as a base, they traced back four thousand six hundred and seventeen years before the Tai Chu era, arriving at the seventh year of Yuan Feng, which corresponds to the year of the Yafeng calendar. In that year, on the day of Jiazi in the eleventh month of winter solstice, the sun and moon were aligned with the constellation Jianxing, and the year star was in the position of Zi, allowing them to obtain the celestial coordinates of the Tai Chu calendar and the new first month.
Xingshe Xing and others said they encountered difficulties in making accurate calculations and proposed to recruit amateur astronomers to revise the calendar together. They eventually established the "Han Taichu Calendar." They selected Deng Ping, Changle Sima Ke, Jiuquan Hou Yijun, Zun, and some other calendar researchers, totaling more than twenty people, including the astrologer Tang Du and Luoxiahong from Ba County. Tang Du was responsible for the celestial observations, while Luoxiahong was tasked with calculating the calendar. Luoxiahong used the method of Lu and Lyu to establish the calendar, explaining, "The volume of Lu and Lyu is one unit, totaling eighty-one inches, which serves as the scale for one day. The length of Lu and Lyu is nine inches, and after one hundred and seventy-one cycles, it returns to the starting point. After three cycles, it reaches Jiazi. Lu and Lyu represent the changes of Yin and Yang, which are the basis for hexagram transformations. Therefore, Huang Zhong represents the original energy, referred to as Lu. Lu is the rule, and everything must adhere to this rule." His method was similar to Deng Ping's.
Therefore, they collectively observed the new celestial phenomena and the movements of the sun and moon, using calculation methods that aligned with those of Luoxiahong and Deng Ping. Their method calculated a month as twenty-nine days and forty-three parts out of eighty-one days. Being half a day ahead was called the solar calendar; not being ahead was referred to as the lunar calendar. The solar calendar indicates that the new moon is calculated based on its visibility before the moon; the lunar calendar means the moon is visible after the new moon. Deng Ping said, "The new moon of the solar calendar always appears before the moon, making it easier to schedule audiences with princes and ministers."
The emperor ordered the adoption of the calendar system based on eighty-one divisions devised by Deng Ping, abolishing the other seventeen relatively crude calendars and ensuring the accuracy of the calendar and the musical laws. Eunuch Chunyu Lingqu rechecked the accuracy of the New Year, the last day of the month, the half-moon day, and the full moon in the "Tai Chu Calendar," all of which were perfectly aligned, like matched jade pieces and strung pearls. Chunyu Lingqu reported the situation, so Deng Ping's calendar was adopted, and Deng Ping was appointed as the Imperial Astronomer.
Twenty-seven years later, in the third year of Yuanfeng, a Grand Historiographer named Zhang Shouwang submitted a memorial saying, "The calendar is a major matter between heaven and earth, established by the heavens. We have always used the Yellow Emperor's 'Tiao Lu Calendar' since the founding of the Han Dynasty. Now that there is an imbalance in the cosmic forces, the problem should lie in the calendar." The emperor ordered the Imperial Astronomer Xianyu Wangren to question Zhang Shouwang, but Zhang Shouwang refused to comply. Xianyu Wangren then requested to join more than twenty people, including the Minister of Agriculture Ma Guang, to carefully examine the accuracy of various calendars by comparing astronomical phenomena such as days, months, phases of the moon, and the solar terms. The emperor approved. He then ordered the Prime Minister, the Imperial Censor, the Grand General, and the Right General to each send a representative to inspect these eleven calendars together in the royal garden of Qingtai in the Shanglin Garden, to determine which calendar was more accurate. Starting from the Winter Solstice on the New Moon of the eleventh month of the third year of Yuanfeng, the calendars were assessed until the twelfth month of the fifth year. Zhang Shouwang's calendar ranked low.
Investigations revealed that the Yellow Emperor's "Tiao Lu Calendar" was never used since the founding of the Han Dynasty. Zhang Shouwang denied the calendar used by the Han Dynasty, claiming it went against the will of heaven, which was a great disrespect! The emperor ordered that his responsibility not be pursued temporarily. The assessment continued until the sixth year of Yuanfeng. The "Tai Chu Calendar" took first place, and the "Tai Chu Calendar" made by Xu Wanqie in Jimo and Xu Yu in Chang'an also took first place. The assessment results of the Yellow Emperor's "Tiao Lu Calendar" made by Zhang Shouwang and Li Xin were poor, and Zhang Shouwang even claimed that more than six thousand years had passed since the time of the Yellow Emperor.
Shu Bao, the Chancellor from Dan'an in Chang'an, and Bei Yu of Anling's *Zhongshi* Calendar stated that from the Yellow Emperor to that time, there were only three thousand six hundred and twenty-nine years, which contradicted Zhang's claims. Zhang also modified the "Emperor's Records," where the ages of Shun and Yu he gave differed from accepted accounts. He also claimed that Hua Yi replaced Yu as emperor, and the Lady of Mount Li also served as emperor, all of which occurred between the Yin and Zhou dynasties, contradicting official history. In fact, the calendar made by Zhang was actually the "Yin Calendar" previously used by the imperial historians.
Zhang also made unfounded claims, asserting that there were five different calendars in use simultaneously and falsely stated that the *Tai Chu* Calendar was short by three-quarters of a day, plus one 750th of a day, resulting in an imbalance of yin and yang, which he claimed was the reason for the great chaos in the world. Critics accused Zhang, a lowly eight-hundred-shi official in Confucian robes, of spouting nonsense and deliberately spreading misinformation to undermine the government. His actions were deemed reckless, and the emperor approved the charges.
Zhang consistently ranked poorly in the annual reviews for three years and remained unconvinced. Later, he was accused again, almost sentenced to death, but was later pardoned. However, he remained unchanged, continued to slander, and was finally demoted to a minor official. Ultimately, the calendar's accuracy had to be verified by astronomical observation. Thirty-six years of use, from the Han Dynasty to the sixth year of Yuanfeng, ultimately proved the calendar's worth.
It is said that Liu Xiang, the esteemed scholar known for his filial piety, revised the calendar six times in his lifetime and wrote "Five Discourses" to clarify the truth of history. His son, Liu Xin, inherited his father's mantle, delved deeper into the research, wrote "Three Systems Calendar" and "Genealogy" to explain the principles in the "Spring and Autumn Annals," summarizing the subtle rules in the calendar. Now, let's turn to this topic.
Studying the "Spring and Autumn Annals" is essentially studying the timing of Heaven, combining human affairs with the rhythms of nature. The book states, "People are born under Heaven; that's fate. Therefore, ritual, propriety, and conduct determine one's destiny. Those who follow will receive blessings, while those who do not will bring calamity upon themselves." The "Spring and Autumn Annals" records events from 242 years of twelve vassal states according to the laws of yin and yang. Spring is when yang is at its height, and all things begin to grow; autumn is when yin is at its height, and all things begin to mature. The events recorded in the "Spring and Autumn Annals" are precise. The rituals emphasize harmony, and the calendar uses intercalary months to adjust yin and yang, ensuring that the common people have enough clothing and food, all to determine a person's destiny! The "Book of Changes" mentions the hexagram of metal and fire overcoming each other, stating, "Tang and Wu revolution, following the will of Heaven and responding to the will of man," and also advises to "maintain an accurate calendar," all to harmonize the relationship between humans and nature.
As the Zhou Dynasty declined and King You died, the Son of Heaven could not even perform normal sacrifices, and the calendar of the state of Lu was incorrect, mistakenly treating the year with the intercalary month as the beginning of the era. Therefore, the "Spring and Autumn Annals" records: "On the day of Yi Hai in the eleventh month, there was an eclipse." At that time, the planet Venus was in the Shen position, but the official responsible for the calendar believed it was in the Jian Xu position, as noted in historical records. In the twelfth year of Duke Ai, the month of Shen, where Antares was located, was mistakenly taken as the month of Jian Hai, leading to questions about why insects did not hibernate. It had been over a hundred years since Duke Wen's time without timely sacrifices, and no one had been able to correct the calendar. Therefore, Zigong wanted to do away with the sacrificial sheep, but Confucius valued this ritual and recorded it in the "Spring and Autumn Annals." The "Classic" states: "On the day of the eclipse on the first day of the tenth month of winter." The "Commentary" explains: "The specific date was not recorded, which was a dereliction of duty by the officials. The Son of Heaven has officials specifically responsible for the calendar, as do the vassal states. These officials hold high positions and are responsible for determining dates, which is a matter of ritual. They must not miss the date and must promptly inform all officials." This underscores the importance of performing sacrifices on time.
The Yuan calendar, from the very start, was simply called "Yuan." According to the ancient texts, "'Yuan' represents the culmination of goodness," meaning that the combination of three virtues is goodness. It also states, "'Yuan' represents the fundamental principle," indicating that the combination of three basic elements constitutes the foundation, hence it is called "Yuan." In the spring season, the activities of the royal family were recorded each month, and these three monthly royal records represent the core principles of the Yuan calendar. These three governing aspects merge into one, using "Yuan Yi" to represent the mathematical relationship between 9³ and 11³ (whose product, while not actually equaling one, is significant in the system). The Yellow Bell is the first note of the primary tone, representing the movement of yang. By multiplying this by six and then dividing by nine, we get the Lin Bell, which is the first note of the fifth tone, representing the movement of yin. These calculations are all based on the laws of the movement of heaven and earth. The upper calculations involve multiplying by six and then doubling, while the lower involve multiplying by six and then halving, both divided by nine. Nine multiplied by six represents the relationship between yin and yang, husband and wife, and mother and child. The primary tone, like a father, generates the fifth tone, like a son, reflecting the cyclical nature of the cosmos. With six primary tones and six fifth tones, the twelve Earthly Branches are determined. With the tonal qualities of the five-note scale, the movement of the ten heavenly stems is also established. The principle of "six in heaven, five on earth" reflects the fundamental nature of numbers. The six qi of heaven descend, producing five flavors. Six and five are the result of the interaction between heaven and earth, and the fundamental basis on which the people rely for survival. Therefore, with the six Jia and five Zi branches, the eleven-year cycle represents the completion of a cycle of the law of the movement of heaven and earth, repeating endlessly. The center of Tai Chi is primordial energy, hence it is the Yellow Bell, with a unit of length called a "yue." By multiplying its length by itself, we get eighty-one, which is the base number of the calendar. This base number (81) formed the foundation for deriving various units of measurement and the entire system of rituals and music.
In the "Book of Changes," the character "yuan" represents the primordial unity from which all things emerge, while in the "Book of Changes," the Taiji symbolizes the beginning of all things. The "Spring and Autumn Annals" detail monthly royal activities during the spring, while the trigrams of the "Book of Changes" encompass the three realms (heaven, earth, and humanity). Even if nothing major happens, the "Spring and Autumn Annals" record the year, month, and day, while the "Book of Changes" represents the four seasons. The "Spring and Autumn Annals" uses terms like "establishment," "division," "arrival," "initiation," and "conclusion" to mark time, while the "Book of Changes" is based on the positions of the eight trigrams. The "Spring and Autumn Annals" record the success and failure of events, while the "Book of Changes" reflects good and bad fortune. The "Spring and Autumn Annals" document court meetings and alliances, while the "Book of Changes" serves as the foundation of great endeavors. Therefore, both the "Book of Changes" and the "Spring and Autumn Annals" elaborate on the unity of heaven and man. The Commentary explains: "The tortoise shell symbolizes the situation, divination the process of calculation. Things first manifest, then take shape, and finally, numbers reveal their meaning."
So, everything starts with "one," right? This "one" is the original source. Then, the "Spring and Autumn Annals" is all about "two," the three realms are "three," the four seasons are "four," and that adds up to ten, making up the Five Elements. Multiply five by ten, and you get the Da Yan number—the Dao's essence is in that "one." The other forty-nine are for doing the calculations. That's why the ancients used yarrow stalks for divination.
We pair numbers, grouping them in twos, threes, and fours, then combine the odd numbers with the nineteenth day of the leap month, add the initial "one," and then repeatedly multiply pairs of these numbers. This is the actual situation of the moon's movement pattern. The sun's cycle is represented by a single "one," which determines the number of days in a month and also dictates the cycles of the sun, moon, and stars, allowing for the calculation of good and bad fortune. The I Ching states: "Heaven is one, Earth is two, Heaven is three, Earth is four, Heaven is five, Earth is six, Heaven is seven, Earth is eight, Heaven is nine, Earth is ten. Five is the number of Heaven, five is the number of Earth; these five positions interact harmoniously. Heaven's number is twenty-five, Earth's is thirty; the total for Heaven and Earth is fifty-five, the source of all change and spiritual power." The total is nineteen, as the I Ching says, "When things reach their limit, they change," hence the leap month calculation. Multiply three by the number of Heaven, nine, then multiply two by the number of Earth, ten; this is the number of cycles. Multiply three by the number of Heaven, twenty-five, and two by the number of Earth, thirty; this is the number of meetings of the new moon and full moon. Multiply the number of cycles, and you can calculate the lunar cycles, new moons, and winter solstice; this is the month of conjunctions. After nine cycles, it returns to the starting point, which is also the first nine cycles of the Yellow Bell.
When recording events, be sure to specify the time of year, even if there is nothing major, and also specify the year and month. Time is used to record solar terms and lunar nodes, while months are used to record seasonal divisions. Solar terms do not necessarily fall within the corresponding month, so solar terms and lunar nodes must fall within the correct months. Therefore, the "Book of Changes" states: "Ancient rulers carefully observed the proper seasons, stepping forth at the beginning, acting correctly in the middle, and returning to completion at the end. By stepping forth at the beginning, the sequence is not violated; by acting correctly in the middle, the people are not confused; by returning to completion at the end, matters are not confused." This is why the virtuous kings valued intercalary months. By using five variables multiplied by the number of conjunctions, one can calculate the first day of the lunation and the winter solstice; this is known as the lunar month. Divide the lunar month into four parts, and use one part multiplied by the lunar month; this is known as the middle method. The middle method involves taking one-fourth of the lunar month and applying it to the calculations. Use the intercalary method to calculate the cycles and winter solstice, then multiply by the lunar method, subtract the middle method, and simplify to obtain a calculated number; this is the method of calculating a lunar month, with a remainder of one seventh. This is the method of calculating the first day of the month. If the first day of the month is not accurate, then it is an intercalary month, meaning that although yin and yang are combined, if the calculation is not accurate, a new month will not be produced. Therefore, the solar method multiplied by the intercalary method is referred to as the annual cycle; three annual cycles comprise a Great Year. The intercalary method of the Great Year is determined based on the anomalies of yin and yang and the three-string intercalary method, a technical term referring to a specific calculation process. The "Book of Changes" records the nine calamities as follows: upon first entering the Great Year, there are one hundred six, with nine being yang; the next is three hundred seventy-four, also with nine being yang; then four hundred eighty, with nine being yang; followed by seven hundred twenty, with seven being yin; then another seven hundred twenty, with seven being yang; next is six hundred, with five being yin; then six hundred again, with five being yang; followed by four hundred eighty, with three being yin; and finally four hundred eighty, with three being yang. In total, four thousand six hundred seventeen years make up one Great Cycle. Among them, four thousand five hundred sixty are normal years, and fifty-seven are calamitous years. Therefore, the "Spring and Autumn Annals" states: "Act correctly in the middle." It also states: "Failing to announce an intercalary month is considered improper. Intercalate according to the proper seasons, seasons to accomplish tasks, tasks to enrich life; the way of governing the people lies therein. Ignoring the intercalary month disregards proper timing, making effective governance impossible."
Therefore, in the spring of the fifth year of Duke Xi of Lu, on the first day of the first lunar month, the winter solstice occurred. Duke Xi personally observed the first day of the lunar month, then ascended the observation platform to look out and record it, which was in accordance with the ritual. All solstices, equinoxes, and other significant celestial events must be recorded for future use. In the second month of Duke Zhao's twentieth year, the winter solstice occurred without a leap month, and the winter solstice did not fall in the expected month. Zishen observed celestial phenomena but didn't get the timing right from the start. Therefore, historical records do not mention the winter solstice, but rather the sun reaching its southernmost point. When the sun is near the constellation Aquila, the shadow is longest at noon, from which the winter solstice can be known. The Dou constellation is adjacent to the Camp constellation, and the star mansion of the Weaver points towards Altair, used for year and month reckoning, hence called star reckoning. The five planets begin their cycles from their starting points, while the sun and moon begin theirs from the middle, resulting in a total of twelve cycles. When the sun reaches its starting point, it is a solar term, and when it reaches the middle of Dou, it corresponds to the twelve earthly branches. Observing its position can determine other positions. Therefore, it is said: "There are only twelve divisions in the ritual calendar, reflecting the fundamental order of heaven." The Classic of Documents says, "In spring, the king's first month," and the commentary adds: "In the first month of Zhou, fire emerges; in summer, it is the third month; in Shang, it is the fourth month; in Zhou, it is the fifth month. The summer numbers receive the mandate of heaven," which established the correct timing of the four seasons.
Each of the three dynasties had its own system of dating, indicating that the three dynasties are cyclical, each taking its turn as dominant, repeating endlessly. This is the way of the five elements. Therefore, three and five are intertwined and give birth to each other. The heavenly dynasty's auspicious energy begins at half past midnight (2 AM), when the sun has just risen, appearing red. The earthly dynasty receives this energy starting at the hour of the Ox (around 1 AM), when the sun begins to change, turning yellow, and by the middle of the hour of the Ox, the sun's color becomes white. The human dynasty receives it starting at the hour of the Tiger (around 3 AM), when the sun's light becomes dark, and by the middle of the hour of the Tiger, the sun's light turns green. Celestial changes begin at the hour of the Rat (11 PM), the changes in the earth's energy start from the hour of the Ox and end at the hour of the Dragon (around 7 AM), and the changes in human energy start from the hour of the Tiger and end at the hour of the Monkey (around 9 AM). Therefore, in the calendar, the heavenly dynasty uses Jia Zi (甲子), the earthly dynasty uses Jia Chen (甲辰), and the human dynasty uses Jia Shen (甲申). The leaders of the Meng (孟), Zhong (仲), and Ji (季) periods take turns as the heads of the dynasties. The cyclical order of the three dynasties was established, starting with the color green for the five elements, and the order remains the same. The five elements and three dynasties were inextricably linked. As the "Zhou Yi" says, "The heavens have three stars, and the earth has five elements," so with the three dynasties and five stars, everything can be understood. The "Book of Changes" states, "The interplay of the five elements creates change, intertwine their numbers. Understand their changes and ultimately form the culture of the world; reach their limits and ultimately establish the image of the world." Above, the Taiji governs the three celestial bodies and five planets; below, the Yuan Qi governs the three dynasties and five elements. For humans, the Huang Ji (皇极) leads the three virtues and five matters, which include benevolence, righteousness, propriety, and the corresponding human affairs. Therefore, the three dynasties are in harmony with the three stars: the sun is in harmony with the heavenly dynasty, the moon is in harmony with the earthly dynasty, and the Big Dipper is in harmony with the human dynasty. The five stars are in harmony with the five elements: water is in harmony with the star associated with the Dragon (辰星), fire is in harmony with Mars (荧惑), metal is in harmony with Venus (太白), wood is in harmony with Jupiter (岁星), and earth is in harmony with Saturn (镇星). The three dynasties and five stars intersect and move. The heavens generate water with one, the earth generates fire with two, the heavens generate wood with three, the earth generates metal with four, and the heavens generate earth with five. The five elements interact cyclically, giving rise to the microcosm, which, when multiplied by the hexagrams of "Qian Kun" (乾坤), forms the macrocosm. Yin and yang are compared and contrasted, interweaving and complementing each other, so the changes of nine and six are reflected in the six realms of existence. Three small changes form a significant change, three significant changes form a scene, two scenes with eighteen changes form hexagrams, and four trigrams form the "Book of Changes," totaling seventy-two changes, which is the product of the three dynasties and the four seasons. Three multiplied by it gives the hexagram of "Qian" (乾), and two multiplied by it gives the hexagram of "Kun" (坤). Multiplying Yang by nine gives 648; multiplying Yin by six gives 432, totaling 1080, a small calculation method for each hexagram of Yin and Yang.
Eight times this amount.
