Sun Wukong is indeed well-versed in the principles of heaven and earth, managing the affairs of the common people with remarkable skill. His abilities are extraordinary, and his legacies are all exemplary. Therefore, everything he created follows a specific order, and even the mysterious and unfathomable can be traced back to their origins; changes and developments all have their reasons, and the final results can also be verified. In ancient times, the Yellow Emperor gathered bamboo on the shady slopes of Kunlun Mountain and listened to the calls of the phoenix at the foot of Qiyang Mountain, establishing musical scales based on natural materials and documenting them according to the sounds of nature. Once the musical scales were established, the Huangzhong, the fundamental pitch, was established; once the numbers were determined, the qi (vital energy) was also established. Thus, this laid the foundation for various measurements and musical scales. This system has remained unchanged by countless emperors. Under Emperor Wu of Han, a dedicated position was created for music coordination, and during the reign of Emperor Yuan, Jing Fang clarified the sixty musical scales, which was done with meticulous attention to detail. During Wang Mang's rule, he even sought out talents nationwide who understood musical scales, and Liu Xin compiled and summarized these materials for submission, resulting in a comprehensive compilation, which Ban Gu subsequently included in his historical records. In the Eastern Han, an official named Yan Chong was also well-versed in musical scales, but unfortunately, his son failed to inherit his skills, and this art was lost. During the Wei dynasty, Du Kui was also proficient in musical laws, and Xun Xu, the head of the Zhongshu, used Du Kui's laws to correct the eight sounds, claiming that the rulers from the Later Han to the Wei were over four parts longer than the ancient rulers. He also obtained the ancient jade laws and named this new set of laws, stating that it conformed to ancient practices, thus altering the musical scales of the Jin dynasty, which led to criticism from the Cavalry Commandant Ruan Xian, who said the sound was too high. After Yongjia, with continuous warfare in the Central Plains, no one cared about the examination of musical scales anymore. This knowledge has survived only in minority regions, with only a handful of musical instruments still in existence.
Now, let's continue.
The Wei family quelled those chaotic rebellions and obtained many ancient musical instruments. The emperor was worried that these instruments were lying idle, which was a shame, so he ordered Gao Lu, the Minister of Ceremonies, to organize the musical scales during the Taihe period. However, this task was left unfinished for a long time. Later, Gao Lu was appointed Inspector of Xiangzhou. Eighteen years later, Gao Lu submitted a memorial stating, "The 'Book of Documents' says, 'to unify laws, measures, and weights', and the 'Analects' states, 'to be cautious in weighing and carefully check the laws'. These four things are the most important for an emperor and the foundation upon which the common people depend for their livelihoods. Of these four, which is the most important? I believe it is the law. This is not a trivial matter, as the law fundamentally derives from the qi of heaven and earth. Confucius said, 'nothing is more important than music'. Thus, the influence of music is considerable. Now, to adjust musical scales and create instruments, without laws, proper coordination is impossible; therefore, the law is the foundation of music."
"I was previously tasked with organizing music, and together with the royal scholar Sun Huiwei and the music master Sun Chong, we studied the 'Rites of Zhou,' 'Guoyu,' and 'Later Han Law and Calendar Records,' using Jing Fang's theory as the standard to determine the laws, adjusting the silk strings with tuning pipes, calibrating the bamboo pipes with law rulers, and distinguishing the eight tones. I have completed these tasks in broad strokes. I have submitted the memorials three times, and the contents are in the previous memorials. I am nearing seventy, growing older every day. I am afraid that I will suddenly die one day without leaving any contribution, leading to a disruption in the musical traditions and leaving regrets after death. This makes me anxious, and I cannot afford to slack off at all. Recently, I met Sun Chong in Ye City. I find him to be intelligent, capable, diligent, and talented. Although he is not a talented ruler, he is very good at scrutinizing and verifying, so I recommend him to teach music. Let him write 'Discussions on the Bells and Chimes' based on my previous research on music, listing the various musical instruments. It can be seen that there is no lack of talent in this world. But now Sun Chong is only teaching music notation to children and has not seriously studied music. I am worried that the work in music theory is being neglected, and the delicate nuances of music theory will be hard to pass down, and learning will also slack off, which goes against my original intention."
"So I want Sun Chong to participate in the research on music theory and bells and chimes, allowing him to learn and grow through practice, which will yield better results. Please take a look at the three memorials I submitted earlier and the 'Later Han Law and Calendar Records,' carefully consider my proposals, as this will help resolve the issues swiftly. In addition, the writer Han Xianzong is knowledgeable, has a strong memory, has a talent for history, and knows a little about music theory. Please let him participate as well. Although I am an official in a foreign land, I follow the ancient practice of recommending talents. I cannot help but speak out, even if it exceeds my authority, it is also for the benefit of the country. I hope you will not dismiss talented individuals due to my candidness." The emperor graciously approved his memorial.
In the fourth year of Jingming, an ancient bronze weight measure was discovered in Bingzhou, and the emperor ordered that it be entrusted to Chong as the standard for establishing musical measurements. During the Yongping period, Chong manufactured a new ruler, using the length of a single grain of millet as the unit of measurement. Later, the Minister of Rites, Liu Fang, was commissioned to revise the musical scales, and he designated the width of a medium-sized grain of millet as one 'fen.' Meanwhile, Lieutenant Yuan Kuang measured the gap between two grains of millet, measuring it with the width of a single grain to define one 'fen.' The three parties presented differing opinions, and after a long debate, no consensus was reached. It wasn't until the nineteenth year of Taihe that Emperor Gaozu issued an order, stipulating that the width of a single grain of millet be used as one 'fen,' and the length of ninety grains of millet as the standard for the bronze ruler. The relevant authorities reported that this was in accordance with previous edicts and that Liu Fang's ruler was the same as the one established by Emperor Gaozu, so Liu Fang's ruler was officially adopted to revise the instruments of metal and stone. Even until the end of the Wuding period, there were no true experts in the laws.
The calendar is a field of study that counts, explores the laws of the universe, and investigates subtle mysteries. It can be used to calculate the movements of the seven celestial bodies (the Sun, Moon, and five planets) and to guide the production and lives of people throughout the world. Since the time of the Yellow Emperor, the methods of calculating and updating the calendar have changed throughout the Xia, Shang, and Zhou dynasties. During the Qin Dynasty and early Western Han Dynasty, the "Zhuanxu Calendar" was used, and the "Three Unifications Calendar" was not implemented until over a hundred years later. In the Eastern Han Dynasty during the reign of Emperor Xiaozhang, the "Four Divisions Calendar" was adopted, and during the Guanghe years, it was changed to the "Qianxiang Calendar." In the time of Emperor Wen of Wei, the calendar created by Han Yi was adopted, and by the time of Emperor Ming of Wei, the "Jingchu Calendar" by Yang Wei was adopted. Up until the Western Jin Dynasty, there were no further changes to the calendar. The Astronomical Bureau was responsible for monitoring celestial phenomena, and each dynasty had its own methods. Although the starting points and final results differed, each had its respective advantages and disadvantages in coordinating the movements of the Sun and Moon and determining time. In the early years of Emperor Taizu's reign, he ordered the Grand Historian Chang Chong to revise the armillary sphere for observing celestial phenomena, continuing to use the "Jingchu Calendar." Over time, the "Jingchu Calendar" became increasingly inaccurate. After Emperor Shizu pacified Liangzhou, he acquired the "Xuanshi Calendar," revised by Zhao Xuan, which he found to be more precise, thus replacing the "Jingchu Calendar." During the reign of Zhenjun, Minister of State Cui Hao compiled the "Wuyin Yuan Calendar," but before it could be implemented, Cui Hao was assassinated, leaving the work unfinished. During the reign of Emperor Gaozu in the Taihe years, he ordered the appointment of Secretary Zhong Lulang Zhang Mingyu as Grand Historian to revise and summarize the calendar, but he passed away before it could be completed. After the capital was moved to Luoyang, there were consecutive southern campaigns, and the emperor also died. During the reign of Emperor Sejong in the Jingming years, the emperor ordered Grand Music Official Gongsun Chong and Grand Music Official Zhao Fansheng to thoroughly study the calendar together.
In the winter of the fourth year of Zhengshi, Gongsun Chong presented a memorial stating: "I previously worked in the Tai Le Bureau, where I studied metal and stone inscriptions in detail. Later, while working in the Secretariat, I researched astronomy and calendars, consulted ancient and modern literature, and carefully analyzed the gains and losses of the calendar. However, the changes of the four seasons, the transformations of the five elements, and the succession of emperors should all align with the original calendar. Modifying the calendar and changing the year names and attire is essential to adapt to the changes of the times and align with the way of heaven. The Book of Changes states that the revolutions of Kings Tang and Wu were successful because they managed the calendar well, resulting in peace throughout the realm. Therefore, the calendars of various dynasties differ. Your Majesty has inherited the mandate of heaven to unify the world; although wars are still ongoing and there is no time to deal with calendar matters, the calendar used during the early years of Wei Jing had errors in its calculation methods, which did not match the actual situation. After Emperor Shizu ascended the throne and unified the country, he ordered Duke Cui Hao of Dongjun, the then Minister of Works, to revise the calendar. Cui Hao is knowledgeable and recompiled the calendar, also writing the "Theory of the Five Elements." At that time, Duke Gao Yun of Xianyang, the Minister of Works, also extensively read various texts, was proficient in the study of the five elements, and wrote works on the Hongfan. However, their studies were not exhaustive enough. After Emperor Gaozong ascended the throne, he adopted the "Jia Yin Calendar" from Dunhuang Zhao, but the astrological calculations of this calendar still had some discrepancies. I have collected different opinions, carefully studied their pros and cons, and re-established a new calendar. Starting from the Jia Yin year, I calculated its gains and losses, and the calculations of astronomical phenomena are precise and straightforward. It has been in use since the Jingming period, hence it is called the "Jingming Calendar." However, how can one claim that the fluctuations in the way of heaven are absolutely accurate? It must be verified through repeated observations before it can be used. Grand Historian Xin Baogui is well-versed in astronomy and calendars; Secretary Jian Zheng Daozhao is exceptionally talented and knowledgeable; Guozijian Doctor Gao Sengyu is the grandson of the former Minister of Works Gao Yun, and his family has been composed of scholars for generations; Shangshu Cibu Minister Zong Jing is knowledgeable and talented, proficient in classics and history; and former Shangshu Minister Cui Bin also has some understanding of astronomy and calendars. I would like to invite these individuals to collaborate on observations and verification in the Secretariat. The critical period is the five days before and after the winter and summer solstices, as reliable verification results can only be obtained during this time. I hope my modest contribution can benefit the country."
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The emperor said, "When calculating astronomical phenomena and calendar systems, it is crucial to be thorough and diligent. Let Minister Fang lead the Imperial Academy along with the scholars from the Four Gates to conduct a thorough study together based on your recommendations."
In the winter of the fourth year of the Yanchang era, Cui Guang submitted a memorial saying, "The Book of Changes states, 'A gentleman uses it to govern the calendar, making the timing clear'; the Book of Documents states, 'The calendar is used to observe the sun, moon, and stars, and thus unify laws, measures, and weights'; Confucius explained the rules of later generations of emperors, saying 'to use the balance carefully, and examine the laws carefully'; The Spring and Autumn Annals record 'the ancient kings established the calendar and implemented it with care from the outset,' and also said 'the emperor has officials specifically responsible for the calendar.' Therefore, since the time of the Yellow Emperor, the Rongcheng family has established the calendar; until the time of Tang Yao, Xihe observed the sun's shadow and established the calendar, all for the accurate grasp of the farming season, emphasizing important matters of the people's livelihood. In the eleventh year of Taihe, I was promoted from a scholar to a writer, in charge of compiling historical books. At that time, the former official Zhang Mingyu calculated the calendar and established the Jichou element, but the preparations were inadequate at that early stage. Later, when the capital was moved to Zhongjing, I was transferred to the position of Taishi Ling, and not long after, he passed away, and the calendar he had established was discarded. I was involved in the historical revision work. In the early years of Jingming, I submitted a memorial requesting that Feng Che Weijun, Taishi Ling Zhao Fansheng, Zuo Lang Zhang Hong, and Yushi Zhong, Taiyue Ling Gongsun Chong, and others work together to establish the calendar, but the work was still incomplete, and Zhao Fansheng passed away, Zhang Hong was transferred to serve as the Changshi of Jingzhou, leaving Gongsun Chong alone to undertake this task. In the early years of Yongping, he said the calendar was basically completed. At this time, Zhang Hong was transferred back to the capital, and I submitted a memorial requesting a revision of the previous calendar, and invited Taishi Ling Zhao Sheng, Taifu Ling Pang Lingfu, and Zhang Longxiang, the son of Zhang Mingyu, to review the classics together and carefully check and improve the calendar with Gongsun Chong and others. However, the mysteries of the cosmos are boundless, and calculating the calendar is extremely complex. Observing and calculating require a long time. Several years passed, and Gongsun Chong and Zhao Sheng passed away successively. Zhang Hong's calendar was based on the Jia Wu and Jia Xu two eras, and he was transferred to serve as the Sima of Yuzhou. Pang Lingfu was also transferred to serve as the Prefect of Puyin. When Zhang Hong arrived in Yuzhou, he continued to establish the Jia Zi and Ji Hai two eras. Only Zhang Longxiang remained in the capital, completing the previous task alone. Because the Wei Dynasty's fortune aligns with the element of water, he established the Jia Zi era, and the archivist Li Ye also participated in the establishment of the calendar, establishing the Wu Zi era. The calendars of these three families were not adopted. Therefore, the recluse scholar Li Shi privately devised a calendar, which is said to conform to historical chronology. I requested his brother Li Yang to hand over the calendar, compare it with the calendars of Zhang Hong and others, in order to understand their strengths and weaknesses. I believe accurately calculating the calendar by observing celestial phenomena is quite challenging. I also requested the summoning of some experts in arithmetic and classics, such as the former Minister of War Sima Gaochuo, the Prefect of the Imperial Guard Lu Daoqian, the former Changshi of Jizhou Zhendong Zuying, the former scholar of Bingzhou Wang Yanye, and the Yezhe Pushe Changjing, etc., to come to the Secretariat every day and review the calendar alongside the historians; the court ministers also visited every fifteen days to examine the strengths and weaknesses of the calendar, and then choose the best calendar to submit to the court for adoption. The deadline is the end of the year. However, as time passes, the system is constantly changing, and the results of ancient and modern chronological studies may also differ, so the calculations of the calendars from the three dynasties show differing start and end times. I participated in this work, but I am old and weak, and have lost the ability to strategize, and I am ashamed of my knowledge of the calendar. Therefore, I have let down both the court and my own expectations, and I am very ashamed.
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Empress Ling decreed, "It can be done as he requested."
In the winter of the fourth year of the Yan Chang era, King Yi of Qinghe, the Grand Tutor, Minister of Works King Cheng of Rencheng, Yuan Hui, the Assistant Minister of the Imperial Secretariat, and Military Minister King Ji of Jiangyang jointly submitted a memorial stating: "The workings of heavenly principles are deep and mysterious, beyond our complete understanding; the shifts in history and the workings of fate are even more enigmatic and unpredictable, so how can we easily draw conclusions based on subjective speculation? Currently, there are widespread discussions, with various opinions emerging, all competing to express their predictions about future development trends, making it difficult to find a unified opinion. Without establishing a clear standard for measurement, we cannot verify whether these claims are true and reliable. Although similar investigations were conducted during the Yongping period, the time was too short and did not involve long-term in-depth research, so we cannot ultimately ascertain the accuracy of these predictions, nor do we fully grasp the extent of the errors. After careful study, we believe that a new wooden sundial should be erected on this year's winter solstice to measure the shadow's length, observing the changes in the shadow diligently for three consecutive years, so that we can know whether these predictions are accurate. This way, we can reach a clear conclusion on what is right and wrong, and those who have been endlessly debating can finally stop arguing, after which we can choose the most reasonable plan from the discussions for further deliberation."
The memorial continued to say that they believed a new sundial should be erected on this year's winter solstice to measure the shadow and observe it continuously for three years, to verify the accuracy of various predictions and thereby quell the debates, ultimately making the correct decision. This suggests that predicting future trends is a complex endeavor that cannot rely solely on subjective speculation; it requires scientific basis and methods. They proposed verifying these predictions through long-term shadow observation, showcasing their rigorous governance philosophy and pragmatic scientific approach. "The heavenly principles are distant and cannot be measured by human feelings; the subtlety of history cannot be gauged by mere intention." These lines further illuminate the core reason behind their cautious decision-making.
Once upon a time, during the Guangfu era, an official submitted a petition stating: the ancient text "Spring and Autumn Annals" records, "The Emperor has officials specifically responsible for the calendar, and the feudal lords have them as well." It also mentions, "Matters must be well-prepared from the very beginning," and "In the end, one must be good at both starting and finishing." All of this is to calculate the yin and yang energies, study the five movements and six energies, determine the movements of the seven celestial bodies (the sun, moon, and five stars), interpret the eight trigrams, establish the concept of the three realms: heaven, earth, and humanity, and formulate the order of the four seasons, then impart this knowledge to the court officials and the common people of the world. The principles of yin and yang, rigidity and flexibility, and benevolence and righteousness are all included within. Therefore, throughout ancient times, all dynasties placed great importance on the calendar, recording it in their classics. Detailed discussions can be found in "Records of the Grand Historian," "Book of Han," and the works of Sima Biao.
I have carefully studied the development of the calendar, which began during the time of the Yellow Emperor. The year Xinmao marked its beginning, continuing until the year Jiayin in the Wei dynasty, spanning over ten dynasties and thousands of years, with different standards and methods used across dynasties, and each region having its own differences. The patterns of changes in the calendar and the accuracy of predictions are quite complex. During the winter of the fourth year of the Yanchang era, General Zhang Hong, Cavalry Commander Zhang Mingyu (Zhang Hong's father), General Long Xiang, and Scholar Li Yexing from three families simultaneously submitted new calendars, all hoping the court would adopt them. Although I do not know much about calendars, I took the initiative to suggest, since I served in the Observation Pavilion, to widely solicit the opinions of Confucian scholars, selecting those who understand both calendar calculations and the classics, along with the Grand Historian's office, to gather materials in the Secretariat, verify the calendars' accuracy with the historians, and then have the Prime Minister and officials check for any errors in the calendar, to decide which calendar to adopt by the end of the year. The Emperor approved my suggestion.
At that time, the Grand Tutor, Grand Marshal, Prince of Qinghe, and other ministers believed that the workings of heavenly principles were very complex and hard to fully understand quickly. They suggested first establishing observation instruments to observe for three years and then choosing the best calendar for modification. The emperor agreed. Therefore, Zhang Hong and his colleagues, together with the former Grand Historian of the Eastern Command, Zu Ying, dedicated themselves to research. After three years of thorough examination, they finally completed this arduous task. Upon careful review, in addition to the calendar previously submitted by Zhang Hong and his two associates, there were also contributions from the Prince Consort and General Lu Daoqian, former Commander Wei Hongxian, General Hu Rong who was also the Grand Historian, as well as Daoist Tong Dao Rong from Yongzhou, Fan Zhongzun from Henan, and Zhang Sengyu from Julu, totaling nine contributors who collectively completed a calendar. This calendar begins in the Renzi year, with the starting pitch of the musical scale being Huangzhong. It not only aligns with ancient principles but also fits modern practical situations, making it arguably the most precise.
Previously, during the reign of Emperor Wu of Han in the Yuanfeng era, the calendar was revised, changing the era name to Taichu, and it was called the "Taichu Calendar"; during the reign of Emperor Wen of Wei in the Jingchu era, the calendar was revised and named the "Jingchu Calendar." Your Majesty, you are exceptionally wise, with merits that surpass those of ancient emperors, and auspicious signs appear frequently—truly a blessing from heaven for Da Wei! The Renzi year belongs to the north in the Eight Trigrams, which is the proper position of water; the turtle is an aquatic animal, reflecting the fortunes of the Wei dynasty; the mother-child correspondence is aptly captured in the poem "Lin Zhi." Therefore, it is suggested to name this calendar the "Divine Turtle Calendar." Now I present this calendar to Your Majesty and request it be submitted to the relevant departments for thorough review. If it can be adopted, it should be kept in the royal archives, and its contents recorded in the historical texts.
The emperor accepted this calendar, issued a general amnesty, changed the era name, and named this calendar the "Zhengguang Calendar," issuing it nationwide. This calendar was jointly revised by the nine contributors, with Long Xiang and Li Yexing as the main responsible persons.
Starting from the Renzi year, until the first year of Duke Yin of Lu, known as the Jimi year, a total of 166,507 days have passed, excluding leap days. Starting from the Jia Yin year, until the year of Duke Yin, known as the Jimi year, a total of 45,307 days have passed, also excluding leap days.
Starting from the Renzi year, until the third year of Weizhengguang (Renyin), a total of 167,750 days have passed, excluding leap days; starting from the Jiashen year, until the second year of Xiaochang (Bingwu), a total of 46,554 days have passed, also excluding leap days. Starting from the Renzi year, until the third year of Weixiaochang (Dingwei), a total of 167,756 days have passed, including leap days; starting from the Jiashen year, until the third year of Weixiaochang (Dingwei), a total of 46,556 days have passed, including leap days.
Zhang (the term for the accumulated leap days over the years, calculated after accounting for leap months): 505 days. (In ancient times, with 19 years having 7 leap months, when the accumulated leap days reach a specific threshold, on the day of the full moon, when the moon appears in the east and a solar eclipse occurs before sunset, the calendar needs to be adjusted to match the celestial phenomena. With over 200 years, there is an extra day, and over 300 years, there is an extra day and a half, causing a deviation in the lunar calendar. Therefore, ancient scholars and scriptures all believed that "the calendar should be revised every 300 years." By reducing leap days, reducing one leap day every 505 years, and reducing one month of leap days every 9,595 years, from the fifth year of Xigong until now, the occurrence of solar eclipses and the lunar calendar's new moon rarely diverge by more than two days, with more cases of conjunction. When the accumulated leap days total a month, it is referred to as a Zhang.)
Zhangrun (the number of leap months in 505 years): 186. (The number of leap months within 505 years, subtracting one-nineteenth of the old calendar.)
Zhangyue (the total number of months in 505 years, including leap months): 6,246 months. (The total number of months in 505 years, including leap months.)
Bufa (referring to Bu, where twelve Zhang constitute one Bu): 6,060 days. (Twelve Zhang make up one Bu, and by this year, the remaining days are insufficient to form a complete unit of measurement.)
Duo Fen (referring to the Duo Fen system, the four-point method): 1,477 days. (The result of the four-point method calculation is 1,515 days, which follows an ancient calculation method. Now reduced by 38 days, because over seven days have been reduced since the fifth year of Xi Gong, which is the closest to the actual situation. Reducing the number of days for 113 years is excessive, so adjustments are needed every thirty years for four solar terms.)
Recording law (referring to a record, where ten parts make one record): 66,000 days. (Ten parts make one record, with ten days remaining.)
Unified law (referring to the unified, where two records make one unified): 121,200 days. (Two records make one unified, with twenty days remaining.)
Yuan law (referring to the Yuan, where three unified make one Yuan): 363,600 days. (Three unified make one Yuan, with no remaining days.)
Daily calculation (referring to the daily calculation, twelve multiplied by the lunar month): 74,952 days. (Twelve multiplied by the number of lunar months gives the daily calculation. Lunar months, leap months within a year.)
The total number of weeks is 2,213,377, which, when calculated using the degree method, equals 365 degrees, which includes the Duo Fen system.
The Qi Law is twenty-four; there are twelve solar terms in a year, each solar term is divided into early and mid, so there are a total of twenty-four solar terms.
The remainder days in a month total twenty-nine, with an additional 39,769 days remaining. This is obtained by dividing the daily calculation by the total number of weeks. The daily calculation is the number of months in a month, and the total number of weeks is the number of days in a month. By dividing the number of months by the number of days, it can be determined that a month is twenty-nine days, and the remaining days, this remainder is the month's pass.
The meeting count is 173, with a remainder of 23,208. Subtracting twenty from five times twenty-three gives one hundred and thirty-five, then multiplying this number by the total number of weeks. Then multiply twenty-three by the daily calculation and divide by this result to obtain one hundred and seventy-three and the remainder.
The meeting pass is 1,298,904. Multiply the daily calculation by the meeting count, then subtract the meeting remainder.
The weekly count is twenty-seven, with a remainder of 41,562. Divide the degree measurement for the first day of the month by the total number of weeks to get twenty-seven days and the remainder.
The total week count is 2,652,266. Multiply the daily calculation by twenty-seven, then subtract the weekly remainder.
The small week is 6,751. The degree measurement for the first day of the month is thirteen degrees, multiplied by the chapter year, then subtract the chapter leap.
The lunar month is calculated as eighty-one thousand one hundred and twelve. You can obtain this number by multiplying twelve by the 'small week,' which corresponds to the degree.
The method for calculating the new moon is as follows:
To calculate the accumulated months, first write down the year you want to calculate, then note the zhang month next to it. Multiply the zhang month by the year to get the accumulated months; the non-integer part is the leap remainder. If the leap remainder exceeds three hundred and nineteen, that year is a leap year.
The method for calculating the new moon day is: multiply the common value by the accumulated months to get the new moon integral, then divide by the new moon integral using the day calculation method to get the accumulated days; the non-integer part is the small remainder. Subtract the accumulated days from sixty to find the large remainder. Record the year and calculate alongside it to determine the date of the new moon in November of the desired year.
The method for calculating the first quarter, last quarter, and full moon days is: based on the new moon day, add seven to the large remainder, the small remainder of twenty-eight thousand six hundred and eighty, and the small fraction of one. If the small fraction reaches four, subtract it from the small remainder; if the small remainder reaches the day calculation method, subtract one from the large remainder; if the large remainder reaches sixty, subtract sixty. This will give you the date of the first quarter. Continue adding to get the full moon day; continue adding to get the last quarter day; continue adding to get the new moon day of the next month.
The method for calculating the twenty-four solar terms is as follows:
This text outlines the ancient methods for calculating astronomical calendars, which can be quite intricate and specialized.
First, the method for calculating the twenty-four solar terms: "First, calculate the remainder of the year since the epoch, then multiply this remainder by a specific coefficient. Then divide this by a value known as 'bu' to get a value referred to as 'jimo'; the remainder is termed 'xiao yu'. Divide 'jimo' by sixty; the remainder is termed 'da yu'. Next, calculate the remainder of the year since the epoch, and determine the date of the winter solstice in the eleventh month of the lunar calendar for that year. To calculate the next solar term, add 'da yu' multiplied by fifteen to the winter solstice date, then add 'xiao yu' multiplied by one thousand three hundred and twenty-four, plus a small fraction (when the small fraction reaches twenty-four, it becomes a 'xiao yu'; when 'xiao yu' reaches a 'bu', subtract one from 'da yu'; when 'da yu' reaches sixty, subtract sixty, then repeat the above steps) to get the date of the next solar term." This passage explains how to calculate the specific dates of the twenty-four solar terms based on the year, involving many professional terms, and understanding requires a certain knowledge of calendrics.
Next is the calculation method for leap years: "Subtract 550 (the chapter year) from the leap remainder, then multiply the remaining number by 12. If the result is greater than or equal to 186, it means there is a leap month in that year; if half of the remaining number is at least 93, it also means there is a leap month in that year. Starting from the eleventh month (lunar November), the calculated leap month is the leap month. The leap month can sometimes occur earlier or later, depending on whether there is a solar term in that lunar month." This passage explains how to determine leap years and the position of leap months in the lunar calendar.
Finally, here is the list of the twenty-four solar terms as directly quoted from the original text:
Winter Solstice (冬至) around the eleventh month, Minor Cold (小寒) in the twelfth month, Major Cold (大寒) around the twelfth month, Start of Spring (立春) in the first month,
Rain Water (雨水) around the first month, Awakening of Insects (惊蛰) in the second month, Vernal Equinox (春分) around the second month, Pure Brightness (清明) in the third month,
Grain Rain (谷雨) around the third month, Start of Summer (立夏) in the fourth month, Minor Fullness (小满) around the fourth month, Grain in Ear (芒种) in the fifth month,
Summer Solstice (夏至) around the fifth month, Minor Heat (小暑) in the sixth month, Major Heat (大暑) around the sixth month, Start of Autumn (立秋) in the seventh month,
End of Heat (处暑) around the seventh month, White Dew (白露) in the eighth month, Autumnal Equinox (秋分) around the eighth month, Cold Dew (寒露) in the ninth month,
Frost Descent (霜降) around the ninth month, Start of Winter (立冬) in the tenth month, Minor Snow (小雪) around the tenth month, Major Snow (大雪) in the eleventh month.
Finally, there is the part about the calculation of solar and lunar eclipses. This part is also quite complicated: "The third method of calculation is to calculate the conjunction of the sun and moon. The method of calculating the date of a solar or lunar eclipse is as follows: first, add the accumulated points since the epoch to the conjunction difference value (using the Jia Shen epoch, the difference is 7,418,784), then divide by the cycle, obtaining the accumulated value, and divide the remainder by the daily calculation, obtaining the degree distance and remainder from the conjunction point to the first day of the eleventh month of that year. To calculate the conjunction point of the next month, add 29 days and 39,769 degrees to the previous month's base, then calculate using the same method. To calculate the degree distance from the conjunction point to the full moon, add 14 days and 57,360.5 degrees to the previous month's base. If the degree remainder exceeds the daily calculation, subtract from the degree value; if it exceeds the cycle, subtract from the cycle; if the degree remainder is not enough to subtract, subtract one degree and add the cycle, to obtain the degree distance and remainder from the full moon to the conjunction point. If the degree distance and remainder from the conjunction point to either the new moon or full moon fall within certain ranges (new moon: 14 degrees to 158 degrees, full moon: 57,360.5 degrees to 47,999.5 degrees), a solar or lunar eclipse will occur." This passage describes how ancient people predicted solar and lunar eclipses, involving many professional terms and complex calculation methods. The entire process requires a deep understanding of ancient astronomical calendars in order to comprehend.
It is said that in the year of Jia Zi, during the conjunction month (when the new moon and sun align in the lunar calendar), the sun and moon perfectly aligned, just like a jade bi; this is referred to as "the sun and moon are like a perfectly aligned jade bi."
Next is the year of Jia Xu; during the conjunction month, the moon and sun were forty-nine degrees apart on the ecliptic, with a remaining distance of thirty-six thousand seven hundred forty-four degrees. In the year of Jia Shen, the moon and sun were ninety-eight degrees apart, with a remaining distance of seventy-three thousand four hundred eighty-eight degrees. In the year of Jia Wu, they were one hundred forty-eight degrees apart, with a remaining distance of thirty-five thousand two hundred twenty-eight degrees. In the year of Jia Chen, they were twenty-four degrees apart, with a remaining distance of forty-eight thousand eight hundred sixteen degrees. Finally, in the year of Jia Yin, they were seventy-four degrees apart, leaving a remaining distance of one thousand six hundred eight degrees.
Now we need to calculate the intersection point (the intersection of the moon's orbit and the sun's orbit) for what month. The method is: first subtract the remaining degrees from the first day of November from the distance difference and remaining degrees calculated earlier. If the subtraction is insufficient, subtract one degree first, then calculate using the specified method, and then add the remaining degrees of the first day of November. If it exceeds the degrees for one day, subtract that amount, and the remaining amount is the day's remainder. Starting from November of the previous year, calculate based on the number of days in each month; if the result is less than a month, that month is when the intersection occurs, and the calculated date is the date of the intersection. If the intersection occurs before the full moon (the fifteenth day of the lunar month), then the first day of this month is the intersection, and the fifteenth features a lunar eclipse; if the intersection is after the full moon, the fifteenth of this month is a lunar eclipse, and the first day of the next month is the intersection. If the intersection happens exactly at the full moon, this month features a lunar eclipse, and the first day of the previous month and the first day of the next month are both intersections; if the intersection happens exactly at the new moon, this month features a solar eclipse, and the fifteenth of the previous month and the fifteenth of the next month are both lunar eclipses. Finally, how do we calculate the time of the next intersection? Add the distance difference and remaining degrees calculated earlier to the date and remaining degrees of the previous intersection. If it exceeds the degrees for one day, subtract that amount, then calculate based on the number of days in each month, starting from the month of the previous lunar eclipse, and you can find out the month and date of the next intersection. This passage discusses ancient astronomical calculations; in modern language, this describes how to predict solar and lunar eclipses.
First, it introduces a method for calculating the moon's position in the ecliptic, called the "method for calculating the moon's position in the ecliptic." The meaning of this passage is: first calculate the conjunction point of the moon and the sun, and then calculate based on some parameters (such as the conjunction difference for the Jia Shen year, which is 7,418,784). If the calculated result is less than a specific value ("conjunction"), then determine the moon's position relative to the ecliptic (south is outside, north is inside) to ascertain whether the moon is on the inside or outside of the ecliptic. If the calculated result is greater than or equal to this value, then the positions inside and outside are reversed. The final result should have certain values subtracted to arrive at a "degree of advance and remainder." Next, add the remainder from the new moon in the eleventh month, and if it exceeds a day's value, subtract a day from the degree. Then adjust according to the number of days in the month to calculate the specific date and time of the solar eclipse. It also mentions the order of occurrence of solar and lunar eclipses, as well as the variation of the moon inside and outside the ecliptic. The phrase "'one in and one out' is a fixed rule" means that the pattern of the moon entering and leaving the inside and outside of the ecliptic is fixed. It also explains the relationship between the new moon and the solar and lunar eclipses; for example, "if it intersects after the new moon and before the full moon, then the position of the moon at the new moon is the same as in November, while the full moon is opposite."
Next, it introduces the method for calculating the starting angle of the shadow when predicting the occurrence of solar and lunar eclipses, called the "method for calculating the starting angle of the shadow." The meaning of this passage is: based on whether the moon is inside or outside the ecliptic, as well as the order of the conjunction and intersection points, determine the direction from which the eclipse shadow begins. If the moon is outside the ecliptic, with the conjunction occurring before the intersection point, the shadow begins from the southeast; if the intersection point occurs before the conjunction, the shadow begins from the southwest. The situation is similar when the moon is inside the ecliptic. If a solar or lunar eclipse occurs at the time of opposition between the sun and moon, the method of determining the starting angle is the same. Finally, it is mentioned that solar and lunar eclipses occur within fifteen degrees before and after the intersection point, with noticeable eclipses occurring within ten degrees, and beyond ten degrees, it is just a meeting of light and shadow.
Finally, it introduces the method for calculating the size of solar and lunar eclipses, called the "method for calculating the eclipse fraction," meaning: subtract the time difference between the new moon and the intersection point from fifteen degrees (the intersection limit), and the remaining value indicates the size of the solar and lunar eclipses.
The last sentence "推合朔入历迟疾盈缩第四" is about how to incorporate the calculated results of the new moon into the calendar, as well as some adjustments in the calendar, such as intercalary months.
This passage talks about the ancient method of calculating calendars, which appears to be quite complex. The first paragraph explains how to calculate which day the first day of the eleventh month of a year (the first day of each month in the lunar calendar) falls on. It uses a method called "integrating the new moon's accumulated data since the epoch," and also considers something called "the difference between delay and speed." An example of the Jia Shen calendar is mentioned, with a delay and speed difference of 1829792. In the end, after all the calculations, the specific date can be determined.
The second paragraph explains how to calculate the first day of the next month. The method is to first add one day, then add a value known as "day remainder" (73159). If the "day remainder" exceeds a certain number of days (the days of the month, possibly), subtract that number of days, and the remainder is the first day of the next month. If the "day remainder" is not enough, subtract one day, then add a value known as "virtual week." This section also lists the "day remainder" for different epochs, such as 63568 for the Jia Zi epoch and 42256 for the Jia Xu epoch, and so on.
The third paragraph explains how to calculate the full moon day (the fifteenth day of each month in the lunar calendar). The method is to first add fourteen days, then add a "day remainder" (57360.5), and then add some other elements to determine the calendar date for the following month.
The last paragraph is a table that records various data on the speed of lunar motion, including "speed of lunar motion and difference," "gain and loss rate," "fullness and contraction," "fullness and contraction integral," and so on. These are used to more accurately calculate the parameters of the moon's movement and the calendar. It seems to be a summary of regularities based on observational data, used to correct calculation results. These data are very professional, and a deeper understanding of ancient astronomical calendars is needed to grasp their specific meanings. In conclusion, this passage describes a complex method of ancient calendar calculation, involving many professional terms and calculation steps.
From the first day to the seventh day, I measured thirteen times each day, totaling two hundred and sixty-six points, increasing by eighty, with a surplus of three thousand four hundred and seventy-seven, with the accumulated total reaching thirty-three thousand eight hundred and twenty-nine points.
From the eighth day to the eleventh day, I measured thirteen times each day. On the eighth day, the score was sixty-one points, dropping by one hundred twenty-five, leaving a surplus of three thousand one hundred twenty-seven, and the total points reached thirty-four thousand seven hundred seventeen. On the ninth day, the score was four hundred thirty-nine points, dropping by two hundred fifty-two, leaving a surplus of three thousand two hundred, and the total points reached thirty-three thousand three hundred twenty-nine. On the tenth day, I measured twelve times, scoring three hundred thirty-eight points, dropping by three hundred fifty-three, leaving a surplus of two thousand seven hundred fifty, and the total points reached thirty-five thousand five hundred thirty-one. On the eleventh day, I also measured twelve times, scoring two hundred thirty-seven points, dropping by four hundred fifty-four, leaving a surplus of two thousand three hundred ninety-seven, and the total points reached twenty-six thousand six hundred twelve.
From the twelfth day to the fourteenth day, I measured twelve times each day. On the twelfth day, the score was one hundred thirty-six points, dropping by five hundred fifty-five, leaving a surplus of one thousand nine hundred forty-two, and the total points reached twenty-one thousand five hundred seventy-two. On the thirteenth day, the score was thirty-five points, dropping by six hundred fifty-six, leaving a surplus of one thousand three hundred eighty-eight, and the total points reached fifteen thousand four hundred ten. On the fourteenth day, I took eleven measurements, scoring four hundred sixty-four points, dropping by seven hundred thirty-one, leaving a surplus of seven hundred thirty-two, and the total points reached eight thousand one hundred twenty-seven.
From the fifteenth day to the twenty-second day, I started to cut back. On the fifteenth day, I measured twelve times, with a score of thirty-six points, an increase of six hundred fifty-five points, which reduced the total by six hundred fifty-five points. On the sixteenth day, I measured twelve times, scoring one hundred ninety points, an increase of five hundred eighty-two points, reducing the total by six hundred fifty-five points, bringing the total reduction to seven thousand one hundred seventy-two points. On the seventeenth day, I measured twelve times, scoring one hundred eighty-nine points, an increase of five hundred two points, reducing the total by one thousand two hundred thirty-seven points, bringing the total reduction to thirteen thousand seven hundred thirty-four points. On the eighteenth day, I measured twelve times, scoring two hundred ninety points, an increase of four hundred one points, reducing the total by one thousand seven hundred thirty-seven points, bringing the total reduction to nineteen thousand three hundred seven points. On the nineteenth day, I measured twelve times, scoring three hundred ninety-two points, an increase of two hundred ninety-nine points, reducing the total by two thousand one hundred forty points, bringing the total reduction to twenty-three thousand seven hundred fifty-nine points. On the twentieth day, I measured twelve times, scoring four hundred ninety-six points, an increase of one hundred ninety-five points, reducing the total by two thousand four hundred thirty-nine points, bringing the total reduction to twenty-seven thousand seventy-nine points. On the twenty-first day, I measured thirteen times, scoring one hundred eighteen points, an increase of sixty-eight points, reducing the total by two thousand six hundred thirty-four points, bringing the total reduction to twenty-nine thousand two hundred forty-four points. On the twenty-second day, I measured thirteen times, scoring two hundred thirty-three points, a decrease of fifty-seven points, reducing the total by two thousand seven hundred two points, bringing the total reduction to twenty-nine thousand nine hundred ninety-nine points.
On the twenty-third day, the temperature was thirteen degrees Celsius, which corresponded to a score of three hundred eighty-eight points, resulting in a loss of two hundred twenty points, reducing the total by two thousand six hundred forty-five points, bringing the total reduction to twenty-nine thousand three hundred sixty-six points.
On the twenty-fourth day, the temperature was fourteen degrees Celsius, which corresponded to a score of twenty-nine points, resulting in a loss of three hundred forty-eight points, reducing the total by two thousand four hundred forty-three points, bringing the total reduction to twenty-seven thousand one hundred twenty-three points.
On the twenty-fifth day, the temperature was fourteen degrees Celsius, which corresponded to a score of one hundred seventy-four points, resulting in a loss of four hundred ninety-three points, reducing the total by two thousand ninety-five points, bringing the total reduction to twenty-three thousand two hundred fifty-nine points.
On the 26th, the temperature was 14 degrees (387 minutes), with a loss of 606 minutes, a reduction of 1,602 minutes, and a decrease of 17,786 points. On the 27th, the temperature was 14 degrees (311 minutes), with a loss of 631 minutes, a reduction of 996 minutes, and a decrease of 11,058 points. On Sunday, the temperature was 14 degrees (339 minutes), with a loss of 650 minutes, a reduction of 365 minutes, bringing the total down to 452 points. The total loss amounts to 9,684 minutes. The method for calculating the size of the conjunction and lunar eclipse is to multiply the remaining days by the profit-and-loss rate, then divide the result by 6,751, and use this to adjust the points to get the final score. If the result is a surplus, subtract it from the remaining days; if it is a reduction, add it to the remaining days. If adding the surplus exceeds the standard for one day, the conjunction will be moved to the next day; if the reduction is insufficient, subtract from the previous day, then add the next day's value and subtract, and the conjunction will be on the previous day. For a lunar eclipse, determine the date and time based on the established remaining days. The method for calculating the time is to divide 6,246 by the established remaining days, and calculate from the starting point of the sub-hour. When there is a remainder in the conjunction, multiply by four, subtract one for the addition, consider two as half, and three as more than half. If there is still a remainder, multiply by three, following the same method; one is strong, half or more is ranked, and less than half is discarded. The combination of strong and weak is referred to as 'less strong', strong and half is called 'half strong', strong and too is called 'too strong', two strong together is called 'less weak', and so on. Then determine the strength based on the hour. The sun's opposition is a break, and the moon is often severely damaged during a lunar eclipse. This text discusses ancient methods of astronomical calculation, which may appear complex at first glance.
The first paragraph talks about what happens after a solar eclipse occurs. "The method for calculating the days after a solar eclipse is as follows: multiply the remaining days by the rate of loss, and add the small fractions of the remaining days." This means that after a solar eclipse, the number of days can be calculated by multiplying the remaining days by a loss rate, and then adding the small fractions of the remaining days. "Then, multiply the remainder of the calendar days by another number to get the numerator, and multiply a smaller cycle by the remaining days of the week to get the denominator. If the result of the numerator divided by the denominator is one, subtract it from the accumulated total." If there is a remainder, add it to the lunar month’s remainder. If the remainder is full, subtract one from the larger remainder to get the number of days after the eclipse. "Continue the calculation as described above." The following calculations are done in the same way.
The second paragraph explains how to calculate the degrees of the sun's movement. "The method for calculating the sun's degrees of movement is as follows: record the days from the beginning of the era to the lunar month, multiply it by the daily degree, subtract a full week, and the remaining days represent the degrees, while any leftover is the remainder." This means to record the days from the beginning of the era to the lunar month, multiply it by the daily degree, subtract a full week, and the remaining days represent the degrees, while any leftover is the remainder. "Start at the twelve degrees before the Ox (which is fifteen degrees before the Dipper). Divide by the constellations, and if it does not complete a full constellation, determine the sun's position at midnight on the first day of the eleventh month." Then, start counting from the twelve degrees before the Ox (fifteen degrees before the Dipper), divide by the constellations, and if it does not complete a full constellation, determine the sun's position at midnight on the first day of the eleventh month.
The third section describes another method for calculating the degrees of the sun's movement. "The method for calculating solar degrees states: set the complete circle at 365 degrees and the doufen (斗分) at 1477, then subtract one from the number of days from the winter solstice to the new moon, and subtract the remaining number from the total degrees of the complete circle. For the remainder at the winter solstice, subtract from the doufen value; if the remainder is insufficient for subtraction, reduce the degree by one, and add the solar degree method, then subtract." This means that first, a complete circle is set at 365 degrees and doufen at 1477, then the number of days from the winter solstice to the new moon is reduced by 1, and the remaining number is subtracted from the total degrees of the complete circle. Next, the remainder from the winter solstice is subtracted from the doufen value, and if it is insufficient, 1 is subtracted from the degrees, adding the solar degree method to complete the subtraction. "The result is the position of the sun at midnight on the new moon of the eleventh month." The final result is the sun's position at midnight on the new moon of the eleventh month.
The fourth section explains how to calculate the sun's position for the next month. "To find the degree of the sun on the next month's day, the method states: for a big month, add 30 degrees; for a small month, add 29 degrees; add one degree for each day; then divide by the next constellation, and finally subtract 1477 from the doufen." This means that for a big month, add 30 degrees, for a small month, add 29 degrees, then add 1 degree for each day, divide by the next constellation, and finally subtract 1477 from the doufen.
The fifth section discusses how to calculate the combined degrees of the moon and sun at the new moon. "The method for calculating the combined degrees of the sun and moon at the new moon states: multiply the annual cycle by the remainder of the new moon, and divide by the chapter month. The result gives the large fraction and the small fraction; if there is a remainder, add it to the midnight sun's degree. If the small fraction exceeds the solar degree calculation, carry over from the degrees." This means to multiply the annual cycle (possibly referring to a cycle) by the remainder of the new moon, divide by the chapter month (possibly referring to a monthly cycle) to get the large and small fractions, then add the small fraction to the degree of the sun at midnight. If the small fraction exceeds the solar degree calculation, carry over from the degrees.
The sixth section calculates the combined degrees of the moon and sun for the next month. "To find the combined new moon degrees for the next month, the method states: add 29 degrees, the large fraction is increased by 3215, and the small fraction is increased by 2455. If the small fraction exceeds the chapter month, carry over from the large fraction; if the large fraction exceeds the solar degree calculation, carry over from the degrees. Then divide by the next constellation, and finally subtract the corresponding value from the doufen total." This means to add 29 degrees, with the large fraction increased by 3215 and the small fraction increased by 2455. If the small fraction exceeds the chapter month, carry over from the large fraction; if the large fraction exceeds the solar degree calculation, carry over from the degrees, then divide by the next constellation, and finally subtract the corresponding value from the doufen total.
The seventh paragraph explains how to calculate the moon's orbital degrees. "The method for calculating the moon's degrees states: record the number of days from the epoch to the new moon, multiply this by the moon's cycle of 81,112, subtract a full circle, and then reduce the remainder using the method of daily degrees to obtain degrees and minutes." This means that first, you note the number of days from the epoch to the new moon, then multiply this number by one lunar cycle (81,112). If it exceeds a full circle, subtract it, and reduce the remainder using the method of daily degrees to get degrees and minutes. "The degrees start from twelve degrees before the Ox constellation, subtracting from the next lunar mansion; if it does not fill the mansion, it is calculated outside, which gives the position of the moon at midnight on the new moon of the eleventh month of the correct calendar year." The final result obtained is the position of the moon at midnight on the new moon of the eleventh month of the correct calendar year.
The eighth paragraph presents another method for calculating the degrees of the moon's orbit. "Another method for calculating the moon's degrees states: multiply the small cycle by the remainder from the new moon as the numerator, and multiply the lunar year by the daily method as the denominator; if the result is one, that is the degree; if it is not enough, divide by the calendar month to get the large fraction, and the remainder is the small fraction. The result is then subtracted from the new moon degrees and minutes, leaving the position of the moon at midnight on the new moon of the eleventh month of the correct calendar year." This means that you use the small cycle multiplied by the remainder from the new moon as the numerator and the lunar year multiplied by the daily method as the denominator. If the numerator divided by the denominator equals one, that is the degree; if it is insufficient, divide by the calendar month to get the large and small fractions, then subtract this result from the new moon degrees, leaving the position of the moon at midnight on the new moon of the eleventh month of the correct calendar year.
In summary, this text describes a rather complex astronomical calculation method that involves many technical terms and steps, making it challenging for modern readers to fully grasp, let alone carry out in ancient times. This reflects the exquisite skill in ancient astronomical observation and calculation.
Let's first calculate the degrees for next month. For a small month (meaning a month with fewer days), add 22 degrees and then 2,651 minutes; for a large month (meaning a month with more days), add 35 degrees and then 4,883 minutes. If the minutes exceed 60, subtract it from the degrees, and then divide the remaining degrees by the degrees of the mansion. If it is not enough for one mansion, it can be disregarded; the remainder is the degree for next month.
Next, let's calculate the degrees the sun travels each day next month. Each day, add 13 degrees and then 2,232 minutes. If the minutes exceed 60, subtract it from the degrees and just keep the degrees, discarding the minutes.
To calculate the degree of the waxing crescent moon (the moon on the eighth and twenty-third day of the lunar month), add 7 degrees to the degree of the new moon (on the first day of the lunar month), then add 2318 large fractions, 5298 small fractions, and 1 micro fraction. When the micro fraction reaches 4, carry over to the small fraction; when the small fraction completes a full month, carry over to the large fraction; when the large fraction reaches a full day, carry over to the degree. By following this method, you can obtain the degree of the waxing crescent moon. Continue adding to calculate the full moon (the fifteenth day of the lunar month), the waning crescent moon, and the new moon of the next month.
The position of the Dipper is 26, the Ox is 8, the Girl is 12, and the Void is 10.
The Scorpion is 17, the Room is 16, and the Wall is 9.
The seven stars of the Black Tortoise in the north add up to 98 degrees (or 1477 out of 2213777 fractions).
The Thigh is 16, the Lou is 12, the Stomach is 14, and the Pleiades is 11.
The Big Dipper is 16, the Beak is 2, and the Can is 9.
The seven stars of the White Tiger in the west add up to 80 degrees.
The Well is 33, the Ghost is 4, the Willow is 15, and the Star is 7.
The Bow is 18, the Wing is 18, and the Arrow is 17.
The seven stars of the Vermilion Bird in the south add up to 112 degrees.
The Horn is 12, the Kang is 9, the Wei is 15, and the Room is 5.
The Heart is 5, the Tail is 18, and the Winnowing Basket is 11.
The seven stars of the Azure Dragon in the east add up to 75 degrees.
The entire celestial sphere is 365 degrees, 6660 fractions, which is 1477 out of 2213777 fractions. Simplify the fractions to obtain the celestial sphere.
This is the sixth method of ancient calendar calculations, associated with the Five Elements, the I Ching, and climate phenomena. This text is quite technical; let's break it down sentence by sentence for better understanding.
First is the "推五行用事日" section: This part explains how to calculate the dates when each of the five elements (water, fire, wood, metal, and earth) each have their ruling dates. It states that each element is dominant for 73 days, with some remainders, including 295 days, 9 minutes, and 3 seconds. Wood is dominant in spring, fire in summer, metal in autumn, and water in winter. To calculate the date when earth is dominant, first find the remainders (small and large) from the start of spring, then add 73 days of wood and those remainders. If the seconds exceed 5, subtract 1 from the minutes; if the minutes exceed 24, subtract 1 from the small remainder; if the small remainder exceeds 60, subtract 1 from the large remainder; if the large remainder exceeds 60, subtract 60. This will yield the date of the Earth King's Day in early spring. Next, add 18 days to the Earth King's Day, along with additional remainders, and calculate using the same method to determine the date of the start of summer. Other dates are calculated in the same manner. Another method is to first calculate the Earth King's Days of the four solar terms (start of spring, start of summer, start of autumn, start of winter) by subtracting 18 days, 1588 days, 20 minutes, and 2 seconds from the remainders of each solar term. If the subtraction is not enough, add 60 before subtracting.
Next is the "推没灭术" section: This part explains how to calculate the dates of "mei." "Mei" probably refers to some astronomical phenomenon, but it's hard to say for sure. It states that starting from the winter solstice, add 1 to the leftovers of "mei," then multiply by the minutes of "mei," and divide by the calculation method for "mei," the result is the "accumulated days," and any excess is termed "mei leftover." Subtract the "accumulated days" from 60 to get the "mei day." To calculate the date of the next "mei," add 69 days and 27764 of "mei leftover" to the previous "mei day." If the "mei leftover" exceeds 31770, subtract 1 from the "mei day"; if the "mei day" exceeds 60, subtract 60. Usually, there are 5 or 6 "mei" in a year, and the day when all remainders are exhausted is referred to as "extinguished day." Another method is to add the days from the winter solstice to the first day of the lunar month to the "mei day," and if the remainders from the winter solstice exceed 60, subtract 1 from the "mei day."
Finally, the "推四正卦术" section: This section is more straightforward, explaining that based on the remainders from the winter solstice, vernal equinox, summer solstice, and autumnal equinox, one can identify the days when the "Kan Gua," "Zhen Gua," "Li Gua," and "Dui Gua" are dominant.
In summary, this text describes a rather complex ancient calendrical calculation method, involving many specialized terms that require a certain level of expertise to understand. Although we translated it sentence by sentence, a deeper study is needed to fully grasp the astronomical and calendrical principles behind it. Ah, this divination is really complicated! First, let's talk about the "Zhongfu" hexagram; after calculations, we add 5,530 days remaining after the winter solstice, divide by 9, and take the remainder as 1. When the micro-fraction reaches five, we deduct it from the small remainder; when the small remainder is full, it is deducted according to the specified method from the remaining days; when the remaining days are full, it is deducted according to the specified method from the large remainder. The final calculated day is the one associated with the "Zhongfu" hexagram. This method is similarly applied to other hexagrams, such as "Jie" plus "Zhen," "Xian" plus "Li," and "Bi" plus "Dui," all of which are similar to "Zhongfu" plus "Kan." Next, we calculate the next hexagram, adding "Kan," with a large remainder of 6, a small remainder of 529, a small fraction of 14, and a micro-fraction of 4. The calculation method is the same as before, with micro-fraction, small fraction, small remainder, and large remainder deducted in order. The final calculated day is the one associated with the "Fu" hexagram. Similarly, "Dazhuang" plus "Zhen," "Gou" plus "Li," and "Guan" plus "Dui" are also like "Zhongfu" plus "Kan." November corresponds to the hexagrams "Weiji," "Jian," "Yi," "Zhongfu," and "Fu"; December corresponds to "Tun," "Qian," "Kui," "Sheng," and "Lin"; January corresponds to "Xiaoguo," "Meng," "Yi," "Jian," and "Tai"; February corresponds to "Xu," "Sui," "Jin," "Jie," and "Dazhuang"; March corresponds to "Song," "Yu," "Gu," "Ge," and "Guai"; April corresponds to "Lv," "Shi," "Bi," "Xiaoxu," and "Qian"; May corresponds to "Dayou," "Jiaren," "Jing," "Xian," and "Shi"; June corresponds to "Ding," "Feng," "Huan," "Lu," and "Dun"; July corresponds to "Heng," "Jie," "Tongren," "Sun," and "Pi"; August corresponds to "Xun," "Cui," "Daxu," "Bi," and "Guan"; September corresponds to "Guimei," "Wuwang," "Mingyi," "Kun," and "Bo"; October corresponds to "Gen," "Jiji," "Shike," "Daguo," and "Kun."
The hexagrams for each month correspond to different meanings, which is rather esoteric. Among them, the four primary hexagrams represent local officials; the "Zhong Fu" hexagram corresponds to the Three Dukes; the "Fu" hexagram signifies the emperor; the "Tun" hexagram stands for the feudal lords; the "Qian" hexagram represents the ministers; the "Kui" hexagram represents the Nine Ministers; and the "Sheng" hexagram returns to the Three Dukes, thus repeating in cycles.
Finally, these hexagrams are also related to the weather! The ninth line corresponds to the upper ninth position, which indicates a clear and mildly warm yang wind; the ninth line corresponds to the upper sixth line, representing a deep red and hot yin rain. The sixth line corresponds to the lower sixth line, representing a white and slightly cold yin rain; the sixth line corresponds to the lower ninth line, representing a twisted dust and cold yang wind. In summary, a yang line in the hexagram indicates a yang wind, while a yin line indicates a yin rain. This practice of fortune-telling is indeed a profound study!
This article discusses the methods of calculating ancient calendars, which may sound somewhat complex, so let’s take it one sentence at a time. The first paragraph talks about the specific methods for calculating solar terms, which can be understood in modern terms as: based on the remainder calculated from the winter solstice (a numerical value in calendar calculations), combined with the day of the Tiger's Crossing (an astronomical phenomenon), plus some specific values (large remainder of five, small remainder of four hundred forty-one, minor division of eight, and micro division of one, etc.), through complex calculations, one can derive the dates of each solar term. These calculation methods are very complex and involve many technical terms, so we won't go into detail here; in short, it is about deriving the dates of each solar term based on the winter solstice and some astronomical phenomena through a series of calculations. The phrase "Ming yi ji, suan wai, suo hou ri" means using these calculation results to determine the solar terms, while the calculations themselves are auxiliary means of calendar computation, with the ultimate aim of establishing the dates of the solar terms.
The following paragraphs list the twenty-four solar terms and the corresponding phenological phenomena for each solar term, in modern terms: starting from the Winter Solstice, they are Winter Solstice (the tiger begins its mating season, the cloud begins to grow, the lychee begins to sprout), Minor Cold (earthworms emerge, deer antlers shed, springs begin to move), Major Cold (geese migrate north, magpies begin to nest, pheasants begin to crow), Start of Spring (chickens begin to lay eggs, east wind melts the ice, hibernating insects begin to stir), Rain Water (fish swim under ice, otters offer fish, wild geese arrive), Insects Awaken (rain begins, peaches bloom, barnacle geese migrate), Spring Equinox (hawks mate, swallows arrive, thunder begins to sound), Pure Brightness (lightning appears, hibernating insects move, hibernating insects come out), Grain Rain (paulownia trees bloom, field mice turn into quail, rainbows appear), Start of Summer (duckweed begins to grow, orioles descend on mulberry trees, crickets start to sing), Grain Full (earthworms come out, melons grow, wild vegetables thrive), Grain in Ear (weeds wither, minor heat arrives, mantises hatch), Summer Solstice (shrikes begin to call, cuckoos fall silent, deer antlers shed), Minor Heat (cicadas start to sing, arisaemas sprout, rose of Sharon blooms), Major Heat (warm winds arrive, crickets inhabit walls, eagles begin to learn), Start of Autumn (decaying grass transforms into fireflies, earth is moist from the summer heat, cool winds arrive), End of Heat (white dew falls, cicadas chirp, eagles prey on birds), White Dew (heaven and earth become serene, violent winds arrive, wild geese arrive), Autumn Equinox (swallows return, birds gather in flocks, thunder ceases), Cold Dew (hibernating insects enter homes, killing energy grows strong, yang qi begins to decline), Frost Descent (water starts to dry up, wild geese arrive as guests, birds enter the water and transform into clams), Start of Winter (chrysanthemums bloom yellow, jackals prey on animals, water begins to freeze), Minor Snow (ground begins to freeze, pheasants enter the water and become mirages, rainbows disappear), Major Snow (ice strengthens, ground begins to crack, hoopoes stop singing). These describe some typical characteristics of animals and plants during each solar term.
The last two paragraphs introduce two other methods for calculating calendars. One section discusses calculating solar terms based on the winter solstice and the beginning of the Tiger, with each five-day interval representing a distinct period. The other section explains the method for calculating the new moon day (the first day of each lunar month), which involves a complex calculation formula involving several steps: "Place the year minus one, add eight, multiply by six rhythms, subtract six thousand, the remainder is the major remainder, calculated outside the Jiazi system, for the new moon day." This also involves many specialized terms, so I won't elaborate here. "The seventh method of calculating the five stars and six communications" refers to a method of calculating celestial phenomena, which is part of ancient astronomy. In summary, the entire article describes the complex methods of ancient calendars and astronomical calculations, involving many specialized terms and calculation methods, which can be somewhat difficult for modern people to understand.
From the year of the Upper Yuan Renzi to the year of Jiwuy in the Spring and Autumn Annals, a total of 166,570 years have passed, not counting in the calculation; up to now, in the second year of Wei Xiping, Dingyou year, a total of 167,745 years have passed, and this does not count in the calculation.
Jupiter has a cycle lasting 2,416,660 days. Mars has a cycle lasting 4,725,848 days. Saturn has a cycle lasting 3,291,021 days. Venus has a cycle lasting 3,538,131 days. Mercury has a cycle lasting 702,182 days.
To calculate the position of the five stars, first subtract one from the number of years from the Upper Yuan to the year you want to calculate, then multiply by the celestial cycle of 2,213,370 days to obtain a number called "the value of six communications." Then use the removal method (a method of calendar calculation) to divide it, and the quotient obtained is the accumulated days of the winter solstice, while the remainder is the minor remainder. Dividing the accumulated days by the sixty-day cycle, the remainder obtained is the major remainder, represented by Jiazi (the sixty Jiazi calendar method), which does not count in the calculation; this is the date of the winter solstice. Then use five hundred and five (the annual age) to divide the minor remainder of the winter solstice, and the resulting quotient, which is also excluded from the calculation, is the time added to the seasonal energy.
Next, calculate the conjunction of the five stars. Divide the number of orbits of each planet by the "six passages of reality" to obtain the quotient as the accumulated conjunction and the remainder as the residual conjunction. Subtract the number of orbits of the planets from the residual conjunction, and what remains is the degree corresponding to the year's entry into the season. Divide by the degree of the day (number of degrees in a day) to get the conjunction degree and remainder of the planets at dawn after the November winter solstice of that year. The calculation methods for Venus and Mercury are slightly different. Subtract the accumulated number of days and the residual conjunction from the accumulated degree to calculate the degree and remainder of the conjunction. If the result equals one, it indicates an evening appearance; if not, it indicates a morning appearance. If the remainder is insufficient, subtract one from the accumulated degree, add the daily degree, and then subtract again. Start calculating from the first twelve degrees before the Ox constellation, divide by the constellations (twenty-eight constellations), and if it is less than one constellation, do not count it. This is the conjunction degree and remainder of the planets at dawn post-winter solstice in November.
Calculate the conjunction of the planets with the moon and the sun: Subtract one from the number of days from the winter solstice new moon (the day of the winter solstice is the new moon, i.e., the first day), add the accumulated degree, then add the small remainder of the winter solstice to the remainder of the degree. If the remainder of the degree exceeds the degree of the day, subtract the degree of the day, then add one degree. This way, the accumulated degree becomes the calculated day, and what remains is the day's remainder. Start calculating from November, divide by the number of days in each month according to the calendar, and if it is less than a month, do not count it. This is the date of the conjunction of the planets with the moon and the sun, taking into account any leap months, if applicable.
To calculate the next conjunction of the moon and the sun, use the number of days and the remainder from the previous conjunction, calculate the number of months and the remainder as before. If the remainder exceeds the degree of the day, subtract the degree of the day, then divide by the number of days in each month according to the calendar, starting from the previous conjunction of the moon. The previous conjunction is not included in the calculation. This is the date of the next conjunction of the moon and the sun. For Venus and Mercury, use the number of days and the remainder of the conjunction, add dawn to get dusk, and add dusk to get dawn. This means that if you know the time of the dawn appearance, adding this number of days will give you the time of the next dusk appearance. The reverse is also true.
Calculate the degree of the next conjunction: Combine the degree and remainder of the planets with those of the previous conjunction. If the remainder exceeds the degree of the day, subtract the degree of the day, start calculating from the previous degree of the conjunction, divide by the constellations, and if it is less than one constellation, do not count it. This is the degree and remainder of the next conjunction. Finally, subtract one thousand four hundred and seventy-seven minutes from this degree.
So, what exactly is all this about? It seems like ancient astronomical records, recording the trajectories of Jupiter (the star of the year) and Mars (the planet of fire). Let's take it step by step.
First paragraph: Jupiter, when it meets the Sun (appears in the same direction), takes a total of 398 days. The remaining time totals 4,780 days. Jupiter moves 33 degrees along the ecliptic, with the remaining degrees totaling 3,303 degrees. A complete orbit is 1,280 degrees. This should be about the data of Jupiter's revolution period and speed, which becomes complicated when explained with modern astronomical knowledge.
Second paragraph: Jupiter, this celestial body, appears in the morning with the Sun, then hides behind the Sun. After 16 days, there are 2,390 days remaining. Jupiter moves 2 degrees, with the remaining degrees being 4,681.5. When it is 13.5 degrees from the Sun, it can be seen in the east in the morning! Its speed is quite fast, moving 11/57 of a degree per day, and 11 degrees in 57 days. Sometimes it slows down to just 0.9 degrees per day, moving 9 degrees in 57 days, and then it stops. It pauses for 27 days and moves again, this time moving backward at a rate of 1/7 of a degree per day, retreating 12 degrees in 84 days. Then it pauses for another 27 days. Then it moves forward again, slowly, moving 0.9 degrees per day, 9 degrees in 57 days. Then it speeds up again, moving 11/57 of a degree per day, and 11 degrees in 57 days. At this point, it moves ahead of the Sun and is no longer visible in the west at night. It slows down, and after 16 days, there are 2,390 days remaining. Jupiter moves 2 degrees, with the remaining degrees being 4,681.5, and finally meets the Sun again. The whole process takes 366 days, with Jupiter moving 28 degrees; hiding behind and in front of the Sun for a total of 32 days, the remaining time is 4,780 days. Jupiter moves 5 degrees, with the remaining degrees being 3,303 degrees, and can once again be seen in the morning. This describes the details of Jupiter's movement, including direct motion, retrograde motion, and periods of stationing, as well as its changing relative position with the Sun.
The last paragraph: Mars takes a total of seven hundred seventy-nine days to align with the Sun, with the remaining time totaling five thousand one hundred eighteen days. A full orbit is nine hundred fifty-two degrees; Mars moves a total of forty-nine degrees along the ecliptic, and the remaining degrees total two thousand one hundred fifty-four degrees. This section mirrors the first, recording the orbit and speed of Mars. These ancient astronomers were remarkably observant!
Mars appears in the morning with the Sun, concealing itself behind the Sun for about seventy-one days, totaling around five thousand five hundred eighty-four days, moving more than fifty-five degrees, which is about four thousand eight hundred forty-five degrees. When it is sixteen degrees away from the Sun, it becomes visible in the east during the morning, moving quickly in a forward direction, traveling fourteen twenty-third degrees each day; it can move one hundred twelve degrees in one hundred eighty-four days. Then its forward speed decreases, moving twelve twenty-third degrees each day, stopping after forty-eight degrees in ninety-two days. After an eleven-day pause, it resumes movement, this time in retrograde motion, moving seventeen degrees out of sixty-two degrees each day, retreating ten degrees after sixty-two days. It stops for eleven days again. It then resumes forward motion, moving quickly, traveling one degree out of fourteen degrees each day; it can move one hundred twelve degrees in one hundred eighty-four days. At this point, it is positioned in front of the Sun, concealed in the west during the evening, moving forward for more than seventy-one days, totaling around five thousand five hundred eighty-four days, moving more than fifty-five degrees, which is about four thousand eight hundred forty-five degrees. Then it aligns with the Sun once more. The total duration of one cycle is six hundred thirty-six days, tracing three hundred thirty degrees; the time spent concealed both in front of and behind the Sun is one hundred forty-three days, totaling around five thousand one hundred eighty days, moving one hundred eleven degrees, which totals approximately three thousand six hundred forty-one degrees, exceeding one circle by forty-nine degrees, which is about two thousand one hundred fifty-four degrees, and finally appears in the morning.
Regarding Jupiter, its conjunction period with the Sun is three hundred seventy-eight days, totaling three hundred forty-one days, moving twelve degrees, which is four thousand nine hundred twenty-four degrees, and a complete circle is five thousand seven hundred nineteen degrees.
Jupiter appears in the morning alongside the sun, hiding behind it for about 170 and a half days in total, moving a total of about 2462 degrees over two cycles. When it reaches 15 and a half degrees from the sun, Jupiter can be seen in the east in the morning. It moves forward at a rate of one twelfth of a degree each day, stopping after 84 days having traveled seven degrees. After stopping for 36 days, it starts moving again, this time retrograde, moving one seventeenth of a degree each day, and retreats six degrees after 120 days. It stops for another 36 days. Then it starts moving forward again, walking one twelfth of a degree each day, traveling seven degrees in 84 days. At this time, it is in front of the sun, hiding in the west in the evening. It moves forward for 18 days, totaling about 170 and a half days, moving a total of about 2462 degrees, and then conjuncts with the sun. The total duration of one cycle is 342 days, during which it moves a total of eight degrees; the time hidden in front and behind the sun is 36 days, totaling 341 days, moving four degrees, about 4924 degrees, and finally appears in the morning again.
Venus, also known as the Morning Star, has a cycle of conjuncting with the sun every 583 days, totaling 5151, with a full circle of 990 degrees, moving 291 degrees. Some sources also suggest that this is the duration of the conjunction cycle.
Brothers, let me tell you about the movement rules of Venus and Mercury; this is something I figured out after a long time. Let's talk about Venus first. Venus appears alongside the sun in the morning, then hides behind the sun for six days, retreats four degrees, and after another ten days, it reappears in the east.
If it moves in retrograde, walking two-thirds of the distance of the sun's orbit in a day, it can retreat six degrees in nine days. If it stops moving, then it stays still for eight days. If it moves forward and is slow, it moves the full distance of the sun's orbit in a day, allowing it to walk thirty-three degrees in forty-five days. If it moves forward quickly, walking one degree plus thirteen thirds in a day, it can walk one hundred and twelve degrees in ninety-one days. If it runs very fast, walking one degree plus thirteen thirds in a day, it can walk one hundred and twelve degrees in ninety-one days, then it runs behind the sun and appears in the east in the morning. After appearing in front of the sun for forty-one days, approximately five thousand six hundred and five degrees, it can walk fifty-one degrees, approximately five thousand six hundred and five degrees, before reuniting with the sun. In total, it appears in the east for two hundred forty-four days, walking two hundred forty degrees, then hides behind the sun for forty-one days, approximately five thousand six hundred and five degrees, walking fifty-one degrees, approximately five thousand six hundred and five degrees, before reuniting with the sun. The appearance in the west is the same.
Appearing together with the sun at night, it appears in front of the sun, hiding for forty-one days, approximately five thousand six hundred and five degrees, walking fifty-one degrees, approximately five thousand six hundred and five degrees, then it moves away from the sun by ten degrees, appearing in the west at night. If it moves forward quickly, walking one degree plus thirteen thirds in a day, it can walk one hundred and twelve degrees in ninety-one days; when it's slow, walking one degree plus thirteen halves in a day, it can walk one hundred and five degrees in ninety-one days; if it moves even slower, moving fifteen-elevenths of the sun's orbit's distance in a day, it can walk thirty-three degrees in forty-five days, then it stops, stays still for eight days, and turns again. If it moves in retrograde, walking two-thirds of the distance of the sun's orbit in a day, retreating six degrees in nine days, it is in front of the sun, appearing in the west at night. Retreating four degrees in six days, it reunites with the sun again. In total, it appears for four hundred eighty days, walking four hundred eighty degrees; it hides in front and behind the sun for eighty-three days, approximately five thousand one hundred fifty-one degrees, walking one hundred and three degrees, approximately five thousand one hundred fifty-one degrees, exceeding a full circle of two hundred eighteen degrees, approximately three thousand six hundred seventy-four degrees, and finally appears in the morning.
Moreover, the planet Mercury, when it aligns with the sun, takes a total of just over 115 days, approximately 5282 hours, and travels over 57 degrees, which takes about 5671 hours, in a cycle of 778 days. "Mercury's alignment lasts for 115 days, with 5282 hours remaining in its cycle; the planet moves 57 degrees (this is also referred to as its alignment with the sun). There are 5671 hours remaining (also known as the alignment with the sun remaining). The orbit is 778 days."
Oh my goodness, the movement pattern of Mercury is truly complex! When it aligns with the sun, it stays hidden behind it for eleven days, then moves back six degrees, is positioned 17 degrees away from the sun, and only appears in the eastern morning after that, remaining stationary for about four days. If it moves slowly, it covers five-sevenths of a degree each day, covering five degrees in seven days. When it moves fast, it moves one degree and a third per day, covering 24 degrees in eighteen days, still appearing in the east in the morning.
Continuing forward, after just over seventeen days (specifically 17 days and a fraction of a day), it has moved just over 44 degrees (specifically 44 degrees and a fraction of a degree), then aligns with the sun again. It can be observed in the eastern sky for a total of 29 days, during which it travels 29 degrees independently, then hides behind the sun for just over 28 days (specifically 28 days and a fraction of a day), moves a little over 34 degrees on its own (specifically 34 degrees and a fraction of a day), and finally aligns with the sun again. The same pattern occurs when observed in the west.
Let's talk about the situation of the planet Mercury, known as Chénxīng, in the evening. When it appears in the evening together with the sun, it is hidden for a little more than seventeen days (specifically, seventeen days and a fraction of a day, about 0.0002 days), and moves a little more than thirty-four degrees (specifically, thirty-four degrees and a fraction of a degree, about 0.00002 degrees), at a distance of seventeen degrees from the sun, and can be observed in the western sky during the evening. If it advances quickly, it moves one degree and one-third each day, covering twenty-four degrees in eighteen days. When it moves slowly, it travels five-sevenths of a degree each day, covering five degrees in seven days, and then stops for four days, still positioned ahead of the sun, appearing in the west in the evening. If it moves backward, it retreats six degrees in eleven days, and can align with the sun in the morning. In total, it can be seen for fifty-eight days, during which it moves forty-six degrees; it is hidden for a little more than fifty-seven days (specifically, fifty-seven days and a fraction of a day, about 0.0002 days) in front and behind the sun, and moves a little more than sixty-nine degrees (specifically, sixty-nine degrees and a fraction of a degree, about 0.00002 degrees), finally reappearing in the morning.
From Dòu (the Dipper) to Niú (the Ox): Star Chronicle, corresponding to the Chǒu hour. From Niú to Wēi (the Danger): Xuánxiāo, corresponding to the Zǐ hour. From Wēi to Bì (the Wall): Zōuzī, corresponding to the Hài hour. From Bì to Lóu (the Lou): Jiànglóu, corresponding to the Xū hour. From Lóu to Bì (the Big Beam): Dàliáng, corresponding to the Yǒu hour. From Bì to Jǐng (the Well): Shíchén, corresponding to the Shēn hour. From Jǐng to Guǐ (the Ghost): Chúnshǒu, corresponding to the Wèi hour. From Guǐ to Zhāng (the Zhang): Chúnhuǒ, corresponding to the Wǔ hour. From Zhāng to Zhěn (the Chariot): Chúnwěi, corresponding to the Sì hour. From Zhěn to Kàng (the Kang): Shòuxīng, corresponding to the Chén hour. From Kàng to Xīn (the Heart): Dàhuǒ, corresponding to the Mǎo hour. From Xīn to Dòu: Xīmù, corresponding to the Yín hour.
