Zhang Zhouxuan, from Chao County, Bohai, was a man of profound knowledge and expertise in various fields, especially astronomy and calendar calculations. He was recommended by the Inspector of Jizhou, Zhao Jiong, and summoned by Emperor Gaozu, who appointed him as a Cloud Cavalry Attendant and assigned him to the Bureau of Astronomy, participating in discussions on calendar calculations. Many of his peers envied him, but while Liu Hui often made incorrect arguments, Zhang Zhouxuan's astronomical calculations were highly accurate, which earned him the Emperor's admiration. The Emperor tasked Yang Su and several other astronomy experts to discuss sixty-one longstanding and difficult problems, putting Liu Hui and Zhang Zhouxuan in a debate. Liu Hui couldn't come up with a single answer, while Zhang Zhouxuan clearly explained fifty-four of the issues. As a result, Zhang Zhouxuan was promoted to Assistant Cavalry Attendant and took on the role of Chief of the Bureau of Astronomy, receiving a reward of one thousand bolts of silk, while Liu Hui and his colleagues were all dismissed.
Zhang Zhouxuan established a new calendar system, noting the errors in the previous calendar. Court Gentleman Yan Minchu submitted a memorial, stating: "During the Han Dynasty, Emperor Liu Bang revised the Zhuanxu Calendar and established the Taichu Calendar, predicting that there would eventually be a day of error. Eight hundred years later, a sage would come to correct it. Now, seven hundred and ten years after the Han Dynasty, someone has completed this task. Isn't this the work of a sage?" The Emperor was delighted and grew to trust and value Zhang Zhouxuan even more.
The calendar formulated by Zhang Zhouxuan differs from ancient calendars in three ways: Firstly, during the Song Dynasty, Zu Chongzhi established a differential method for calculating the precession, resulting in a gradual shift of the winter solstice point that no longer follows the old rules. Every forty-six years, the winter solstice point will move one degree. During the Liang Dynasty, Yu Guang believed that Zu Chongzhi's algorithm had too much error, so he changed it to one hundred and eighty-six years for the winter solstice point to move one degree. Zhang Zhouxuan took these two algorithms into account and, due to the long history and many errors found in ancient texts, he adopted a compromise between the two as a new standard of measurement. This way, the calculation of the position of the winter solstice point will gradually shift each year, moving one degree every eighty-three years, which aligns with both the records of day length and star positions from the time of Emperor Yao and those in the Han Dynasty calendar, proving the accuracy of his algorithm both before and after.
Zhou Maxian developed a calendar called the "Bingyin Yuan Calendar," which includes methods for converting yin and yang, including methods for adding and subtracting time and calculating advances and retreats. This was a significant innovation. At that time, most astronomers and calendar experts could not understand it. Even though Zhang Bin utilized this calendar, he was unable to fully comprehend it or conduct thorough verification. Zhouxuan believed that the problem of whether to add or subtract time early or late was illogical because the changes in solar terms are not consistent, and determining based on the moon is illogical. Therefore, he listed the changes in the gains and losses of the sun and moon according to the twenty-four solar terms, which is actually due to the different speeds at which the sun moves and the moon chases the sun, resulting in the new moon (the first day of the lunar month) sometimes occurring early and sometimes late. He examined the situation of early or late additions in previous calendars and identified a pattern of gains and losses. The sun moves more quickly from the autumn equinox to the spring equinox, covering one hundred and eighty-two degrees in one hundred and eighty-two days; from the spring equinox to the autumn equinox, it moves slower, covering one hundred and seventy-six degrees in one hundred and eighty-two days. Each solar term corresponds to its own speed of movement.
When Zhang Bin formulated the calendar, he introduced the concept of outer limits, meaning that even if the conditions for a solar eclipse are met, it may not necessarily occur, a detail he did not fully clarify. Zhi Xuan explained that the sun travels along the ecliptic, completing a circle in a year; the moon travels along its own orbit, completing a circle in a little over twenty-seven days. The orbits of the moon and the sun intersect, with the moon crossing the ecliptic roughly every thirteen days before returning to it after another thirteen days, in a continuous cycle. When the moon crosses the ecliptic, it is called a node, and if the new moon phase (first and fifteenth day of the lunar calendar) is within fifteen degrees before or after the node, a solar eclipse will occur. If the moon is on the inner side of the ecliptic, towards the north, solar eclipses are easier to observe; if the moon is on the outer side of the ecliptic, towards the south, even if it is at the node, a solar eclipse will not occur, making the phenomenon rarer. Therefore, based on previous calendars, he established additional limits, calculating errors for each solar term based on the proximity to the node, correcting the calculation of solar eclipses, thereby clarifying the calculations.
Zhi Xuan's calendar had seven unprecedented aspects: first, in ancient calendars, the movements of the five planets were considered fixed, and there were no reliable patterns for their appearances, disappearances, or changes in brightness. Zhi Xuan calculated their true speeds of movement, which differed from the results of ancient calendars, with errors sometimes exceeding thirty days! For example, if Mars appears during the Rain Water solar term, you need to add twenty-nine days; if it appears during the Minor Snow solar term, you need to subtract twenty-five days. Even though the average appearance time was adjusted, the actual appearance time was still used for calculations. The waxing and waning of other planets followed similar patterns, with varying degrees of error. People of that time found it challenging to grasp the reasoning behind these accumulated observations.
Secondly, ancient astronomers used to say that Mercury, often referred to as the Morning Star, only appears once in a long time, and this was a common belief among ancient calendars. However, its appearance cannot be accurately predicted. Shen Kuo summarized the law through long-term observations, knowing that the Morning Star can sometimes be seen in a year, and sometimes not, which is influenced by the gravitational pull of other celestial bodies. They will influence one another and may appear simultaneously. For example, if Mercury appears in the morning during the Rain Water solar term (Yushui), it may not be visible; but if it appears in the morning during the Awakening of Insects solar term, between 18 and 36 degrees from the sun, and at the same time one of Jupiter, Mars, Saturn, or Venus is visible, then Mercury can be seen.
Thirdly, ancient calendars calculated planetary motion within a fixed framework, and once a planet appears, its future trajectory is calculated according to this law. However, the speed of their motion and the timing of their appearances and disappearances cannot be accurately predicted. Shen Kuo found through long-term observations that the speeds, stops, and retrogrades of the five visible planets: Jupiter, Mars, Mercury, Venus, and Saturn differ from the results calculated by ancient calendars, with some differing by more than 80 days and positions differing by more than 80 degrees. For example, when Mars first appears, if it appears at the beginning of Winter, it moves 177 degrees in 250 days; but if it appears at the beginning of the Summer Solstice, it only moves 92 degrees in 170 days. Actual observations verify that both ancient and modern calculations can be remarkably accurate.
Fourthly, ancient calendars calculated the size of solar eclipses using average values, but the results often do not align with actual observations. Shen Kuo found through long-term observations that the moon's speed is influenced by Jupiter, Mars, Saturn, and Venus. When the moon is close to these four stars, its speed is faster, and it is slower when it is far away. Only when the distance exceeds fifteen degrees does it return to its original motion pattern. Therefore, he determined the size of solar eclipses according to this principle.
Fifth point, in ancient calendars, the calculation of the new moon and full moon dates (the first and fifteenth day of the lunar month) was done using the same method. Zhoudian discovered through long-term observation that the position and time of solar eclipses vary depending on the location of observation. The height, size, and timing of solar eclipses vary at different locations, as well as the depth and speed of the eclipse. Therefore, the predicted time will also vary, all of which must be judged based on actual celestial phenomena.
Sixth point, ancient calendars believed that the size of a solar eclipse is related to the degree of alignment between the sun and moon: at a distance of fourteen degrees, the eclipse is partial; at thirteen degrees, the eclipse is two-thirds; at ten degrees, the eclipse is three-thirds; for each degree closer, the eclipse increases by one part; when completely aligned, the eclipse reaches its maximum. However, the actual situation is not always as predicted; sometimes the calculations predict a smaller eclipse, but the actual eclipse is larger; sometimes the calculations predict a larger eclipse, but the actual eclipse is smaller. Ancient calendars did not explain the reasons clearly. Zhoudian discovered through long-term observation that near the alignment point, the moon does not fully cover the sun, leading to a smaller eclipse; when the moon is five to six degrees from the alignment point, the eclipse is at its peak; afterwards, as the distance increases, the eclipse becomes smaller. This pattern repeats around the winter solstice, but near the summer solstice, the pattern is different. Based on these patterns, he developed a more accurate method for calculating solar eclipses.
Seventh point, ancient calendars believed that during the spring and autumn equinoxes, day and night are equal in length. Zhoudian discovered through long-term observation that in reality there is a difference; during the spring and autumn equinoxes, daytime is about fifteen minutes longer than nighttime, due to the changing speed of the sun's movement.
These were all insights that Zhoudian alone comprehended; his reasoning was exceptionally meticulous, earning him admiration for his precise calculations. He passed away during the Daye period.
Xu Zhicang is from Gaoyang. His grandfather taught him from an early age. Once his mother fell ill, he started studying medical books, and the more he learned, the more proficient he became. He eventually earned a reputation as a renowned physician. He warned his sons, saying, "As sons, if you can't even understand food or medicine, how can you call yourselves filial?" So his medical skills were passed down from generation to generation. He later became an official in the Liang Dynasty, rising to the rank of Cavalier Attendant. His father, Xu Jing, was a counselor to the Prince of Wuling. Xu Zhicang became famous for his medical skills at a young age, and during the Chen Dynasty, he became a Cavalier Attendant. After the fall of the Chen Dynasty, Emperor Yang of Sui appointed him as a Cavalier Attendant and sent him to Yangzhou.
Coincidentally, Prince Xiaowang of Qin, Yang Jun, fell ill, so the emperor quickly summoned him. Yang Jun dreamed one night that his deceased wife, Cui Shi, was crying and saying, "I was meant to welcome you, but I heard that Xu Zhicang is coming. If he comes, he will surely make you suffer. What are we going to do?" The next night, Yang Jun dreamed again that Cui Shi said, "I have come up with a solution. I will hide in the underworld." When Xu Zhicang arrived, he took Yang Jun's pulse and said, "The illness has penetrated deep into the bone marrow and will soon flare up. There is no cure." As predicted, Yang Jun passed away just a few days later. The emperor was amazed by his remarkable medical skills and rewarded him with one hundred rolls of cloth. After Emperor Yang of Sui ascended the throne, Xu Zhicang had already retired at home. Whenever the emperor felt unwell, he would send eunuchs to consult him, sometimes even sending people to bring him to the palace and help him onto the imperial bed. Xu Zhicang's prescriptions always proved effective in treating illnesses. He passed away peacefully at home at the age of eighty.
Xu Cheng, the kinsman of Xu Zhicang, was also famous for his medical skills. His father, Xu Shi, served as the Minister of Rites and Chief of the Central Army during the Liang Dynasty. He followed Liu Zhongli to Chang'an, where he was renowned alongside Yao Sengyuan and was appointed as one of the Three Officials of the Imperial Court. Xu Cheng was very knowledgeable, inheriting his father's expertise and excelling in medical skills. He later served as the Chief Pharmacist and Grand Adviser, and was made Count of Hechuan. Both father and son were renowned for their superb medical skills during the Zhou and Sui dynasties. The historical records are brief on this matter, so it is supplemented here.
As for Wan Baochang, little is known about him. His father was named Da Tong, who initially defected to the Qi Dynasty alongside the Liang general Wang Lin. Later, he tried to secretly return to Jiangnan, but his plan was exposed and he was killed. Wan Baochang was subsequently made a musician, and he excelled in music theory and various musical instruments. He presented a set of jade chimes to the Emperor of the Qi Dynasty. Once, during a meal conversation about musical tones, Wan Baochang picked up chopsticks and some random objects in front of him and imitated various pitches by tapping with the chopsticks, producing harmonious sounds of various musical tones. People at the time greatly appreciated it.
However, from the Zhou Dynasty to the Sui Dynasty, he was largely overlooked. During the reign of Emperor Yang of the Sui Dynasty, Pei Guo Gong Zheng Yi and others were responsible for establishing new musical scales, initially settling on the Huang Zhong scale. Even though Wan Baochang was a skilled musician, Zheng Yi and the others often consulted with him, but many of his suggestions were not adopted. Later, when Zheng Yi's musical scales were finalized and performed for the Emperor, the Emperor called for Wan Baochang to ask for his opinion. Wan Baochang said, "This is the music of a fallen state; Your Majesty should not listen to it!" The Emperor was displeased. Wan Baochang then explained in detail that the music was sorrowful and dissolute, lacking the refinement of traditional court music, and requested to use a standard measure to define the scales and adjust the musical instruments. The Emperor agreed.
Wan Bao frequently made various musical instruments by imperial order, with a pitch two pitches lower than the one set by Zheng Yi. He also wrote 64 volumes of "Scores of Music," detailing the method by which the eight sounds form palace tones, as well as techniques for changing strings and moving the bridge pins. He established 84 tones, 144 notes, and a total of 1,800 combinations of sounds. People at the time said that the theory of revolving palace tones was already in the "Rites of Zhou," but since the Han and Wei dynasties, those knowledgeable about music struggled to understand it. When they witnessed Wan Bao's unique creation, they found it utterly ridiculous. However, when he was asked to perform, he could immediately play the music without hesitation, astonishing everyone who witnessed it.
He improved and created countless musical instruments, but his musical style was refined yet understated, not favored by the people of that time. Those in the Ministry of Ceremonies who excelled in music marginalized him. Prince Su Kui, who prided himself on his musical mastery, especially envied Wan Bao. Su Kui's father, Su Wei, held significant power at the time, and all those who engaged in musical discourse relied on him, together belittling Wan Bao. Wan Bao repeatedly complained to the court officials, and Su Wei questioned him, asking where he learned his skills. A monk told Wan Bao, "The Emperor likes auspicious signs, and whenever someone mentions them, the Emperor is pleased. You should say you learned from a foreign monk and claim that the musical theory was passed down by Buddhist Bodhisattvas. The Emperor will be pleased. Then you can promote what you have done." Wan Bao followed the monk's advice and answered Su Wei accordingly. Angrily, Su Wei said, "The music passed down by foreign monks is from the Western Regions, not what we should perform in China!" This issue ultimately fizzled out.
Wan Bao once listened to the music played at the Ministry of Ceremonies and began to cry. When asked why, he said, "This music feels both lascivious and mournful, and soon there will be countless deaths in the world due to war." At the time of peace, those who heard him dismissed his words. By the end of the Deyuan period during the Sui Dynasty, his words were proven true.
Bao Chang was a destitute man with no children. When his wife saw him fall ill, she secretly took all his money and possessions and fled. Bao Chang was left hungry and cold, with no one to take care of him; he eventually starved to death. Before he died, he burned the books he had written, saying, "What use are these things?" A few volumes were salvaged from the flames and later circulated, and people mourned his fate.
During the Kaihuang era, scholars such as Zheng Yi, He Tuo, Lu Ben, Su Kui, and Xiao Ji studied classical texts and composed music together, which were widely used at the time. However, none of them possessed the same innate musical talent as Bao Chang. An Maju, Cao Miaoda, Wang Changtong, and Guo Lingle were skilled composers and top musicians of the time. They also studied Zheng Sheng, but Bao Chang's music compositions belonged to the realm of refined music. Though these individuals did not openly endorse Bao Chang, they all admired him in their hearts, thinking of him as a godlike figure.
There was a musician named Wang Lingyan who was also very knowledgeable in music theory. During the reign of Emperor Yang of Sui, he was preparing to travel to Jiangdu, and his son followed him. His son played a rearranged version of "An Gongzi Qu" on the Hu pipa outside the house. When Wang Lingyan heard it in the bedroom, he was taken aback and sprang to his feet, saying, "This is bad, this is bad!" He hurriedly called out to his son and asked, "When did this tune become popular?" His son replied, "It only became popular recently." Wang Lingyan then cried sadly and told his son, "You must not go with them; the emperor will not return." When his son pressed for an explanation, Wang Lingyan responded, "The tonal structure of this melody is irreversible, and the tonal structure represents the monarch, so this is my judgment." Ultimately, Emperor Yang of Sui was indeed assassinated in Jiangdu.
The history books say: yin-yang divination and fortune-telling have been taught by sages, although they cannot be completely believed or completely denied. If people can promote the right path, they can benefit society; if their behavior goes against morality, they will face the consequences. Therefore, ancient sages would warn people not to act recklessly. Wei and Lai's physiognomy and qi analysis, Yu and Zhang's calculations of surplus and deficiency, even those like Luo Xia, Gaotang, Xu Fu, and Zhu Jian cannot compare to them. Bo Chou's tortoise divination can discern the will of the spirits; Geng Xun's astrolabe can precisely measure celestial events; Bao Chang's musical theory can skillfully capture the harmony of the Gong and Shang scales. Although they are not as good as the great masters of ancient times, they were still leading figures of their era. Xu's acupuncture techniques are commendable as noted in historical records; Xiao Ji's discussion of yin and yang is somewhat overstated.
