《天原发微(鲍云龙)》Vol. 5

This passage discusses how the ancients distinguished sui from nian, and, drawing on Shao Yong’s theory, discusses the cycles of heaven and earth.

First, there is the term “Bailiu” (Hundred-Six). In ancient calendrical systems there was the doctrine of “Yangjiu and Bailiu” (a cyclical number of calamity), according to which the operation of the heavenly Dao includes disasters such as floods and droughts. The original text says, “One hundred and six years, together with three hundred and seventy-four years, make four hundred and eighty years.” The commentator takes this to be the number “six times eight,” and says the doctrine originates in Wei Heshan’s (Wei Liaoweng’s) Yaoyi.

The author Bao Yunlong comments: The histories say that the Han dynasty suffered the “calamity of Yangjiu”; in Yao’s time there was a great flood lasting nine years, and in Shang Tang’s time a great drought lasting seven years. From this one may infer the pattern of such calamities. Yet Yao and Shun dissolved these upheavals through virtue; floods and droughts came from the numbers of Heaven, and so need not always conform to this cycle. The calamities of the Han, by contrast, arose from human action and cannot be blamed entirely on Heaven. Hence the old saying: “When Heaven makes calamity, it may still be avoided; when one makes calamity oneself, one cannot escape (huan, to evade).”

Next the text discusses calendrical method. The duty of the Taishi (Grand Scribe, the official in charge of astronomy and the calendar) was to rectify sui and nian so that affairs could be ordered. Counting twelve months by the zhongqi (the solar seasonal points such as the winter and summer solstices) gives a total of about 365 and one quarter days, and this is called sui; counting twelve months by the shuo (the first day of each lunar month) gives a total of 354 days, and this is called nian. Compared with each other they differ; spoken of loosely, there is no difference. The Erya, “Shitian” (“Explaining Heaven”), records that in the Tang-Yu era the term was zai, in the Xia dynasty sui, in the Shang dynasty si, and in the Zhou dynasty nian.

Finally, quoting Zhu Xi, the text relays Shao Yong’s (Kangjie’s) theory. Shao Yong held that one yuan is divided into twelve hui, totaling 129,600 years; from the great heaven and earth down to the small units of year, month, day, and hour, the pattern is the same. In the first hui, 10,800 years, heaven begins to form; in the second hui, 10,800 years, earth begins to solidify; in the third hui human beings and the myriad things begin to arise, which is called kaiwu (“opening of things”), corresponding to the yin hour (symbolizing dawn and the first birth of things). By the xu hour (symbolizing dusk), the myriad things close off, human beings and things gradually perish, and heaven and earth are in a half-light, half-dark condition, like the alternation of day and night. When one yuan comes to an end, heaven and earth will again be opened anew.

Tianyuan Fawei (Bao Yunlong): A Vernacular Interpretation

Reckoned from the perspective of the single Qi of heaven and earth, the transformations within a single day and night can already be seen clearly. From this year’s winter solstice to next year’s winter solstice is one cycle of Qi’s movement. Divide this cycle into two: the first half belongs to Yang, the latter half to Yin. Divide it further into four, and they are the four seasons of spring, summer, autumn, and winter. The Qi of spring and summer is like exhaling, while the Qi of autumn and winter is like inhaling; in reality, it is all the same Qi in motion.

When Yang Qi has risen to its fullest and is about to wane, Yin Qi is born in its wake; when Yin Qi is exhausted, Yang Qi is born again. When Qi has been used up, it disperses—this is what is meant by “waxing and waning” (xiaozhang). As heaven moves through one month, the sun roughly completes one revolution. Yet there are also larger cycles of transformation, and one should not be bound to any single fixed period of time.

The author comments: Qian and Kun are the two doors of the Yijing (Classic of Changes), while the Fu and Gou hexagrams are the hinge that determines their opening and closing. At the Zi hour, when Yang Qi first arises, the Qian door opens and Yang Qi begins to stir; this is what is called “heaven opens at Zi.” By the Yin hour, when the handle of the Big Dipper points toward this direction, Yang Qi opens out, its image being Zhen, and the myriad things sprout and emerge from it. This is the result of the dispersal of Qian Qi, and so its movement stops only at the Si hour. At the Wu hour, when one Yin first arises, the Kun door closes; Yin Qi gradually grows and Yang Qi gradually wanes, and the myriad things withdraw and gather. This is the function of the Xun hexagram: Kun Qi gathers and stores the myriad things away, and it does not stop until the Hai hour. One opening and one closing are like two doors: when one opens, the other closes. When Yang Qi arrives, Yin Qi is born; when Yang Qi withdraws, the door closes.

From this we can see that the earlier Confucians’ saying—“If one can fully extend it, heaven and earth transform and nurture the myriad things, and grasses and trees flourish; if one cannot extend it, heaven and earth close off and the worthy withdraw”—also depends on human beings alone. If Yao, Shun, Yu, Tang, Wen, and Wu were in positions of authority, there would be prosperous ages like those of Tang-Yu and Shang-Zhou, with clear government and moral order. If not, upright scholars are imprisoned and enslaved, poison spreads throughout the four seas, books are burned and scholars buried, and the world falls into disintegration; men like Shi Dong and Zhu Wen corrupt human relations and overturn heaven and earth. At such a time, if no rescue is applied, the sun and moon lose their light, the cosmos grows dark, and human beings and the myriad things naturally cannot but move toward extinction. Alas! This is truly difficult to speak of.

Explanation of the General Meaning of the Original Text

This passage says that the ancients believed the beginning of celestial phenomena occurred in the Zi month, the opening of the earth in the Chou month, and human reproduction in the Yin month; these three months could all serve as the beginning of a year. Thus the three dynasties of Xia, Shang, and Zhou in turn used different beginnings of the year: the Xia took the Yin month as “Human Rectitude” (with the Yin month as the first month), the Shang took the Chou month as “Earthly Rectitude” (with the Chou month as the first month), and the Zhou took the Zi month as “Heavenly Rectitude” (with the Zi month as the first month).

However, the calendar was ultimately meant to arrange agricultural work and daily activities, so the calculation of years and months should be based on the needs of human life. Confucius said, “I have obtained the calendar of the Xia dynasty.” Those who explain this sentence believe that what Confucius referred to should have been a work of the Xia Xiao Zheng type; the reason he praised it is that the seasons it established were correct and the agricultural arrangements it indicated were also appropriate.

Notes

The three time-markers (the months corresponding to the three Earthly Branches Zi, Chou, and Yin, namely the eleventh, twelfth, and first months): The ancients used the Earthly Branches to record months, and these three could each serve as the beginning of the year.

Human Rectitude, Earthly Rectitude, and Heavenly Rectitude: These refer to the three different systems for the beginning of the year adopted by the three dynasties, namely the “Three Rectitudes.”

Xia Xiao Zheng: A chapter in the Da Dai Liji, recording astronomical phenomena, seasonal phenomena, and agricultural affairs month by month; it is important material for studying ancient calendars.

Someone asked: Why did the Shang and Zhou, in changing the zhengshuo (the orthodox beginning of the year and month), fail to attain the correctness that the Xia calendar had? The reply: Although yang qi first sprouts from the Yellow Bell (Huangzhong, the first of the twelve pitch standards, corresponding to the yang qi at the winter solstice), and the beginning of the year was set at the Zi month, the yang qi is still hidden in the earth, and its function of transforming and generating the myriad things cannot yet be seen. Only when the Chou month gives way to the Yin month are the “Three Yangs” that gradually increase after the winter solstice fully present; then the east wind arrives, the virtue of Wood flourishes, and the spring qi responds accordingly. The ancient sages took this as the starting point for the growth of the myriad things. Therefore, in fixing the beginning of the year, one should take as the standard the season that everyone can see, yet no one can clearly explain its underlying root.

By the time of the Shang and Zhou, because they had gained the world through military conquest, they changed the zhengshuo and established it as the system of a dynasty, so as to renew the eyes and ears of the world; thus arose the doctrine of the “Three Standards” (Santong)—that the Xia, Shang, and Zhou each took a different month as the beginning of the year, succeeding one another in a cycle. If judged by the Dao of Heaven, the generative function is not evident; if judged by terrestrial patterns and human affairs, the rationale for changing the year is also unclear, and even the order of the four seasons and the Five Phases loses its proper center. Therefore Confucius examined and regulated the institutions of the Three Kings and honored the Xia calendar.

I have examined the various traditions: although the calendars of the Three Dynasties differed in the beginning of the year, they all counted the months starting from the Yin month. When the feudal lords came to court or assembled, and when the calendar was promulgated and granted to the people, all acted according to the zhengshuo; but in ordering the months, all took the Yin month as the first. The “Yixun” chapter of the Book of Documents says, “In the twelfth month, on the day Yichou.” The Shang took the Chou month as the beginning of the year, and therefore treated the twelfth month as the first month. “Yichou” is merely a sexagenary day designation, not the first day of the month, so it was not used to determine the new moon. As for cases of changing the zhengshuo without changing the numbering of the months, traces can still be found in the classics and histories. The Zhou took the Zi month as the beginning of the year, yet the Book of Odes says, “In the fourth month is summer; in the sixth month the heat arrives.” The season of the “arriving heat” is still counted from the Yin month, which shows that the numbering of the months did not change. The Qin took the Hai month as the beginning of the year, and the Records of the Grand Historian records that in the twelfth month of the thirty-first year of the First Emperor, it was renamed “La” and called “Jiaping.” The La sacrifice originally belonged to the Chou month; since the Qin took the Hai month as the first month, the La month became the third month.

Some say that “the eleventh month” was already “Jian Hai.” “Jian X” means taking the month corresponding to a particular Earthly Branch as the beginning of the year (the first month). The Xia took the Yin month as the first month, the Yin (Shang) took the Chou month, and the Zhou took the Zi month. This claim is incorrect. The Records of the Grand Historian record that in the thirty-first year of the First Emperor of Qin, the twelfth month was renamed “La,” though the La month was originally the Jian Chou month. If Qin had taken the Hai month as the first month, then the La month would have been the third month. The reference to “the eleventh month” still counts from the Yin month, which shows that Qin did not change its method of counting months.

In the thirty-seventh year, it is recorded that on the Guichou day of the tenth month the First Emperor set out on a journey, and in the eleventh month he arrived at Yunmeng. It then records that on the Bingyin day of the seventh month the First Emperor died, and in the ninth month he was buried at Mount Li (present-day Lintong, Shaanxi). The tenth and eleventh months are written first, and the seventh and ninth months afterward, showing that Qin took the tenth month as the beginning of the year, but the counting of months still began with the Yin month and was not changed. Qin edicts also say that the beginning of the year was changed, and that court congratulations all began on the first day of the tenth month. Qin inherited from the Zhou. If it had really changed the numbering of the months, then the Zhou tenth month would have become the Jian You month; how could it still be Jian Hai? The Han continued to use the Qin calendar, and the histories record “in the winter, the tenth month, of the first year,” which shows that what was changed was the beginning of the year, while the numbering of the months was not changed. This is already quite clear.

Next consider the statement of Kong Anguo of the Han. He held that spring was the Jian Zi month, on the grounds that the Three Dynasties not only changed the beginning of the year but also changed the numbering of the months, and took the beginning of the year as the start of the four seasons. The “Great Declaration” in the Book of Documents says, “On Wuwu in the first month”; the “one” is a scribal error for “three.” Since he took “the first month” to be the Jian Zi month, and the canonical text also calls it spring, he made the Jian Zi month into the spring season. He did not realize that what the “Great Declaration” actually refers to is the first month, the first month of spring, namely the Jian Yin month. On his account, the four seasons would be completely disordered, which is utterly unreasonable. Winter cannot be spring, and cold cannot be warm; this should be clear without any need for debate.

Someone cites Zheng Xuan’s commentary on the Poems, saying that “Wei mo zhi chun” refers to the last month of spring in the Zhou calendar, corresponding to the first month of spring in the Xia calendar. This is an error inherited by the Han Confucians. The “mo chun” mentioned in “Chen Gong” of the Zhou Hymns is precisely late spring, when new fields should be opened. Now the barley and wheat are about to ripen, and one may receive the bright blessing of the Lord on High.

The Xia calendar took as its standard the season when wheat and barley were about to ripen; that was the month established in Chen (the third month of the Xia calendar), and so the Xia dynasty treated late spring as spring. This is quite clear. When Zheng Xuan annotated the Classic of Poetry, he too failed to grasp the principle involved, and his explanation of this matter was not sufficiently careful. If this were not so, then the Shang dynasty would have treated late winter (the twelfth month of the Xia calendar) as spring, and the Zhou dynasty would have treated midwinter (the eleventh month of the Xia calendar) as spring; the order of the four seasons would then be inverted and thrown into confusion, and none would accord with the proper Way. Could it be that the sages of the Xia, Shang, and Zhou dynasties were carrying out the decrees of the Way of Heaven?

It is also said: The Zhou people took the month of Zi as the first month. Although this accorded with the governing order of the Way of Heaven, when Confucius discussed the way of governing the state he advocated taking the Xia calendar as orthodox, because the Xia calendar could clearly display the beginning and end of Yin-Yang.

Yang qi begins in the month of Zi (at the winter solstice, when the first yang is born) and ends in the month of Si (when yang qi reaches its fullness); yin qi begins in the month of Wu (at the summer solstice, when the first yin is born) and ends in the month of Hai (when yin qi reaches its fullness). If one speaks in terms of the qi of the four seasons, however, yang qi begins in the month of Yin and ends in the month of Wei, while yin qi begins in the month of Shen and ends in the month of Chou. These two accounts appear to differ slightly, but what is at issue is no more than the positions of two months.

At the Zi position, although the first yang has already been born, it has not yet emerged from the earth. At the Yin position, the image of the Tai hexagram becomes manifest; only then does the qi of the three yangs rise out of the ground, and the mild qi begins from this point. The Si position is the Qian hexagram: the six yangs have already reached their height, but the mild qi has not yet come to an end. At the Wu position, although the first yin has already been born, it does no harm to the yang qi; only when the Wei position is reached and the image of the Dun hexagram appears does the mild qi come completely to an end. At the Hai position the six yins have already reached their height, but the qi of severe cold and congelation is not completely exhausted until the Chou position. At the Shen position, when the qi of severe cold first begins to arise, the principle is similar.

Shao Yong’s (Kangjie’s) theory of the twelve hui holds that at the Zi period heaven first existed but earth did not yet exist; at the Chou period earth existed but humanity did not yet exist; at the Yin period humanity first appeared. Heaven, earth, and humanity all began from these points. Thus the three dynasties took Yin, Chou, and Zi as the starting points for establishing the first month; in each case they took the point of beginning and fixed it as the head of the year. Therefore it is said: the first-month establishments in the three months Zi, Chou, and Yin all belong to the months of the three yangs. As for the Qin dynasty taking the month of Hai as the first month, that was entirely without principle.

This passage discusses the “Twelve Sovereign Hexagrams” (shier bigua) in the Xiantian Diagram (Diagram of Prior Heaven), that is, the use of hexagram images to represent the waxing and waning of Yin-Yang Qi through the twelve months of the year. The bigua are hexagrams of the sovereign and represent the advance and retreat of Yin and Yang.

On the left are the yang hexagrams, from the Zi month to the Si month. Yang Qi begins to generate at the Zhen position; a second yang line appears at the Dui position, forming the Lin hexagram; thereafter, from Lin it rises to the Qian palace, in sequence Tai, Dazhuang, Guai, and Qian, ending with the Si month (the fourth month). On the right are the yin hexagrams, from the Wu month to the Hai month. Yin Qi begins to generate at the Xun position; a second yin line appears at the Gen position, forming the Dun hexagram; thereafter, from Dun it descends to the Kun palace, in sequence Pi, Guan, Bo, and Kun, ending with the Hai month (the tenth month).

Among the yang hexagrams, the Zhen palace takes one and the Qian palace takes four; among the yin hexagrams, the Xun palace takes one and the Kun palace takes four. This shows that Yin-Yang Qi is faint and slow at the beginning and later becomes abundant and rapid. In the faint and slow stage, it can nurture the myriad things and nourish their root; in the rapid and intense stage, it can cause the myriad things to grow and decline and complete their functions.

The Kan and Li palaces are not assigned a hexagram count, indicating that the two Qi of water and fire circulate between Heaven and Earth and are present everywhere. Their not being listed separately precisely shows that they exert their function within all things.

The twelve sovereign hexagrams are laid out in a flat sequence and correspond to and stand opposite the four seasons, so the twenty-four solar terms and the seventy-two hou (seasonal periods) can all be arranged within them in order without confusion. The correspondences of the various Xiantian Bagua (Eight Trigrams) palaces also each have a fixed order. Among the twelve sovereign hexagrams, the Qian and Kun palaces alone occupy eight of the positions. Therefore Qian and Kun are regarded as the father and mother of the myriad things; the growth, gathering, and hiding of the myriad things all arise from this.

Shao Yong said: The methods of ordering the world originated with Fuxi, matured in the time of Yao, were transformed through the Three Kings of Xia, Shang, and Zhou, reached their extreme with the Five Hegemons of the Spring and Autumn period, and were cut off in the Qin dynasty. The order and disorder, rise and decline of the world all cannot escape this pattern.

Here Shao Yong uses his image-number numerology (xiangshu) to explain the cycles of time. “It began with Fuxi, when things were opened forth at Yin” means that in Fuxi’s era the myriad things began to transform and be born, corresponding to Yin among the twelve Earthly Branches. “It was completed with Yao, when yang became pure at Si” means that in Yao’s time yang qi was pure and flourishing, corresponding to the Si position. “It was transformed by the Three Kings, when yin was born at Wu” means that in the transformations of the three generations of Xia, Shang, and Zhou, yin qi began to sprout from the Wu position. “It reached its extreme with the Five Hegemons, when the way of yang was already exhausted” means that by the time of the Five Hegemons of the Spring and Autumn period, yang qi had already been used up. “It was cut off with Qin, and so was bounded off” means that after the Qin dynasty, the way of governance was blocked and no longer flowed through.

The way of governance of the sage kings Shao Yong speaks of—Fuxi, Huangdi, Yao, Shun, Tang of Shang, Wu of Zhou, and Wen of Zhou—as well as the ethical relations between father and son and between ruler and minister, were all obstructed after the Qin dynasty and could no longer be put into practice.

Finally, he also says that the Yi begins with the Three August Ones, the Shu with the Two Emperors, the Shi with the Three Kings, and the Chunqiu with the Five Hegemons. This correlates the origins of the Confucian classics with the various eras, showing that each classic reflects the age in which it arose.

The author borrows the four seasons of spring, summer, autumn, and winter to metaphorize the patterns of ordered governance in successive ages. The age of the Two Sovereigns (ancient sage-kings, traditionally figures such as Fuxi and Shennong) was like spring; the age of the Five Emperors (Huangdi, Zhuanxu, Diku, Yao, and Shun) was like summer; the age of the Three Kings (Yu of Xia, Tang of Shang, King Wen and King Wu of Zhou) was like autumn; and the age of the Five Hegemons (the feudal lords who dominated during the Spring and Autumn period) was like winter. The Seven Warring States were the residual force of winter. The Han founded the state on the kingly Way but was not yet pure; the Jin had only the hegemonic Way and had it in excess. The Three Kingdoms were the mighty champions among the hegemons; the Sixteen Kingdoms were a thicket of hegemons. The successive Southern Dynasties were a borrowed carriage for the hegemonic enterprise, while the Five Dynasties were merely a temporary lodging for it. The Sui and Jin in relation to the Tang were like younger brothers to an elder brother, a relation of dynasties succeeding one another in sequence. The separatist regimes across the land at the end of the Sui were the afterwaves of the hegemonic enterprise; the independent military governors at the end of the Tang were its lingering light; and the later Five Dynasties were like fading stars at sunrise.

The author holds that before Yao there were also ages similar to that of the Five Hegemons. Within the great cycles there are naturally small cycles, which require careful discrimination; it is only that the world cycles of remote antiquity cannot be verified, while those of recent times can be seen clearly.

Shao Yong (a Northern Song Neo-Confucian scholar and author of the Huangji Jingshi) believed that within the categories of Huang (Sovereign), Di (Emperor), Wang (King), and Ba (Hegemon), each in turn contains Sovereign, Emperor, King, and Hegemon. Taking the Han dynasty as an example: those who governed by wuwei (non-action) belonged to the Sovereign, such as Emperor Gaozu and Emperor Hui; those who transformed people through kindness and trust belonged to the Emperor, such as Emperor Wen; those who controlled through intelligence and force belonged to the Hegemon, such as Emperor Wu. Emperor Xuan of Han practiced the kingly Way through the hegemonic Way; Emperor Wu of Han practiced the hegemonic Way through the kingly Way. This is like spring, summer, autumn, and winter of the four seasons interweaving with one another. If the hegemonic Way is further mixed with the customs of the Yi and Di barbarians, it is even lower. Alas! How fortunate it would be to encounter the age of the Three Sovereigns (the earliest sage-kings of antiquity, whose identities are variously given)!

It is also said: In the Qi (vital energy) cycles of heaven and earth, when they turn from north to south there is ordered rule, and when they turn from south to north there is chaos; after chaos has lasted long, they again turn from north to south. The Heavenly Dao and human affairs are both like this.

This passage uses Shao Yong’s (posthumous title Kangjie) calendrical numerology of “yuan, hui, yun, and shi” to infer the order and disorder of successive dynasties. Yuan-hui-yun-shi is his temporal system: one yuan divides into twelve hui, one hui into thirty yun, and one yun is 360 years. The author holds that the Dao of Heaven is like human affairs: when the cyclical Qi (vital energy) moves from north to south, there is order; when it moves from south to north, there is disorder; and when disorder reaches its extreme, it turns back again from north to south.

He divides one yun into four stages by the twelve Earthly Branches. From Zi to Mao, there is yang within yin, and the way of order is about to arise. From Mao to Wu, there is yang within yang, the zenith of ordered rule. From Wu to You, there is yin within yang, and signs of disorder are about to emerge. From You to Zi, there is yin within yin, the extreme of disorder.

Shao Yong’s Xiantian Tu (Pre-Heaven Diagram) represents this process through the hexagrams of the Zhouyi. From the Tai hexagram to the Pi hexagram, one passes through the Gu hexagram; from Pi back to Tai, one passes through the Sui hexagram. Tai and Pi are opposed; Gu and Sui are opposed. Within Gu, yin Qi is in command; yang Qi is halted by the Gen trigram, yin evil seeps in through the Xun trigram, and so Pi follows. Within Sui, yang Qi is stirred upward by the Zhen trigram, and the yin of the Dui trigram moves in response; the people rejoice without end, and there is nothing unsuitable in an age of peace and tranquility. The author holds that the four hexagrams Pi, Tai, Gu, and Sui are precisely the gateways through which one enters and exits, comes and goes, between the Heavenly Gate, the Earthly Door, the Human Path, and the Ghost Region.

Counting past events in forward order—from Zi to Wu, with the Zhen, Li, Dui, and Qian trigrams, the image of ordered times—is forward movement; inferring future events—from Wu to Zi, with the Xun, Kan, Gen, and Kun trigrams, the image of disordered times—is reverse movement. If one observes with one’s back to the north and facing south, one can see this reverse direction.

Applied specifically to history: from the Tang to the Five Dynasties, about 360 years elapsed, with order and disorder each occupying half. From the Qiande era of the Song (963) to the present, there is again the number of one jiazi cycle; during this period southern forces held power, and the Qi of the south arose accordingly, crossing over the north and causing turmoil. Shao Yong calculated by numbers and held that sixty jiazi, namely 360 years, correspond to the number of one shi among the twelve shi of a single day.

The author further reckons from the jiachen year of Emperor Yao; to the present there have already been 3,660 years, but converted to the scale of heavenly time, this corresponds to only 122 shi. He laments the swiftness of time and says that the changes from ancient to modern times within heaven and earth are no more than a single day drawing toward dusk.

Finally, the author quotes Shao Yong: the sage understands the principle of the changes of day and night, and therefore can view ten thousand times through one time and ten thousand ages through one age. He records these calendrical calculations within the cyclic numbers of the twelve hui, and, sighing over the end of this cyclic number, is moved.

The numerical pattern of the earth’s seasonal ordinances begins with “two.” Multiplying “two” by six gives twelve, the twelve months of the year; extending this, multiplying by four and by three yields the twenty-four solar terms and the seventy-two seasonal periods (hou). Within the twelve sovereign hexagrams—the twelve hexagrams such as Fu, Lin, and Tai allocated to the twelve months—are contained the seventy-two seasonal periods; within the four cardinal hexagrams (Kan, Li, Zhen, and Dui) are contained the twenty-four solar terms; within the sixty hexagrams are contained the three hundred sixty days.

Regarding the arrangement of the solar terms, in the Han dynasty the initial system took Jingzhe as the medial qi of the first month and Yushui as the nodal term of the second month; it was only changed in the late Western Han. The order in the Hanshu, “Lülizhi” (Treatise on Pitch and Calendar), is: in the first month, Lichun is the node and Yushui the medial qi; in the second month, Jingzhe is the node and Chunfen the medial qi. This is because hibernating insects begin to be startled in the first month and are stirred more strongly by the second, so the names of the terms were fixed accordingly. The Santong Calendar (the calendar established by Liu Xin of the Western Han) instead took Guyu as the third month’s node and Qingming as the third month’s medial qi. If we examine the Tongguayan and the calendar of the time, Qingming should be the third month’s node and Guyu the medial qi, with the rest the same as in the Lülizhi.

The “Monthly Ordinances” in the Book of Rites records the phenology of the twelve months, but its format is not uniform: in some cases it first states the solar term and then the phenological signs; in others the reverse. In the months containing the two solstices (winter and summer) and the two equinoxes (spring and autumn), the seasonal time is recorded once again. This is because the two solstices are the beginning and end of Yin-Yang, and the two equinoxes are the meeting of Yin-Yang; these are the most important among the seasonal nodes, and therefore the sage kings gave them particular attention.

The Yijing says, “Kan is the hexagram of due north,” and also, “Dui is due autumn,” and also, “The former kings closed the passes on the solstice day.” The phrase “closed the passes on the solstice day” comes from the Xiang Commentary on the Fu hexagram; it means that on the day of the winter solstice the passes were closed, merchants and travelers did not set out, and the ruler did not tour the four quarters, so as to quietly nourish yang qi.

The later divisions of the solar terms and seasons were already present in the Yijing (Book of Changes). The Kan trigram is the trigram of due north; that Zhen is in the east, Dui in the west, and Li in the south needs no further explanation. The Dui trigram corresponds exactly to autumn, namely the autumn equinox; from this one can infer that Zhen corresponds to the spring equinox, Li to the summer solstice, and Kan to the winter solstice. The Great Image Commentary to the Fu hexagram says, “At the solstice, close the gates,” referring to the winter solstice. By the same reasoning, the character shen—suspected to be a scribal error for zhen—corresponds to the summer solstice. Those who understand the Yijing can infer by analogy, from the images of the trigrams and hexagrams, the changes in the qi of the waxing and waning of yin and yang.

Mr. Wei of Heshan (the Southern Song scholar Wei Liaoweng) said: Autumn is the “middle of yin” within yin qi, and spring is the “middle of yang” within yang qi.

Yin qi begins in the fifth month and ends in the tenth, so the seventh and eighth months are the middle of yin. Although the middle of yin also contains yang qi, yin still predominates. Yang qi begins in the eleventh month and ends in the fourth, so the first and second months are the middle of yang. Although the middle of yang also contains yin qi, yang still predominates.

Zhu Xi (Master Zhu) said: From this year’s winter solstice to next year’s winter solstice is simply one qi circulating. If it is divided into two sections, spring and summer belong to yang, and autumn and winter belong to yin; if divided into four sections, they are the four seasons; subdivided further, they are the twenty-four solar terms and seventy-two seasonal phases (hou), all of which come from this one circulation.

The twenty-four qi are the twenty-four solar terms by which the ancients divided the year according to the sun’s position on the ecliptic. Each term is separated from the next by about half a month. They are explained in order below:

First month: the Lichun (Beginning of Spring) node (within Yushui), and Yushui (Rain Water)—ice and snow melt and become rain. Viewed from above, snow disperses and turns into rain; the north wind freezes the rain and it becomes snow, while the east wind blows the snow apart and it turns back into water.

Second month: the Jingzhe (Awakening of Insects) node (within Chunfen). Jingzhe means that hibernating insects are awakened by thunder and crawl out of their burrows.

Third month: the Guyu (Grain Rain) node (within Qingming). Qingming means that all things grow, fresh and clean, bright and luminous. Guyu means that rain moistens, and from this the hundred grains grow.

Fourth month: the Lixia (Beginning of Summer) node (within Xiaoman). Xiaoman means that when the growth of all things reaches this point, they begin gradually to become full and plump.

Fifth month: the Mangzhong (Grain in Ear) node (within Xiazhi). Mangzhong refers to the time when awned grains can be sown.

Sixth month: the Xiaoshu (Minor Heat) node (within Dashu). Xiaoshu and Dashu are two segments distinguished within the extremely hot season: the beginning of the month is Xiaoshu, and mid-month is Dashu.

Seventh month: the Liqiu (Beginning of Autumn) node (within Chushu). Chushu means that the heat is about to retreat and hide away.

Eighth month: the Bailu (White Dew) node (within Qiufen). Bailu means that Yin qi gradually grows heavier, and dew condenses and turns white.

Ninth month: the Hanlu (Cold Dew) node (within Shuangjiang). Hanlu means that the dew air is cold and about to condense into frost.

Tenth month: the Lidong (Beginning of Winter) node (within Xiaoxue). Xiaoxue: the beginning of the tenth month is Xiaoxue.

Eleventh month: the Daxue (Major Snow) node (within Dongzhi). In the eleventh month the weather turns cold; this is called Daxue.

Twelfth month: the Xiaohan (Minor Cold) node (within Dahan). Xiaohan and Dahan are likewise two segments distinguished within severe cold: the beginning of the twelfth month is Xiaohan, and mid-month is Dahan.

The scripture also says that each of the twenty-four qi lasts a little more than fifteen days; each qi is further divided into two halves, making forty-eight segments in all, each lasting a little more than seven and a half days. In the Zhouli (Rites of Zhou) there is the expression “eighteen arrows for the day,” meaning that one qi corresponds to one arrow (the clepsydra arrow used for timekeeping in antiquity). The twenty-four qi are further divided so that each set of three hou amounts to a little more than five days; therefore the year is also divided into seventy-two hou.

Master Ou says: The seventy-two pentads (hou) each correspond to one mid-node (the midpoint of a solar term). The pentad at the beginning of a solar term is called the “pentad”; when the pentads are accumulated in order, one obtains the corresponding hexagram. What corresponds to a mid-qi is the next hexagram; what is named according to the Five Phases taking turns to govern is the Gong hexagram. When these stalk numbers (ce) are added up one by one, one arrives at the beginnings of spring (Wood), summer (Fire), autumn (Metal), and winter (Water) (the “fourteen” is understood according to the original character as fourteen days). Establishing nodes at the transitions of the four seasons gives the periods in which the Earth phase governs.

The lines of the twelve sovereign hexagrams (Fu, Lin, Tai, and so on, each corresponding to one of the twelve months) correspond to the mid-nodes of the seventy-two pentads. The preceding pentad is the first pentad, referring to the three days before the shuoqi (the starting point of a solar term); the following pentad is the second pentad, referring to the three days after the shuoqi. Similarly, by accumulating the stalk numbers, one obtains the beginnings of spring Wood, summer Fire, autumn Metal, and winter Water, while the nodes between the four seasons are governed by the Earth phase.

This passage discusses using the hexagrams of the Yi (Book of Changes) to calculate the solar terms and phenological periods of a year.

Each line of the twelve sovereign hexagrams (shier bigua)—that is, the twelve waxing-and-waning hexagrams that represent the growth and decline of Yin-Yang through the twelve months—corresponds to one of the seventy-two phenological periods (qishier hou), the year being divided into seventy-two hou of about five days each. For each hexagram, the first three days are the “initial hou,” belonging to the new-moon qi (shuoqi, the qi around the first day of the lunar month); the latter three days are the “secondary hou.” Dividing inner and outer in this way, the sixty hexagrams correspond to the 360 days of the year.

A year has twelve months, and each month also has a middle qi (zhongqi). The middle qi is governed by the “public hexagram” (gonggua), and the secondary hexagrams are arranged in order after it. For example, at the winter solstice in the eleventh month, the first line (a six) of the Kan hexagram is “Fu” (Zhongfu), which is where the middle qi lies. The hou attached to the Fu hexagram is Zhun, corresponding to three days; at Minor Cold, the second line (a nine) of the Kan hexagram is Zhun, and beyond it are the Grandee Qian (Modesty) and the Minister Kui (Divergence)—all of these are secondary hexagrams.

The four beginnings (Lichun, Lixia, Liqiu, and Lidong) belong respectively to the Four Phases of Wood, Fire, Metal, and Water; they are the nodal days of the first month of each of the four seasons and also the times when the Five Phases begin to take effect. The four corner positions—Gen, Xun, Qian, and Kun—each govern one of the six qi; Chen, Xu, Chou, and Wei are the four seasonal transition months, belong to Earth, and are the times when the Earth phase takes effect. Kan, Li, Zhen, and Dui are the four cardinal hexagrams; each hexagram’s two lines govern five hexagrams, forming the operations of one month. The Beginning of Spring occupies the position of Qian and Kun: one line governs two and a half hexagrams, and six lines govern fifteen hexagrams, making three months into one season.

In summary, the four seasons multiplied by six make the twenty-four solar terms. Separately speaking, there are jie, qi, and hou, each with its own order and not confused with the others.

The above is my own superficial understanding, and it may not accord with Ouyang Xiu’s original intent. There is another theory: the Jia and Si months each change six times, and over the twelve months there are seventy-two changes; calling these “hou” is also plausible.

The Sitianl Examination states: seventy-two is the number generated by the transformations of the Five Phases and the fundamental rule of calculation. The yarrow-stalk number of Yang is thirty-six; multiply it by two. The yarrow-stalk number of Yin is twenty-four; multiply it by three. The numbers of Yin and Yang are all in complete accord. The seventy-two hou (phenological periods, dividing the year into seventy-two seasonal segments) are also derived from this.

The seventy-two hou were used by the Imperial Astronomical Bureau in compiling calendars, and they are extremely refined. I once sought their underlying principle without success; after pondering all night and a long while thereafter, I suddenly understood: these are the yarrow-stalk numbers of the Qian and Kun hexagrams. In the Qian hexagram each line is thirty-six; two lines make seventy-two, and six lines make two hundred sixteen. In the Kun hexagram each line is twenty-four; three lines make seventy-two, and six lines make one hundred forty-four. Using these to calculate a year, the full number of three hundred sixty days is included. Distributing them further among the Five Phases: Water, Wood, Fire, and Metal each govern one season, totaling four times seventy-two, or two hundred eighty-eight days; another seventy-two days are still needed to complete a full cycle. Earth is therefore used to make up the deficiency. Earth occupies eighteen days in each of the four seasons, namely the four months of Chen, Xu, Chou, and Wei. In addition, six days of each month belong to Earth, corresponding to the six lines of the monthly sovereign hexagram (the hexagram that uses line images to represent the monthly waxing and waning of Yin and Yang), thereby displaying the Five Phases; without Earth, this would be impossible. In the four seasons of the year and the six days of each month, Earth is lodged within them as the place of transition. Thus within heaven and earth, the myriad people, myriad things, myriad affairs, and myriad transformations all rely on it as the ground of birth, growth, harvest, and storage; for this reason it is called “hou.” The reader should pardon my ceaseless pondering; in truth, this is merely the transformation of the heavenly stems Jia and Ji combining to produce Earth.

Zhang’s Discourse on the Observation of Things: The four seasons and eight solar terms of a year each divide into three stages of change. Ten days make one xun (ten-day period); three xun make one month; nine xun make one season; and thirty-six xun complete all four seasons. Five days make one hou (phenological period); three hou make one qi (solar term); nine hou make one jie (node); and seventy-two hou complete one cycle of the eight jie.

Heaven has four seasons; each season has four months; when the four seasons are finished. Here likewise five days make one hou, three hou one qi, nine hou one jie, and seventy-two hou cause the eight jie to cycle endlessly.

Heaven has four seasons; each season has four months; each month has forty days. Four times four is sixteen; from each number one must be subtracted, so in fact each season has three months and each month thirty days. Although the total count of the four numbers is four, the “one” within them is often unused; the numbers actually used are three and nine. Therefore three xun make one month, and three months—ninety days—make one season.

Five days make one hou: a month has six hou; five times six equals thirty days. Three hou make one qi: three times five is fifteen days. Nine hou make one jie: nine hou exactly complete the eight jie, and the cycle of solar terms then comes full circle.

The author says that he often felt regret for the calendar officials of his time: they only remembered the names of the hou but did not deeply investigate the principles within them. He therefore explains them item by item, so that people will not, like ordinary folk, use them every day without knowing why.

The Names and Meanings of the Seventy-Two Hou

The hou “In mid-eleventh month, earthworms coil”: Taking the winter solstice as the starting point, it is based on the first epoch of the Jiazi Shangyuan calendar.

The hou “The east wind thaws the ice” (Dongfeng jiedong): It is based on the new calendar that takes Rain Water in the first month as the first solar term.

First month

From Beginning of Spring to Rain Water (General Account of Phenology)

The spring wind—also called Tiaofeng and Shufeng—blows away the cold freezing Qi, and ice and snow begin to melt. Hibernating insects begin to stir slightly, but they do not yet crawl out of their burrows; only in the second month will they be startled into emerging.

During severe cold, schools of fish swim beneath the ice and press close to the ice surface to warm themselves. In the first lunar month, as Yang Qi returns, the fish begin to swim toward the surface and draw near the ice. At this time the fish are fat and delicious, and otters first display the fish they have caught on the bank before eating them; the ancients called this “the otter’s fish offering.” Wild geese return north from the south, about to go back to their northern dwelling places.

The Tongguayan (a Han-dynasty apocryphal text) says: at Beginning of Spring pheasants call and hens incubate eggs; at the Rain Water solar term Tiaofeng blows. Winds of violent force are called fierce winds. Wind moves plants and trees and makes them give forth sound, and so it is said that plants and trees sprout and stir; this is the season when one can plow and plant.

Second Month

Peach blossoms open, corresponding to the Awakening of Insects solar term. After another five days, the canggeng (oriole) begins to call. The canggeng is also called Huangliliu, Wuhuang, and Chuque; the people of Qi called it “Boshui,” which is close to the call of today’s cuckoo. The ancients also believed that in spring eagles transform into doves, and in autumn doves transform back into eagles.

The Xuanbird is the swallow. Swallows come in spring, build nests under the eaves, and incubate eggs, symbolizing marriage. Therefore Jiandi, mother of Qi, ancestral founder of the Shang people, swallowed a swallow’s egg and gave birth to Qi.

Yang Qi is pressed within by Yin Qi and cannot rush out; Yang Qi strikes with force, and thus thunder is produced. Thunder is the sound of Yang, and lightning is the light of Yang. When Yang Qi is on the outside and Yin Qi attaches to it, it flickers and becomes lightning. When Yang Qi is weak, the light does not appear; when Yang Qi gradually flourishes and strikes Yin Qi, the light then manifests, and so it is called “the beginning of lightning.”

Third Month

In the original text, this section contains only the month heading and no body text.

Third Month

The paulownia trees begin to flower. Field mice turn into ru (a small quail-like bird). Another interpretation says that field mice belong to the yin kind; when yang qi is abundant, they transform into ru, and when yin qi becomes dominant, the ru turn back into mice.

The rainbow is colored light formed when yin and yang qi converge. The male rainbow, bright and intensely colored, is called “the bright and full”; the female rainbow, pale and thin, is called “the subtle union.” If pure yin qi overwhelms yang qi, no rainbow appears. When the clouds are thin and sunlight passes through gaps to shine on raindrops, a rainbow forms.

Ping is duckweed; it is also called ping and zao—these are all water plants. The calling dove (the quege, which resembles a mountain magpie but is smaller, blue-black, short-tailed, and noisy, hence its name) ruffles its feathers, and the silkworms are about to hatch. When migratory birds fly, they strike their wings together; this spurs on the farm work. The hoopoe (a bird with a crest on its head) alights on the mulberry tree; it is also called the yajiu and is the weaving crow. Its descent onto the mulberry tree signals that women should devote themselves to sericulture, a fundamental task. The “Neizai” section of the Rites of Zhou says: In mid-spring, the queen leads the titled ladies to gather mulberry leaves in person, and when the Great Fire star (the Heart mansion) is in the sky, they soak the silkworm eggs.

Fourth Month

Louguo is the croaking frog, that is, the toad. The commentary on the “Guoshi” section of the Rites of Zhou says: When summer yang qi is at its height, the toad’s croak is especially loud. Earthworms are yin creatures; sensing the true yang qi, they emerge from the ground. The Wang gourd is red in color and grows in response to fire qi. The bitter herb flowers and, responding to fire qi, turns bitter in taste. Micao belongs to the grasses (such as the caoli and similar plants); because its branches and leaves are fine and soft, it is called micao. In the months when yang qi is vigorous, yin-type grasses cannot withstand the yang qi and wither and die.

Fifth Month

The Tianyuan Fawen is a Daoist classic. This passage focuses on phenology, explaining the seasonal phenomena recorded in the Liji · Yueling (Monthly Ordinances) and using Yin-Yang Qi to account for the causes of the transformations of the myriad things.

Mid-Summer (Fifth Month):

The praying mantis gives birth to its young. It is also called “tianlang” and “buying.” The egg case it lays is called “piaoxiao.” In the Yan and Zhao regions it is called “Shili”; in the Qi and Qi regions it is called “Shuma Guzhe.” This insect begins to call in the seventh month, a sign that cold Qi is about to arrive. The climate of Bin is rather cold, so it does not begin to call until the fifth month.

The “fantong” is the hundred-tongue bird; the text says it is what is today called the “xiama.” Some say that the base of its tongue adheres to one side of the oral cavity and the tip curves inward; others say that upon dissection and observation, the tongue is found to be turned backward. Zheng Xuan did not accept this explanation. From this it can be known that the fantong bird begins to call in spring and gradually stops by the fifth month. Because its calls are highly varied, it receives the name “reverse-tongue.” It is also possible that the toad’s tongue is naturally structured this way, and for that reason alone it cannot be called “reverse-tongue.”

Deer belong to the Yin category; when they sense Yin Qi, they shed their antlers. This is why physicians use deer antler velvet to supplement Yin. Cicadas also belong to the Yin category; they sense Yin Qi and call. Banxia (Pinellia) is a medicinal herb; its growth at this time shows that Yin Qi has reached its extreme and Yang Qi is beginning to sprout.

Sixth Month:

Warm winds begin to blow, and the warm, generous Qi reaches its peak in late summer (the sixth month). Crickets, also called “cuzhi,” are born in the earth. In late summer their wings gradually mature, but they still cannot fly far, so they remain by the walls; by the seventh month they can fly far into the fields.

Hawks sense the Yin Qi of autumn, give rise to a killing intent, and begin practicing seizing prey. Jiao Gan, a Han-dynasty Yijing scholar, asked: “In mid-autumn doves transform into hawks, and in mid-spring hawks transform into doves. How can there be a hawk practicing in the sixth month?” Zhang Yi replied: “Although hawks are transformed from doves, there are originally true hawks that can practice.”

Decaying grass receives summer heat and damp Qi and transforms into fireflies. The text does not say “transform” because the firefly is no longer decaying grass. The soil is moist, and stifling heat steams upward; heavy rain then descends.

After the Beginning of Autumn, cool winds gradually rise: this is the season of cold and coolness. White Dew condenses, matching the color of autumn, which belongs to Metal. The cold cicada cries because it has received the upright Qi of Yin. The hantiao, also called the cold cicada, resembles a cicada but is slightly smaller. At this time green hawks and red hawks kill black birds but do not eat them immediately; this is their way of repaying their root to Heaven and Earth (repaying the source, in gratitude for Heaven and Earth’s nurturing grace). This also shows that without autumn’s work of austere severing, the Qi of Heaven and Earth would not begin to withdraw, and the five grains could not ripen.

Eighth month: the wild geese come flying. In the first month of spring, the text speaks of migratory birds flying in from outside; here it speaks of migration from north to south. The dark bird (the swallow) goes back—this is the seasonal phase of mid-autumn. Swallows come in spring and leave in autumn, returning to their former hiding places; at this time flocks of birds store food in preparation for winter’s storage.

Hibernating insects open their portals when thunder sounds, so here the text records that they close their portals when thunder withdraws. The expression shuhu means “to seal the door”; yun refers to the door leaf. They seal the crevices around the door leaf, making the formerly bright opening a little smaller. At this time the weather is still warm, and people still need to go in and out; only in the tenth month, when the cold is extreme, are the doors completely sealed tight. Thunder sounds in the Yang Qi of the second month and is silenced in the Yin Qi of the eighth month. Because Yin Qi contracts, water begins to dry up. The Guoyu says: when the Chenjiao star appears, the rainy season ends; when the Tiangen star appears, the streams dry up. After the rainy season ends, Yin Qi gradually grows stronger; when the water has dried up, bridges can be built and crossings made.

In the eighth month, the Mao and Bi lodges of the twenty-eight lunar mansions govern rain. When the Tiangen star appears between the Di and Fang lodges, the Chenjiao star is visible at the same time. At the start of the ninth month the Tiangen star appears; by the end of the ninth month, the two are about twenty-one days apart.

Ninth month: what follows records the seasonal phases of the ninth month.

Migratory Birds and Phenology in Mid-Autumn and Late Autumn

The hongjiu (a migratory bird that the ancients regarded as a “guest” coming and going with the seasons) is called the “host” if it arrives in mid-autumn, and the “guest” if it arrives in late autumn. Another explanation is that the birds that come in mid-autumn pass on, while those that come in late autumn remain as guests.

The phenological changes of autumn roughly correspond to the growth and decline of Yin-Yang. Birds entering water and transforming into clams is a manifestation of yang Qi concealing itself; chrysanthemums putting forth yellow blossoms whose color is rich and full corresponds to the strength of yin Qi. The author holds that five yin lines cannot completely strip away one yang line; therefore plants and trees must send forth their essence as blossoms in order to preserve their vitality. When plants wither, turn yellow, and shed, this is a return to the root. Hibernating insects (those dormant in the soil) all lower their heads downward, following the yang Qi as it hides within.

Hunting Sacrifice and Predation

In autumn jackals first display their prey on the ground as if making a sacrifice, and only then hunt and eat birds and beasts. In the first month of autumn, hawks display the birds they have caught; flying birds are small in body, so their transformations are rapid. In the last month of autumn, jackals sacrifice beasts; the quadrupeds they hunt are larger in body, so their transformations are slow.

Tenth Month: Water Freezes and Yin Flourishes

After the solar term Frost Descends, water begins to freeze. Frost is the precursor of solid ice; this is the meaning of the Zhouyi’s Kun Hexagram saying, “Treading on frost, solid ice arrives.” The ground begins to freeze; when water freezes, the ground must freeze. Pheasants enter the water and transform into shen; shen are large clams. This too is a manifestation of yang Qi hidden within.

Rainbows accordingly hide and are no longer seen. In late spring yang is stronger than yin, so rainbows first appear; in the first month of winter yin is stronger than yang, so rainbows hide and are unseen. Heavenly Qi rises. From the fifth month the first yin Qi is generated; by the tenth month the six yin have all risen, and the six yang have already receded. The celestial bodies are above, and yang Qi returns to emptiness. Therefore what is said to “rise upward” is earth Qi; the six yin preside below, and so it is said to “descend.” Yang Qi hides in the earth, yin Qi closes and solidifies, and thus winter is formed.

Eleventh Month: Magpies Do Not Call

Magpies do not call in the eleventh month. When birds call at night, it is yin creatures seeking the dawn (yang); therefore when they sense the first birth of one yang, they no longer call.

(The “eleventh month” is a solar-term subheading; the above is only a brief explanation based on the text as it stands.)

The Phenological Signs of the First Month of Winter (the Tenth Month) and the Second Month of Winter (the Eleventh Month)

The hedan (a night-calling bird) no longer calls. Its nighttime calling is a way of seeking dawn; it belongs to the yin category and seeks yang qi. When it senses the first birth of one yang, it stops calling. Tigers begin to mate, also because yin creatures sense yang qi and come together. The liting grass puts forth new shoots, and fragrant herbs, sensing yang qi, become more fragrant. Earthworms knot themselves because they come out from underground with their heads bent downward. As yang qi begins to stir, the earthworms want to stretch their heads upward, but their bodies are obstructed, so they curl into knots.

The mi deer’s antlers fall off: deer are yang beasts, and at the summer solstice they sense the first birth of one yin and shed their antlers; mi deer are yin beasts, and at the winter solstice they sense the first birth of one yang and shed their antlers. Springs begin to surge; this is the image of the Kan trigram, produced by the yang of Heavenly One.

The Phenological Signs of the Twelfth Month

Wild geese begin to migrate north; they fly from south to north. The early ones fly north as early as the eleventh month, while the late ones do not fly north until the second month. Magpies begin to build nests because they can foreknow the workings of the seasons and sense the climatic omens of the coming year, so they build early. Pheasants call; pheasants are fire animals, and sensing yang qi they make sound, so they call. Hens begin to lay eggs; chickens are wood animals, and they take form by attaching to yang qi, so they lay eggs at the Beginning of Spring solar term. This is because the Beginning of Spring falls in this month.

Birds of prey hunt. At this time the killing qi is at its height, so hawks and falcons gather and fiercely seize swift flying birds. “Yan” means fierce. Lakes and marshes freeze very thick, because the ice is solid through to the depths, showing that the ice is thick. At this time the sun’s position is in the Xuanxiao region, that is, in the positions of the three lunar mansions Nü, Xu, and Wei.

Making the earth ox: this is a matter of going out and starting work. The Chou month belongs to earth, and earth can overcome water, so an earth ox is made to escort away the cold qi and prevent yin qi from becoming a disaster in the coming year.

The above seventy-two phenological signs each have their meaning. Seeing the scene gives rise to feeling, and one can use them to express reflections on the seasons and animals; therefore they are specially recorded.

The Commentary on the Spring and Autumn Annals says: at the nodes of fen (the spring and autumn equinoxes), zhi (the summer and winter solstices), qi (the Beginning of Spring and Beginning of Summer), and bi (the Beginning of Autumn and Beginning of Winter), one must record cloud qi and physical phenomena in order to make preparations.

The fen (spring and autumn equinoxes) serve to send off cold qi, so that yin-cold qi will not harm the coming year. The seventy-two hou (the year is divided into seventy-two phenological periods, each about five days long) each have their meaning. Seeing scenes and objects gives rise to feelings, through which one may express sighs over the changes of the seasons and the myriad things; therefore I have specially recorded them.

The Chunqiu Zhuan (that is, the Zuo Zhuan) says: at the times of fen, zhi, opening, and closing, one must record cloud qi and phenomena, to keep them for verification.

These four terms refer to four solar terms: fen is the spring and autumn equinoxes; zhi is the summer and winter solstices; opening (qi) is the beginning of spring and the beginning of summer; closing (bi) is the beginning of autumn and the beginning of winter. Kong Yingda of the Tang dynasty held that the two solstices are the beginning and end of yin-yang, while the two equinoxes are the intersection of yin-yang; these are the most important solar terms, and so the ancients observed cloud qi on these days. “Wu” means color. The Bao Zhangshi (an official in the Zhou dynasty responsible for observing celestial phenomena) said: according to the five-colored cloud qi, one distinguishes auspicious and inauspicious events, floods and droughts. Green foretells insect pests, white foretells mourning, red foretells war or famine, black foretells floods, and yellow foretells a good harvest. All this is observing the colors of the cloud qi beside the sun to verify omens, and by this means inferring the twelve fenye (the terrestrial regions corresponding to celestial mansions), to determine whether the corresponding state would have abundance or famine.

The Bao Zhangshi also said: one uses twelve kinds of phenomena to observe whether there is harmony between Heaven and Earth.

“Wind” means “qi.” The ancients blew the twelve pitch pipes, using them to measure and observe the wind qi of the twelve double-hours, and thereby distinguish auspicious signs from anomalies. Today the method of blowing the pitch pipes to observe the winds no longer exists.

The Explanation of Wind and Ancient Methods of Wind Observation

Wind is Qi (vital energy). The ancients all used the method of blowing pitch pipes to observe and determine the wind Qi of the twelve double-hours, thereby distinguishing auspicious and inauspicious signs and ominous or auspicious portents. Pitch pipes were a set of standard pipes used in antiquity both to fix pitches and to practice divination by observation; they were divided into the twelve Yin-Yang pitches. Today the method of blowing the pitch pipes no longer exists, and this branch of learning has been lost.

The Zuo Zhuan records that when the Chu army attacked Zheng, the music master Shi Kuang blew the pitch pipes and sang to observe the strength or weakness of the Chu army. He sang the “North Wind” and then the “South Wind.” The tone of the South Wind was not vigorous enough and consisted mostly of decaying sounds; therefore he judged that the Chu army would not succeed, and later it indeed returned without accomplishment. Note: what Shi Kuang blew were pitch pipes: the North Wind corresponded to pitches such as Wuyi and Jiazhong, while the South Wind corresponded to pitches such as Guxi. From the weakness of the South Wind’s tone, one could infer that Chu would achieve nothing.

Wang Zhaoyu (a Northern Song scholar) said that the twelve winds arise from the directions of the twelve earthly branches and are produced by the combination of the six Qi of heaven and earth. The Zhen position produces the Mingshu wind, the Li position the Jing wind, the Dui position the Changhe wind, and the Kan position the Guangmo wind; these four winds are the winds of the four cardinal trigrams. The Gen position produces the Tiao wind (the Beginning of Spring is also called the Tiao wind), the Xun position the Qingming wind (the Beginning of Summer is also called the Qingming wind), the Kun position the Dong wind (the Beginning of Autumn is also called the cool wind), and the Qian position the Buzhou wind (the Beginning of Winter is also called the Buzhou wind); these four winds are the winds of the four corner trigrams. Adding the four beginnings (Beginning of Spring, Beginning of Summer, Beginning of Autumn, and Beginning of Winter) and speaking in terms of the Bagua (Eight Trigrams), combining them with the four beginnings yields the twelve winds. The eight winds are assigned to the Bagua.

Zhu Xi’s Theory of Qi Transformation

Zhu Xi (a Southern Song Neo-Confucian) said that between heaven and earth there is only one Qi. When Qi first arises, it is spring; when it grows to its fullest, it is summer; when it contracts, it is autumn; when it recedes and congeals, it is winter; and the following year it begins again from spring. Benevolence and righteousness are like Yin-Yang, and the four beginnings (the sprouts of benevolence, righteousness, propriety, and wisdom) are like the four seasons. Dividing out the four seasons and the four beginnings is like the eight nodes. This is merely the waxing and waning, the increase and decrease, of one Qi. One divides into two, two divides into four; three times four gives twelve, twelve times two gives twenty-four, and twenty-four times three gives seventy-two; from this it scatters into ten, a hundred, a thousand, and ten thousand—nothing more than the principle of “heaven three, earth two” (the ancients used the number three for heaven and two for earth to summarize the numbers of heaven and earth).

Pitch Standards and Sound: Appendix (this section discusses the relationship between pitch standards and sound)

Zhu Xi said: The Qi (vital energy) of heaven and earth all emerges upward from within the earth. This Qi has rising and descending phases and should be divided into six stages. Beginning at the winter solstice, the first layer of yang Qi rises from below; by the fourth month, when the six yang [phases] are full, it recedes, and the yin Qi beneath then arises. By matching these with the pitch standards, one can see the changes of climate.

The Grand Master (Taishi), the Zhou official in charge of music and pitch standards, administered the six yang pitch standards and the six tong. The six yang pitch standards are yang sounds; the six tong—that is, the six yin pitch standards—are yin sounds. This shows that sound has Yin-Yang distinctions and that each has its own correspondences.

Huangzhong corresponds to the Qi of the Zi position and is established in the eleventh month (the ancients called the month indicated by the handle of the Big Dipper “establishing” [jian]); its corresponding star field is Xingji (one of the twelve celestial divisions, the division correlating the heavens with earthly regions). Dalü corresponds to the Qi of the Chou position and is established in the twelfth month, corresponding to Xuanxiao. Taicu corresponds to the Qi of the Yin branch position and is established in the first month, corresponding to Juzi. Yingzhong corresponds to the Qi of the Hai position and is established in the tenth month, corresponding to Ximu.

Taicu is assigned to the Qian palace and is the second of the yang sounds, matched with the nine-in-the-second line of the Qian hexagram; the Kun palace is assigned Yingzhong, that is, the six-in-the-third line. This is a yang pitch standard matched with a yin pitch standard, with yang as the governing principle and yin coming to unite with it. The remaining months can largely be inferred by the same pattern. The month established at Mao is Jiazhong; at Xu, Wuyi; at Chen and You, Guxi and Nanlü, respectively corresponding to such star fields as Jianglou, Dahuo, Shouxing, and Daliang, and they interlace with one another. The month established at Si is Zhonglü; at Shen, Yize; at Wu and Wei, Ruibin and Linzhong. These pitch pipes pertain to the fourth through seventh months; their corresponding star field is Shishen, and the stars Chunshou, Chunwei, and Chunhuo also interlace with one another.

The stars and luminaries move through the twelve celestial divisions; the pitch standards correspond to the twelve months and are used to harmonize the Dao of Heaven with human affairs. First, the Yin-Yang Qi is distributed through the four seasons, assisting the sage king in participating in and assisting heaven and earth, thereby establishing the supreme principle of centrality and harmony.

It is also said: Among the Three Systems (Santong), the establishment at Yin is the human system, at Chou the earth system, and at Zi the heaven system. These are the three systems in ancient calendrics that take different months as the beginning of the year (the Xia took the Yin month as first, the Yin-Shang took the Chou month, and the Zhou took the Zi month), corresponding respectively to the human, earth, and heaven systems.

Heaven takes the Huangzhong pitch as its foundation; its pipe is nine cun long, belongs to the Qian trigram, and matches the number of Heaven. Earth takes the Linzhong pitch as its foundation; it is six cun long, belongs to the Kun trigram, and matches the number of Earth. Humankind takes the Taicu pitch as its foundation; it is eight cun long and matches the number of the Bagua. None of the three pipes has a fractional remainder; their dimensions are exact and leave no odd fraction.

Linzhong occupies the Wei position, where the qi of Huangzhong is exhausted. The heavenly-earthly pattern on Linzhong appears at the Si position and becomes fully formed only at Wei in the southeast; it too has no fractional remainder. The pitch pipes take the yin-yang numbers nine and six as their rule; nine multiplied by nine yields eighty-one, the general framework of one primal cycle, and the pattern is thereby completed. After another nineteen years, with seven intercalary months established, the calendrical chapter is fully completed, likewise without remainder.

Therefore the sage kings of the Three Dynasties ought to have fixed the beginning of the year by these three pitches, in order to accord with the seasons of Heaven, spread the Way of Earth, and instruct human affairs. The Xia calendar is taken as primary because human harmony prevails, and the harmony of Heaven and Earth then resonates in response.

The three palaces are: Yuanzhong as the Heaven Palace, Hanzhong as the Earth Palace, and Huangzhong as the Human Palace.

Yuanzhong is Jiazhong. It is born from the qi of the Fang and Xin lodges and is Dachen (the Xin lodge, the Bright Hall of the Heavenly Thearch); hence it is called the Heaven Palace. It is a yin note yet is paired with a yang pitch. In sacrifices to Heaven, four notes are used (meaning four notes are combined in performance), while Huangzhong, Taicu, and Guxi are not used. Hanzhong is Linzhong. It is born from the qi of the Wei position, stands in the Kun direction, and is where the Heavenly Altar and Earth Spirit are located, beyond the three lodges Jing, Yu, and Gui; hence it is called the Earth Palace. In sacrifices to Earth, four notes are used: Linzhong, Taicu, Dalu, and Guxi. Huangzhong is born at the Zi position; above Zi are the qi of the Xu and Wei lodges, which preside over the ancestral temple; hence it is called the Human Palace. In ancestral temple sacrifices, four notes are used: Huangzhong, Taicu, Yingzhong, and Dalu. The three palaces are each used for the sacrifices to Heaven, Earth, and humans; from each palace as root, the notes jue, zhi, and yu are generated in mutual relation and are obtained by extending the calculation according to the notes.

It is also said: when the pitch pipes are used to observe the qi (the ancients placed reed ash in the pitch pipes so that it moved with the qi and thus measured the solar terms), there is not the slightest error.

The twelve pitches (lülü) can respond to and verify the Qi (vital energy) of the solar terms without any deviation.

The “pitch” (lü) is also called “zhong.” “Zhong” carries the meanings of “center” and “response”; “response” refers to verification by blowing ashes. The specifications of a pitch pipe are nine fen in circumference and three fen in inner diameter. Taking the Huangzhong (Yellow Bell) pitch pipe as the standard, it is buried at the zi position (due north, the first of the twelve earthly branches), with the top of the pipe nine cun from the ground and its opening facing south. From this orientation, the positions of the other pitches can be inferred. The inner membrane of reeds from Henei is burned into ash (jiafu ash) and used as the qi-testing material, while bamboo from Jinmen Mountain in Yiyang is used to make the pitch pipes.

The twelve pitch pipes are buried in a sealed chamber, corresponding to the directions of the four seasons. The positions from zi to si and from wu to hai belong to “greater Yin-Yang”; when the six yin and six yang are paired, they belong to “smaller Yin-Yang.” This method of calculation originates from the twelve-pitch theory of Jing Fang of the Western Han.

The twelve pitches are divided into two categories. When yang pitches occupy yang positions and yin pitches occupy yin positions, this is called “obtaining the position”; among these, five pitches each generate five sons. When yang pitches occupy yin positions and yin pitches occupy yang positions, this is called “losing the position”; likewise, five pitches each generate three sons. The text uses multiplication and addition of numbers to calculate these relationships, finally combining them into the number sixty, which corresponds to the days of the sixty Jiazi cycle.

Seven pitches, including Huangzhong and Taicu, each govern one day and serve as the master of that day. The remaining fifty-three pitches correspond in turn to other days; paired six and seven, they complete one cycle, which is the sixty days of one Jiazi cycle.

The twelve pitches further give rise to twelve modes, a scale system based on the pitches.

The Twelve Lü and the Sixty Lü

Jing Fang’s pitch system was this: each lü can be divided into five tones, so the twelve lü together make sixty tones; the sixty lü then further generate three hundred sixty sounds, corresponding to the three hundred sixty days of the year. If each of the twelve lü is paired with the seven notes to form a mode, the total is eighty-four modes. The so-called diao (mode) is what is used to harmonize sounds.

The Huainanzi says: in the three hundred sixty lü, each takes the lü of its current month as mother and one mid-season qi (zhongqi) as child. Their fractional values are determined according to the day and branch (sexagenary day) on which they fall; then, matching them with the seven notes, one takes the stem-branch of that day as the standard. In the sound at the winter solstice, the five tones (gong, shang, jiao, zhi, yu) and the seven notes are harmonized here and fully contained within it. Within this there is also a distinction between principal tones (zhengsheng) and subsidiary tones (zisheng).

One Lü Generates Five Tones

A single lü can generate the five tones. Taking Huangzhong (the first of the twelve lü, belonging to zi and corresponding to the zi month, the month of the winter solstice) as an example: at the zi position there are five tones—Jiazi is zhi, Bingzi is yu, Wuzi is gong, Gengzi is jiao, and Renzi is shang; these are the five tones of Huangzhong. Dalü (one of the twelve lü, belonging to chou) also has five tones; the five tones of Yichou, Dingchou, Jichou, Xinchou, and Guichou are the same as these. The remaining lü, from the mao month through the hai month, all follow this pattern.

Zhu Xi’s Account

Zhu Xi said: each of the twelve lü takes its own lü as gong and from this generates four lü. For example, with Huangzhong as gong, Taicu is shang, Guxi is jiao, Linzhong is zhi, and Nanlü is yu; these are the notes of the Huangzhong scale. If Linzhong is taken as gong, then Nanlü is shang, Yingzhong is jiao, Taicu is zhi, and Guxi is yu; these are the notes of the Linzhong scale.

Vernacular Explanation

Each of the twelve lü corresponds to a Gong position, and from this the five tones—Gong, Shang, Jue, Zhi, and Yu—are distinguished; only then are the sounds of the sixty lü considered complete. This does not mean that taking Huangzhong as Gong, Taicu as Shang, Guxi as Jue, Linzhong as Zhi, and Nanlü as Yu is fixed and unchanging. The twelve lü (Huangzhong, Dalü, Taicu, Jiazhong, Guxi, Zhonglü, Ruibin, Linzhong, Yize, Nanlü, Wuyi, and Yingzhong) are simply standard pitches arranged in order of length.

In the Huangzhong yun, whether generated upward or downward, the lengths all follow in accord, so each can take the proper tone of its own lü. As for the remaining sixty lü, each of the five tones governs a day in turn. Whichever day comes around, the corresponding lü serves as that day’s Gong; thus the five tones’ Gong, Shang, Jue, Zhi, and Yu alternate in succession. This is called “rotating to form the Gong” (xuanxiang weigong).

Zhu Xi also explained the method for the mutual generation of Gong pitches. Taking Dalü as Gong, Dalü takes Huangzhong’s number eighty-one; subtracting one part from three gives fifty-four, and it generates Yize downward. Yize in turn takes Linzhong’s number fifty-four; adding one part to three gives seventy-two, and it generates Jiazhong upward. All the other lü are treated analogously.

The rule for the numbers of the pitch pipes is this: all yang lü generate upward and govern “growth” (xi), so one part is added to three and the pipe length increases; all yin lü generate downward and govern “decay” or “collection” (mie), so one part is subtracted from three and the pipe length decreases.

This passage discusses the "three-part loss and gain" method (sanfen sunyi) of the ancient pitch-pipe system, that is, calculating the relative pitch of each note by increasing or decreasing the length of a pipe by one third.

A long pipe can generate a short pipe: subtract one third from the long pipe and one obtains a shorter pipe; this is called "lower generation." A short pipe can generate a long pipe: add one third to the short pipe and one obtains a longer pipe; this is called "upper generation." Taking Huangzhong (the first of the twelve pitches, with a pipe length of nine cun) as an example, subtracting one third gives six cun, yielding Linzhong. Linzhong is six cun; adding one third of that (about two cun) gives eight cun, yielding Taicu (the pitch of the first lunar month). The remaining pitches are all calculated in this way.

Then, using the "Gong number" (with nine as the base: nine times nine is eighty-one, the fundamental value of the gong pitch), one calculates the five tones. The gong pitch is 81; subtracting one third (27) gives 54, which is the zhi pitch; 54 plus one third (18) gives 72, which is the shang pitch; 72 minus one third (24) gives 48, which is the yu pitch; 48 plus one third (16) gives 64, which is the jue pitch. These three-part loss and gain numbers of the five tones are all patterns formed naturally.

Finally, it discusses the distinction between lü and lü: the six lü of the yang class belong to yang and areplaced on the left; the six lü of the yin class belong to yin and are placed on the right. The two have different directions of movement, just like the order in which yin and yang are arranged in divination methods.

The generation relations among the twelve lü (pitch-standards) are divided into “downward generation” (xiasheng) and “upward generation” (shangsheng), that is, the three-part subtraction-and-addition method: take one third of the length of the pitch pipe; subtracting one part is downward generation, adding one part is upward generation.

From Huangzhong to Zhonglü, generation proceeds downward in sequence. This corresponds to the section from zi to si, when Yang Qi rises and Yin Qi recedes; therefore, when a yang lü generates a yin lü it is called downward generation, and when a yin lü generates a yang lü it is called upward generation. From Ruibin to Yingzhong, generation proceeds upward in sequence. In the section from wu to hai, Yin Qi rises and Yang Qi recedes, so the situation is reversed: when a yang lü generates a yin lü it is called upward generation, and when a yin lü generates a yang lü it is called downward generation. The change occurs at wu, and therefore Ruibin must repeat upward generation. This is what Jing Fang, Ma Rong, and Zheng Xuan all say; Ban Gu, by contrast, advocates sequential downward generation.

The Jiazhong pipe is a little more than three cun and seven fen long; its pitch is somewhat high and constricted, and it does not correspond to the Meng and Zhong pitch-standards. Spring is the Qi of growth for the ten thousand things, and Zheng Xuan regards the arising of Yang as rising. But after Yang Qi descends, where should it ultimately return? It is better to discuss this through the divination method (the method of casting hexagrams and tracing their progression).

The Qian hexagram corresponds to jia and ren and moves left; Kun corresponds to yi and gui and moves right. The six Yin and six Yang each move according to their directions, and thus the order of the lü is determined. The upward generation of Dalu gives the zhi note; the downward generation of Yize gives the shang note. The upward generation of Jiazhong gives the yu note; the downward generation of Wuyi gives the jue note.

The sixty lü are correlated with the sixty hexagrams: arranged leftward from Huangzhong to Zhishi is upward generation; arranged rightward from Linzhong to Chishi is downward generation. Qian is positioned at zi and moves left; Kun is positioned at wei and moves right. Zhun, Meng, Tai, Pi, Xiaoguo, and the other hexagrams likewise each have their own position and direction. These seven hexagrams proceed in an interwoven manner, and the changes of the lü are determined according to them.

If one adopts the simplified method, it does not go beyond the six Yang and six Yin of the two hexagrams Qian and Kun. Zi, yin, chen, wu, shen, and xu correspond to Huangzhong, Taicu, Guxi, Ruibin, Yize, and Wuyi, like the leftward rotation of Qian; this is the yang lü generating downward. Wei, si, mao, chou, hai, and you correspond to Linzhong, Zhonglü, Jiazhong, Dalu, Yingzhong, and Nanlü, like the rightward turning of Kun; this is the yin lü generating upward. This is Zheng Xuan’s theory of the divination method, derived from Yang Xiong’s Taixuan.

Jing Fang held that each lü contains the transformations of the five notes and extended this into sixty hexagrams, beginning with the Zhongfu hexagram. After seven days, it again corresponds to the lü of the winter solstice (Huangzhong). In fact, all of this arises from Zhishi; before the winter solstice, it is the root of the lü-calendar. Yang Xiong (Ziyun) and Jing Fang truly understood these principles.

The North Star remains fixed at the center, and the Niu Star serves as the celestial pivot. That fixed point is actually one degree beyond the end of the Niu Star. I am not skilled at observing the heavens and am not qualified to understand this principle deeply.

The Beginning and End of the Gong Numbers

Huangzhong (the name of a pitch pipe, taken as the standard pitch and counted as one), Linzhong (two), Taicu (three), Nanlü (four), and so on are the lü numbers arranged in sequence; the ancients used them to record the order of “gong.” The North Star stays centered and unmoving, like the pivot of a door, and is called “Tianshu” (Heavenly Pivot). Its unmoving position is in fact about one degree from the end of “Niuxing” (the pivot star near the Northern Dipper). The author modestly says that he is not good at observing the heavens and considers this point difficult to understand.

The beginning and end of the gong numbers are the starting and stopping points of the twelve lü. The twelve lü in order are Huangzhong, Linzhong, Taicu, Nanlü, Guxi, Yingzhong, Yibin (that is, Ruibin), Dalu, Yize, Jiazhong, Wuyi, with Zhonglü as the twelfth. This calculation is called “Sanfen Sunyi” (three-part division, subtracting and adding): from a yang lü one derives downward to obtain a yin lü, and from a yin lü one derives upward to obtain a yang lü; when the derivation reaches Zhonglü, the twelve lü have completed one full cycle. Upward derivation is called “shangsheng” (upward generation), and downward derivation is called “xiasheng” (downward generation). Huangzhong generates zhi by upward generation and generates Linzhong by downward generation, yielding shang; Taicu generates yu by upward generation, and Nanlü generates jiao by downward generation. Each lü governs the five notes, and the twelve lü together make sixty notes. Nanlü is placed in the last position, and so it is said that they “end with Nanlü.” The text also says that Zhonglü generates Zhishi by upward generation, and Zhishi generates Qumie by downward generation; generating upward and downward in turn, they finally return to Nanlü (called “Nanshi” in the original). The sixty lü are complete at this point.

The Three Powers and the Seven Beginnings

The “Three Powers” are heaven, earth, and humanity. Heaven takes Huangzhong as its beginning, earth takes Linzhong as its beginning, and humanity takes Taicu as its beginning. The “Seven Beginnings” are the Three Powers plus the beginnings of the four seasons: Guxi is the beginning of spring, Ruibin (written “Kuibin” in the original) is the beginning of summer, Nanlü is the beginning of autumn, and Yingzhong is the beginning of winter. These four are called the “Four Beginnings,” and together with the Three Powers they make the Seven Beginnings.

If only the two altered notes were used to form modes, the pitches of winter and summer would be missing, and the four seasons would be incomplete. Therefore each gong must have five modes; adding the two modes of altered gong and altered zhi makes seven modes in all. The “Yue Ling” (Monthly Ordinances) chapter of the Book of Rites records only the five notes and does not mention the altered gong and zhi.

Correspondence Between the Six Lines and the Six Pitch-Standards

The six lines of the Qian hexagram correspond to the six yang pitch-standards, in order as follows: the initial nine, Huangzhong (corresponding to the Fu hexagram); the nine in the second place, Dalü (the Lin hexagram); the nine in the third place, Taicu (the Tai hexagram); the nine in the fourth place, Jiazhong (the Zhuang hexagram); the nine in the fifth place, Guxi (the Guai hexagram); and the top nine, Zhonglü (the Qian hexagram itself). Huangzhong, this yang qi, first arises in the eleventh month (the Zi month); thereafter yang qi gradually grows from below upward, which is called “lower generation.”

The six lines of the Kun hexagram correspond to the six yin pitch-standards, in order as follows: the initial six, Ruibin (that is, Ruibin, one of the twelve ancient pitch-standards; the original text writes “Shen,” which should be an error for “Gou,” the hexagram name corresponding to the fifth month); the six in the second place, Linzhong (the Dun hexagram); the six in the third place, Yize (the Pi hexagram); the six in the fourth place, Nanlü (the Guan hexagram); the six in the fifth place, Wuyi (the Bo hexagram); and the top six, Yingzhong (the Kun hexagram itself). Ruibin, this yin qi, first arises in the fifth month (the Wu month); yin qi grows from below upward, which is also “lower generation.” Some hold that yin qi is generated from above downward, so it may also be called “upper generation.”

Eight-Eight and the Eight Winds

“Eight-eight” refers to an arrangement in units of eight, used to symbolize the winds of the eight directions. Among the eight winds, pitch-standards in the same position are like husband and wife, while those in different positions are like mother and child. Hence it is said: “The pitch-standard takes a wife, and the mother gives birth to a child.” This means that when pitch-standards generate one another, the same position is “taking a wife,” while a different position is “the mother giving birth to a child.”

Generative Relations Among the Twelve Pitch-Standards

The patterns by which the twelve pitch-standards generate one another all take eight as a group. The relation of upper and lower generation stops at Zhonglü. Yin-yang generation, however, begins with Huangzhong and proceeds in a leftward rotation. For example, Huangzhong generates Linzhong with an interval of eight double-hours between them; the other pitch-standards follow by analogy, all observing the numerical principle of “three Heaven and two Earth”: three times three yields nine, and two times three yields six. Nine belongs to yang and six to yin; nine and six are precisely the expression of the Dao of yin and yang, husband and wife, and mother and child.

The initial nine of Huangzhong and the initial six of Linzhong both occupy the first position of the initial line; they are a pair of “same-position” husband and wife, joined together above Linzhong, and then generate Taicu upward. The nine in the second place of Taicu occupies the second position and forms with the first position a “different-position” relation of mother-child generation. Therefore it is said: what the yang pitch-standard generates is the same-position husband and wife; what the yin pitch-standard generates is the different-position mother and child.

Blowing the Pitch-Pipes to Know Auspiciousness and Inauspiciousness

In ancient times, the Grand Master held the matching pitch-standard and judged auspiciousness and inauspiciousness by listening to sounds in the army, and on this basis issued orders. The Book of King Wu’s Troop Dispatch says that on the day the ruler sends forth troops, he must use the pitch-standard of the same position to match the day and time, thereby conforming to the Way of Heaven.

The Grand Preceptor (Taishi) held the standard pitch pipe (“tonglü,” the basis for fixing pitch), listened to the sounds within the army, judged auspicious and inauspicious signs accordingly, and announced them to everyone. This passage comes from the Book of King Wu’s Dispatch of Troops: on the day the king sends forth troops, the soldiers form ranks, the commanders shout loudly, and the music officials blow the pitch pipes in response.

According to the Five Phases, each tone governs a different aspect. The Shang tone belongs to Metal; since Metal is hard and decisive, its sound is strong and firm, indicating a powerful army. The Jue tone belongs to Wood; since Wood is crooked or straight, its sound is bent and disordered, indicating wavering soldiers and lost morale. The Gong tone belongs to Earth; Earth governs growth and can bear, and its sound is harmonious and smooth, indicating harmony between officers and soldiers, of one mind. The Zhi tone belongs to Fire; Fire is impetuous and vehement, so its sound is urgent, indicating commanders who are impatient and quick to anger. The Yu tone belongs to Water; Water is weak, soft, and hidden, and its sound is faint, indicating that military prestige is not roused.

(Note: The twelve pitches are twelve pitch pipes used to fix pitch; the Five Tones are Gong, Shang, Jue, Zhi, and Yu, respectively assigned to Earth, Metal, Wood, Fire, and Water among the Five Phases.)

Shi Kuang said: “I heard the song of the north wind, and I also heard the song of the south wind. The south wind was not strong and mostly gave forth sounds of mourning and ruin; Chu will surely not succeed.” The so-called north wind refers to pitches to the north of such pitches as Jiazhong and Wuyi; the south wind refers to pitches to the south of Guxi and Nanlü. The pitch Qi of the south had not arrived, and therefore there were many sounds of mourning and ruin. The ancients all used blowing the pitches and singing the winds to foreknow victory and defeat. To produce sound and chant was called “song.”

Shao Yong said: “Yuanjiu is bland and tasteless; the great sound is faint and hard to hear.” Yuanjiu was the plainest wine in ancient sacrificial rites, with a light flavor; the grandest sound is instead subtle, just as Laozi said, “the great sound is faint and hard to hear.”

At the winter solstice, the first Yang is newly born and stirs in the Yellow Palace (the palace of Huangzhong, the pitch pipe corresponding to the zi position), like the brewing of yuanjiu; Yang Qi is nurtured in secrecy, waiting to manifest.

At the winter solstice, the first yang is just born, stirring at the position of Huangzhong (the first of the twelve pitches and the standard for fixing pitch), like the first breath of yuanjiu (unseasoned wine used in ancient sacrifices) at the beginning of brewing. Its flavor lies in flavorlessness; this is music without sound. Zhou Dunyi (a Northern Song Neo-Confucian) said: “The tones of music are plain and not excessive.” When music is plain, the desiring mind becomes calm; when it is harmonious, the restless mind dissolves. The centered and correct sound of Huangzhong is the root for determining pitches, so one need not deliberately distinguish gong and shang; the pitches naturally become established.

I once greatly admired the story of Wan Baochang (a Sui dynasty music theorist): when eating with others, he struck miscellaneous vessels and earthen pots with chopsticks, and they naturally formed pitches; he could even distinguish high and low and evaluate rhythm. Unfortunately, there was no one at the time who understood music. Suzi (a Song dynasty literatus) said: “If there were no Nanguo Ziqi (a figure in Zhuangzi’s ‘Discussion on Making All Things Equal’) in the world, then the pipes of earth (the sound of wind through myriad openings) could not be heard—how much less the pipes of heaven (the natural sounds of the world)?” Ouyang Xiu said: “Musical instruments will decay, and sound is difficult to convey in words. Alas, is there truly no way for sound to be handed down?”

Between heaven and earth, where is there no pitch or music? It operates together with sun and moon, cold and heat, darkness and light, wind and rain between heaven and earth. From antiquity to the present, from dawn to dusk, birds and beasts cry out, apertures and openings respond—all are natural sounds. High mountains and flowing water, yellow pipes and earthen drums—none are not the music of heaven and earth. Why must one wait for metal, stone, silk, and bamboo to be played before sound can be considered transmitted?

It is also said: when the yang pitch-standards respond to the yin pitch-standards, sound is thereby born. Sound belongs to the yang pitch-standards, and the yang pitch-standards belong to yang. The pitch-standards have opening and closing; with one opening and one closing, myriad sounds arise. Ten sounds are paired with ten pitch-standards; among the ten heavenly stems, five belong to yang, and the five sounds are the combined number of the ten stems. In trigrams, this number corresponds to Qian, Dui, Li, and Zhen; in time, to yuan, hui, yun, and shi (cosmic chronological units established by Shao Yong of the Northern Song); in pitch, to the sounds of sun, moon, stars, and constellations. Using sound to lead tones, using yang pitches to lead yin pitches, within this are further distinguished levels such as greater yang, lesser yang, greater firmness, and lesser firmness. Sound is born from the sun and paired with the ten heavenly stems from jia to gui; downward it initiates twelve tones on earth. There are about one hundred and sixty sounds, of which one hundred and twelve are actually used.

The yin pitch-standards respond to the yang pitch-standards, and tones are thereby born.

Tone is lü, and lü belongs to Yin. Among the Yin lü there is leading and responding; one leads and one responds, and from this arise countless sounds. The twelve tones are paired with the twelve lü, and among them the six Yin lü—Dalü, Jiazhong, Zhonglü, Linzhong, Nanlü, and Yingzhong—correspond to the double-hours represented by the twelve Earthly Branches. Thus, in terms of trigrams, they correspond to the four trigrams Kun, Gen, Kan, and Xun; in terms of time, to years, months, days, and double-hours; and in terms of pitch and sound, to the tones of water, fire, earth, and stone.

Tones are used to respond to the pitch standards, and lü to respond to the pitch pipes; their numbers are divided into different levels such as Greater Softness (Tairou), Lesser Softness (Shaorou), Greater Yin (Taiyin), and Lesser Yin (Shaoyin). Tones are born at the position of chen; matched in order from yin to chou, they respond above to the ten Heavenly Stems. There are approximately 192 tones, of which 152 are actually used.

The study of pitch standards and lü expounded by Shao Yong (a Northern Song Yijing scholar, style name Kangjie) reveals secrets of the Prior Heaven (xiantian) learning that were never transmitted, and it is not the same as the systems of Yang Xiong’s Taixuan or the Taichu Calendar.

The Xuan (referring to Yang Xiong’s Taixuan) takes the heavenly number three (an odd number) as the basis for counting. Three times three makes nine; this is the root number of the Three Unities of Heaven, Earth, and Humanity, and it accords with the normative numbers that likewise begin from the Huangzhong pitch (the first of the ancient twelve pitches and the standard for the lengths of pitch pipes). Master Shao (Shao Yong, the Northern Song Neo-Confucian philosopher), in his Jingshi lülü, instead takes the earthly number four (an even number) as the basis. Four times four makes sixteen, which derives from “the Two Modes give rise to the Four Images” (the Two Modes are Yin and Yang; the Four Images are Greater Yang, Lesser Yang, Lesser Yin, and Greater Yin); this is the numerical principle in the Changes.

Yin and Yang are further divided into old and young, and these are used to distinguish sound and tone from the pitches. Four is substance; five and six are function: five is sound and tone, six is the pitches. If within substance one further divides substance and function, then sound is substance and tone is function; if within function one further divides substance and function, then the pitches are substance and sound and tone are function. The Taixuan and Taichu take zi through si exclusively as yang pitches and wu through hai as yin pitches, so that sound and tone are thereby united as one body. Master Shao’s pre-heaven numbers, by contrast, take the ten Heavenly Stems exclusively as yang pitches and the twelve Earthly Branches (the twelve double-hours) as yin pitches.

To match sound and tone with the pitches, one must understand the calculations of three times three and four times four; only then can the study of the pitches be explained. Most people, ancient and modern, who discuss sound and tone conflate them; only with Master Shao’s doctrine does it become precise and thorough.

Those who are proficient in bell pitches can discern tones and sounds, and thereby know whether the world is ordered or chaotic.

Shao Kangjie (that is, Shao Yong, posthumously titled “Kangjie”) was traveling on Longmen Mountain and rested in a stone forest. Suddenly a withered branch fell nearby. He said to Lord Fu and Lord Han, who were with him: “This tree will soon be cut down.” On the return journey, he looked around and saw that the area was indeed completely bare. It turned out that the auxiliary capital was then under construction, and the trees in this area had all been cut down. Only then were his words fulfilled. Other cases, such as the flourishing and decline of peonies, the calls of cuckoos, and the order and chaos of the world, all follow the same principle. I excerpt one or two examples below.

In the Han dynasty, Cai Yong (courtesy name Bojie) passed by Gaoqian Pavilion in Kuaiji and saw bamboo in the rafters of the pavilion. Among them, the sixteenth joint on the east side could be made into a flute. Later, the flute made from it indeed had a remarkable sound, and people called it the “Ke Pavilion flute.” This was inferring its sound from the shape of the bamboo. He also took scorched paulownia wood from a guest house and made the “Scorched-Tail Zither”; this was inferring its sound from the wood having been subjected to vibration.

Once a neighbor was playing the qin. Cai Yong saw a praying mantis about to catch a cicada, and when he heard the qin sound, he knew that there was a killing aura in it. This was inferring the human heart from sound.

In the Sui dynasty, Wan Baochang was thoroughly versed in music and pitch standards. He told Emperor Wen of Sui: “The music established by Zheng Yi is the sound of a doomed state; Your Majesty should not listen to it.” He also once heard the Court of Imperial Sacrifices, the office in charge of rites and music, perform, and after hearing it he wept without stopping. When someone asked him why, he said: “The music is decadent and vehement, and it mourns for the realm; the world will soon be locked in mutual slaughter.” At that time the realm was at the height of its prosperity, and all who heard these words thought he was mistaken. Only by the late Daye era of Emperor Yang of Sui (605–618) were his words fulfilled.

There was also a Wang Lingyan, who heard his son playing the pipa outside the door. The tune was “An Gongzi.” He asked in great alarm: “When did this tune arise?” His son replied: “It has only recently appeared.” Lingyan wept and said to his son: “You must by no means follow the emperor to Jiangdu (present-day Yangzhou, where Emperor Yang made his southern tour); once the emperor leaves on this journey, he will never return. This tune belongs to the Gong tone and has the image of departing and not returning; that is how I know.” Later it was indeed as he had said.

In the Tang dynasty, when Li Sizhen listened to music, he said: “When the Gong tone cannot command the Shang tone, it is a loss of harmony between ruler and minister; when the Jue tone and the Zhi tone are mutually discordant, it is suspicion between father and son.” The ancients analogized the five tones (gong, shang, jue, zhi, yu) to human relations: Gong is ruler, Shang is minister, Jue is the people, Zhi is affairs, and Yu is things. Thus, upon hearing the tones fall out of order, one can infer changes in human affairs and in the relations between ruler and minister, father and son.

According to records, someone heard the wailing for the dead, profuse and sorrowful, and declared: “If the state is free of trouble, the crown prince will instead bear the blame.” Before long the crown prince was indeed deposed. Another person calculated his own date of death, prepared a coffin and burial garments in advance, and died on that day.

During the first month of the first year of the Shenlong era, when the Tang music official Pei Zhigu was performing music at the ancestral temple, he said to Yuan Xingchong, “The sound of metal and stone is harmonious and melodious; I fear that the descendants of the Tang royal house will have a great celebration.” That month, Zhongzong (Tang Zhongzong Li Xian) was indeed restored to the throne. Another man, while riding, heard a horse neigh mournfully and said, “The master will fall from the horse and die.” Seeing the ornaments on a newlywed making a sound, he said, “In the end the bell sounds will scatter.” When later checked, all matched what had been said. Likewise, what Zheng Xiangru told Zheng Qian could also infer honor and disgrace, success and failure, and life and death. In the Song dynasty, Shaochangbo Dou Yan (Dòu Yǎn; the title Shaochangbo refers to Vice Minister of Rites) used counting rods to deduce that a chair would break, and asserted that the brothers’ lifespans and emoluments would be without error. Dou Wan was proficient in musical pitch and skilled at distinguishing sounds, and so could calculate such things.

From this it may be inferred that in the numerological arts of foreknowing victory and defeat, fortune and misfortune, there were many skilled practitioners from the Qin and Han onward, but only the Northern Song Yijing scholar Shao Kangjie (Shao Yong) grasped their subtle essence.

Shao Yong held that human nature is quiescent; when quiescence reaches its extreme, it turns to movement. This movement belongs to Yang and is not emotional desire; it is merely the first stirring at the beginning of heaven and earth, that initial movement which “sees the mind of heaven and earth.” A person in the mother’s womb is likewise an “opening,” likewise initial Yang; at the moment of birth, it is “opening things and completing affairs” (opening the ten thousand things and bringing affairs to completion). Only then does emotional movement arise, and only then can movement be observed.

In calculations based on sound, the Former Heaven numbers have 256 positions, and one begins calculating only from sheng. Shao Kangjie used 264 characters as “character mothers” (mu, i.e., mother), comprehensively encompassing the lülü (ancient pitch standards, here standing by extension for the numbers of sound); of these, 112 characters were actually used to encompass sheng, and another 152 to encompass yin. Sheng and yin are mutually combined through fanqie (the ancient method of joining two characters to indicate pronunciation), each yielding 17,024 sounds. Sheng corresponds to rhyme; yin corresponds to the character mothers. Sheng is divided into the four tones—level, rising, departing, and entering; yin is divided into the five articulations—labial, lingual, velar, dental, and guttural. Sheng is further divided into inner and outer; the sounds of the eight turns distinguish opening, issuing, gathering, and closing; then they are further divided into pi, qing, xi, and zhuo. Finally, the sheng hexagrams are placed on the left and the yin hexagrams on the right.

This passage uses Yin-Yang, the Five Phases (Wood, Fire, Earth, Metal, Water), the five notes, and the pitch pipes (lülü) to explain how Heaven, Earth, and humanity are mutually connected.

First, the hexagram lines. The outer three lines of a hexagram are called “hui,” and the inner three lines are called “zhen.” Looking horizontally at each group of three lines to see which trigram it forms, these two trigrams together are named Jiji, an image hexagram. From this one observes the hexagram image to judge good and bad fortune; the crucial point is calculated entirely from sound, and listening and discrimination must be carefully scrutinized, without the slightest error.

Then it cites the words of the Venerable Yichuan (a former worthy quoted here): with one opening and one closing, the four tones—level (ping), rising (shang), departing (qu), and entering (ru)—are complete; with one leading and one responding, the four methods of vocal production—opening, issuing, gathering, and closing—are complete. When the four tones are complete, the ten thousand sounds arise from them; when the methods of vocal production are complete, the various rhymes and tones are formed from them. The yang pitch pipes change with Heaven, the yin pitch pipes transform with Earth; opening follows Yang and emerges, closing follows Yin and enters; leading follows the hard and rises, responding follows the soft and descends. In this way, the pitch pipes and sounds are matched, and the principles of gong, zhi, yu, and jue each attain their proper correctness.

Yang corresponds to the sun and to fire; Yin corresponds to the moon and to water. The hard corresponds to the stars and to metal; the soft corresponds to the lunar mansions (chen) and to earth. When the sun, moon, stars, and lunar mansions accord with metal, wood, water, fire, and earth, Heaven and Earth are rectified. The sun corresponds to the eyes and the color of fire; the moon to the ears and the sound of water; the stars to the nose and the Qi (vital energy) of metal; chen to the mouth and the taste of earth. When the colors, sounds, Qi, and tastes of the eyes, ears, mouth, and nose are rectified, the human Dao is rectified.

Therefore, one who understands the way of the pitch pipes and sound can use it to handle affairs among Heaven, Earth, and humanity. The pitch pipes resonate with one another; sound gives rise to the dispositions of Heaven, Earth, and the myriad things; their principles are all embodied here.

This passage is not the main text of a scripture but a collation note, that is, the editor’s record of textual variants. It lists the character and word differences between the original block-printed edition of Tianyuan Fawei—written by Bao Yunlong in the Yuan dynasty and chiefly concerned with Yijing principles, celestial phenomena, and calendrical calculations—and the Siku Quanshu edition, and explains which character form has been adopted.

It can be broadly divided into three types. The first consists of characters corrected according to the Siku Quanshu edition: in the original text, “qi” was changed to “xun,” “jing” to “ji,” “Qin” to “Tai,” “yi” to “yi,” “jia” to “shen,” “Zhu” to “Song,” “wei” to “shui,” “yi” to “san,” “ji” to “xu,” “shui” to “bing,” “yin” to “yang,” and “xian” to “hong.” These are mostly errors involving graphically similar forms.

The second type merely notes that the Siku Quanshu edition has a certain character, without explaining what the original text was: for example, “ba” is given as “bo,” “Yidi” as “Qin Sui,” and “ya” as “ou.”

The third type consists of entries whose character forms are difficult to distinguish and are suspected of being misprints or transcription errors: for example, in the “Mouwu” entry the Siku Quanshu edition reads “Anmu yi,” which is unintelligible on its face and should be checked against the original book or other editions.

In addition, several items appear repeatedly in the content (such as items 8 and 9, and near the “Mouwu” and “hong” entries); this is a problem of transcription or typesetting and does not affect the above collation conclusions.

This passage consists of the collation notes to Tianyuan Fawei (by Bao Yunlong), recording textual differences between the base edition and the Siku Quanshu edition. It is not the main scriptural text, so there is no cultivation or ritual content requiring interpretation. According to the entry notes, the situation is roughly as follows. For entries 23 and 24, the base edition omits the characters er (“two”) and shi (“beginning”), which are supplied according to the Siku edition. For 25, “ice” originally appeared as “water” in the base edition and was changed according to the Siku edition. For 26, “crow” differs in character form between the two editions, a matter of variant characters. For 27, “Yang” originally appeared as “Yin” in the base edition and was changed according to the Siku edition. For 28, “fierce” originally appeared as “you” in the base edition and was changed according to the Siku edition. For 29, “thing” originally appeared as “color” in the base edition and was changed according to the Siku edition. For 30, “chen zai” originally appeared as “zai chen” in the base edition; the word order was changed according to the Siku edition. For 31, “after” originally appeared as “thick” in the base edition and was changed according to the Siku edition. For 32, “ben” appears as “genben” in the Siku edition. For 33, “degree” originally appeared as “add” in the base edition and was changed according to the Siku edition. For 34 and 35, “tai” originally appeared in both places as “da” in the base edition and was changed according to the Siku edition. For 36, “bianzheng” originally appeared as “huanbian” in the base edition and was changed according to the Siku edition. For 37, “jiang zhang xi” appears as “jiang gong shi” in the Siku edition. For 38, “south wind” originally appeared as “north wind” in the base edition and was changed according to the Siku edition. For 39, “therefore” originally appeared as “time” in the base edition and was changed according to the Siku edition. For 40, “tai” originally appeared as “da” in the base edition and was changed according to the Siku edition. For 41, “beside” appears as “front” in the Siku edition.

Among these, changes to wording related to “celestial phenomena,” the “Five Phases,” and similar matters affect the understanding of the original meaning. For example, the differences between “south wind” and “north wind,” and between “Yang” and “Yin,” must be based on the emended text.

Collation Notes

This passage is a record of textual comparison between the base text and the Siku Quanshu edition. In a few places the base text has omitted characters or variant readings, which the editor has corrected or noted according to the Siku Quanshu edition. Entry 42: the base text omits the two characters zhi and nai; they have been supplied according to the Siku Quanshu edition. Entry 43: the base text omits the two-character phrase zhiluan, "order and disorder"; it has been supplied according to the Siku Quanshu edition. Entry 44: for the character bao, the Siku Quanshu edition has qian. When the same entry appears again, it has tai instead; the two records are inconsistent. Entries 45 and 46: for the character mu meaning "nurse/governess," the Siku Quanshu edition uniformly has mu meaning "mother." Entry 47: for the character yi, "one," the Siku Quanshu edition has er, "two." Entry 48: the Siku Quanshu edition has an additional character wei after ming.

Title and Author

Tianyuan Fawei, juan 11, was compiled by Bao Yunlong (courtesy name Jingxiang, a Yuan dynasty scholar) and collated by Fang Hui (sobriquet Xugu, a Yuan dynasty scholar) and Wan Li.

Guaqi (Hexagram Qi)

Gua qi is an important theory in Han dynasty Yijing studies. It assigns the sixty-four hexagrams to the solar terms of the year, explains changes in heavenly timing through the waxing and waning of Yin-Yang, and from this deduces the auspicious and inauspicious in human affairs and politics. This juan takes this as its title and presumably discusses this system.

The theory of hexagram qi began with the Zhongfu hexagram. Jing Fang of the Western Han transmitted it to Jiao Gan, who had obtained it from a recluse. He assigned the four cardinal hexagrams Kan, Li, Zhen, and Dui to govern the four directions respectively, like local officials such as regional lords and inspecting officials. The use of Kan, Li, Zhen, and Dui corresponds to the four solar terms of winter solstice, summer solstice, spring equinox, and autumn equinox. Each of the four seasons is dominated by one kind of qi: spring belongs to Wood, summer to Fire, autumn to Metal, and winter to Water. Each hexagram governs a period of time, and on this basis one prognosticates the auspicious or inauspicious, good or evil character of each day.

The lines of the remaining sixty-four hexagrams each govern one day, amounting to about 360 days, with five and a quarter days left over. Each day is divided into eighty fen, counted from midnight; five days make four hundred fen, and a quarter day is twenty fen. The sixty-two hexagrams within the sixty hexagrams—that is, the sixty hexagrams each receive six days and seven fen—each receive seven fen.

The Bo hexagram represents the exhaustion of yang qi at the end of the ninth month; in the tenth month the purely yin Kun hexagram is in charge. The Kun hexagram occupies six days and seven fen; after Kun comes to an end, the Fu hexagram marks the first birth of one yang—this is the process from the full exhaustion of Bo to the rebirth of yang qi. In between there is one Kun hexagram, totaling six days and seven fen; taking the round number, one says seven days. The author Bao Yunlong holds that, reckoned by the month hexagrams, between Bo and Fu there lies one Kun hexagram; reckoned by the period hexagrams, each month has five hexagrams. The above is found in the Yiwei tu.

Jing Fang took the xiaoxi (waxing-and-waning) hexagrams as primary: the xi hexagrams (those in which yang qi gradually grows) he called Taiyin (Greater Yin); the xiao hexagrams (those in which yang qi gradually wanes) he called Taiyang (Greater Yang); the remaining hexagrams he called Shaoyin (Lesser Yin) and Shaoyang (Lesser Yang).

Mr. Cai of Xishan (Cai Shen) said: Shao Kangjie (Shao Yong) also adopted the formulation of six days and seven fen, while Yang Ziyun (Yang Xiong) used it as the basis for composing the Taixuan.

The Taixuan (Yang Xiong’s imitation of the Zhouyi) and the Jingshi (Shao Yong’s Huangji Jingshi shu) both set aside the four cardinal hexagrams Kan, Li, Zhen, and Dui, and instead use “six days and seven fen” (a Han-dynasty Yijing method for reckoning time, according to which each hexagram corresponds to roughly six and one-seventh days) to coordinate the sixty hexagrams with timekeeping.

Zixia (a disciple of Confucius, traditionally regarded as one of the authors of the Yizhuan) said: when the lines of the sixty-four hexagrams complete one cycle, from Kun back to Fu, seven line-positions are traversed in all, and so it is called “seven days.” Hu Yuan (courtesy name Anding, a Northern Song educator) explained further: each line passed through counts as one day, and the sixty hexagrams together have 360 lines, exactly corresponding to the 360 days of a year. Between each pair of adjacent hexagrams there is a space of seven days. In addition, hexagrams have different usages in which a line represents a year, a month, or a day; the statement “seven days” is meant to explain changes in gua qi (the ancient doctrine that hexagram images correspond to solar terms and the movement of Yin-Yang).

Viewed from the process of xiaoxi (the growth and decline of Yin and Yang), from the Beginning of Winter, the solar term of the tenth month, to Major Snow, the solar term of the eleventh month, from Kun, the hexagram of pure Yin, to Fu, in which a single Yang is first born, is approximately seven days. Most explanations by the various schools derive from Zixia. Scholars of the Western and Eastern Han, in transmitting classical learning, all adopted the doctrine of “six days and seven fen.”

In the Song dynasty, Wang Zhaosu, Wang Mei, and Song Xian began to write essays in refutation. Wang Zhaosu held that the old commentaries and subcommentaries all violated Confucius’s original intent: the tenth month is purely the Kun hexagram, yet Yang qi still remains within, which is why the top six line of Kun in the Yi has the line statement “dragons battle in the wild.” If one reckons by six days and seven fen and treats Kun as the end point of the tenth-month solar term, then the time when the single Yang returns would be fifteen days earlier than the winter solstice; it is thus clear that the “seven days” doctrine can hardly be applied to the numbers in the Yiwei (the Han-dynasty apocryphal and prognostication learning attached to the classics).

Hu Dan refuted this, saying: in the Western Han, Jing Fang used gua qi to infer good and bad fortune, and his predictions mostly came true; in the Eastern Han, Lang Yi’s learning of six days and seven fen was the most refined. Six days and seven fen are the real numbers of the hexagram lines, whereas the days of a year are a nominal number; the days lacking in each month must be supplied by intercalation. Wang Zhaosu did not understand the mystery of intercalary numbers, which is why he raised doubts about “fifteen days before the winter solstice.” Unfortunately, the texts of the wei books have been scattered and lost, and Jing Fang and Lang Yi long ago passed away.

Zhu Zhen (courtesy name Zifa, a Southern Song Yijing scholar) commented: Wang Zhaosu knew only the general outline and did not understand the principle that the four cardinal hexagrams govern the four directions and the sixty hexagrams are distributed in sequence.

Zhaosu understood only the general outline of the intercalary numbers and had not grasped their subtleties; that is why he doubted the saying that “the winter solstice should fall around the fifteenth day.” Unfortunately, most of the weft texts attached to the classics have been lost, and Jing Fang, the Western Han Yijing scholar, had long since died. Zhu Zhen (courtesy name Zifa, a Song scholar) said: Zhaosu knew only the outline but did not understand the principle that the four cardinal trigrams (Kan, Li, Zhen, and Dui, each governing one of the four directions) govern the sixty hexagrams, with each hexagram presiding over the days of one period. The twenty-four solar terms all fall under the governance of the four cardinal trigrams; the remaining five and one-quarter days accumulate year by year and become intercalation. Each hexagram governs six days and seven fen, and the advance and retreat of the solar terms are produced by just such shifting. For example, the Bo hexagram of the ninth month passes through about five hexagrams—Gen, Jiji, Shike, Daguo, and others—before changing into Kun; the tenth month is Kun, and after passing through about five hexagrams—Weiji, Jian, Yi, Zhongfu, and others—it changes into Fu. Bo and Fu are thirty days apart, and the Fu hexagram governs the winter solstice. The mid-qi of the winter solstice begins with Zhongfu; seven days after Zhongfu comes the Fu hexagram. Hence it is said, “After seven days comes the return”—this is the movement of the heavenly Dao.

Among Confucian scholars of successive ages, only Yang Xiong (Western Han scholar and author of the Taixuan) grasped its essential purport. The Taixuan arranges the nine numerical orders as Xuan 1, Zhong 2, Xian 3, Cong 4, Geng 5, Mou 6, Kuo 7, Han 8, and Chen 9, forming the “Zhong image.” At the winter solstice node in which Zhongfu lies, the sun begins at the first degree of the Niu lunar mansion, the handle of the Big Dipper points to the zi position, the pitch pipe corresponds to Huangzhong, and this is the eleventh month of the Xia calendar. When the sun moves to the fifth degree of Niu, one revolution is completed; the saying “the Zhou image returns at seven-five-one; after seven days comes the return” refers to this principle.

From Yang Xiong, Ma Rong, Zheng Xuan, Song Zhong, Yu Fan, Lu Ji, Fan Wang, and others, all transmitted this learning, yet Zhaosu criticized it—why? Wang Mei had already refuted Kong Yingda’s (a Tang classicist) criticism of Wang’s commentary. Song Xian further condemned the practice of Jing Fang, Guan Lang (a Northern Wei Yijing scholar), and others of using the Yi to promote the arts of Liuren, Dunjia, divination and invocation, and Yin-Yang numerical derivation, holding that therein was no intention of the sage. Why not take this hexagram as the month and this line as the day? Why do the solar terms not begin with another hexagram but precisely with Zhongfu? Zhu Zhen retorted: What Kong Yingda and Wang said about the Yi-weft Xiaoxi hexagrams cannot be criticized. The Liuren calculation of days and hours likewise comes precisely from the numbers of Kan and Li in the Yi.

Dunjia assigns the Nine Palaces to the positions of Heaven and Earth, and from this derives the principles of the Hetu (River Chart) within the Yi. This only grasps one aspect of the Yi and cannot exhaust it entirely. Others say that the scholars borrowed Rendun (the art of the Six Ren) to expound the Yi in order to win over the people of the world, not realizing that Rendun originally emerged from the Yi. If this is so, why should those who expound the Yi need to rely on Rendun?

The sage elaborated the patterns of the waxing and waning of Yin-Yang (xiaoxi) in order to reveal the signs of things’ gain and loss, survival and destruction. People today believe only the principle of hardness and softness, advance and retreat; they do not believe the doctrine of xiaoxi, nor do they believe the learning of the Yiwei (the Han-dynasty apocryphal texts that interpret the Yi). They also hold that Guaqi (the system correlating hexagrams with solar terms) does not begin with the Zhongfu hexagram. This is like counting all day long without knowing the positions of two and five—how could such a person be considered good at reading?

At the winter solstice of the yiwei year of the Yuanzhen era (1295), Mr. Fang Xugu (Fang Hui, whose sobriquet was Xugu) wrote to the author, saying: Zhu Xi held that the winter solstice should be reckoned from the first degree of the Ox mansion; this was the ancient method. In the jiazi year of the third year of Emperor Wen of Han, the winter solstice was at the twenty-second degree of the Ox mansion; by the jiazi year of the first year of Xingyuan of Tang (784), it was at the ninth degree of the Dipper mansion. A span of 961 years, a difference of twelve degrees. Now, on the seventh day of the eleventh month of the first year of Yuanzhen, the winter solstice is at the eighth degree of the Winnowing Basket mansion, having receded another twelve degrees; five days after the winter solstice, it is again at the third degree of the Dipper mansion. Why then still cling to the old theory and insist that the winter solstice must enter the Ox mansion in order to conform to ancient celestial phenomena?

The author replied: When one examines remote antiquity, it is difficult to make them entirely consistent. The calendar says that in the time of Yao the winter solstice was at the first degree of the Emptiness mansion, while He Chengtian says it was at the tenth degree of the Girl mansion; the Yuanjia Calendar of the Liu Song of the Southern Dynasties fixed the winter solstice at the seventeenth degree of the Dipper mansion, while the Yue Ling Yaoyi says it was at the fourteenth degree of the Dipper mansion.

The Dayan Calendar, compiled during the Kaiyuan era of the Tang, determined that at the winter solstice the sun stood at ten degrees in the Dou mansion (one of the Twenty-Eight Mansions); by the Song dynasty Tongyuan Calendar, the winter solstice had come to be at two degrees in Dou. Ancient calendars took the midpoint of zi (midnight) as the beginning of the day, whereas Li Chunfeng used the beginning of zi (11 p.m.) as the starting point; thus their calculations differed by two ke (one ke being about fifteen minutes). His contemporaries likewise admired his precision.

Broadly speaking, the two Qi of Yin-Yang are uneven; they push against and displace one another, waxing and waning, and only then do they form a year. Qi has fullness and contraction, advance and retreat; such is its nature, and it merely goes back and forth among the mansions Ji, Dou, Niu, and Nü. Yang Xiong’s Taixuan, in saying “it enters the Niu mansion and corresponds to the Fu hexagram,” likewise derives from the Taichu Calendar of the Western Han. All these relied on results already verified at the time and simply took their approximate values as standards. Later calendars, though differing in branches and details, share the same root and should not be lightly censured.

Zhu Xi said: those skilled in making calendars must establish a broad, large number to contain errors—this is very true. As for the doctrine of “six days and seven fen,” earlier scholars have analyzed it in great detail, so there is no need to say more here.

The Xiang Commentary on the Ge hexagram says: “Fire within the lake: this is Ge. The noble person therefore regulates the calendar and clearly determines the four seasons.” Water and fire overcoming one another symbolizes change; observing this hexagram image, the noble person revises the calendar so that the seasonal ordinances are clearly distinguished.

On the day of the winter solstice, the sun starts from one degree in the Qianniu star region and moves rightward (from west to east). Passing through the twelve stations and traversing the twenty-six degrees of the Dou mansion, it returns to its starting point in Qianniu, thus completing one cycle, and the calendar likewise changes by one round. Qianniu (one of the Twenty-Eight Mansions) belongs to the fire position, while Xingji (one of the twelve stations) belongs to the water position; the sun and moon meet here, like fire within water. This is the calendrical epoch of the Upper Primordial Taichu calendar, reckoned from the winter solstice, and in hexagram-qi (guaqi) theory it corresponds to the third month. The Taixuan (by Yang Xiong) calculates on this basis and uses it to replace the “day-change” (ri ge) doctrine recorded in historical texts.

The Zhongfu hexagram stands in the forty-ninth position in the Xugua (Ordering of the Hexagrams), exactly at the node of the Dayan number (the number used in divination); placed sixtieth, it corresponds to the degrees of the celestial circuit. The sixty hexagrams comprise three hundred sixty lines, each line governing one day. The Upper Classic begins with Qian at jiazi; passing through Tai at jiaxu and Shike at jiashen, it reaches Li, making thirty hexagrams and one hundred eighty days, exhausting three jiazi cycles. The Lower Classic begins with Xian at jiawu; passing through Sun at jiachen and Zhen at jiayin, it ends with Jie at guihai, likewise thirty hexagrams and one hundred eighty days, completing one annual circuit. From this, the reckoning of days takes the solar terms as its guiding framework, and the nodes of Heaven and Earth and the transformations of the four seasons are all determined thereby.

Next, the four hexagrams Zhongfu, Xiaoguo, Jiji, and Weiji are allocated to the four cardinal hexagrams Kan, Li, Zhen, and Dui, corresponding to zi, wu, mao, and you, and representing winter, summer, spring, and autumn respectively. The four seasons are paired two by two, forming the eight nodes: fen (the spring and autumn equinoxes), zhi (the winter and summer solstices), opening (the Beginning of Spring and Beginning of Summer), and closing (the Beginning of Autumn and Beginning of Winter). Each line is worth fifteen days and corresponds to the seventy-two seasonal periods (hou).

Earlier scholars said that hexagram-qi begins with Zhongfu; this is incorrect. Zhongfu merely starts its reckoning from jiazi. The Qian hexagram takes the eleventh month as its starting point; when yang qi reaches the si position, the solar terms come to an end. The hexagram of the tenth month receives guihai: yin qi arises from the wu position and ends at the hai position, and the year is then reckoned complete. The further statement that Zhongfu also belongs to the eleventh month, beginning at jiazi and ending with Weiji, is because hexagram-qi is always calculated from the medial qi of the preceding month. In the Taixuan, “Zhong” is matched with Zhongfu and with the initial six line of Kan and fixed as the eleventh month, when the medial qi first arises and corresponds to the Upper Primordial. The Taichu calendar takes the new-moon dawn winter solstice of the eleventh month as the epoch for beginning calculations; this is the first link in calendrical reckoning.

Zhongfu (Xun above, Dui below) and Xiaoguo (Zhen above, Gen below), together with Jiji and Weiji (based on the bodies of Kan and Li), are collectively called the “Six Children.” The qi of lesser yang and lesser yin is distributed through the four seasons, forming the seasonal periods of the year.

Shao Yong (style name Kangjie, commonly known as Shaozi) said: In the Western Han, Luoxia Hong changed the Zhuanxu Calendar (Zhuanxu li) into the Taichu Calendar (Taichu li), and Yang Xiong (courtesy name Ziyun), relying on the Taichu Calendar, composed the Taixuan (Great Mystery). The Taixuan takes “one separated by five hexagrams” as its grouping, and its qi rises from the center. Thus the first head, “Zhong” (Center), uses three to form a triad with Heaven and two to pair with Earth; the “leaning numbers” (yishu) it uses are not the proper numbers of Heaven and Earth but are established in imitation of them.

Kangjie also said: The Taixuan perhaps understands the heart of Heaven and Earth. The so-called “heart” refers to Kun reaching its extreme and generating Qian, beginning at the time of the winter solstice; this is the starting point of the pitch-calendar (the ancient system of pitch pipes and calendrical reckoning). It plumbs the profound and extends to the vast, and accords with divine principle to this degree. Therefore his poem says: “If there were no Master Yang’s learning of Heaven and Man, how could there be Zhuang Sheng’s inner and outer chapters?” When the first yang stirs and the myriad things have not yet grown, the sage thereby sees the heart of Heaven and Earth. The hexagram qi begins with Zhongfu and is verified after seven days. Because the Zhongfu hexagram is empty within and symbolizes the human heart, it corresponds to the Han Taichu Calendar. The Zhuanxu Calendar takes the tenth month as the beginning of the year, while the Lianshan takes the Gen hexagram as its first.

Ziyun took the eighty-one heads of the Taixuan, with nine zan in each head, for a total of 729 zan. A zan is a yao. Two zan correspond to one day; each zan corresponds to six shi (an ancient shi being about two hours); one shi yields six ce, and one zan yields thirty-six ce, matching the number of yao lines in the hexagram qi of the sixty hexagrams. Each hexagram is about six days and seven fen, while each Taixuan head is about four and a half days. When one head’s number is distributed over four days, a remainder remains; when two heads are combined to make nine days, it divides exactly. Yin heads take yin numbers as dominant, and yang heads take yang numbers as dominant. Five occupies the middle of two and four; five belongs to Earth and is located at the center. One, two, three, and four are the generative numbers and stand before five; six, seven, eight, and nine are the completed numbers and stand after five.

Master Zhu (Zhu Xi) said: The Taixuan is entirely a study of Jiao Yanshou’s method of calculating hexagram qi.

Jiao Yanshou and other schools differ in their accounts of the positions and correspondences of the hexagrams in the Yi. In the King Wen Bagua directions, Qian is in the northwest and Xun in the southeast; Kun is in the southwest and Zhen in the east—positions wholly different from those in other accounts. Another account takes Zhen as east, Dui as west, Li as south, and Kan as north to be the directions of the Yi hexagrams; still another holds that the twelve sovereign hexagrams (the twelve message hexagrams representing the twelve months) are assigned to the twelve chen (earthly branches).

It was only when Jiao Yanshou (a Western Han Yi scholar) established the method of gua-qi governing the days that these two accounts were combined into one: on the one hand, the four cardinal trigrams Kan, Li, Zhen, and Dui and their twenty-four lines were used to correspond to each day and each time; on the other hand, the twelve sovereign hexagrams were used to correspond to the twelve months. He further took the remaining forty-eight of the sixty-four hexagrams and assigned them respectively to the duke, marquis, minister, and grandee, and from this arose the doctrine of “six days and one-seventh” (each hexagram governs six days and one-seventh of a day, so as to match the number of days in a year).

Yang Xiong’s Taixuan modeled itself on gua-qi but changed the names: it took the “Zhong” hexagram as the beginning of the winter solstice and made it correspond to the initial period of the winter solstice; it took the position of the top nine line of the “Nourishment” hexagram to correspond to the end of Major Snow. The Taixuan holds that “Zhong” is the place where yang qi first begins to sprout, and therefore corresponds to the beginning of the winter solstice; the “Yang” and other encomia correspond to the end of Major Snow. This is based on the gua-qi order of the Yi, only with the names changed. Gua-qi uses Kan, Li, Zhen, and Dui to govern the twenty-four solar terms; the Taixuan, by contrast, starts from “Zhong” and advances by alternating four and six, using this to govern the twenty-four solar terms.

As for the numbers adopted by the Taixuan, they originate in the Hetu (River Chart). In the Hetu, one and six both belong to Water and form one lineage; two and seven both belong to Fire and form one companionship; three and eight both belong to Wood and form one friendship; four and nine both belong to Metal and return together to one Dao; five and ten both belong to Earth and mutually guard and uphold one another. This exactly accords with the numbers by which Heaven and Earth generate and complete things. By this one draws analogies to human affairs: the dignity of robes and garments is taken from three and eight; the awe of armor, helmets, and halberds is taken from four and nine; the order of ruler and minister is taken from two and seven; the sacrifices to ghosts and spirits are taken from one and six; the offerings of wine and food are taken from five and five. The reason it does not mention “five” by itself is that five plus five makes ten, which is already contained therein.

Yang Xiong's Taixuan completely imitates the Yijing. The Taixuan is constructed entirely from multiples of three, while the Yijing uses multiples of four. Since it was originally composed in imitation of the Yi, by reading the Yi alongside the passages it imitates one can gain a rough understanding of what it means.

The section titles of the Taixuan are mostly taken from the names of Yijing hexagrams: for example, "Zhou" corresponds to Fu (Return), "Tong" to Meng (Youthful Ignorance), "Zeng" to Yi (Increase), "Jiao" to Tai (Peace), and "Yi" to Yang (Nourishment). Sometimes one shou corresponds to one hexagram; sometimes two or three shou correspond to one hexagram, and these are used to explain calculation methods involving units such as fen and miao. Among them, "Xuanchong" is equivalent to the Xugua of the Yizhuan, "Xuancuo" to the Zagua, "Xuanshu" to the Shuogua, and "Xuanwen" to the Wenyan. All of these are modeled on the Yi.

The generative sequence of the Yi is: one generates two, two generates four, four produces eight, and eight times eight gives sixty-four hexagrams, where it stops. The Taixuan, by contrast, is: one generates three, three generates nine, nine multiplies into nine, and nine times nine gives eighty-one, where it stops. Each Yi hexagram has six yao; six times six yields 384 yao. The Taixuan has nine "zan"; it separates out the generation of metal, wood, water, and fire, which combine into eight, and then adds earth, which occupies the center and holds fast to the one, to make nine. Nine times nine multiplies until 729 zan are complete. Both contain the principle of the Five Phases.

In the Yi, two multiplies four, four multiplies eight, eight multiplies sixty-four, and sixty-four multiplies 384; this is broadly based on the idea in the Hetu of "Heaven three, Earth four"—that is, taking four as the original number of Earth while using three as the number of Heaven. For this reason Fuxi stacked three yao into six yao to form a hexagram. The numbers of the Taixuan, by contrast, originate in the Huangzhong pitch (the standard pitch of ancient music).

Taking nine cun as the hollow circumference and dividing each cun into nine fen: taking one third of it yields “three,” corresponding to Heaven, Earth, and Humanity, the “Three Powers.” Three times three is nine, which is what the Hong Fan calls the “Nine Categories.” The Earth number four tripled is twelve, corresponding to the “Twelve Sovereign Hexagrams” of the twelve months of the year (the twelve hexagrams that use hexagram images to represent the months). The Heaven number five tripled is fifteen, corresponding to the fifteen days in one solar term. The Earth number six tripled is eighteen, that is, the hexagram image is formed after eighteen transformations.

Huangzhong (the standard pitch of ancient music theory, first of the twelve pitches) begins at the zi position, and its number is “the one of Heaven.” Proceeding by tripling in order: one at zi, three at chou, nine at yin, twenty-seven at mao, eighty-one at chen, two hundred forty-three at si, and seven hundred twenty-nine at wu. Then from wu through the five earthly branches wei, shen, you, xu, and hai, one obtains 177,147. This is the number for the mutual generation of Jing Fang’s sixty pitches, and it is recorded in the commentary to the “Treatise on Pitch and Calendar” in the Book of Han.

Taking the 365 days of the Taixuan as the base, multiplying each day by eighty-one yields 29,565 fen; adding the remainder of a quarter day (about twenty fen), the total is about 29,585 fen. Using this method to calculate each zan and each solar term, all can be made to correspond. Therefore it says, “Drinking below, drinking above, emerging from and entering the nine voids.” “Xuan” is the head of the myriad spirits.

Yang Ziyun (Yang Xiong) was deep in thought and skilled at exploration. His probing of the wonders of the increase and decrease of Yin-Yang may be said to have applied the mind extremely deeply. Zhang Pingzi (Zhang Heng) praised his mystery as having reached the utmost of the Dao. He once had others debate Yin-Yang matters with him, and compared the works of the two hundred years since the founding of the Han dynasty to the “Five Classics.”

The statement “Heaven and the sun move in crossing courses, Yin-Yang alternate, death and life intertwine, and the myriad things thereby become entangled” means that the sun and moon move in alternating courses, Yin-Yang change in turn, life and death intertwine, and the myriad things are thereby bound up and cannot be untangled. This passage also emphasizes the keenness of his inquiry.

The movements of celestial phenomena become disordered; Yin-Yang alternates and changes; life and death intertwine. The myriad things grow and reach completion within this entanglement. This means: when the po (the yin spirit-soul in the human body) is born, it manifests the death of the po; when the po dies, it manifests the beginning of life. Life and death succeed one another, and thus the myriad things complete themselves in endless cycles.

It further says: by observing the patterns of the dragon and tiger (manifestations of the two qi of Yin-Yang) and comprehending the principle of the tortoise (the ancients divined with tortoise shells and used tortoise imagery to investigate the principles of heaven and earth), one can establish heaven’s warp, earth’s weft, and human conduct. Heaven divides into yin and yang—this is heaven’s warp; earth divides into vertical and horizontal—this is earth’s weft; humans divide into obscurity and clarity—this is human conduct. This means heaven is the warp and earth the weft; north-south is the warp and east-west the weft. The distinctions between day and night, brightness and darkness, and the worthy and the foolish are all contained therein.

The sun rises and sets; one day and one night make a day. Yin-Yang goes once and comes once, and from this the myriad things are born. This means: in summer the daylight lasts as long as sixty ke (an ancient unit of time; a day and night were divided into one hundred ke), and in winter the night is also sixty ke long. The longest night does not exceed the winter solstice, and the longest day does not exceed the summer solstice. The night of the winter solstice is not as long as the day of the summer solstice; therefore the number of daylight ke is greater.

It further says: Yang qi is born at zi (due north), and Yin qi is born at wu (due south). The northwest is the zi position, where Yang qi comes to an end; the southeast is the wu position, where Yin qi comes to an end. This means Yang qi starts from zi and ends at wu; Yin qi starts from wu and ends at zi. In the southwest there is still a faint Yang, so only when it reaches the northwest does Yang qi exhaust itself; in the northeast there is still a faint Yin, so only when it reaches the southeast does Yin qi reach its extreme. The way of Yang is always abundant, while the way of Yin is always deficient—that is, Yang qi is fully deployed, while Yin qi uses only half.

North and south determine position, and east and west connect the qi mechanism. The fixing of position by zi and wu is the root of Yin-Yang; when the Wood qi of the east is vigorous, the Metal qi of the west declines and dies, and the two qi correspond and communicate.

When it comes to the sun and moon, it says: the sun has south and north; if it did not reach the extreme points of south and north, there would be no distinction between winter and summer. The moon has going and coming; if it did not go and come, the new moon and dark moon could not be formed. The sage observes the subtle, hard-to-see changes in the movement of Yin-Yang and follows the order of the sun, moon, and Yin-Yang to calibrate the calendar. Broadly speaking, the sun travels south to the Jianniu lunar mansion (the position of the winter solstice) and north to the Dongjing lunar mansion (the position of the summer solstice).

The ancients regarded the south as the place where yang Qi is most abundant (Taiyang, the Great Yang), and the north as the place where yin Qi is most abundant (Taiyin, the Great Yin). When the essence of yang Qi reaches the south, it is summer; when the essence of yin Qi reaches the north, it is winter. At the end of the month (hui), the moon appears in the west, and the sun seems to leap out from the west; on the first day (shuo), the moon appears in the east, while the sun hides to the side. These phenomena are explained separately in the “Taiyang Chapter.”

The following explains the method of calculating pitches by numbers. The Earthly Branches correspond in order to numbers: zi and wu are nine, chou and wei are eight, yin and shen are seven, mao and you are six, chen and xu are five, and si and hai are four. From this one derives that the total of the yang pitches (the six yang pitches among the twelve, called lü) is forty-two, and the total of the yin pitches (the other six yin pitches, called lǚ) is thirty-six; together they make seventy-eight. In cases where the number is eight, the two branches chou and wei revolve cyclically, and only the yin pitch can be obtained, not the yang pitch.

The Heavenly Stems are also assigned numbers by the same method: jia and ji are nine, yi and geng are eight, bing and xin are seven, ding and ren are six, and wu and gui are five. The five tones (gong, shang, jue, zhi, and yu) come from the Heavenly Stems: jia and yi belong to jue, bing and ding to zhi, geng and xin to shang, and ren and gui to yu. The twelve pitches, in turn, come from the twelve double-hours (that is, the Earthly Branches), and they are the root of the pitch system. Sound has emotion as its essence, and pitch standards are used to harmonize sound; when the two are in harmony, the eight sounds—the eight categories of instruments made of metal, stone, silk, bamboo, gourd, earth, leather, and wood—arise from this.

On the whole, this is an expression of the Five Phases and numerical principles. Later generations used this to discuss the numerology of Shao Kangjie (Shao Yong of the Northern Song, who was skilled in image-number studies), yet they did not realize that its roots lie precisely here.

The Taixuan takes “three” as its starting number. “Taixuan” is “Taiji” (the Supreme Ultimate), used to symbolize the ruler’s position. The three domains refer to Heaven, Earth, and Man, corresponding to the “Three Powers”—Heavenly Mystery, Earthly Mystery, and Human Mystery. The three domains also symbolize the Three Dukes; each domain contains three provinces, making nine provinces in all, which symbolize the Nine Ministers; each province contains three divisions, making seventy-two divisions in all, which symbolize the grand officers.

On the Dao of Heaven it establishes “beginning, middle, end”; on the Dao of Earth, “above, middle, below”; on the Dao of Man, “thought, misfortune, blessing.” The Yi divines good and bad fortune through the changes of hexagrams and lines, while the Xuan divines by penetrating the principles of affairs. The Taixuan uses the shou (head) as its unit, and each shou contains nine zan (appraisals), just as one hexagram in the Yi contains six lines. The zan of each shou are all rooted in the Five Phases (Wood, Fire, Earth, Metal, Water), in order: Zhong corresponds to one, Water; Zhou to two, Fire; Zan to three, Wood; Xian to four, Metal; Shao to five, Earth; Li to six, Water; Shang to seven, Fire; Gan to eight, Wood; Ni to nine, Metal; the numbers stop at nine. Among the nine zan of each shou, the first and sixth belong to Water, the second and seventh to Fire, the third and eighth to Wood, the fourth and ninth to Metal, and the fifth to Earth. The fifth zan is the ruler of the whole shou, just as the fifth line is the master of a hexagram in the Yi.

The Taixuan consists of eighty-one shou, paired two by two. The first shou is the beginning of Yang, the second the beginning of Yin. Odd-numbered shou belong to Yang, even-numbered shou to Yin; odd is paired with odd, even with even, and although the meanings they govern are different, they are mutually opposed.

The Preface to the Taixuan says, “It patrols riding the six jia, and meets with the Dipper.” This means that the calculations of the Taixuan run cyclically according to the six jia (the six groups of jiazi used in stem-and-branch time reckoning) and coincide with the movement of the Northern Dipper; this is the main purport of its calendrical reckoning. The cycle of the Taixuan is like the Northern Dipper having a Dipper head; both come into being through mutual opposition.

The preface to the Taixuan (Supreme Mystery) says: It traverses and governs the Liujia (the cycle of days reckoned by the heavenly stems and earthly branches) and conjoins with the Northern Dipper (Beidou). This is the general purport of the Taixuan’s calendrical reckoning. The Taixuan has qiman (surplus and fractional remainders in the calendar), comparable to the Northern Dipper having an intercalary month. The eighty-one heads begin from the middle; each head marks the degree at sunset on the first day of each month, taking the Northern Dipper as its basis. The seasons are easy to rectify and are visible, whereas calendrical reckoning by the Northern Dipper is difficult to discern clearly and easily goes awry. If the intercalary qi accords with the Northern Dipper without error, then both intercalation and the calendar are accurate.

It further says: The Taixuan measures the sun by day and the Dipper by night; it does not involve the moon. This is because the sun and the Dipper are ever full and ever pointing, and can serve as standards; whereas the moon waxes and wanes, is large and small, and moves fast or slow without constancy, so it is not recorded.

The degrees of the twenty-eight lunar mansions (xiu) in the diagram are not the actual twenty-eight lunar mansions in the sky, but refer to the positions reached by the solar terms and seasonal phenomena. The degrees at sunset on the first day of each month are roughly close to those recorded in the “Yueling” chapter of the Liji (Book of Rites).

The Taixuan’s diagram explanation says: From Zi to Chen, from Chen to Shen, and from Shen to Zi, all are governed by the character Jia. Zhang, hui, tong, and yuan (calendrical cycle units of the Taixuan) are concealed together with lunar eclipses; this is the Way of the Taixuan.

Wu Ji of Yulin explains: In the year of the upper epoch of the Taichu calendar, at dawn on the jiazi new-moon day of the first month, the winter solstice fell exactly without a fractional remainder. After this, one thousand five hundred and thirty-nine years later, it again met jia...