《天原發微》Vol. 11

Chapter Eleven of the Tianyuan Fawei discusses the theory of "hexagram qi" (guaqi), a divination system transmitted by Jing Fang and Jiao Gan of the Han dynasty. This theory correlates the sixty-four hexagrams with the seasonal climatic changes throughout the year.

The core principle states that the four cardinal hexagrams—Kan (Water), Li (Fire), Zhen (Thunder), and Dui (Lake)—representing the four directions (north, south, east, and west), govern the four seasons respectively:

• Kan corresponds to the winter solstice,
• Li to the summer solstice,
• Zhen to the spring equinox,
• Dui to the autumn equinox.

The remaining sixty hexagrams evenly divide the 360 days of the year, with each hexagram presiding over approximately six days and seven "parts" (an ancient time unit where one day equals 80 parts; "seven parts" roughly equates to 2 hours and 6 minutes in modern terms). Notably, the Bo hexagram (symbolizing the exhaustion of yang qi) appears at the end of the ninth month, followed by the purely yin Kun hexagram governing six days and seven parts. After this, the Fu hexagram, representing the rebirth of yang qi, takes over. The interval from Bo to Fu spans exactly seven days, giving rise to the saying "seven days for the return" (qiri laifu).

Jing Fang, the Han dynasty scholar of the Yi Jing, categorized hexagrams into four types:

• Great Yin (hexagrams of increasing yin qi),
• Great Yang (hexagrams of increasing yang qi),
• Lesser Yin,
• Lesser Yang.

Later commentaries reference various scholars:

• Cai Yuanding (Master Xishan) of the Song dynasty noted that Shao Yong (Kangjie) also adopted the "six days and seven parts" framework.
• Yang Xiong (Ziyun) drew upon this system when composing the Tai Xuan Jing.
• Both Zixia and Hu Yuan (Hu Anding) interpreted "seven days" as symbolizing the cyclical nature of hexagram qi, where the six lines of a hexagram represent six days, and the seventh line marks the completion of a seven-day cycle.

The text concludes by explaining how the lines of hexagrams can symbolize different temporal units in the guaqi theory: some lines represent a year, others a month. The "seven days" mentioned in the Fu hexagram illustrate the cyclical pattern of hexagram qi. Specifically, the period from the beginning of winter (the tenth month's solar term) to heavy snow (the eleventh month's solar term) serves as a crucial timeframe for observing these qi transformations.

This passage examines the historical debates surrounding the "Six Days and Seven Parts" (六日七分) hexagram-Qi theory in ancient Yijing studies. From the Han to the Song dynasties, scholars held divergent interpretations of the "return in seven days" (七日来复) concept in the Zhouyi, which describes the seven-day transition from the Kun hexagram to the Fu hexagram.

Han dynasty scholars generally adopted the "Six Days and Seven Parts" framework, dividing the solar year of 365¼ days among sixty hexagrams, with each hexagram governing 6 and 7/80 days. However, by the Song dynasty, scholars like Wang Zhaosu, Wang Shu, and Song Xian began questioning this calculation.

Wang Zhaosu argued that if following the "Six Days and Seven Parts" method, the conclusion of the Kun hexagram would leave fifteen days remaining before the winter solstice—contradicting the "seven days" principle. He observed that even during the tenth month (governed by the pure Yin Kun hexagram), Yang Qi remained latent (as seen in shepherd's purse growing and "dragons battling in the wilderness"), demonstrating Yin-Yang transformation as a gradual process.

Hu Dan countered Wang Zhaosu's position, defending the precision of the hexagram-Qi theories developed by Jing Fang of the Western Han and Lang Yi of the Eastern Han. He maintained that "Six Days and Seven Parts" resulted from meticulous astronomical calculations, comparable to the sophisticated intercalary month system. Wang's fifteen-day discrepancy, according to Hu, stemmed from misunderstanding these calendrical refinements.

Zhu Zhen (style name Zifa) elaborated further: The four cardinal hexagrams (Zhen, Li, Dui, Kan) govern the four directions while sixty hexagrams distribute the solar year. Seasonal transitions are all subsumed under the four cardinal hexagrams, with residual time accumulating into intercalary months. Tracing from the Bo hexagram in the ninth month through Kun in the tenth to Fu in the eleventh month reveals a thirty-day progression of gradual changes across multiple hexagrams. The Fu hexagram corresponds precisely with the winter solstice, which begins its solar term (中气) with the Zhongfu hexagram—seven days later manifesting as Fu hexagram, embodying the "movement of heaven" (天行).

Among historical scholars, Yang Xiong's Taixuan Jing (太玄经) most profoundly captured this system's essence, correlating hexagram-Qi transitions with nine praise-markers (赞) like "Central, Extended, Following." When the sun reaches 1° of the Ox constellation during winter solstice—aligned with the Huangzhong pitch (黄钟) in the twelve-tone system and the eleventh month in the Xia calendar—this complete system was transmitted through scholars like Yang Xiong, Ma Rong, Zheng Xuan, Yu Fan, Lu Ji, and Fan Wang. Wang Zhaosu's generation, however, raised objections, with Wang Shu refuting Kong Yingda's commentary on Wang Bi's annotations, and Song Xian dismissing earlier theories entirely.

This discourse reveals the evolution of hexagram-Qi theory within Yijing studies, showcasing both continuities and ruptures between Han dynasty image-number (象数) exegesis and Song dynasty principle-based (义理) interpretations. At its core lies the challenge of correlating hexagrams with astronomical calendrics and the natural rhythms of Yin-Yang fluctuation.

This passage addresses issues in ancient calendrics and divination arts. Figures like Jing Fang and Guan Lang appropriated the name of the "Yijing" (Classic of Changes) to promote practices such as Liuren (a divination method), Qimen Dunjia (Daoist esoteric arts), sacrificial divination, and yin-yang numerology—all of which had strayed from the original intent of the sages (referring to the Yijing's authors).

A common challenge arises: Why must specific months correspond to particular hexagrams, or certain days align with specific line statements? For instance, why does the winter solstice calculation begin with the Zhongfu hexagram? Zhu Xi countered this by noting that Kong Yingda, the great Han dynasty Confucian scholar, documented in his "Zhouyi Zhengyi" the logical coherence of the "hexagram-qi theory" (matching the sixty-four hexagrams to solar terms). Systems like Liuren divination referencing time-positions or Dunjia's nine-palace division (directional arrangements in Qimen Dunjia) all ultimately derive from the Kan and Li hexagrams in the Yijing and the Hetu (River Chart) diagram—they simply emphasize different aspects of the Classic's principles.

Master Fang Xugu's correspondence during the winter solstice of 1295 (Yuanzhen era) discussed calendrical discrepancies: Zhu Xi maintained that the sun resided at the first degree of the Ox constellation during winter solstice per ancient standards. Yet historical records show that from Emperor Wen of Han to the Tang dynasty—spanning 961 years—the solstice point had shifted twelve degrees. By Yuanzhen's first year, it had receded further to the eighth degree of the Winnowing Basket constellation, then five days later to the third degree of the Dipper. How could one rigidly adhere to ancient assertions that the solstice sun must occupy the Ox constellation?

Examining historical annals reveals inherent inconsistencies in calendrical data: During Emperor Yao's reign, the winter solstice aligned with the first degree of the Emptiness constellation, yet He Chengtian recorded it at the tenth degree of the Girl constellation. The Yuanjia calendar of Song placed it at the seventeenth degree of the Dipper, while the "Yueling Yaoyi" noted the fourteenth degree. The Tang dynasty's Dayan calendar marked the tenth degree, whereas the Song's Tongyuan calendar adjusted this to the second degree. Even the ancient convention of midnight (mid-zi hour) as the day's start was modified by Li Chunfeng to the zi hour's beginning—a mere two ke (approximately thirty minutes) difference that contemporaries praised for its precision. Such variations stem from the inherently irregular movements of yin and yang qi, where natural fluctuations in annual cycles inevitably produce subtle discrepancies.

This passage examines the correspondence between ancient astronomical calendrics and the hexagrams of the Yijing (Book of Changes). Ancient astronomers established calendars through celestial observations, with the region between the Ox Star (Niuxiu) and the Dipper constellation holding particular significance. Zhu Xi maintained that the key to proper calendrical calculation lay in establishing a broad foundational framework capable of encompassing diverse astronomical phenomena.

The text describes how the winter solstice sun aligns with the first degree of the Ox Star, then moves rightward through twelve celestial divisions (ancient astronomers divided the ecliptic into twelve equal segments) until reaching the 26th degree of the Dipper, before returning to complete its cycle at the Ox Star's first degree. The Ox Star corresponds to the Fire position, while the Stellar Chronogram (Xingji) corresponds to the Water position. The convergence of sun and moon here creates the imagery of the Ge hexagram ("Fire in the Marsh"). This served as the reference point for the ancient Taichu calendar (Han dynasty), corresponding to the third month in the "hexagram-Qi" theory.

The sixty-four Yijing hexagrams map onto the annual cycle: the thirty hexagrams of the Upper Canon correspond to the first 180 days of the solar year, while the thirty hexagrams of the Lower Canon match the latter 180 days. The Qian hexagram begins on the first Jiazi day, Tai hexagram on the tenth Jiaxu day, Shihe hexagram on the twentieth Jiashen day, concluding with Li hexagram as the thirtieth. The Lower Canon commences with Xian hexagram on the first Jiawu day, Sun hexagram on the tenth Jiachen day, Zhen hexagram on the twentieth Jiayin day, ending with Jie hexagram on the final Guihai day. Thus the sixty hexagrams' 360 lines (yao) each represent one day, completing the annual cycle.

Regarding seasonal divisions, the Jie hexagram signifies "heaven and earth having proper measures makes the four seasons distinct," while the Ge hexagram denotes "heaven and earth transforming makes the four seasons distinct." The four hexagrams Zhongfu, Xiaoguo, Jiji, and Weiji correspond to the cardinal directions of north (zi), south (wu), east (mao), and west (you), symbolizing the four seasons. Each hexagram's six lines represent fifteen days, forming the system of twenty-four solar terms and seventy-two pentads. However, the author notes that previous claims about the cycle beginning with Zhongfu are inaccurate—the proper calculation should commence with the Qian hexagram on the first Jiazi day.

This passage discusses the correspondence between ancient calendrical systems and hexagram symbolism. During the Western Han Dynasty, Luo Xiahong reformed the Zhuanxu Calendar (an ancient timekeeping system) to create the Taichu Calendar, upon which Yang Xiong (courtesy name Ziyun) based his Canon of Supreme Mystery (Taixuan Jing). The text mentions that "hexagram qi" (the theory correlating hexagrams with solar terms) always begins calculation from each month's "central solar term" (twelve of the twenty-four solar terms).

Specifically, the Taixuan Jing pairs the Zhongfu hexagram (one of the sixty-four hexagrams) with the initial six-line of the Kan hexagram, representing the winter solstice—the central solar term of the eleventh month when yang qi first emerges. This moment marks the starting point of calendrical calculations. Both Zhongfu (comprising Xun above and Dui below) and Xiaoguo hexagrams (Zhen above and Gen below) belong to the "Six Offspring Hexagrams" (referring to Zhen, Xun, Kan, Li, Gen, and Dui). These hexagrams' qi movements distribute across the four seasons, forming the annual cycle of solar terms.

Shao Yong (Kangjie) regarded the Taixuan Jing as capturing the essence of celestial and terrestrial movements. At the winter solstice, when the Kun hexagram (pure yin) reaches its zenith, the Qian hexagram (pure yang) begins stirring—the fundamental principle behind musical temperament and calendrics. Yang Xiong's theory resonates with the divine Dao, much like Zhuangzi's concept of "internal and external correspondences."

The text also notes differences between calendrical systems: the Zhuanxu Calendar begins its year in the tenth month, while the Lianshan Yi takes the Gen hexagram as its primary symbol. In contrast, the Taixuan Jing employs eighty-one "headers" (units analogous to hexagrams), each containing nine "eulogies" (equivalent to lines), totaling 729 eulogies—with two eulogies corresponding to one day. Each eulogy further correlates with six time periods, and each period matches six "counting stalks" (divination tools), creating a system harmonized with the qi movements of sixty hexagrams.

Zhu Xi observed that the Taixuan Jing system drew from Jiao Yanshou's hexagram-qi theory but differed from King Wen's arrangement of the eight trigrams (with Qian in the northwest and Kun in the southwest). Here, the number "five" occupies the position between two and four, symbolizing earth virtue (De). The first four numbers (1-4) represent generative numbers, while the latter four (6-9) signify completion numbers, embodying the cosmological principle of heaven and earth's creative process.

This passage discusses the correspondence between Yang Xiong's Canon of Supreme Mystery (Taixuan Jing) from the Han Dynasty and the Book of Changes (Yijing). Ancient scholars aligned the eight trigrams (Qian, Kun, Zhen, Xun, Kan, Li, Gen, Dui) with cardinal directions—Zhen representing east, Dui west, Li south, and Kan north. Another system matched the twelve sovereign hexagrams (Fu, Lin, Tai, Dazhuang, Guai, Qian, Gou, Dun, Pi, Guan, Bo, Kun) with the twelve double-hours of the day.

Jiao Yanshou of the Han Dynasty developed the "Hexagram-Qi (Qi)" theory, synthesizing these approaches: the 24 lines of the Kan, Li, Zhen, and Dui trigrams corresponded to the 24 solar terms, while the twelve sovereign hexagrams represented the twelve months, further subdivided into 48 hexagrams symbolizing official ranks (Duke, Marquis, Minister, Grandee). This gave rise to the "six days and seven parts" calendrical calculation method.

The Taixuan Jing emulated this hexagram-Qi framework but introduced modifications: it designated the Zhongfu hexagram as the start of the winter solstice and the top line of the Yi hexagram as the end of Major Snow. The text used the "Center" hexagram to symbolize the winter solstice's nascent Yang energy, while the "Nourishment" hexagram, paired with the "Qi" and "Ying" annotations, represented late Major Snow. Though terminology differed, the sequence followed the Yijing's hexagram-Qi progression.

Numerologically, the Taixuan Jing drew from the Hetu (River Chart) system's symbolic pairings: 1 and 6 shared origins, 2 and 7 were companions, 3 and 8 formed alliances, 4 and 9 walked the same path, and 5 with 10 stood guard together. These combinations carried distinct meanings: 3 and 8 signified attire, 4 and 9 represented martial power, 2 and 7 mirrored ruler-subject relations, 1 and 6 connected to spirit worship, and 5 (or 10) symbolized sustenance.

A key distinction lies in the Taixuan Jing's adoption of a ternary system, mirroring yet diverging from the Yijing's binary foundation. Where the Yijing derived its 64 hexagrams from the four images (Lesser Yang, Greater Yang, Lesser Yin, Greater Yin) and eight trigrams, the Taixuan Jing built its 81 "sections" (shou) from the triad of Heaven, Earth, and Humanity. For instance, its "Cycle" (Zhou) corresponds to the Yijing's "Return" (Fu), "Youth" (Tong) to "Darkness" (Meng), and "Increase" (Zeng) to "Benefit" (Yi)—sometimes with one-to-one mappings, other times multiple sections matching a single hexagram to elaborate finer distinctions. The Taixuan Jing's "Mystical Charges" (Xuan Chong) parallels the Yijing's "Sequence of Hexagrams," "Mystical Alternations" (Xuan Cuo) mirrors "Miscellaneous Hexagrams," and "Mystical Numbers" (Xuan Shu) equates to "Explaining the Trigrams"—a structural homage to the Yijing's framework.

This scripture primarily elucidates the calculation principles of ancient numerology and astronomical calendrics. The four elements—Metal, Wood, Water, and Fire—each occupy one portion, interacting with the two energies of Yin and Yang to form six forces. Through multiplying six by six, the sixty-four hexagrams are derived, giving rise to the three hundred and eighty-four lines (yao, the fundamental units of hexagrams). Here, the "Xuan" (referring to the profound principles of the Taixuan Jing, or Classic of Supreme Mystery) divides the generative patterns of Metal, Wood, Water, and Fire using the "Nine Praises," supplemented by the Earth element's principle of "Guarding the One" (Shou Yi). By multiplying nine by nine, the complete system of seven hundred and twenty-nine praises is ultimately achieved.

Both the Yijing (Book of Changes) and the Taixuan Jing adhere to the principles of the Five Phases (Wuxing). The Yijing's calculation method progresses in layers—two multiplied by four, four multiplied by eight—culminating in the complete system where sixty-four hexagrams are multiplied by eighty-four. This originates from the multiplicative relationship between the Heavenly number three and the Earthly number four in the Hetu (an ancient mystical diagram). Thus, four is taken as the base number for Earth, while Heaven is calculated using three. Fuxi, therefore, overlapped three lines to form six, completing the hexagram structure.

The mathematical framework of the Taixuan Jing derives from the Huangzhong pitch pipe (an ancient musical standard), which measures nine inches in length and nine fen in hollow circumference. Through tripling increments, it symbolizes the patterns of Heaven and Earth: tripling the Heavenly number three yields the "Nine Categories" (jiuchou, the nine great principles); tripling the Earthly number four produces the "Twelve Sovereign Hexagrams" (shier pi gua, corresponding to the twelve months); tripling the Heavenly number five results in fifteen days forming one solar term; and tripling the Earthly number six generates the eighteen transformations that shape the hexagrams. This tripling progression begins at the zi hour (midnight) and, through continuous multiplication across the twelve double-hours, ultimately reaches the number 177,147—the generative figure of Jing Fang's sixty musical pitches (an ancient tonal system).

The text further notes that the Taixuan Jing takes the 365 days of a year as its foundation, multiplying each day by eighty-one and adding the fractional quarter-day, totaling slightly more than 29,585 units. Each "praise" (zan, a textual unit in the Taixuan Jing) and each solar term precisely corresponds to this computational system, demonstrating its capacity to encompass the cyclical patterns of Heaven and Earth. "Xuan" is revered as the wondrous governing principle.

Finally, it mentions Yang Xiong (courtesy name Ziyun), a man skilled in deep contemplation of the mysteries of Yin-Yang waxing and waning, who earnestly sought to deduce these principles. Zhang Heng (courtesy name Pingzi) also praised him for pushing Daoist techniques to their utmost limits, sparking later discussions.

This passage presents ancient Yin-Yang theory's insights into the celestial movements. It elucidates several key concepts:

The alternation of Yin and Yang resembles the cycle of day and night, manifested in the varying daylight hours between winter and summer solstices. Yang energy (Qi) begins germinating during the Zi hour (11pm-1am), reaching its peak at the Wu hour (11am-1pm), while Yin energy follows the opposite pattern, starting at Wu hour and peaking at Zi hour. In spatial terms, Yang exhausts itself in the northwest, while Yin culminates in the southeast.

The cosmic operating principle follows: Heaven uses north-south as its warp threads, Earth employs east-west as weft threads. Like fabric weaving, this celestial warp-and-weft interweaving creates all phenomena. Solar and lunar movements also obey patterns: when the sun moves south to the Altair position (Niuxiu), it marks winter solstice; when traveling north to the Well constellation (Dongjing), summer solstice occurs. The moon appearing in the west on the last day of a lunar month is called "tiao," while its appearance in the east on the first day is termed "ceni."

The text also records a numerical system: Zi-Wu corresponds to number nine, Chou-Wei eight, Yin-Shen seven, Mao-You six, Chen-Xu five, Si-Hai four. Combined, these yield forty-two Yang musical pitches and thirty-six Yin pitches, totaling seventy-eight - resonating with the Tiangan-Dizhi combinations like Jia-Ji.

These theories reflect ancient scholars' systematic observations of celestial movements, diurnal/seasonal changes, forming an explanatory framework for natural laws that became integral to early astronomy, calendrics, and Yin-Yang/Five Phases (Wuxing) theory.

This scripture primarily elucidates the correspondence between ancient musical temperament and the numerical principles of the Five Phases (Wuxing). It first explains the generative principle of musical temperament: the pitch standards originate from the pairing of celestial stems and earthly branches. The Huangzhong pitch (first among the twelve temperaments) begins at the Zi position, with the Wu position corresponding to the Zi palace, hence all numbers are based on nine. The combinations of stems and branches form different numbers—for instance, Jia (first stem) paired with Si (sixth branch) makes nine, Yi (second stem) with Geng (seventh stem) and Chou (second branch) makes eight, Bing (third stem) with Xin (eighth stem) and Yin (third branch) makes seven, and so forth.

The Yang pitches correspond to odd numbers nine, seven, and five, whose multiples sum to forty-two; the Yin pitches correspond to even numbers eight, six, and four, summing to thirty-six—together totaling seventy-eight. The five tones (Gong, Shang, Jue, Zhi, Yu) correspond to the ten celestial stems: Jia and Yi belong to Jue, Bing and Ding to Zhi, Geng and Xin to Shang, Ren and Gui to Yu. The twelve temperaments derive from the twelve earthly branches, while the eight sounds (metal, stone, silk, bamboo, gourd, earth, leather, and wood) emerge from these correspondences. These form the fundamental principles of musical temperament and the origin of Five Phases numerology.

The subsequent "Profound Meaning" section expounds the Tai Xuan numerical system: Tai Xuan (Supreme Mystery) signifies the Taiji (Supreme Ultimate), representing the sovereign position. It divides into three realms—Heavenly Mystery, Earthly Mystery, and Human Mystery—corresponding to the three powers of heaven, earth, and humanity. Each realm contains three provinces (totaling nine provinces symbolizing the nine ministers), with each province comprising three departments (seventy-two departments representing officials). The heavenly way manifests in beginning, middle, and end; the earthly way in upper, middle, and lower; the human way in thought, calamity, and fortune. The divination method of Tai Xuan resembles the Yijing (Book of Changes) but emphasizes "penetration" as its distinctive feature.

The Tai Xuan numerology originates from the Five Phases: one represents Water, two Fire, three Wood, four Metal, and five Earth, cycling through to nine before restarting. Each "head" (chapter) contains nine praises, where the first praise corresponds to Water, the second to Fire, and so on, forming a complete Five Phases cycle. These numerical correspondences with Five Phases attributes constitute the foundational framework of Tai Xuan numerology.

This passage from Tianyuan Fawei primarily discusses the calculation principles of ancient astronomical calendars. At its core, it uses the movement of the Northern Dipper (Dou) as the calendrical benchmark, since the Dipper's motion is stable and observable, whereas the moon's waxing and waning phases are too variable to serve as a constant reference.

The text mentions the arrangement of "eighty-one sections": odd numbers represent Yang, even numbers represent Yin, with odd matching odd and even matching even, forming a structure of Yin-Yang correspondence. Much like how the fifth line dominates a hexagram in the Yijing (Book of Changes), this system also takes "five" as its central organizing principle.

The key to calendrical calculations lies in coordinating the Dipper's movement with the 60-year cycle of the sexagenary system (Liujia). Just as calendars require intercalary months to correct discrepancies, this system employs a "displacement-adjustment" mechanism. By observing the position of the Northern Dipper among the twenty-eight lunar mansions at sunset on the first day of each month, solar terms can be precisely calibrated.

Wu Ji's commentary elaborates on the calendrical cycles: 1,539 years constitute one "unified cycle" (tong), while three such cycles (4,617 years) form one "grand cycle" (yuan). Within this, 19 years make up a "chapter," and 27 chapters (513 years) form a "convergence," recording the complete cycle of solar-lunar conjunctions. This calculation method begins from a Jiazi year, cycles through Jiachen and Jiashen, and ultimately completes one grand yuan cycle.

All these computations aim to achieve precise alignment between the calendar and celestial phenomena. When solar terms perfectly coincide with the Dipper's positions, it confirms the correct placement of intercalary months and the overall accuracy of the calendar. The text particularly emphasizes that this system primarily observes the sun and Northern Dipper rather than relying on the moon, precisely because lunar phases are too irregular and unstable.

This passage elucidates the sophisticated calculations of ancient calendrical astronomy. The ancients observed that a solar year actually consists of 365 and 1/4 days, yet their standard calendar accounted for only 365 days. The surplus was reconciled through the intercalation of leap months. Just as the lunar cycle doesn't perfectly align with the solar year, the "shuofen" (fractional lunar phase) method was employed for synchronization.

The fundamental calendrical computations began from the winter solstice of the first Jiazi year (the celestial origin epoch), using the star Altair (ancient astronomical reference point) as the starting marker. The sun's annual circuit spans 365 and 1/4 degrees, while twelve lunar phases complete a year. Through strategic intercalation to adjust the seasons, they ultimately derived the precise 365.25-day cycle. However, the ancient Zhuanxu Calendar fell short by 3/4 day, while the Taichu Calendar exceeded by half a day—both discrepancies stemming from the natural principle where odd-numbered Yang quantities overflow and even-numbered Yin quantities remain deficient.

Shao Yong's (Kangjie) Huangji Jingshi calendar, though employing different calculations, similarly attained marvelous precision. He allocated the four primary hexagrams—Qian (Heaven), Kun (Earth), Kan (Water), and Li (Fire)—to govern the four seasons, with each hexagram presiding over six solar terms. For instance, Kan governed from winter solstice to awakening of insects, while Li ruled from spring equinox to grain in ear, thus correlating all twenty-four solar terms with corresponding hexagrams. The year divides into four phases: the winter solstice's midnight hour (zi) marks cosmic inception, the spring equinox's dawn hour (mao) signifies life's emergence, the summer solstice's noon hour (wu) represents flourishing vitality, and the autumn equinox's dusk hour (you) denotes harvest—each phase symbolized by sixty-four hexagrams.

Notably, the awakening of insects (second month solar term) embodies all things sprouting, while the beginning of spring (tenth month solar term) symbolizes nature's withdrawal. This arrangement originates from the unique Yin-Yang transitional positions of the yin hour (3-5 AM) and xu hour (7-9 PM) within the diurnal cycle, mirroring the equinoxes' balancing function in the annual rhythm.

The relationship between the moon's movement and seasonal transitions is fundamentally determined by the interaction of celestial and terrestrial Qi (vital energy). The earth nurtures all things through the mechanism of Qi circulation—celestial Qi arrives first, and earthly phenomena subsequently respond to it.

Qi typically arrives half a month in advance because its movement is expansive and abundant, while the moon's orbit appears swifter and more contracted. As Guan Ziming observed: "When Qi arrives beyond the expected time, it's called 'Qi excess'; when it falls short, it's called 'new moon deficiency.'" The discrepancies between Qi phases and lunar cycles accumulate over time. Occasionally, solar terms may occur on the last day of a lunar month (Hui day), necessitating intercalary months to recalibrate the calendar to its original state.

The Jingshi classic, rooted in the primordial cosmic order (Xiantian), calculates both Zhongqi (the solar terms falling in mid-month) and new moon phases from the same starting point. The "hexagram-Qi" system (matching the 64 hexagrams to seasonal transitions) follows the primordial numerical sequence, selecting Zhongqi as the governing force for each month. Whether in grand cycles (Yuan-Hui-Yun-Shi) or minor cycles, calculations always begin from Zhongqi—this embodies the principle of "centering on harmony and correctness."

Hexagram diagrams reveal: The Grand Cycle Method follows Jingshi's rules, commencing from the celestial stem-branch combination Xing-Jia-Chen-Zi; the Minor Cycle Method adheres to the Hexagram-Qi Chart, starting from the stem-branch combination Jia-Si-Meng days. Heaven's Dao operates holistically—Qi's essence originates from the four cardinal directions (Zi-Wu-Mao-You). Thus, the Grand Cycle's Jiazi corresponds to the winter solstice, with all 24 solar terms anchored to these cardinal points. Qi's movement manifests through the four seasonal commencements (Start of Spring, Summer, Autumn, Winter), so the Minor Cycle's Jiayin aligns with the Start of Spring, with all solar terms rooted in the four seasonal initiators (Yin-Shen-Si-Hai).

Song Dynasty scholars noted: In the Primordial Diagram, the left sector begins with Zhen hexagram's initial line representing the winter solstice, progresses through Li and Dui hexagrams' midpoints at the spring equinox, and culminates at Qian hexagram's terminus transforming into the summer solstice. The right sector starts with Xun hexagram's initial line marking the summer solstice, traverses Kan and Gen hexagrams' centers at the autumn equinox, and returns to Kun hexagram's endpoint reverting to winter solstice.

Regarding the clockwise and counterclockwise movements in hexagram diagrams, predecessors have provided detailed explanations. The "already manifested" hexagrams (Qian-1, Dui-2, Li-3, Zhen-4 representing Yang's growth phase) arrange south-to-north, while Qi circulation flows north-to-south. Yang Qi first emerges in Zhen hexagram, hence Shao Yong (Shaozi) designated the winter solstice's midnight (Zi hour midpoint) as Fu hexagram (corresponding to mid-November). The twelfth month's Chou hour beginning marks minor cold, matching Kan, Zhun, and Yi hexagrams; mid-month's major cold corresponds to Zhen, Shike, and Sui hexagrams. The first month's Yin hour start signals the Start of Spring, aligning with Wuwang and Mingyi hexagrams; mid-month's rainwater matches Bi, Jiji, and Jiaren hexagrams. The second month's Mao hour commencement brings awakening of insects, corresponding to Feng, Li, and Ge hexagrams; mid-month's spring equinox aligns with Tongren and Lin hexagrams. The third month's Chen hour beginning ushers in clear brightness, matching Sun, Jie, and Zhongfu hexagrams; mid-month's grain rain corresponds to Gui and Kui hexagrams.

This scripture explains how ancient Daoism divided the year into Yin and Yang halves, using the sixty-four hexagrams to correspond with the twenty-four solar terms. From the Beginning of Summer (Lixia) to the Summer Solstice (Xiazhi), thirty-two hexagrams belong to Yang, representing spring and summer; from the Summer Solstice to the Winter Solstice (Dongzhi), another thirty-two hexagrams belong to Yin, representing autumn and winter.

In detail: At the Beginning of Summer, the hexagrams Lü and Tai correspond; during the Grain Full (Xiaoman) solar term, the hexagrams Daxu, Xu, and Xiaoxu apply; in the fifth month's Grain in Ear (Mangzhong), the hexagrams Zhuang, Dayou, and Guai appear, culminating at the Summer Solstice with the final line of the Qian hexagram. These Yang hexagrams move in direction from west to north.

After the Summer Solstice, the Yin hexagrams begin: in the sixth month's Minor Heat (Xiaoshu), the hexagrams Daguo, Ding, and Heng correspond; during Great Heat (Dashu), the hexagrams Xun, Jing, and Gu apply; in the seventh month's Beginning of Autumn (Liqiu), the hexagrams Sheng and Song appear; during End of Heat (Chushu), the hexagrams Kun, Weiji, and Xie apply; in the eighth month's White Dew (Bailu), the hexagrams Huan, Kan, and Meng correspond; during Autumn Equinox (Qiufen), the hexagrams Shi and Dun appear; in the ninth month's Cold Dew (Hanlu), the hexagrams Xian, Lü, and Xiaoguo apply; during Frost's Descent (Shuangjiang), the hexagrams Jian, Jian, and Gen appear; in the tenth month's Beginning of Winter (Lidong), the hexagrams Qian and Pi correspond; during Minor Snow (Xiaoxue), the hexagrams Cui, Jin, and Yu apply; in the eleventh month's Major Snow (Daxue), the hexagrams Guan, Bi, and Bo appear, culminating at the Winter Solstice with the final line of the Kun hexagram.

The year contains eight major solar terms (Winter Solstice, Beginning of Spring, Spring Equinox, Beginning of Summer, Summer Solstice, Beginning of Autumn, Autumn Equinox, and Beginning of Winter), each corresponding to two hexagrams, totaling sixteen; the remaining sixteen solar terms each correspond to one hexagram, making forty-eight in total. Including other variations, all sixty-four hexagrams align with the annual climatic cycle. This theory of hexagram-Qi (Guagi) was used to determine time and complete the yearly cycle, reflecting the patterns of Heaven-Earth and Yin-Yang transformation. Zhu Xi (Master Zhu) summarized this system using the "Two Solstices and Two Equinoxes" (Xiazhi, Dongzhi, Chunfen, Qiufen), while the author elaborates on its principles through detailed analysis of specific hexagrams.