《天原發微》Vol. 10

This passage primarily discusses the ancient system of using the number twelve as a foundation for calculating temporal cycles. In the Song Dynasty scholar Bao Yunlong's (style name Jingxiang) work Tianyuan Fawei (The Subtle Origins of Heaven), he cites theories by Shao Yong (Kangjie) and others, proposing that the movements of heaven and earth can be divided and calculated using a duodecimal system.

Shao Yong's Huangji Jingshi (Supreme Principles Governing the World) is a text for astronomical and calendrical calculations, where twelve special hexagrams (known as "ruling hexagrams") correspond to twelve temporal units ("hui"), much like the twelve months in a year. He proposed that one day has twelve two-hour periods (shichen), one year has twelve months, one "yun" (cycle) contains twelve "shi" (generations), and one "yuan" (epoch) consists of twelve "hui." This duodecimal pattern can be extended infinitely—from calculating a single shichen to a full day, from a day to a month, from a month to a year, and even to grand cycles spanning 129,600 years.

Jing Fang of the Han Dynasty introduced the "Hexagram-Qi Theory," which divides solar terms using the "six days and seven parts" method, an approach also adopted by Shao Yong. Zheng Xuan (Zheng Shi) believed that the sun and moon meet twelve times annually, and ancient sage-kings used this to demarcate the four seasons. By grasping the broad framework through hexagrams ("hexagram-Qi outlines the essentials"), studying details with the Tai Xuan Jing (Canon of Supreme Mystery), and deriving subtleties through Huangji Jingshi (Supreme Principles), one could calculate the patterns of heaven, earth, the sun, the moon, and the rise and fall of dynasties.

Sima Qian (the Grand Historian) proposed grand historical cycles: minor changes every thirty years, moderate changes every century, major changes every five hundred years, with three major changes forming one "ji" (1,500 years), and three "ji" completing a full cycle (4,500 years).

Finally, the passage summarizes Shao Yong's "Yuan-Hui-Yun-Shi" system: one "yuan" (epoch) contains twelve "hui" (like twelve months in a year), one "hui" consists of 360 days (like 360 days in a year), totaling 4,320 "shi" (like 4,320 shichen in a year). The smallest unit, the day, is called "yuan"; the month is "hui"; the movement of stars is "yun"; and the changes in shichen are "shi." This system likens time to a wheel turning in cycles ("revolving leftward with heaven"), completing 360 revolutions each year.

This passage elucidates the ancient Daoist theory concerning temporal cycles and cosmic operational principles, focusing on the calculation methods and inherent patterns of the "Great Cycle" (一元).

The fundamental temporal unit is explained as follows: A day contains twelve double-hours (时辰), thus a year comprises 4,320 double-hours. Thirty years constitute one generation (一世), while a Great Cycle spans 129,600 years. In the grand transformation of the cosmos, a single year represents merely a basic unit. From the largest cycle (元) to the smallest division (辰), these temporal units progress hierarchically until reaching their limits, at which point transformative change occurs.

Specifically: One Great Cycle equals 129,600 years; one period (会) equals 129,600 months; one movement (运) equals 129,600 days; one generation equals 129,600 double-hours. These numerical relationships emerge from natural patterns rather than artificial constructs.

The text then details the waxing and waning of Yin-Yang: The first six periods represent growth phases (息), while the latter six signify decline phases (消). This mirrors the annual cycle where Yang energy ascends from the eleventh month (子) to the fourth month (巳), and Yin energy grows from the fifth month (午) to the tenth month (亥). The 75th lunar mansion corresponds to the Awakening of Insects solar term, while the 315th mansion aligns with the Beginning of Winter.

Regarding calendrical calculations: Although the actual solar year contains 366 days (due to Qi excess) and the lunar year 354 days (due to moon phase deficiency), the "Supreme Principles" (经世) employs a 360-day base year to conceal deeper operational laws. The Yang phase ascends from the eleventh to fourth months, peaking at the end of the fourth month; the Yin phase rises from the fifth to tenth months, culminating at the tenth month's end. Each phase contains six residual voids, totaling twenty-four, corresponding to the 384 lines of the sixty-four hexagrams.

The four fundamental hexagrams—Qian (Heaven), Kun (Earth), Kan (Water), and Li (Fire)—occupy the cardinal directions as unchanging templates. The remaining sixty hexagrams with their 360 lines perfectly match the 360-day cycle. This computational system embodies the laws of Yin-Yang fluctuation, containing profound operational mysteries.

Finally, the text notes the celestial configuration during Emperor Yao's reign (唐尧时期): Beginning at the 180th lunar mansion in the Gui position, corresponding to the 2,157th double-hour in the Shen position. This demonstrates how ancient sage-kings established calendars based on the operational laws of heaven and earth.

The moon's movement follows the patterns of the Five Phases (Wuxing), and by tracing its path upward, one can comprehend its trajectory. Ancient sages divided time into twelve phases—the first six representing growth and the latter six representing decline—with the entire cycle perfectly corresponding to the 360-day waxing and waning of Yin and Yang.

This describes the calculation method of the "Epochal Scripture Cycles" (Yuanjing Hui), a Daoist temporal unit: twelve months correspond to twelve "assemblies" (hui), and 360 days correspond to 360 "revolutions" (yun). Using the "Primordial Epoch" (Yuan zhi Yuan), the largest temporal unit, as the basis for division, each assembly contains 10,800 "epochal fractions," and each revolution contains 360 "epochal fractions." The total division of the grand cycle, called "One Epoch" (Yi Yuan), amounts to 129,600 "Primordial Epochs." Within this, the Yang number 360 represents advancement, while the Yin number 360 represents retreat—together forming a combined total of 720 numerical values.

An alternative division splits the cycle into thirty parts, corresponding to the thirty days of a month, advancing and receding over sixty days in accordance with the grand revolution cycle. This is the calculation system of "Assembly Scripture Revolutions" (Hui Jing Yun): thirty days in a month correspond to thirty revolutions in one assembly. Observing the moon's movement, there are variations in speed (referred to as "tiao ru," indicating the moon's faster and slower phases), creating an actual total of sixty revolutions. From the sun's movement, the alternation of day and night also follows an advance-retreat pattern, and when combined with the tiao ru variations, the actual counted days in a month reach 120, and one assembly reaches 120 revolutions.

Further subdivision divides the 129,600 numerical values into twelve parts, corresponding to the twelve double-hours (shichen) of a day and their six-day cycle of advance and retreat. This is the calculation method of "Revolution Scripture Generations" (Yun Jing Shi). In this system: twelve double-hours in a day correspond to twelve generations in one revolution, sixty seconds make one fen (minute), thirty fen make one double-hour, and a full day totals 4,320 seconds. The 129,600 seconds precisely equal the total seconds in thirty days. The complete count of years in one revolution amounts to 559,872,000 seconds, which is the numerical value of the "Tai Hexagram" (symbolizing prosperity and smoothness).

The so-called "six-day advance and retreat" refers to a cycle of transformation. If one day is likened to a year, then six days equate to six years. In a minor revolution cycle, advancing sixty years is equivalent to ten transformations, while in a grand revolution cycle, it constitutes one complete transformation. The Dao of Heaven operates on a base of six for its transformations, always leaving a remainder. The smallest six-day cycle corresponds to six double-hours, forming one sexagenary (Jiazi) cycle.

This scripture expounds the Daoist theory of temporal cycles and cosmic operation, primarily divided into two systems: the Grand Cycle (大运) and Minor Cycle (小运).

The Grand Cycle system operates on a complete 60-year period (called "one celestial revolution" or 一周天), corresponding to the cyclical movement of the Five Phases (Wood, Fire, Earth, Metal, Water). Beginning from the Jiazi year (甲子年), the celestial stems and earthly branches pair to complete one full revolution after 60 years. These six decades are further subdivided into six 10-year periods, each corresponding to one "yun" (运) or phase of energy.

The Minor Cycle system uses a 6-year basic period aligned with the transformations of the "Six Climatic Qi" (六气: wind, cold, summer heat, dampness, dryness, and fire). These six energies generate twelve variations (matching the twelve earthly branches) in their celestial-terrestrial movement, ultimately forming the complete 60-year cycle. Whether in the 60-year Grand Cycle or the 60 transformations of the Minor Cycle, both ultimately correspond to the annual cycle of 366 days (including intercalary surplus).

The text further details temporal measurements: 360 double-hours (时辰) constitute one "generation" (世, 30 years), with each double-hour divisible into 180 "miao" (杪, the smallest time unit). One day contains 4,320 fen (分), though only half this value (2,160 miao) is used in practice. Temporal movement follows patterns of waxing-waning and advance-retreat: from the midnight-to-noon period (子时 to 巳时) representing Yang Qi's growth phase, to the noon-to-midnight period (午时 to 亥时) marking its decline. The Grand Cycle primarily manifests the waxing-waning principle, while the Minor Cycle embodies advance-retreat dynamics. One complete annual cycle of day-night alternation comprises 730 standard units (referring to 365 fundamental units each for Yin and Yang).

This passage explains a complex temporal calculation system from ancient Chinese astronomical calendars. The ancients used the "Tai Xuan" system (an ancient astronomical calendar method) to measure time, considering one full day as comprising both daylight and night. Through special calculations, they divided the 365-day year into distinct cycles.

Several key concepts are mentioned here: the solar surplus (extra time in the sun's movement) and lunar deficit (shortfall in the moon's movement) cancel each other out, leaving a remainder of 12 days. Multiplying these 12 days by ten yields 120 days. Adding these 120 days to 720 days (equivalent to two years) gives a total of 840 days—more than twice the standard 360-day year.

The ancients also divided each day into daylight and nighttime portions, incorporating intercalary months (additional months added to align the calendar with astronomical phenomena) into their calculations. The extra six days were distributed across the six Jia cycles (the sixty-year Jiazi cycle), forming sixty smaller cycles. These six intercalary days, combined with the previous 120 days, totaled 126 days—considered the optimal period for human activities.

In the six-number system, daylight and nighttime were each allotted equal halves, while the moon's movement varied in speed (with "tiao" indicating faster movement and "nü" indicating slower movement), creating twelve distinct periods. Through this division, temporal progression could be calculated: 60 days forward, 60 days backward, and six such cycles making 360 days. Adding six days forward and six days backward created seven segments of waxing and waning time, ultimately using fourteen "hui" (an ancient time unit) to form 720 days—all calculated using only half-values.

Another interpretation holds that twelve days forward count as 120, and twelve days backward also as 120. Adding the solar surplus of six days and the lunar deficit ("shuoxu," the discrepancy between synodic and actual moon phases) of six days yields 252 days in total. This forms the foundation of the greater and lesser cycles (with the greater cycle referring to celestial motion and the lesser to specific temporal divisions).

Overall, the complete celestial cycle number is 384, but only 360 are actually used. A standard year consists of 360 days, yet according to the "Huangji Jingshi" calculations, nine out of twelve "hui" make 270 days. Within one "yuan" (a grand cycle) of 360 cycles, only 240 are practically applied, with intercalary additions not exceeding 252 cycles—this being the method for calculating the "Eight Kaiwu Hui" (eight critical temporal nodes).

From the perspective of celestial motion, a year uses 360 days; from the perspective of earthly growth cycles—from vegetation sprouting to ground freezing—only 252 days are actually utilized. Thus, the "guaqi" chart (depicting seasonal changes) shows 384 days in day-count but 256 in hour-count (with ancient days divided into twelve "shichen"), totaling 3,072 hours—the basis for distinguishing greater and lesser cycles. The entire system uses twelve temporal boundaries of progression and regression to form the 360-day cycle, supplemented by six days of forward and backward movement to complete the calculations.

This passage from Tianyuan Fawei (The Subtle Origins of Celestial Cycles) primarily elucidates the operational patterns of Yin-Yang and the principles of calendrical calculations. The alternating movements of Yin and Yang each comprise 360 units when viewed separately, yet their combination also totals 360, as the Yang number encompasses the Yin number, forming a complete cycle. Thus, the Grand Celestial Cycle (referring to major cosmic periods) employs intercalation methods (calendar adjustments for solar-lunar synchronization) to manifest the generative relationship between standard and intercalary numbers in Heaven-Earth Yin-Yang dynamics—identical in essence but distinct in manifestation.

Regarding the Minor Cycles (shorter-period calculations), a base number of 129,600 years is adopted, wherein thirty percent constitutes "transition numbers" (intermediary figures for Yin-Yang alternation) and seventy percent represents "applied numbers" (practically utilized figures). The Grand Cycle embodies fundamental laws, while Minor Cycles demonstrate concrete applications—the two being mutually complementary. Within foundational principles, the applied number is 360; in practical applications, it becomes 252. Transition numbers signify the concealed power of Yin, whereas applied numbers express the manifest power of Yang. Heaven governs overarching patterns, while Earth manages specific implementations.

Viewed through the lens of one cosmic epoch (129,600 years), applied numbers occupy seventy percent and transition numbers thirty percent, symbolizing Yang Qi's predominance over Yin Qi. This manifests as Heaven claiming seven parts above and Earth three below, corresponding to Kan-Li (Water-Fire in the Bagua) and the Mao-You (east-west) axes, thereby forming the division between day and night. Yang Qi's encroachment upon Yin Qi resembles daylight's annexation of nighttime, aligning with the "three celestial, two terrestrial" principle (Yang number three, Yin number two).

Concretely:

• In a single day, the period from Yin hour (3-5 AM) to Xu hour (7-9 PM) constitutes applied time.
• Annually, the span from "emergence of life" (spring equinox) to "withdrawal of life" (autumn equinox) designates 90,720 years out of 129,600 as applied years.
• Daily, seventy percent (252 ke, ancient quarter-hours) is allocated to applied time.
• Seasonally, winter's three months are excluded; nocturnally, the third watch (11 PM-1 AM) remains unused.

The winter solstice, summer solstice, spring equinox, and autumn equinox evenly divide 360 degrees into 180-degree segments—midpoints of Yin-Yang waxing and waning. As Zhu Xi explained:

• From winter solstice to spring equinox, Yang Qi grows halfway—hence "division" (fen).
• From spring equinox to summer solstice, Yang Qi peaks—thus "culmination" (zhi).
• Post-summer solstice, Yang Qi declines to halfway by autumn equinox, reaching its nadir at winter solstice.

The concluding reference to "the 106-year and 9-year cycles" pertains to ancient calendrical catastrophe theory, where nine years within every 106 require special vigilance for disruptions caused by Yin-Yang disharmony.

The Tianyuan Fawei passage discusses two main themes: the cyclical patterns of floods and droughts, and different concepts of time measurement.

The first part explains disaster cycles in ancient calendrics. According to calendrical records, 19 years make a zhang (chapter), 4 zhang form a bu (section), 20 bu constitute a tong (system), and 3 tong complete a yuan (epoch) totaling 4,560 years. It mentions "yang nine" referring to nine consecutive years of drought, while "yin nine" indicates nine years of floods. Historical examples include Emperor Yao's nine-year deluge and King Tang of Shang's seven-year drought. However, the author emphasizes that during Yao and Shun's virtuous reigns, natural disasters caused minimal harm, whereas Han Dynasty calamities stemmed largely from human misrule—as the ancient saying goes: "Heaven-sent disasters may be avoided, but man-made calamities prove inescapable."

The second part distinguishes between sui (solar year) and nian (lunar year). A sui measures 365¼ days by the 24 solar terms, while a nian counts 354 days by lunar phases. Different dynasties used distinct terms for time units: the Tangyu era called it zai, the Xia sui, the Shang si, and the Zhou nian.

Finally, it cites Zhu Xi's explanation of Shao Yong's "Epochs-Cycles-Revolutions-Generations" theory: 12 hui (cycles) form a 129,600-year grand cycle. The first hui (10,800 years) sees heaven opening, the second earth forming, and the third (Tiger hour) witnessing life's emergence (kaiwu), until the eleventh (Dog hour) brings universal extinction (biwu). Like day and night, when a yuan ends, heaven and earth renew. Using diurnal metaphor, winter solstice to winter solstice completes one qi cycle—yang dominant in the first half, yin in the latter. This cyclical framework applies universally from small-scale (daily cycles) to cosmic epochs.

This passage elucidates the cyclical patterns of cosmic Yin-Yang movement. The four seasons operate like respiration—spring and summer exhale Yang Qi, while autumn and winter inhale Yin Qi, representing the circulation of a single vital energy. When Yang Qi ascends to its zenith, it naturally declines, allowing Yin Qi to emerge; when Yin Qi retreats to its nadir, Yang Qi begins its renewal. Expended Qi dissipates, manifesting this perpetual waxing and waning.

Celestial motion follows cycles: the sun completes a monthly orbit while larger cosmic rhythms unfold, never confined to a single pattern. The Qian (Heaven) and Kun (Earth) hexagrams serve as gateways to transformation, with the Fu (Return) and Gou (Encounter) hexagrams acting as pivotal hinges. From Zi hour (11 PM–1 AM), when Yang Qi first stirs, Qian's gate opens as the Zhen hexagram (Thunder), initiating growth as Qian distributes energy until Si hour (9–11 AM). At Wu hour (11 AM–1 PM), Yin Qi emerges, closing Kun's gate as the Xun hexagram (Wind), where Yin recedes and Yang expands—Kun gathers energy until Hai hour (9–11 PM). These gates alternate like paired doors: one opens as the other closes, activated by Yang Qi's arrival and sealed by its departure.

Thus, ancient sages observed: "When expansion prevails, heaven and earth teem with vitality, and flora thrives; when contraction dominates, the cosmos stagnates, and sages withdraw." Human agency determines these outcomes. Under enlightened rulers like Yao, Shun, Yu, Tang, and the Zhou kings Wen and Wu, golden ages flourished (Tang-Yu, Shang-Zhou), illuminating the world. Conversely, tyrants like Qin Shi Huang (book-burner), Shi Ke, and Zhu Wen (Five Dynasties despots) corrupted natural order, plunging existence into darkness where neither humans nor creatures could thrive. Such epochs transcend mere celestial omens—they embody cosmic collapse. Alas, words fail to capture this fully!

Supplementary note: Heaven opens at Zi hour (midnight), Earth closes at Chou hour (1–3 AM), and humanity is born at Yin hour (3–5 AM). The Big Dipper's handle aligns with these three months (Zi, Chou, Yin), each serving as calendar origins. The Three Dynasties rotated these systems: Xia used Yin month (human alignment), Shang adopted Chou month (earth alignment), and Zhou followed Zi month (heaven alignment). Yet agricultural planning demands human-centered calendars, hence Confucius praised: "I obtained the Xia calendar"—scholars identify this as texts like Xia Xiaozheng, valued for precise solar terms and farming synchronization.

Question: Why were Shang-Zhou calendar reforms less accurate than Xia's?

Answer: Though Yang Qi germinates at the winter solstice (Huangzhong pitch), and Zi month (Zhou's calendar) marks its inception, this nascent Yang remains subterranean—not yet manifesting its life-nourishing potency.

This passage examines the historical evolution of ancient calendar reforms. It explains that in antiquity, the Yin month (the first month of the lunar calendar) was originally considered the beginning of the year, as it marked the start of spring and the renewal of all living things. During the Shang and Zhou dynasties, after rulers established their authority through conquest, they began altering the designation of the first month (known as "correcting the zhengshuo") to assert the legitimacy of their new regimes, forming the "Three Systems" calendar framework.

However, the author argues that these artificial modifications to the first month designation did not align with natural rhythms: the Shang dynasty used the Chou month (lunar December) as its first month, the Zhou dynasty adopted the Zi month (lunar November), and the Qin dynasty even designated the Hai month (lunar October) as its first month. Historical records reveal that while official calendars changed the first month designation, commoners maintained the traditional sequence of months ("month numbering") beginning with the Yin month. For instance, references to the fourth and sixth months in the Book of Songs, or the Qin dynasty's renaming of the traditional twelfth month (originally Chou month) as "Jiaping," demonstrate that folk practices continued following the Xia calendar's monthly sequence.

The author particularly notes that Confucius praised the Xia dynasty calendar (which used the Yin month as its first month) precisely because it best corresponded with the cyclical patterns of the four seasons. Although the Han dynasty officially retained the Qin practice of beginning the year in the tenth month, people's daily lives still followed the convention of starting the year with the Yin month. Through numerous historical examples, this text reveals the discrepancy between official calendar systems and folk practices, as well as the tension between natural laws and political expediency.

This discussion examines the relationship between the "zhengshuo" (the calendrical starting month of the year) in ancient calendars and the division of the four seasons. Han dynasty scholars maintained that although the Xia, Shang, and Zhou dynasties altered their calendrical starting months, the sequence of months within the four seasons remained unchanged.

The text points out that Kongshi (likely Kong Anguo) mistakenly regarded the winter month of Zi (the 11th lunar month) as the beginning of spring. In reality, the first month of Mengchun (the 1st lunar month) marks spring's commencement. Counting Zi as spring would disrupt the natural order of seasons—winter cannot be spring, nor can cold be warmth, as this is self-evident.

Some cite Zheng Xuan's (Zhengshi) commentary on the Book of Songs, where he equates the late spring of the Zhou calendar (the 3rd month) with the early spring of the Xia calendar (the 1st month), another error perpetuated by Han scholars. The poem "Chen Gong" states, "In late spring, prepare new fields," when barley is about to ripen—clearly describing the 3rd Xia month (the Chen month). Zheng Xuan's interpretation is thus inaccurate. If this logic were followed, the Shang dynasty would regard late winter (the 12th month) as spring, and the Zhou dynasty mid-winter (the 11th month) as spring, completely inverting the seasons. How could this align with the sagely kings' governance principle of harmonizing with celestial timing?

Later, the text notes that although the Zhou dynasty's use of the Zi month (11th month) as the year's start conformed to heavenly patterns, Confucius still advocated the Xia calendar when discussing governance, as it better reflects the waxing and waning of Yin-Yang. Yang Qi begins to stir in the Zi month but has yet to emerge above ground; by the Yin month (1st month), the "Tai Hexagram" (三阳开泰) marks the full emergence of three Yang lines, and warm energy spreads across the land. Even in the Si month (4th month), when the "Qian Hexagram" reaches peak Yang, warmth persists. Similarly, Yin Qi first arises in the Wu month (5th month) but does not yet suppress Yang; only after the Wei month (6th month) and the "Dun Hexagram" does warmth recede. Harsh cold begins in the Shen month (7th month) and fully dissipates by the Chou month (12th month).

Shao Yong's (Kangjie) theory of the twelve cosmic cycles parallels this, proposing two perspectives on Yin-Yang's cyclical movement: fundamentally, it begins at Zi and Wu, while phenomenologically, it starts at Yin and Shen—differing by two solar terms, yet both conform to natural law.

The Tianyuan Fawei discusses the origin of the Three Powers (Heaven, Earth, and Humanity) and the waxing and waning patterns of Yin-Yang. First regarding temporal orientations: the Zi hour (midnight) marks the beginning of Heaven, the Chou hour (early dawn) signifies Earth's formation, and the Yin hour (morning twilight) witnesses the emergence of humanity. These three celestial hours represent the primordial commencement of the Three Powers, which is why the Xia, Shang, and Zhou dynasties each selected these hours to initiate their respective first lunar months.

The text references the "Twelve Sovereign Hexagrams" (shier pigua), a Daoist system where twelve specific hexagrams correspond to the monthly fluctuations of Yin-Yang throughout the year. The left progression from Zi to Si (November to April) represents six months of ascending Yang Qi. Beginning with the Fu hexagram (symbolizing thunder) from the Zhen palace, Yang energy gradually intensifies through the Lin, Tai, Dazhuang, and Guai hexagrams, culminating in the pure Yang of the Qian hexagram. Conversely, the right progression from Wu to Hai (May to October) depicts six months of growing Yin Qi. Starting with the Gou hexagram (symbolizing wind) from the Xun palace, Yin energy progressively deepens through the Dun, Pi, Guan, and Bo hexagrams, ultimately arriving at the pure Yin of the Kun hexagram.

Notably, the Zhen palace employs a single Yang line, while the Qian palace uses four Yang lines; the Xun palace initiates with one Yin line, and the Kun palace culminates with four Yin lines. This demonstrates how Yin and Yang energies begin subtly and develop slowly, yet manifest powerfully and rapidly in their later stages. The Kan (water) and Li (fire) hexagrams aren't separately listed because water and fire energies perpetually circulate between Heaven and Earth—seemingly invisible yet omnipresent.

Shao Yong (a Northern Song Confucian scholar) maintained that this cosmological system originated during Fuxi's era, reached perfection under Emperor Yao, underwent transformations during the Three Dynasties (Xia, Shang, Zhou), and peaked during the Spring and Autumn period's Five Hegemons before being severed after the Qin dynasty. Fuxi initiated civilization during the Yin hour; Emperor Yao's reign corresponded to the zenith of Yang energy (the Si month); the Three Dynasties period witnessed Yin's initial emergence (Wu month); by the Five Hegemons era, Yang energy was exhausted, and the Qin dynasty ultimately disrupted this celestial cycle. Shao Yong divided history into four phases—Imperial (huang), Thearchic (di), Kingly (wang), and Hegemonic (ba)—corresponding to four relational paradigms (father-son and ruler-minister), asserting that all cosmic flourishing and decline operates within this immutable pattern.

This passage explores the patterns of historical evolution and the cyclical nature of order and chaos. The author posits that historical development mirrors the rotation of seasons: the era of the Three Sovereigns (Sanhuang) was as pure as spring, the Five Emperors (Wudi) period flourished like summer, the age of the Three Kings (Sanwang) reached maturity akin to autumn, while the Five Hegemons (Wuba) marked a wintry decline. Subsequent dynasties follow this seasonal pattern—for instance, the early Han dynasty (Emperors Gaozu and Hui) embodied spring-like governance through Wuwei (non-action), Emperor Wen's reign exemplified summer's benevolent De (Virtue), and Emperor Wu's era reflected autumn's martial vigor.

The text introduces the theory of "celestial-terrestrial Qi (vital energy) cycles": when cosmic Qi flows southward, the world enjoys peace; when it shifts northward, chaos ensues. This alternation between order and disorder mirrors the waxing and waning of Yin-Yang—order, like Yang energy, is brief (occupying one-third of the cycle), while chaos, resembling Yin, dominates two-thirds. Using Shao Yong's "epochal cycles" (Yuanhui Yunshi) framework, the author calculates 360-year periods where the Zi-to-Mao hours (midnight to dawn) symbolize nascent Yang within Yin, heralding order, while the Wu-to-You hours (noon to dusk) signify growing Yin within Yang, foretelling turmoil.

The passage concludes with a lament: how fortunate to live in an era as harmonious as the Three Sovereigns' golden age! This historical perspective intertwines celestial Dao (the Way) with human affairs, interpreting dynastic rise and fall through the natural rhythms of Yin-Yang transformation.

This scripture elucidates the cyclical patterns governing celestial movements and dynastic rise and fall. The alternation between the Tai (Peace) and Pi (Stagnation) hexagrams from the Book of Changes mirrors the shifting fortunes between north and south. During the transition from Tai to Pi, the Gu (Decay) hexagram emerges, symbolizing how Yin energy dominates while Yang is suppressed. Conversely, the Sui (Following) hexagram appears when transitioning from Pi to Tai, marking Yang's revival and Yin's submission.

Heaven and Earth operate through two directional cycles: the Shun (forward) cycle from midnight to noon (Zi to Wu hours), corresponding to the Zhen, Li, Dui, and Qian hexagrams representing orderly governance; and the Ni (reverse) cycle from noon to midnight (Wu to Zi hours), aligned with the Xun, Kan, Gen, and Kun hexagrams signifying chaotic eras. The author employs six sexagenary cycles (360 years) as a historical unit - from the Tang to Five Dynasties period spanning three and a half cycles of mixed order and chaos, with six more cycles passing after the Qiande era of Song dynasty.

The text notes that the grand celestial cycle initiated during Emperor Yao's Jiachen year has lasted 3,660 years to present - merely equivalent to 122 double-hours (about 10 days) in cosmic timescale. Sages comprehend eternity by observing the present, just as understanding day and night reveals the principle of cyclical alternation.

The second section discusses calendrical systems: earthly phenomena follow binary foundations, generating twelve months (2×6), twenty-four solar terms (2×12), and seventy-two pentads (2×36). Early Han dynasty originally placed Jingzhe (Insects Awaken) in the first month and Yushui (Rain Water) in the second month, corrected only by late Western Han. The Lüli Zhi records: after Lichun (Spring Begins) comes Yushui in the first month; after Jingzhe comes Chunfen (Spring Equinox) in the second month. This adjustment reflected natural patterns - insects begin stirring in the first month but become fully active in the second.

This passage primarily explains the division principles of the twenty-four solar terms in ancient calendars, along with their correspondence to the waxing and waning of Yin and Yang.

The ancient Santong Calendar designated Grain Rain (Guyu) as the principal solar term of the third month and Clear and Bright (Qingming) as the secondary solar term, which differs from modern calendars that instead place Clear and Bright as the principal term and Grain Rain as the secondary one. This discrepancy stems from varying observational perspectives on the transformations of Yin and Yang across different calendrical systems. The Monthly Ordinances (Yueling), when documenting the seasonal changes across twelve months, particularly emphasizes the significance of the winter solstice (Dongzhi) and summer solstice (Xiazhi) (the "Two Extremes"), as well as the spring equinox (Chunfen) and autumn equinox (Qiufen) (the "Two Divides"). This is because the Two Extremes represent the zenith of Yin and Yang, while the Two Divides mark their convergence—making them the four most pivotal junctures among the solar terms.

The Book of Changes (Yijing) contains references such as "the Kan trigram corresponds to due north" and "the Dui trigram corresponds to mid-autumn," along with mentions that "the ancient kings closed the city gates on the solstices"—all of which implicitly incorporate the concept of solar terms. The Kan trigram aligns with the winter solstice, Dui with the autumn equinox, Zhen with the spring equinox, and Li with the summer solstice. Through the trigrams of the Yijing, one can deduce the patterns of Yin and Yang's cyclical growth and decline.

Wei Heshan elaborated: Autumn belongs to the "Yin within Yin," while spring belongs to the "Yang within Yang." Yin energy begins in the fifth month and concludes in the tenth month, making the seventh and eighth months the period of Yin's greatest intensity. Yang energy begins in the eleventh month and concludes in the fourth month, with the first and second months being the peak of Yang's dominance. Although Yin and Yang always contain traces of each other, each has its own primary and secondary phases.

Zhu Xi further clarified: The span from this year's winter solstice to the next forms a complete cycle of Yin and Yang transformation. This cycle can be divided into two halves (spring-summer as Yang, autumn-winter as Yin), or further subdivided into four seasons, twenty-four solar terms, and even seventy-two pentads (hou). The twenty-four solar terms specifically include:

• First month: Beginning of Spring (Lichun) and Rain Water (Yushui)
• Second month: Waking of Insects (Jingzhe) and Spring Equinox (Chunfen)
• Third month: Clear and Bright (Qingming) and Grain Rain (Guyu)
• Fourth month: Beginning of Summer (Lixia) and Grain Full (Xiaoman)
• Fifth month: Grain in Ear (Mangzhong) and Summer Solstice (Xiazhi)
• Sixth month: Minor Heat (Xiaoshu) and Major Heat (Dashu)
• Seventh month: Beginning of Autumn (Liqiu) and End of Heat (Chushu)
• Eighth month: White Dew (Bailu) and Autumn Equinox (Qiufen)
• Ninth month: Cold Dew (Hanlu) and Frost Descent (Shuangjiang)
• Tenth month: Beginning of Winter (Lidong) and Minor Snow (Xiaoxue)
• Eleventh month: Major Snow (Daxue) and Winter Solstice (Dongzhi)
• Twelfth month: Minor Cold (Xiaohan) and Major Cold (Dahan).

This passage elucidates the astronomical calendrical system of the twenty-four solar terms and seventy-two pentads (hou), along with their correspondences with hexagram images and the Five Phases (Wuxing).

Regarding seasonal transformations: When snow melts it becomes rainwater, descending from heaven as precipitation. The cold north wind forms snow, while the warm east wind transforms it into water. At the Awakening of Insects (Jingzhe), hibernating creatures stir from their burrows; during Grain Rain (Guyu), nourishing showers moisten the hundred grains. The Clear and Bright (Qingming) period brings purity and luminosity to all things, while Lesser Fullness (Xiaoman) marks the initial plumpness of crops. Grain in Ear (Mangzhong) is the sowing season for awn-bearing grains. Lesser Heat (Xiaoshu) and Greater Heat (Dashu) distinguish degrees of summer intensity, while the End of Heat (Chushu) signifies the retreat of scorching qi. White Dew (Bailu) arrives as yin qi intensifies and dew turns white; Cold Dew (Hanlu) follows when dew grows chilly, nearing condensation. Lesser Snow (Xiaoxue) and Greater Snow (Daxue) occur in the tenth month (smaller) and eleventh month (larger) respectively, while Lesser Cold (Xiaohan) and Greater Cold (Dahan) manifest in the twelfth month's beginning (smaller) and mid-month (larger).

Each solar term spans approximately fifteen days, further divisible into forty-eight "qi periods" of about seven and a half days each. The Rites of Zhou (Zhouli) records the ancient practice of changing timekeeping arrow shafts every eighteen days, thus forming the annual cycle of seventy-two pentads.

Concerning hexagram correspondences: The seventy-two pentads align with the sixty-four hexagrams, where each mid-term (zhongqi) corresponds to a governing hexagram. Subsequent transformations can be deduced through hexagram prognostication. The Five Phases (Wood, Fire, Earth, Metal, Water) correspond to seasonal transitions: Beginning of Spring (Lichun) belongs to Wood, Beginning of Summer (Lixia) to Fire, Beginning of Autumn (Liqiu) to Metal, and Beginning of Winter (Lidong) to Water, with Earth governing the transitions between seasons. The line changes of twelve principal hexagrams (pi hexagrams) reflect the seventy-two pentads' transformations, with each solar term's three-day preamble and aftermath corresponding to distinct hexagram shifts. For instance, the Winter Solstice (Dongzhi) in the eleventh month aligns with the first yin line of the Kan hexagram, while Lesser Cold (Xiaohan) corresponds to Kan's second yang line—these hexagram transformations mutually validate climatic characteristics.

(Note: "Houce" refers to instruments for calculating solar terms; "Weice" denotes methods for determining seasonal transitions; "gong hexagrams" and "pi hexagrams" are specific hexagram classifications; "Zhongfu," "Fu," "Zhun," etc. are names of Yi Jing hexagrams.)

In the primordial operation of the cosmos, the four seasons—spring, summer, autumn, and winter—correspond respectively to the four cardinal directions represented by the Bagua (Eight Trigrams): Qian (Heaven), Kun (Earth), Gen (Mountain), and Xun (Wind). The months of Chen, Xu, Chou, and Wei mark the periods when Earth's De (Virtue/Power) governs, while the four primary trigrams—Kan (Water), Li (Fire), Zhen (Thunder), and Dui (Marsh)—each preside over a cardinal direction.

Each line (yao) within a trigram governs two half-trigrams, two lines command five trigrams to form a month, and six lines regulate fifteen trigrams, manifesting six climatic characteristics. Three months constitute a season. Viewed holistically, the four seasons multiplied by six lines yield the twenty-four solar terms; examined in detail, each term further divides into three pentads (five-day periods), creating an impeccably ordered system.

Regarding climatic patterns, some scholars posit that in the Jia-Si year cycle, each month undergoes six transformations, totaling seventy-two changes across twelve months—termed "pentads." This interpretation holds validity. Astronomical records from the ancient Directorate of Astronomy (Sitianjian) reveal that the number seventy-two originates from the Five Phases (Wood, Fire, Earth, Metal, Water) evolutionary principle: the Yang number thirty-six doubled equals seventy-two, while the Yin number twenty-four tripled also yields seventy-two—a perfect convergence of Yin-Yang numerology.

The ancient calendrical master Wang Sijian's application of seventy-two pentads in calendar-making demonstrates extraordinary sophistication. Prolonged contemplation reveals its foundation in the line calculations of the Qian and Kun trigrams: each line of Qian represents thirty-six, two lines seventy-two, and six lines two hundred sixteen; each line of Kun represents twenty-four, three lines seventy-two, and six lines one hundred forty-four. Applied annually, this system manifests as three hundred sixty days.

Among the Qi (vital energy) of the Five Phases, Water, Wood, Fire, and Metal each govern seasons totaling two hundred eighty-eight days, leaving seventy-two days to complete the annual cycle. Earth's De supplements this deficit—allocating eighteen days per season corresponding to Chen, Xu, Chou, and Wei months, with six Earth-governed days distributed monthly, mirroring the six lines of the trigrams. Thus Earth's De permeates the entire year, with its nourishing Qi sustaining all beings monthly across seasons.

All living things between Heaven and Earth rely on this cyclical rhythm for growth, harvest, and storage—hence the term "pentad." True comprehension requires recognizing that the seventy-two pentads transcend mere Jia-Si year variations, embodying the crystallized wisdom of ancient celestial observation.

Zhang Shi's Guantreatise proposes: The four seasons and eight nodal points (such as the Beginning of Spring) each contain three pentadic transformations, calculated decimally... (subsequent content missing)

This passage from Tianyuan Fawei primarily discusses temporal divisions and phenological phenomena in ancient calendrical systems. It first explains time measurement methods: Three xun (旬, 10-day periods) form one month; nine xun constitute a season; thirty-six xun complete the annual cycle of four seasons. Five days make up one hou (候, pentad); three hou form one qi (气, 15-day solar term); nine hou compose one jie (节, 45-day node); seventy-two hou complete the celestial circuit of eight major seasonal nodes (节气).

Each season contains four months of forty days each, yet the "three-used, one-reserved" counting method was practically adopted—discarding ten days to calculate each month as thirty days, making one season three months or ninety days. The author criticizes contemporary calendar officials for merely recording phenological names without deeper investigation, emphasizing the need for thorough textual research to prevent people from using these systems without understanding their significance.

Regarding the starting point of the seventy-two hou, two theories exist: One begins with "earthworms knotting" on the winter solstice's jiazi day (following the Upper Origin calendar), while another starts with "east winds thawing ice" in the first month (per the Five Dynasties-era Ma Chongxu's revised calendar, which places the Rain Water solar term at the beginning).

Detailed phenological interpretations:

In the first month, spring winds disperse cold (east winds thaw ice); hibernating creatures stir but remain underground (dormant insects begin moving); fish ascend from deep waters toward icy surfaces (fish rise to ice); otters ceremonially arrange caught fish (otters sacrifice fish); wild geese return northward (swan geese arrive). The Tonggua Yan records pheasants calling and hens brooding at the Start of Spring, while the Rain Water solar term brings east winds stirring plant growth—signals for spring plowing.

Second-month phenomena include: peach blossoms heralding the Awakening of Insects; five days later, orioles (canggeng) begin singing—this bird bears multiple names like huangliliu or boshu (modern cuckoos, named for their "boshu"-like calls); followed by shijiu (also cuckoos). Together, these natural phenomena formed the ancient phenological calendar system guiding agricultural activities.

This scripture primarily elucidates the relationship between the transformations of Yin-Yang and natural phenomena in the seasonal cycle. In the third lunar month, eagles transform into turtledoves, only to revert back to eagles by autumn. The arrival of swallows (Xuan birds) to build nests near human dwellings during breeding season symbolizes marriage and procreation, reminiscent of the legendary birth of Qi after the Shang dynasty's Jiandi swallowed a bird's egg. Thunder results from Yang Qi bursting forth when enveloped by Yin Qi, while lightning manifests as radiant sparks when emerging Yang Qi clashes with Yin forces—when Yang energy grows strong enough, it pierces through Yin's veil to become visible.

Additional phenomena in the third month include: the blossoming of parasol trees, field mice (Yin creatures) transforming into quails (Yang creatures) under flourishing Yang energy, though they revert to rodents should Yin regain dominance. Rainbows form through the convergence of Yin and Yang Qi, vanishing when Yin completely overpowers Yang; they appear only when sunlight filters through thin clouds to illuminate raindrops. Duckweed begins to grow, turtledoves flap their wings (signaling the impending silkworm season), and hoopoe birds alight on mulberry trees, reminding women to focus on sericulture. Palace matrons lead noblewomen in mulberry-leaf gathering during mid-spring, using the month when Antares dominates the night sky to bathe silkworm eggs.

By the fourth month, mole crickets (frog-like insects) chirp in midsummer, while earthworms (Yin creatures) respond to Yang energy by surfacing. The fire-dominated phase turns snakegourds red and lends bitter herbs their characteristic taste. Delicate plants like pepperweed wither in this month of pure Yang, unable to thrive.

The fifth month brings praying mantises (also called "sickle mantises"), whose egg cases (oothecae) have regional colloquial names. Shrikes begin calling (foretelling the cold of the seventh month), while mimic thrushes—capable of imitating countless birds—fall silent. These phenomena collectively embody the cyclical waxing and waning of Yin and Yang energies in the natural world.

This scripture describes the phenological changes in nature during the transition between summer and autumn seasons, as well as the waxing and waning patterns of Yin and Yang energies.

Regarding animal behaviors: The toad's tongue grows on the side of its mouth, curling inward at the tip. There is a bird called "reverse-tongue" (or possibly referring to the toad's tongue) that begins singing in spring and gradually stops by the fifth month, producing varied calls. Deer belong to Yin creatures - when they sense Yin energy, they shed their antlers, which is why deer antler velvet is used in Chinese medicine to nourish Yin. Cicadas are also Yin creatures that begin chirping when sensing Yin energy, coinciding with the growth of Pinellia ternata (a medicinal herb), marking the peak of Yin energy and the initial emergence of Yang.

In the sixth month, warm breezes begin blowing as crickets (also called "weaving promoters") develop in the soil. Their newly formed wings cannot yet carry them far, so they cling to walls. Hawks sensing Yin energy develop hunting instincts and begin practicing combat skills. Rotten grass in the humid summer heat produces fireflies (though not through transformation, as fireflies don't revert back to rotten grass). The earth becomes moist during this period with frequent heavy rains.

When the seventh month arrives with cool winds and white dew appears, autumn cicadas (small green cicadas with red markings) begin singing. Hawks demonstrate gratitude and restraint by not eating prey immediately after capture. The world takes on an austere quality as crops ripen.

By the eighth month, wild geese arrive from the north while swallows (dark birds) begin their southern migration for winter. Various bird species start storing delicacies for winter. Dormant insects that opened their burrows during the second month's thunder begin repairing them in the eighth month when thunder ceases (partially closing entrances while weather remains warm, fully sealing them only when cold arrives in the tenth month). Waters begin drying up during this time, as the ancient saying goes: "When the Chen star appears, the rainy season ends; when the Tian'gen star appears, waters dry up completely."

This passage records natural phenomena and the principles of Yin-Yang transformation from the eighth to twelfth lunar months, using celestial signs and seasonal indicators to illustrate the waxing and waning of cosmic energies.

In the eighth month, when the Mao and Bi constellations govern the skies, rainfall predominates. The Tian'gen star appears between the Di and Fang constellations in the Chen position. By early ninth month, the Jiao constellation emerges, and Tian'gen reappears at month's end, spanning twenty-one days between its first and final appearances.

During the ninth month, migrating wild geese arrive in two waves: those arriving in mid-autumn (eighth month) as the host flock, and late-autumn (ninth month) arrivals as guests. The transformation of sparrows into clams symbolizes the shift from Yang's dynamic flight to Yin's hidden stillness. Chrysanthemums are specially noted for their yellow blooms, which burst forth precisely when Yin energy peaks—yet even when five layers of Yin accumulate, they cannot extinguish the last spark of Yang, hence the flowers' radiant display. Like eagles "sacrificing" birds in the seventh month, jackals perform ritual offerings before hunting, though beasts manifest these transformations more gradually than birds due to their greater physicality. Leaves yellow and fall as vegetation returns to its roots, while insects bow their heads in hibernation—all aligning with Heaven's timing as Yang withdraws inward.

By the tenth month, ice begins forming on water and frost hardens the earth. Pheasants transform into giant clams (shen), another manifestation of Yang converting to Yin. Rainbows disappear—visible in late spring when Yang flourishes, they vanish in early winter as Yin dominates. Now celestial Qi (Yang) ascends skyward while terrestrial Qi (Yin) sinks earthward, their separation creating winter's closed energy system.

In the eleventh month, night-calling owls (yin creatures yearning for Yang) cease their cries upon sensing Yang's first stirrings. Tigers begin mating, another Yin response to emerging Yang. The mallow plant emits fragrance upon detecting Yang's revival. Earthworms coil downward, their movement constrained yet still responding to Yang's impulse. Yin-associated elk shed antlers at winter solstice when receiving Yang's touch—mirroring how Yang-associated deer shed antlers at summer solstice. Springs show faint movement, signaling the first stirring of Yang within the Kan (Water) trigram.

The twelfth month (though not detailed here) marks the critical transition where exhausted Yin gives birth to new Yang. The preceding observations foreshadow this pivotal "return of the solitary Yang" at solstice. Through these seasonal transformations, the text vividly demonstrates the Daoist cosmological view that "Yang is born from Yin's exhaustion, and Yin arises from Yang's completion."

This passage primarily discusses ancient methods of predicting auspicious or inauspicious events and climatic changes by observing natural phenomena.

The first section explains the behavioral patterns of birds such as wild geese, magpies, and pheasants across different months. Wild geese migrate from south to north, with the earliest beginning their journey in this month and the latest not departing until the second month. Magpies, capable of foreseeing the coming year's weather, start building their nests early—some as soon as the eleventh month. Pheasants, being fire-attribute birds, sing in response to the rising Yang Qi. Domestic chickens, as wood-attribute birds, lay eggs when Yang Qi gathers. Hawks and falcons hunt with particular ferocity during this time due to the prevailing killing energy (Sha Qi). When ponds and marshes freeze thick and hard, it indicates that the cold has penetrated deep within. The ancients crafted earthen oxen (clay sculptures of oxen) to dispel the cold and prevent Yin Qi from harming the next year's harvest. Each of these seventy-two pentads (ancient divisions of the year into seventy-two natural phenomena) carries its own significance, evoking emotional responses as people observe how seasonal changes affect all living things.

The second section describes how the ancients predicted fortune by observing cloud colors. During key solar terms such as the Spring and Autumn Equinoxes, Summer and Winter Solstices, and the beginnings of each season (Start of Spring, Summer, Autumn, Winter), they recorded cloud formations and natural signs. The solstices (Summer and Winter) mark the extremes of Yin and Yang, while the equinoxes (Spring and Autumn) represent their harmonious balance. The Bao Zhang officials (ancient astronomers and calendar specialists) interpreted five cloud colors to determine omens: blue-green signaled insect plagues, white foretold mourning events, red indicated warfare and famine, black warned of floods, and yellow heralded bountiful harvests. By observing the hues of clouds near the sun, they could foresee disasters or prosperity in different regions.

The third section mentions how the ancients used the twelve musical pitches (ancient tonal system) to observe wind energy shifts across the twelve time periods (shichen), thereby assessing fortune. During the Spring and Autumn period, the Jin state’s court musician Shi Kuang played melodies representing the north and south winds to gauge the strength of the Chu army, predicting their failure. Unfortunately, this method of using musical tones to measure wind patterns has been lost to time.

This passage primarily discusses ancient Chinese understanding of the relationship between winds, seasonal nodes, and musical temperament, integrating natural phenomena with the theories of Yin-Yang and the Five Phases (Wood, Fire, Earth, Metal, Water).

Regarding wind classification, ancient scholars identified twelve winds corresponding to the twelve earthly branches' directions. Four principal winds originated from the cardinal directions: the Ming Shu wind from Zhen gua (east), the Jing wind from Li gua (south), the Chang He wind from Dui gua (west), and the Guang Mo wind from Kan gua (north). Four additional winds came from the intercardinal directions: the Tiao wind from Gen gua (northeast, also called Tiao wind during the Beginning of Spring), the Qing Ming wind from Xun gua (southeast, also called Qing Ming wind during the Beginning of Summer), the Liang wind from Kun gua (southwest, also called Liang wind during the Beginning of Autumn), and the Bu Zhou wind from Qian gua (northwest, also called Bu Zhou wind during the Beginning of Winter). Thus, the eight trigrams combined with four seasonal nodes (Beginning of Spring, Summer, Autumn, and Winter) formed the twelve-wind system.

Ancient people believed the eight winds corresponded to the eight trigrams, while the twelve winds matched the twelve musical tones. When deploying troops, they would predict battle outcomes by playing pitch pipes - the sounds indicating victory or defeat.

Zhu Xi explained that between Heaven and Earth, only one Qi circulates, its growth and transformation creating the four seasons: spring Qi during generation, summer Qi at its peak, autumn Qi during contraction, and winter Qi in retreat, cycling annually without end. Just as humaneness and righteousness resemble Yin-Yang, the four virtues (humaneness, righteousness, propriety, wisdom) parallel the four seasons, further divisible into eight seasonal nodes - all manifestations of one Qi's waxing and waning.

Regarding musical temperament and climate, Zhu Xi held that celestial Qi rises from within the earth, its ascent and descent divisible into six stages. Beginning at winter solstice, Yang Qi emerges from its deepest level, reaching full maturity by the fourth month's six Yang periods, after which Yin Qi begins growing. The twelve musical pitches could verify these climatic changes.

The Grand Maestro (ancient music official) governed six Yang pitches (Liu Lü) and six Yin pitches (Liu Tong), the former matching Yang tones, the latter Yin tones. For instance: Huangzhong pitch corresponded to Zi-position Qi (eleventh month, Zi month), aligning with the stellar mansion Xingji; Dalü to Chou-position Qi (twelfth month, Chou month), matching Xuanxiao; Taicu to Yin-position Qi (first month, Yin month), corresponding to Ju Zi; Yingzhong to Hai-position Qi, etc. These correlations embodied the ancient cosmological view integrating astronomy, calendrics, and musical temperament.

When the moon moves, the stars align with the Ximu constellation (one of the Seven Mansions of the Azure Dragon in the east), just as the Taicu pitch (a yang tone among the Twelve Pitches) corresponds to the direction of the Qian hexagram. The second yang line (九二) of the Qian hexagram pairs with the third yin line (六三) of the Kun hexagram's direction, represented by the Yingzhong pitch (a yin tone among the Twelve Pitches). In this pairing of yin and yang pitches, the yang tone always leads while the yin tone follows, establishing a pattern that persists throughout.

The text then describes the corresponding pitches for each month: the second month (建卯) aligns with Jiazhong, the ninth month (建戌) with Wuyi, while the third month (建辰) and eighth month (建酉) correspond to Guxi and Nanlü, respectively. These pitches interact with the movements of celestial mansions such as Jianglou (from the White Tiger's western mansions), Dahu (Heart Mansion), Shouxing (Horn and Neck Mansions), and Daliang (Stomach and Hairy Head Mansions). The fourth month (建巳) matches Zhonglü, the seventh month (建申) with Yize, while the fifth month (建午) and sixth month (建未) align with Ruibin and Linzhong. These four months' pitches coordinate with celestial patterns like Shichen (Three Stars Mansion), Chunshou (Well Mansion), Chunwei (Wings and Chariot Mansions), and Dahu (Heart Mansion), harmonizing the Qi of heaven and earth through stellar correspondences.

The twelve celestial cycles (i.e., the zodiac) and twelve monthly pitches regulate the Dao connecting heaven and humanity. First dispersing their Qi through the four seasons, they assist sage-kings in establishing cosmic order and the principle of harmonious balance.

Regarding the Three Systems Calendar: the Yin month (first month) represents the Human System, the Chou month (twelfth month) the Earth System, and the Zi month (eleventh month) the Heaven System. The Heaven System corresponds to the Huangzhong pitch pipe of nine inches (the yang number of the Qian hexagram), the Earth System to the Linzhong pitch pipe of six inches (the yin number of the Kun hexagram), and the Human System to the Taicu pitch pipe of eight inches (the number of the Eight Trigrams). These three pitch standards leave no fractional remainders. Linzhong occupies the Wei position (southwest), where the Qi of Huangzhong concludes. The patterns of heaven and earth begin manifesting from the Si position (southeast) and complete at Wei, with pitch standards following the yin-yang principles of nine and six. The ultimate number 81 (9×9) forms one cosmic cycle, completed in 19 years with seven intercalary months—all without fractional remainders. Thus, the sage-kings of the Three Dynasties adopted these three pitches as their calendar foundations, aligning with cosmic movements and human affairs, particularly emphasizing the Xia calendar (beginning with Yin) because harmonious human affairs naturally resonate with cosmic harmony.

Concerning the Three Palaces: Huanzhong (i.e., Jiazhong) represents the Celestial Palace, Hanzhong (i.e., Linzhong) the Earthly Palace, and Huangzhong the Human Palace. Huanzhong receives Qi from the Heart and Room Mansions—the Celestial Sovereign's Bright Hall—hence its designation as the Celestial Palace. Though fundamentally a yin tone, it follows yang pitch movements, employing four tones (excluding Wuyi, Taicu, and Guxi) for celestial sacrifices. Hanzhong receives Qi from the Wei position's Kun palace, corresponding to regions beyond the Well and Ghost Mansions where earthly deities dwell, thus named the Earthly Palace. Earth sacrifices employ four tones (Linzhong, Taicu, Dalü, and Guxi).

This scripture primarily elucidates the correspondence between ancient musical tones and the cosmic principles of Yin-Yang, as well as the specific methods of using pitch pipes to measure seasonal qi (energy) and determine time.

Regarding musical tones and rituals: The Huangzhong tone (first of the twelve pitch standards) corresponds to the Zi position in earthly branches, beneath the qi field of the Xu and Wei constellations, governing ancestral temple ceremonies. Four specific tones—Huangcu, Yingzhong, and Dalü—are employed in ancestral worship, representing the sacrificial functions of Heaven, Earth, and Humanity respectively. Each tone generates three notes—Jue (horn), Zhi (zither), and Yu (flute)—within its own tonal palace, determined through tonal classification systems.

The pitch pipe method for measuring qi: Ancient practitioners used specially crafted pitch pipes (Huangzhong pipes measuring 0.3 cun in diameter with 0.9 cun inner diameter) buried at the Zi position, nine inches below ground with openings facing south. The procedure involved burning reed membranes from Henei into ash, placing them in bamboo pipes specially made from Jinyang's Golden Gate Mountain, then burying all twelve pitch pipes in an enclosed chamber. When seasonal qi arrived, the corresponding pipe's ash would be stirred—gentle movement indicated harmonious Yin-Yang, vigorous movement foretold ruler-minister disharmony, while complete stillness symbolized tyrannical rule. During winter solstice when earthly qi peaks, the ash disperses completely. This method precisely determined solar terms, with only the corresponding pipe's ash dispersing each month.

Musical tones and Yin-Yang: The twelve pitch standards correspond to twelve months—six Yang tones from winter solstice to April, six Yin tones from summer solstice to October. Both solstices always occur mid-month, with days before winter solstice still considered Yin and those before summer solstice still Yang, matching the twelve earthly branches and twelve hexagrams.

Origins of musical tones: Legend recounts the Yellow Emperor dispatching Ling Lun westward to gather bamboo for pipes. Six Yang tones were created from male phoenix calls, six Yin tones (Lü) from female phoenix sounds. Zhu Xi held that all tones originate from Huangzhong, while the Taixuan Jing states sounds emerge from the sun and pitch pipes from celestial stems. Original pipes used bamboo before transitioning to bronze. The Huangzhong palace tone corresponds to Earth (Wu-Ji) in the Five Phases, while Taicu's shang tone matches Metal (Geng-Xin).

This passage discusses the correspondence between ancient musical tones and the cosmic principles of Heaven-Earth and Yin-Yang, with particular emphasis on the foundational importance of the Huangzhong pitch standard.

The text first explains the relationship between the six musical pitch standards (ancient tonal system) and the five notes (Gong, Shang, Jue, Zhi, Yu). The metal element and Guxian pitch correspond to the Jue note, associated with the numbers nine (Jia-Si) and the Wood phase (Jia-Yi). The Linzhong pitch matches the Zhi note, connected to the number seven (Bing-Xin) and the Fire phase (Bing-Ding). The Nanlü pitch aligns with the Yu note, relating to the number six (Ding-Ren) and the Water phase (Ren-Gui). Yingzhong serves as the variable Gong note, while Ruibin functions as the variable Zhi note. These five primary notes form the standard tones, supplemented by two variable tones to create harmonic balance. Before the Shang dynasty, only five tones were used; the Zhou dynasty later incorporated two additional tones (Wen and Wu) to form a seven-tone system.

The text then employs social hierarchy as a metaphor for musical harmony: the Shang note symbolizes ministers with defined responsibilities, the Jue note represents commoners with established occupations, and the Yu note signifies all things maintaining their proper forms—all embodying stability. In contrast, the Gong note represents the sovereign governing all affairs, while the Zhi note symbolizes adaptability to constant change. Since neither can remain fixed, the two variable tones are necessary for regulation.

Next, it describes the Yin-Yang attributes of the twelve pitch standards (complete tonal system): the Zi pitch is Yang while Chou is Yin, with six Yang pitches initiating sequences and six Yin pitches providing intervals. The Dalü pitch assists Huangzhong in dispersing Yang Qi, the Jiazhong pitch helps Taicu nurture the Qi of growing things, Zhonglü regulates central Qi to support Guxian, Linzhong aids Ruibin in governing crop growth, Nanlü assists Yize in completing all things, while Yingzhong symbolizes Yin Qi responding to Wuyi in storing creation. These pitch standards serve to observe the cosmic interplay of Heaven-Earth and Yin-Yang energies.

The passage particularly emphasizes Huangzhong as the fundamental standard: measuring exactly nine inches (each inch divided into nine parts), it represents the origin of all phenomena. Yang Qi is born at the Zi hour (midnight), which corresponds to the Huangzhong pitch. Since nine is the ultimate Yang number, the pitch standard is nine inches long. Both the Taichu calendar and the Taixuan Jing take 81 (9×9) as their numerical foundation, and similarly, all royal regulations follow this principle. As Ouyang Xiu noted, ancient pitch regulators used millet grains to establish standards of measurement: aligning grains determined length, their volume determined capacity, and their weight determined balance. All three derive from the Huangzhong standard—thus those who understand music can establish measurement systems, and conversely, measurement systems can be used to determine musical standards.

Through these correspondences between musical tones and cosmic-social order, the text illustrates how ancient systems used musical theory to comprehend and regulate universal harmony, with special focus on Huangzhong's role as the fundamental benchmark.

The Tianyuan Fawei primarily discusses the correspondence between ancient musical temperament and the yin-yang principles of heaven and earth. The ancients used the twelve pitch pipes (the ancient musical temperament system) to simulate the patterns of celestial movement. Among them, the six pitch pipes from Huangzhong to Zhonglü belong to yang, while the six from Ruibin to Yingzhong belong to yin, forming a grand yin-yang structure. Each yang pitch pipe alternates with a yin pitch pipe in their arrangement, creating smaller yin-yang relationships.

Specifically, the measurement of musical temperament takes Huangzhong as the standard: the width of one millet grain equals one fen, ten fen make one cun, ten cun make one chi, ten chi make one zhang, and ten zhang make one yin, thus establishing the five degrees (units of length). The entire system of weights and measures was constructed in this manner.

Jing Fang, a music theorist of the Han dynasty, further subdivided the twelve pitch pipes: among them, five pitch pipes (Huangzhong, Taicu, Guxian, Linzhong, and Nanlü) occupy the proper positions of yin and yang, each generating five tones, totaling twenty-five tones. Another five pitch pipes (Dalü, Jiazhong, Zhonglü, Yize, and Wuyi) are in irregular yin-yang positions, each generating three tones, totaling fifteen tones. The remaining two pitch pipes (Ruibin and Yingzhong) lie at the boundary of yin and yang, each generating four tones, totaling eight tones. Altogether, this produces sixty musical tones, corresponding to the sixty-year Jiazi cycle. Among these, seven pitch pipes govern one day each, while the remaining fifty-three combine to form a complete cycle.

This system of musical temperament can generate abundant variations: each of the twelve pitch pipes contains five notes, totaling sixty notes; these sixty notes further produce three hundred and sixty tones, corresponding to the number of days in a year. Each pitch pipe can also generate seven tones, forming eighty-four modes (musical scales). The Huainanzi records that the three hundred and sixty pitch pipes take the monthly corresponding pitch as the "mother tone" and the solar terms as the "child tones," harmonizing with the seven-tone system. This allows the performance of balanced five-note and seven-tone melodies on specific occasions such as the winter solstice. Additionally, there is a distinction between zhengsheng (standard pitch) and zisheng (derived pitch).

This theory tightly integrates musical temperament with astronomy, the calendar, and the yin-yang Five Phases, embodying the ancient worldview of "harmony between heaven and humanity." Through the mathematical relationships of musical temperament, it seeks to reveal the deeper patterns governing the movement of heaven and earth.

This passage explains the principle of matching the ancient Chinese musical system of "Twelve Pitches" with the "Five Tones." Each of the Twelve Pitches (pitch standards like Huangzhong and Dalü) can serve as the Gong (tonic note), from which the other four scale degrees are derived.

Taking the Huangzhong pitch as an example: when Huangzhong is the Gong, Taicu becomes the Shang, Guxian the Jue, Linzhong the Zhi, and Nanlü the Yu. These five tones form a complete scale system. Similarly, if Linzhong is used as the Gong, the other tones shift accordingly.

Each of the twelve pitches can rotate in this way to serve as the Gong, producing sixty possible tonal combinations (12 pitches × 5 tones). This rotational method is called "Xuangong" (pitch rotation). In this process, the generation of pitches follows the "Rule of Thirds": Yang pitches (aligned with the directions of Zi, Wu, Si, and East) use "adding one-third" (lengthening the pipe by one-third), while Yin pitches (aligned with Wu, Si, and West) use "subtracting one-third" (shortening the pipe by one-third).

For instance, a Huangzhong pipe measuring nine inches, when shortened by one-third (three inches), produces a Linzhong pipe of six inches. This method of pitch generation reflects the philosophical concept of Yin-Yang waxing and waning—long pipes generating short ones represent Yang giving birth to Yin, while short pipes generating long ones represent Yin ascending to Yang.

Note: The Twelve Pitches correspond to the twelve semitones in modern music, while the Five Tones (Gong, Shang, Jue, Zhi, Yu) roughly equate to the pentatonic scale (do, re, mi, sol, la). The "Rule of Thirds" was a crucial method for calculating pipe lengths in ancient Chinese acoustics.

This passage explains the ancient system of musical temperament generation and the principles of Yin-Yang movement. In numerical calculations for musical pitches, adding two to six yields eight cun (inches), which corresponds to the length of the Taicu pitch pipe (an ancient tuning instrument) for the first lunar month. Other pitches are derived similarly.

Using the numerical system of the Gong (宫, fundamental tone), multiplying nine by nine gives eighty-one as the Gong pitch. Subtracting one-third (twenty-seven) yields fifty-four, representing the Zhi (徵) pitch. Adding eighteen produces seventy-two for the Shang (商) pitch. Subtracting twenty-four gives forty-eight for the Yu (羽) pitch, and adding sixteen results in sixty-four for the Jue (角) pitch. These five tones are calculated through the "method of adding and subtracting thirds," all following natural patterns.

Musical pitches alternate in leftward and rightward movements, much like divination methods. From Huangzhong to Zhonglü, the generation is downward (下生, descending), signifying rising Yang Qi and receding Yin Qi. From Ruibin to Yingzhong, the generation is upward (上生, ascending), indicating rising Yin Qi and receding Yang Qi. At noon (午时), a transformation occurs, so Ruibin must regenerate upward. Scholars such as Jing Fang, Ma Rong, and Zheng Xuan all agreed with this principle, but Ban Gu argued that Ruibin should descend to generate Jiazong, which would shorten the pitch sequence and contradict the vital energy of spring growth. Zheng Xuan explained it through the rise and fall of Yang Qi, but a better analogy is divination: the Qian (乾, Heaven) hexagram moves leftward from Jia and Ren, while the Kun (坤, Earth) hexagram moves rightward from Yi and Gui. True nature follows the movement of the six Yin and six Yang lines.

Specifically, Ruibin resides in the seventh palace, ascending to generate Dalü (a Zhi pitch) and descending to generate Yize (a Shang pitch), ascending to generate Jiazong (a Yu pitch), and descending to generate Wuyi (a Jue pitch). The sixty-pitch system corresponds to the sixty hexagrams: from Huangzhong moving leftward to "Zhishi" is upward generation, while from Linzhong moving rightward to "Chishi" is downward generation. Among the sixty hexagrams, Qian moves leftward from the Zi position, and Kun moves rightward from the Wei position. Others, such as the Tun, Meng, Tai, Pi, and Xiaoguo hexagrams, each have their own left-right movement patterns. Seven hexagrams interweave in motion, and the musical pitches actually imitate this principle. Simply put, they follow the movement of Qian and Kun’s six Yang and six Yin lines: Zi, Yin, Chen, Wu, Shen, and Xu correspond to the six pitches—Huangzhong, Taicu, Guxi, Ruibin, Yize, and Wuyi—rotating leftward like Qian, called "pitch descending generation." Wei, Si, Mao, Chou, Hai, and You correspond to the six pitches—Linzhong, Nanlü, and others—rotating rightward like Kun.

This passage discusses the correspondence between ancient musical temperament and astronomical calendrics, focusing primarily on the generative principles and symbolic meanings of the twelve-tone Lü system (the ancient Chinese musical scale). Here's a modern interpretation in sections:

On the generation of musical tones:

The twelve Lü (ancient pitch standards) cycle sequentially starting from Huangzhong (Yellow Bell), with yang pitches generating yin counterparts downward and yin pitches generating yang counterparts upward. Specifically: Huangzhong generates Linzhong, which in turn generates Taicu, then producing Nanlü, and so on until Zhonglü completes the twelve tones. Subsequently, Zhonglü ascends to regenerate Huangzhong as the zhi note and descends to produce Linzhong as the shang note, creating sixty tonal variations. Nanlü occupies the terminal position in this cycle, hence referred to as "culminating at Nanlü."

Astronomical correlations:

The North Star (Polaris) appears stationary as the celestial pivot, yet actually moves slightly beyond the tip of the Dipper's handle by about one degree—a motion detectable only by skilled astronomers. The musical tones correspond to solar terms: the Zhongfu hexagram represents the seventh day after winter solstice, matching Huangzhong pitch, while actual seasonal transitions begin earlier with the "Zhishi" pitch before the solstice.

Three Powers and Seven Origins:

The Three Powers (Heaven, Earth, Humanity) correspond respectively to Huangzhong (Heaven), Linzhong (Earth), and Taicu (Humanity). The Seven Origins combine seasonal beginnings with the Three Powers: Guxian (spring), Ruibin (summer), Nanlü (autumn), and Yingzhong (winter) form the four seasonal origins, totaling seven when combined with the Three Powers. Each modal system requires two altered tones (bian-gong and bian-zhi) to complete the seven-note scale, though the "Monthly Ordinances" only records the pentatonic system.

Qian-Kun hexagrams and musical tones:

Qian hexagram's six lines correspond to six yang pitches: initial nine (Huangzhong, matching Fu hexagram), nine-two (Dalü, Lin hexagram), nine-three (Taicu, Tai hexagram), nine-four (Jiazhong, Zhuang hexagram), nine-five (Guxian, Guai hexagram), and top nine (Zhonglü, Qian hexagram). Beginning with Huangzhong's nascent yang in the eleventh month, this shows yang energy's gradual growth. Kun hexagram's lines similarly correspond to six yin pitches (not elaborated in the original text).

The initial six line of the Kun hexagram corresponds to Ruibin (one of the twelve pitch standards), symbolizing the second six line of the Gou hexagram; Linzhong corresponds to the third six line of the Dun hexagram; Yize corresponds to the fourth six line of the Pi hexagram; Nanlü corresponds to the fifth six line of the Guan hexagram; Wuyi corresponds to the top six line of the Bo hexagram; Yingzhong ultimately returns to the Kun hexagram. Beginning from Ruibin in the fifth month, when Yin qi first emerges, its downward development is called "descending generation," though it may also be termed "ascending generation."

The number eight-eight symbolizes the winds from the eight directions. Pitch standards in corresponding positions resemble marital relationships, while those in different positions resemble parent-child relationships. Thus, it is said that the Yang pitches (lü) form marital unions, while the Yin pitches (lü) give birth to offspring. The mutual generation of the twelve pitch pipes all follows the eight-eight principle, with ascending and descending generations ultimately converging at Zhonglü. The mutual generation of Yin and Yang begins from Huangzhong and rotates leftward. For example, Huangzhong generating Linzhong requires eight double-hours, as does the generation of other pitch standards. This applies the principle of "three for heaven and two for earth": three times three yields nine (Yang number), and two times three yields six (Yin number). Nine and six symbolize the Dao of Yin-Yang, marital unions, and parent-child relationships. The initial nine of Huangzhong and the initial six of Linzhong both occupy starting positions, symbolizing the marital union dwelling together. When Linzhong ascends to generate Taicu's second nine, the second position relative to the first represents the parent-child relationship in different positions. Hence, it is said that what the lü generates are marital unions dwelling together, while what the lü generates are parent-child relationships dwelling apart.

By playing the pitch pipes, one can foresee auspicious or inauspicious signs. The Grand Maestro (music official) holds the pitch pipes to listen to the army's sounds and determine fortune. Historical records of King Wu's military campaigns state: when the ruler marches to war, as soldiers form ranks and shout, the Grand Maestro blows the pitch pipes to measure the tones. If the Shang tone (western metal) is obtained, victory is certain, for metal's nature is firm; if the Jue tone (eastern wood) is obtained, morale scatters, for wood's nature is pliant and changeable; if the Gong tone (central earth) is obtained, officers and soldiers unite, for earth's nature is inclusive; if the Zhi tone (southern fire) is obtained, commanders grow impatient, for fire's nature is fierce; if the Yu tone (northern water) is obtained, military strength weakens, for water's nature is yielding. Master Kuang (musician of the Spring and Autumn period) once said: "When I played the north wind mode and then the south wind mode, I found the south wind mode lacked strength and was filled with lifeless qi, foretelling Chu's inevitable defeat." The north wind refers to pitch standards north of Jiazhong and Wuyi, while the south wind refers to those south of Guxi and Nanlü. The southern pitch standards lack sufficient qi, hence their lifelessness—all discerned through playing the pipes and listening to their sounds.

Shao Yong (Northern Song Confucian scholar) remarked: Aged wine appears bland and flavorless, while the music of heaven grows sparse. At the winter solstice, when Yang qi stirs in the position of Huangzhong's Gong, it resembles fine wine in fermentation—its true flavor lies deeply concealed.

This passage explores the fundamental nature of sound and musical tones, revealing their intrinsic connection with the cosmos. Through the perspectives of several renowned scholars, the author illustrates how sound permeates all existence.

The discussion begins with Zhou Dunyi's (Master Zhou) insight: Truly sublime music is subtle yet never excessive. Gentle melodies can pacify desires, while harmonious sounds dissolve restlessness. Take the Huangzhong pitch (the foundational tone in ancient twelve-tone temperament) as an example—it achieves natural harmony without deliberate pursuit of the five-note scale (gong, shang, jiao, zhi, yu). The author cites the story of Wan Baochang (Sui dynasty musician) who created spontaneous rhythms by tapping an earthen jar with chopsticks during meals—a natural music few contemporaries appreciated.

Su Shi (Master Su) and Ouyang Xiu (Master Ou) observe the scarcity of true connoisseurs like Nanguo Ziqi (an ancient sage who understood the "music of heaven"). While instruments may decay, the essence of sound transcends verbal expression. Why must sound be deliberately transmitted? The universe itself resonates with musical patterns—woven into celestial movements, seasonal transitions, and atmospheric phenomena. From dawn to dusk across the ages, all creatures participate in this cosmic symphony, creating natural "high mountains and flowing waters" (metaphor for spiritual resonance). Must we wait for zithers and flutes to acknowledge sound's existence?

The text then elaborates on the Yin-Yang principles governing musical tones:

Yang pitches (lü) resonate with yin modes (lǚ) to generate sounds. Sound belongs to yang lü, whose opening-closing dynamics produce infinite variations. Ten sounds correspond to ten pitch standards, aligning with the heavenly stems. Five yang sounds combine these stems, corresponding to the Qian, Dui, Li, and Zhen hexagrams in the Bagua, matching temporal units (yuan, hui, yun, shi) proposed by Shao Yong, and embodying celestial harmonies. Sounds guide tones as lü guides lǚ, with numerical distinctions between greater/smaller yang and greater/smaller firmness. Born from solar cycles and paired with stems (Jia to Gui), they connect with twelve earthly tones—totaling 160 potential sounds, though only 112 find practical use.

Yin modes (lǚ) respond to yang pitches (lü) to create tones. Tone belongs to yin lǚ, whose call-response relationship yields infinite modulations. Twelve tones match twelve modes, synchronized with earthly branches. Six yin lǚ combine these branches, corresponding to Kun, Gen, Kan, and Xun hexagrams, temporal units (year, month, day, hour), and elemental resonances. Tones harmonize with sounds as lǚ coordinates with lü, numerically distinguished by greater/smaller softness and greater/smaller yin. Born from lunar phases and paired with branches (Yin to Chou), they ascend to celestial sounds—totaling 192 potential tones, with 152 in actual practice.

The passage concludes by honoring Shao Yong's (Master Shao) theories that unveil cosmic mysteries through musical temperament, bridging classics like Taixuan and Taichu. This exemplifies China's unique tradition of correlating acoustics with universal principles.

This passage discusses two main aspects: the correspondence between musical tones and cosmological numbers, and historical anecdotes demonstrating how masters of music could foresee events through their understanding of sound.

The first part explains the relationship between musical tones and numerical systems. Ancient scholars used the odd number "three" to represent heaven. Multiplying three by three yields nine, corresponding to the Three Fundamentals (heaven, earth, and humanity) that all originate from the foundational Huangzhong pitch (the first of the twelve ancient musical tones). Shao Yong (courtesy name Kangjie), in his Supreme Principles Governing the World, employed the even number "four" to symbolize earth. Multiplying four by four produces sixteen, derived from the Book of Changes concept of the Two Modes generating the Four Images. Musical tones were categorized into young and mature yin-yang states, with sounds and pitch-pipes (ancient tonal systems) taking four as their substance and five or six as their function. Sounds themselves have substance and function: tones as substance, notes as function; pitch-pipes also distinguish substance and function: pipes as substance, musical expressions as function. The Canon of Supreme Mystery and Grand Inception Calendar designate the hours from midnight to noon (zi to si) as yang pitches, and noon to midnight (wu to hai) as yin pipes. Shao Yong's theory of innate numbers uses the ten heavenly stems as yang pitches and twelve earthly branches as yin pipes. True mastery of music requires understanding these multiplicative operations of three-by-three and four-by-four.

The second part presents stories of musical adepts: Shao Kangjie predicted a tree's felling after observing a dead branch fall at Longmen Mountain, which later came true; Eastern Han scholar Cai Yong (courtesy name Bojie) identified bamboo suitable for crafting the famed "Keting Flute" and created the "Scorched Tail Zither" from burnt tong wood; he once detected murderous intent in a neighbor's zither music while watching a mantis stalk a cicada; Sui dynasty master Wan Baochang, upon hearing music composed by Zheng Yi, foretold it as an omen of national collapse, which soon befell the Sui.

These accounts illustrate how genuine musical mastery enables anticipation of human affairs through sound, because musical principles resonate with the fundamental patterns of heaven and earth.

This passage records several remarkable instances where ancient sages predicted the future through music and sound.

The first account tells of a man named Wang Lingyan who, while lying down, heard his son playing the pipa composition "Fan'an Gongzi" outside. Suddenly overcome with alarm, he tearfully warned his son: "You must never follow the emperor to Jiangdu—the sovereign will certainly not return. This melody's gong mode (one of the ancient five tones) departs without returning, from which I know the outcome." The prediction later proved accurate.

Next, the Tang dynasty's Li Sizhen discerned ominous patterns while listening to music: the gong tone failed to summon the shang tone (symbolizing discord between ruler and ministers), while the jue and zhi tones clashed (representing suspicion between father and son). He foretold national turmoil and the crown prince's downfall—predictions fulfilled when the prince was deposed. Li even calculated his own death date and passed away as scheduled.

Pei Zhigu of the Tang dynasty, during a grand ancestral temple ceremony, heard harmonious bell and chime sounds and prophesied the Tang court's joyous event—the restoration of Emperor Zhongzong. His other predictions proved equally precise: hearing a horse's mournful whinny foretold its rider's fatal fall, while detecting certain jade ornament sounds at weddings predicted the couples' eventual separation.

Song dynasty scholar Dou Yan, a master of musical theory, accurately predicted his brothers' lifespans and fortunes by calculating the deterioration of a wooden chair. These accounts demonstrate that since Qin-Han times, many possessed sound-based divination skills, yet only the great Song Confucian Shao Yong (Master Kangjie) truly grasped its profound principles.

Shao Yong believed human nature is fundamentally still—when stillness reaches its extreme, movement arises. This movement is pure yang, untainted by emotion, resembling the primordial state of heaven and earth. The human fetus similarly mirrors cosmic beginnings, with true "initiating creation and completing affairs" beginning at birth when emotional activity emerges. Through analyzing 256 sound variations, he summarized musical principles in 264 characters—112 representing sheng (initial sounds) and 152 representing yun (rhymes)—which could combine through fanqie (traditional phonetic notation) to produce 17,024 sound permutations. Sounds were classified by four tones (level, rising, departing, entering) and five articulation points (lips, tongue, teeth, palate, throat), with further distinctions including internal/external eight rotations, open/closed, clear/muddy variations.

This passage describes ancient methods of divination through sounds and hexagram imagery. On the left, low-pitched (zhuo) tones correspond to hexagram lines, while on the right, high-pitched (qing) tones match other lines. The six lines of a hexagram are divided into two parts: the outer three lines are called "hui" (regret), and the inner three are called "zhen" (constancy). Viewed horizontally, they form two combined hexagrams known as the "Jiji Diagram" (既济图, symbolizing completion), through which auspicious or inauspicious outcomes are determined.

Master Yichuan (a Song Dynasty scholar) explained: The opening and closing variations of sounds create the four tones (平上去入) of classical Chinese phonetics. The interplay of call-and-response encompasses four articulation methods—opening, expanding, gathering, and closing. With these four tones, all possible sounds emerge; with these four articulations, all musical temperaments arise. Musical temperaments shift according to celestial phenomena, while musical modes (吕) adapt to geographical influences. Opening follows the expansion of Yang Qi, while closing aligns with the contraction of Yin Qi. High tones ascend with the vigor of strength, and low tones descend with the softness of yielding. Thus, when temperaments and modes harmonize with sounds, the five notes of the pentatonic scale (宫商角徵羽) each find their proper place.

Yang corresponds to the sun and fire; Yin to the moon and water. Strength mirrors the stars and metal, while softness reflects the planet Chen (辰星) and earth. When sun, moon, stars, and the Five Phases (Wood, Fire, Earth, Metal, Water) each occupy their rightful positions, heaven and earth operate smoothly. Eyes perceive colors, ears discern sounds, noses detect scents, and mouths distinguish flavors. When these sensory faculties function properly, the human Dao remains upright. Therefore, understanding the principles of musical temperaments and sounds enables one to properly manage the affairs of heaven, earth, and humanity. The mutual resonance of musical temperaments generates sounds, and herein lies the manifestation of the natural order governing all things in creation.

(Note: This passage reflects Daoist cosmological philosophy, which correlates musical temperaments, hexagrams, and the natural world, positing that variations in sound and hexagram imagery mirror the operating principles of the universe.)