《易數鉤深圖遺論九事》

This passage recounts two pivotal cosmological narratives from Daoist Yijing (Book of Changes) tradition:

1. The Legend of Fu Xi Receiving the River Chart

In remote antiquity during Fu Xi's reign, the mythical dragon-horse emerged from the Yellow River bearing the renowned "River Chart" (Hetu). Its numerical configuration revealed: nine above the head, one beneath the feet, three on the left and seven on the right, two and four forming the shoulders, six and eight as the legs, with five occupying the central position. Remarkably, all straight-line summations (horizontal, vertical and diagonal) equal fifteen - the origin of the Yijing's principle of "three and five producing transformations through intricate numerical patterns." Fu Xi thereby established the Five Phases (Wuxing) numerology: Yang qi begins at the winter solstice (midnight position) as the source of all growth, while Yin qi arises at summer solstice (noon position) as the foundation of contraction. Their harmonious interaction generates the myriad beings.

The River Chart numbers correspond to Five Phase theory: Heaven's one-water (Kan), Earth's two-fire (Li), Heaven's three-wood (Zhen), Earth's four-metal (Dui), and Heaven's five-earth (center) represent the generative numbers. However, solitary Yin cannot birth nor isolated Yang grow, hence completion numbers were paired: midnight with Earth's six, noon with Heaven's seven, dawn with Earth's eight, dusk with Heaven's nine, and center with Earth's ten. Thus the Eight Trigrams (Bagua) were established, later doubled to form sixty-four hexagrams with three hundred eighty-four lines - revealing the sages' profound wisdom in creating symbols to observe cosmic patterns.

2. King Wen's Evolution and Confucius' Exegesis

Millennia after Fu Xi, during the ninth year of King Zhou's tyrannical reign, the imprisoned King Wen of Zhou developed the Zhouyi system. Five centuries after King Wen's passing, Confucius emerged to deeply study the Yijing's Dao, declaring "When the River brought forth the Chart and the Luo produced the Writing, the sages took them as models" - signifying Fu Xi alone could comprehend the dragon-horse's auspicious revelation, and Confucius alone could elucidate the River Chart's mysteries. These intricate numerical patterns connect Heaven and Earth while encompassing all phenomena, containing within them celestial-human transformations and spiritual secrets.

The second section explains the sixty-four hexagrams' derivation method: The sages observed cosmic phenomena while applying the River Chart's numerical complexities - surveying celestial patterns above and terrestrial configurations below, drawing parallels from the human body nearby and all creatures afar. They established the six-line symbols to complete the triune Dao of Heaven-Earth-Humanity, ultimately employing the fourfold divination process (referring to the yarrow stalk casting procedure) to exhaustively explore the principles governing all transformations.

This scripture explains the origin and numerical principles of the Bagua (Eight Trigrams) and the mysteries of the Dayan numbers (the total count of yarrow stalks used in divination).

The Bagua evolved from the Four Symbols (Shaoyang, Laoyang, Shaoyin, and Laoyin). Specifically:

• The number for Water is 6; subtracting 3 lines (the basic trigram strokes) forms the Kan trigram (☵), while the remaining 3 lines distribute to the Hai position to form the Qian trigram (☰).
• The number for Metal is 9; subtracting 3 lines forms the Dui trigram (☱), while the remaining 6 lines distribute to the Wei position to form the Kun trigram (☷).
• The number for Fire is 7; subtracting 3 lines forms the Li trigram (☲), while the remaining 4 lines distribute to the Si position to form the Xun trigram (☴).
• The number for Wood is 8; subtracting 3 lines forms the Zhen trigram (☳), while the remaining 5 lines distribute to the Yin position to form the Gen trigram (☶).

Among the Five Phases (Wood, Fire, Earth, Metal, Water), only Metal, Wood, Water, and Fire are specifically mentioned because they govern the four seasons, while Earth permeates all seasons. The sages observed natural phenomena and used numbers and trigram lines to model the patterns of Heaven and Earth.

Regarding the Dayan numbers (the total yarrow stalks for divination):

• The total is 50 stalks, but only 49 are used (symbolizing the primordial state of chaos).
• The number 50 represents the ultimate numerical expression of Heaven and Earth, capable of calculating transformations and comprehending the spiritual realm.
• Of the 49 stalks, one is set aside unused, symbolizing the ineffable mystery of the Taiji (Supreme Ultimate, the cosmic origin).
• Through this divination method, the numerical values of the Qian and Kun trigrams (216 and 144) are determined, totaling 360, corresponding to the days of a year.

The text also lists the harmonious numerical relationships between Heaven and Earth:

• Heaven’s 4 pairs with Earth’s 9 to generate Metal.
• Heaven’s 7 pairs with Earth’s 2 to generate Fire.
• Heaven’s 5 pairs with Earth’s 10 to generate Earth.
• Heaven’s 1 pairs with Earth’s 6 to generate Water.
• Heaven’s 3 pairs with Earth’s 8 to generate Wood.

These numerical combinations are natural laws of Heaven and Earth, not human inventions. Even Fuxi (Fu Xi Shi), though born with divine wisdom, merely acted in accordance with the Dao of Heaven. Scholars throughout history have offered varying interpretations of the "Dayan numbers," but the core idea always revolves around the harmonious interplay of Yin-Yang in Heaven and Earth.

This passage primarily discusses the relationship between numbers and the generation of the Five Phases (Wuxing), as well as the principle behind the Eight Trigrams (Bagua) evolving into the sixty-four hexagrams. Here's a modern interpretation:

Regarding the generation of the Five Phases:

1. The sum of the numbers four, six, eight, and ten equals fifty-five, representing the "five positions" (the paired locations of odd and even numbers). When Yin and Yang combine, they generate the Five Phases, which in turn produce all things within the five directions.

2. For instance, Heavenly One (a Yang number) combines with Earthly Six (a Yin number) to generate Water, much like parents giving birth to children. Other numerical pairings follow the same pattern: Earthly Two with Heavenly Seven generates Fire, Heavenly Three with Earthly Eight generates Wood, Earthly Four with Heavenly Nine generates Metal, and Heavenly Five with Earthly Ten generates Earth.

3. Each numerical pairing reserves an "empty position," symbolizing the parents' hidden potential to generate the Five Phases. These Five Phases assist Heaven and Earth in producing all things—this transformation between Yin and Yang is profoundly mysterious.

4. Wood and Fire govern the flourishing of all things, while Metal and Water govern their completion. Earth has no fixed position but is distributed throughout the four seasons. As the sages said: "Essence (Jing) and Qi form material substance, while wandering spirits (Shen) produce transformations."

Regarding the evolution of the trigrams:

1. The Eight Trigrams are formed through four operations and eighteen transformations. They represent the foundation (minor completion), and their extension and expansion give rise to the sixty-four hexagrams.

2. The sixty-four hexagrams encompass the Dao of the Three Powers (Heaven, Earth, and Humanity), the origin of all things, the patterns of Yin and Yang, and the mysteries of spirits and deities. To avoid excessive complexity, let's use the Qian (Heaven) hexagram as an example of these transformations:

• Qian represents Heaven
• It transforms into Gou (Heaven-Wind)
• Dun (Heaven-Mountain)
• Pi (Heaven-Earth)
• Guan (Wind-Earth)
• Bo (Mountain-Earth)
• Jin (Fire-Earth)
• Dayou (Fire-Heaven)

These seven hexagrams all derive from transformations of the Qian hexagram.

This passage reveals the profound connections between numbers, the Five Phases, and hexagram imagery, demonstrating the ancient wisdom of using numerical reasoning to deduce cosmic patterns. The concept of the "empty position" is particularly significant, symbolizing the potential for transformation.

This scripture primarily discusses key points regarding the transformations of Yin-Yang and hexagram relationships in the Book of Changes (Yijing):

The first section explains the concepts of "wandering soul" and "returning soul":

The Book of Changes states that "the wandering soul signifies transformation," where the seventh transformation is the wandering soul and the eighth is the returning soul. The returning soul refers to reverting to the original form of the generated hexagram, with all other transformations following this pattern.

The second section explains how to distinguish Yin and Yang hexagrams:

The Qian (Heaven) hexagram symbolizes heaven and is thus called the father; the Xun (Wind), Li (Fire), and Dui (Lake) hexagrams—three Yin hexagrams—are derived from Qian.

The Kun (Earth) hexagram symbolizes earth and is thus called the mother; the Zhen (Thunder), Kan (Water), and Gen (Mountain) hexagrams—three Yang hexagrams—are generated from Kun.

In Yang hexagrams, Yin lines are more numerous (one Yang line and two Yin lines), symbolizing one ruler and two subjects (Zhen, Kan, and Gen are all Yang hexagrams).

In Yin hexagrams, Yang lines are more numerous (two Yang lines and one Yin line), symbolizing two rulers and one subject (Xun, Li, and Dui are all Yin hexagrams).

In Yang hexagrams, the single Yang line represents the ruler, while the two Yin lines represent the people—this harmonious relationship is called the "Way of the Noble One."

In Yin hexagrams, the two Yang lines represent rulers, while the single Yin line represents the people—this inverted relationship is called the "Way of the Petty Person."

The third section discusses "recovering the heart of heaven and earth":

From Fuxi’s hexagram chart, the number six appears in the Hai position, representing the place of the old Yin in the tenth month. At this time, Yin energy reaches its peak (six is the number of Yin).

The Qian and Kun hexagrams govern the transformations of Yin and Yang. The cycle of "returning in seven days" is inseparable from the nature of these two hexagrams (Qian uses the Yang number nine, Kun uses the Yin number six).

From the Zi month (eleventh month), when the first Yang emerges, to the Si month (fourth month), Qian dominates; from the Wu month (fifth month), when the first Yin emerges, to the Hai month (tenth month), Kun dominates.

Between Zi and Wu lies the number six in the Hai position, representing six days. Six is the number of old Yin, and the return of young Yang is symbolized by seven days.

Though Yin energy is at its peak in the tenth month, Yang energy already lies latent beneath it (hence the growth of the lichen plant). Similarly, when pure Yang prevails in the fourth month, Yin energy lies hidden beneath (hence the withering of the mi grass).

Kong Yingda noted that the Hai position in the tenth month spans thirty days, yet the sages did not say "returning in one month" but instead used hexagram correspondences with the six-day and seven-part divisions. This can be proven by the Jiji hexagram’s second line: "The woman loses her veil; do not pursue, it will return in seven days," where "seven days" hints at the cycle of transformation. Master Lu also stated that the alternation of Yin and Yang often follows a seven-day cycle.

By the Zi month (winter solstice in the eleventh month), the celestial wheel turns left, the earth’s axis turns right, and the interaction of Yin and Yang energies generates all things. By the next winter solstice, all things return to their origin. The "origin" is the "heart," and in terms of Yin and Yang energies, it is....

This scripture primarily discusses the transformations of Yin-Yang and the operating principles of Heaven and Earth:

1. The Ebb and Flow of Yin-Yang:

• Yang Qi reaches its zenith at the summer solstice (the Si position), while Yin Qi peaks at the winter solstice (the Hai position), representing the fundamental cyclical pattern of Yin-Yang.
• Just as day and night alternate, the waxing of Yang Qi corresponds to the waning of Yin Qi, and the resurgence of Yang leads to the retreat of Yin—an eternal process of transformation.

2. The Heart of Heaven and Earth:

• Heaven and Earth nourish all things through silent, effortless functioning, achieving growth without deliberate action.
• The sage aligns with this cosmic mind, relinquishing personal attachments to follow natural patterns.

3. Structure of the Yi Jing (Classic of Changes):

• Divided into two sections, the first part contains 30 hexagrams focused on pure Yang (beginning with Qian and Kun, representing celestial and terrestrial creation), while the latter 34 hexagrams depict Yin-Yang interactions (commencing with Xian and Heng, illustrating the way of marital union).
• The final hexagrams, Jiji (Already Across) and Weiji (Not Yet Across), employ states of completion and incompletion to warn about the principles of prosperity and decline, elucidating the proper relationship between ruler and subject.

4. Revelations for Cultivation:

• One should not forcibly seek the "Heart of Heaven and Earth," for it manifests naturally through the operation of all things.
• The genuine sage appears to practice Wuwei (non-action), yet in truth acts in perfect accordance with the Dao.

(Note: In this text, "Qi" (炁) refers to vital energy; the "Qian Zao Du" is an apocryphal Han Dynasty text attributed to Confucius; "Jiji/Weiji" are the names of the Yi Jing's final two hexagrams.)

This scripture primarily discusses two aspects: the dialectical relationship between the "Ji Ji" (Already Fording) and "Wei Ji" (Not Yet Fording) hexagrams from the Book of Changes (Yijing), and the specific method of divination using yarrow stalks.

The first part explains:

The teachings of sages remind us that when matters reach completion (Ji Ji), we must consider potential issues arising from incompleteness (Wei Ji); when matters remain unfinished, we should maintain caution, accepting the current state while awaiting the right moment. The conclusion of Ji Ji heralds the beginning of Wei Ji, much like when a fox crosses a river—Ji Ji represents the head getting wet first, while Wei Ji signifies the tail inevitably following. This cyclical continuity mirrors the ceaseless interplay of Yin-Yang in heaven and earth. Thus, when perfection is achieved, how can one not remain vigilant?

The second part details the divination method:

Regarding the number "three years," Master Lu explains this follows the pattern of Yang numbers unfolding. The Yijing's calculation method operates through hierarchical temporal units: years governing months, years governing days, months governing ten-day weeks, and days governing two-hour periods. Therefore, when referring to "days," one ce (calculation unit) represents one two-hour period; when speaking of "years," one ce equals one month. Hence "three days" and "three years" are both multiples of nine. "Seven days" combines nine with two-six, while "ten-day week" and "ten years" combine nine-six-seven-eight. Months alternate between long and short, years include intercalary months—thus when discussing "months," half of the seven-eight combination symbolizes a lunar cycle; when discussing "years," the nine-six line numbers fully represent an intercalary year. Three ten-day weeks make a month, with eight months symbolizing the extreme Yin number twenty-four; three years include one intercalary month, with intercalary days corresponding to the 384 hexagram lines. Three hundred sixty ce match the days in a year, while 384 lines correspond to accumulated intercalary days. These represent the sages' exquisite calculation methods—not arbitrary inventions—thus perfectly harmonizing with the natural rhythms of heaven-earth and Yin-Yang.

The final section describes the actual divination procedure (yarrow stalk method):

Using fifty yarrow stalks for divination, forty-nine are actually employed while one remains unused. This unused stalk holds crucial significance—it enables the entire divination process. The specific operation involves: holding the forty-nine stalks between both hands, symbolizing the undifferentiated chaos before heaven-earth separated; dividing them into two bundles representing the division of heaven and earth; taking one stalk from the left hand to place between the little finger, symbolizing the Three Powers (heaven-earth-humanity); counting the left-hand stalks in groups of four to represent the four seasons; and placing the remainder between fingers to symbolize intercalary months.

This passage explains the ancient methods of divination using yarrow stalks and the theory of musical temperament in modern terms:

Divination Section:

When ancient practitioners performed divination with yarrow stalks, they would divide 49 stalks into four portions (counting by fours), placing the remainder aside (the "hanging one"). Since there were two intercalary months every five years, this division process was repeated twice (the "double hanging"). Through three such divisions (three counting operations), a single hexagram line (yao) could be determined. After eighteen transformations (ten and eight changes), a complete hexagram would be formed.

Music Temperament Section:

The Yellow Emperor sent music master Ling Lun to the Daxia region east of Mount Kunlun to select bamboo of uniform thickness. They cut segments between the nodes to make pitch pipes. The longest pipe, Huangzhong (Yellow Bell), served as the fundamental pitch standard (the basis of temperament), capable of producing twelve tones (twelve pitches) by imitating the calls of phoenixes (six male calls and six female calls).

Rules of Temperament Generation:

• The initial Yang line of the Qian hexagram corresponds to Huangzhong, the first of the Yang pitches
• The initial Yin line of the Kun hexagram corresponds to Dalü, the first of the Yin pitches
• Calculations followed the "three heavens and two earths" method: Yang pitches used nine as base, Yin pitches used six
• Huangzhong (9) multiplied by six yields 54, corresponding to Linzhong
• Different pitches relate like mother and child (Huangzhong generates Linzhong with Dalü's assistance)
• Same pitches relate like husband and wife (Dalü must harmonize with Huangzhong to generate the six pitches)

Yin-Yang Transformations:

When Yang energy reaches the Wu-Ji direction, Huangzhong governs the fifth month (Ruibin month). At the winter solstice in the eleventh month when Yang energy first emerges, the Huangzhong pitch begins its function. When Yin energy first appears in the fifth month, the Qinggong pitch must be withdrawn to produce Zhonglü.

Finally, it mentions Jing Fang of the Han Dynasty understood the sixty-pitch generation method:

• Higher pitches generating lower ones follow "three generates two" (upper generates lower)
• Lower pitches generating higher ones follow "three generates four" (lower generates upper)
• Yang energy descends in generation, while Yin energy ascends in movement

(Note: The pitch names in parentheses refer to the ancient twelve-tone system, corresponding to modern musical scales.)

This passage explains the generative principles of the "Twelve Lü Pitch Standards" in ancient Chinese music theory, and how this system expands from twelve to sixty pitch standards. In modern terms:

The Yin-Yang generation pattern of musical pitches works as follows: Yin pitches (Lü) generate Yang pitches when ascending, while Yang pitches generate Yin pitches when descending. For instance, the Zhonglü pitch generates Zhishi when ascending, which in turn generates Qumie when descending. Through this alternating ascent and descent up to the Nanshi pitch, a total of sixty pitch standards are formed—analogous to how the Eight Trigrams (Bagua) evolve into sixty-four hexagrams.

Specific generative relationships include:

• The Huangzhong pitch (Yang) combining with Dalü (Yin) produces Linzhong
• The Taicu pitch (Yang) combining with Zhonglü (Yin) produces Nanlü
• The Linzhong pitch (Yin) combining with Ruibin (Yang) regenerates Taicu
• The Wuyi pitch (Yang) combining with Yingzhong (Yin) produces Jiazhuang

The Huangzhong pitch, measuring nine inches, serves as the foundation. Using the "Method of Adding and Subtracting a Third" (a mathematical tuning technique):

• Subtracting a third from Huangzhong (six inches) produces Linzhong
• Adding a third to Linzhong (eight inches) generates Taicu
• Each successive pitch's tube length is precisely calculated through this method

Notably, the Ruibin pitch (4.9 inches) intersects with the Qinggong tone at the Wuji position (representing central Earth in Five Phases theory), ultimately returning to Huangzhong to complete the cycle. This expansion from twelve to sixty pitch standards demonstrates the sophisticated calculations and cosmological worldview embedded in ancient Chinese music theory.

(Note: The Twelve Lü Pitch Standards formed China's ancient chromatic scale, while the "Method of Adding and Subtracting a Third" determined new pitches by increasing or decreasing tube lengths by one-third.)

This passage is from Yishu Goushen Tu Yilun Jiushi (Nine Supplementary Discussions on the Diagram of Profundity in the Numbers of the Changes), which discusses the ancient theory of correlating musical temperament with the numerical principles of the Yijing (Book of Changes). In modern terms:

It describes a rule of musical generation by mutual production. The phrase "descending to generate while extinguishing below Linzhong" refers to the generative method of the Linzhong pitch (one of the twelve ancient pitch standards)—derived from a certain tone descending in mutual production (ancient musical temperament followed the "rule of adding and subtracting a third"). However, it does not fully transition into the southern system of pitches.

"Southern affairs" refers to the southern pitch system (the ancients correlated musical pitches with cardinal directions). Here, it explains that the southern pitches emerge beside Ruibin (another pitch name). The entire passage describes how the cycle of musical generation completes a full period when it reaches the southern system.

This theory integrates music, mathematics, and cosmology, embodying the ancient concept of "harmony between heaven and humanity." Musical temperament was not merely an artistic concept but also a manifestation of the natural order of the cosmos.