Inner Twelve Months and Twelve Tones

離巽繩離目。網目謂之罟，兩目相連，結繩為之網罟也。離，雉佃也。兌、巽為魚，漁也。

The hexagram Li (Fire) says: Xun (Wind) is the rope, and Li (Fire) is the eye. The eye holes on a net are called "gu," and with two eyes connected, tying ropes together makes a net. Li is also the wild chicken, which can be hunted; Dui (Lake) and Xun (Wind) are fish, which can be caught. This is what the Great Treatise says about Fuxi making ropes into nets to hunt and fish, which is derived from the hexagram Li.

益乾金斷巽，斷木也，四之上成坎，坎為益揉之初成。震，揉木也，入坤土而巽於前，斷木為耜也。動於後，揉木為未也。

The hexagram Yi (Benefit): The metal of Qian cuts the wood of Xun, which is called 'cutting wood'; the fourth line moves upward to form Kan, which is the beginning of Yi hexagram's action of shaping wood. Zhen is the action of shaping wood, the wood is inserted into the earth of Kun, with Xun hidden in front, which is cutting the wood to make a plowshare; when it moves forward, it is shaping the wood into a plow. This is what the Great Treatise says about Shen Nong 'carving wood into a plowshare and bending wood into a plow, which is derived from the hexagram Yi'. The original text 'wei' is actually 'le'.

噬嗑眾離日在上，為日中。坤眾在下，為市眾為民。離有伏，兌為羸，具坤往之致天下之民，聚大下之貨也。以坤交乾，交易也。

The hexagram Shihhe states: The trigram Li (Fire) with the sun in the upper position signifies 'noon'; the trigram Kun (Earth) with the multitude in the lower position signifies a market, where 'multitude' refers to the people. Within Li is concealed Dui (Lake), which represents goods that can be carried, and with the multitude moving towards it, it attracts people from all over the world and gathers goods from everywhere. Using Kun to meet Qian (Heaven) signifies trade. This is what the Great Treatise says: Shennong established the market at noon, gathering the people from all over the world and collecting goods from everywhere, engaging in trade and then departing, each returning to their proper place. This is derived from the hexagram Shihhe. The original text '大下' is actually '天下'.

乾乾，坤無為，六子自用，垂衣裳而天下乾在上為衣。

The Qian hexagram: Qian remains at ease in its position, while Kun does nothing. The six subordinate hexagrams each perform their functions, thus achieving the state of "governing the world by wearing robes and keeping a simple demeanor." Qian occupies the upper position, symbolizing the upper garment.

坤坤在下為裳。裳，下體之飾也。

The sixth hexagram, K'un, is associated with the lower position, symbolizing the lower garment. The lower garment is clothing that covers the lower part of the body. Together with the previous statement, this forms what the Great Treatise says about the Yellow Emperor, Yao, and Shun: "They governed the world by simply wearing robes, which was derived from the hexagrams of Qian and K'un."

渙乾金剖巽，浮於坎上，剖木為舟也。火上銳，刻木為楫也。

The Hexagram of Dispersing: Heaven metal splits Wind wood, allowing it to float on Water. This is making a boat by hollowing out wood. The shape of fire is pointed at the top, which is making an oar by carving wood. This is what the Great Treatise says: "Hollowing out wood to make a boat, carving wood to make an oar; the usefulness of boats and oars in crossing water that is not passable, is derived from the Hexagram of Dispersing."

隨坤牛而震足，驅之服牛也。震作足馬，上六引之。引，重也。內卦近，外卦遠，上六在外卦之外，致遠也。

The hexagram "Following" states: Earth (Kun) represents the ox and Zhen represents the foot, driving it forward is like harnessing an ox cart; Zhen also represents a good-running horse, with the sixth line at the top pulling it. "Pulling" means bearing a heavy load. The inner trigram is near, the outer trigram is far, and the sixth line is outside the outer trigram, hence "reaching far away." This is what the Great Treatise says: "Harnessing oxen and riding horses, bearing heavy loads and reaching far away, benefiting the world, is derived from the hexagram 'Following.'"

豫《豫》，《謙》之反也。《謙》，艮為門，九三之四又為門，重門也。艮為手，坎為堅，震為聲，手擊堅木而有聲，擊柝也。坤為闔戶，而坎盜逼之，暴客也。

The hexagram Yu: Yu is the reverse of the hexagram Qian. In Qian, Gen represents a gate, and the line nine in the third position moves up to the fourth position to form another gate, making two gates stacked on top of each other, which is called "chong men" (double gates). Gen represents the hand, Kan represents a hard object, and Zhen represents sound; using the hand to strike a hard wooden block and produce a sound is called "ji tuo" (striking a wooden block), which is the act of beating a drum to signal the night watch. Kun represents a tightly closed gate, while the thief represented by Kan approaches forcefully, which is called "bu ke" (sudden intruders). This is what the Great Treatise says: "Chong men ji tuo, yi dai bu ke, ge qu zhu Yu."

小過兌金斷巽木，斷木為杵也。巽木入坤土，掘地為臼也。坎，陷也。臼之象，杵動於上，臼止於下，四應初，三應上，上下相應，杵、臼之利也。坎變巽股，萬民濟也。

The "Small Crossing" hexagram: The metal of the Trigram Dui cuts the wood of the Trigram Xun, which is made into a pestle; the wood of Xun is inserted into the earth of the Trigram Kun, which is dug into to make a mortar. The Trigram Kan represents a depression, which matches the image of a mortar. The pestle is above and moves, while the mortar is below and remains still; the line Six in the Fourth corresponds to Six at the Beginning, and Nine in the Third corresponds to Six at the Top, with upper and lower parts corresponding, thus forming the benefit of pestle and mortar for pounding rice. When the Trigram Kan changes to the "thigh" of the Trigram Xun, all the people receive sustenance. This is what the Great Treatise says: "Cutting wood to make a pestle, digging the earth to make a mortar, the benefit of pestle and mortar sustains the people, which is taken from the 'Small Crossing' hexagram."

睽《睽》，《家人》之反也。《家人》，巽為木，巽、離為絲，坎為弓，弦木為弓也。兌金刻木而銳之，刻木為矢也。兌庾乾剛，威天下也。

The hexagram Kui is the reverse of the hexagram Jiaoren. In Jiaoren, Xun represents wood, Xun and Li represent silk threads, and Kan represents the bow. When silk threads are strung on wood, a bow is formed. The metal of Dui sharpens the wood into an arrow. The solemnity of Dui combined with the strength of Qian is sufficient to subdue the world. This is what the Great Treatise says: "To make a bow from wood and string, to make an arrow by sharpening wood, the utility of bows and arrows to subdue the world, is derived from the hexagram Kui."

大壯《大壯》自《還》來，一變《中孚》。艮為居，兌為口穴之象。穴，居也。再變大《大畜》，乾在上，天際也，野之象。巽入變艮，而止野處也。三變《大壯》，震壯木在上，棟也。乾天在下，宇也。巽風隱，兌澤流，待風雨也。《大壯》則不橈矣。

The hexagram Great Strength comes from the hexagram Retreat, with the first change leading to the hexagram Middle Trust. The mountain (Gèn) represents stopping and dwelling, and the lake (Duì) represents the mouth, which is the image of a cave; the cave is the dwelling place. The second change leads to the hexagram Great Accumulation. Heaven (Qián) at the top represents the sky's edge, which is the image of the open field; the wind (Xùn) enters and transforms into the mountain, indicating stopping in the open field to rest. The third change leads to the hexagram Great Strength. The strong wood (Zhèn) above represents the beams, and Heaven (Qián) below represents the house; the wind (Xùn) is blocked, and the marsh (Duì) water flows away, indicating protection against wind and rain. With the hexagram Great Strength, the roof beams will not bend. This is what the Great Treatise says: "In ancient times people dwelled in caves and lived in the open fields, but later sages replaced this with houses and buildings, with beams above and eaves below, to guard against wind and rain, which is derived from the hexagram Great Strength." The original text's "return" should be "Retreat."

大過《大過》自《遯》，一變《訟》，乾見坤隱，不封也。再變巽木，而兌金毀之，不樹也。三變《鼎》，離為目，兌澤流喪也。上九變而應三，坎兌為節，不變喪期，無數也。木在澤下，中有乾人，棺槨也。葬則棺周於身，槨周於瓪棺，土周於槨，大過也。

The hexagram Great Excess comes from the hexagram Retreat. The first change produces the hexagram Strife, with Heaven appearing and Earth hidden, hence "not sealing," meaning not piling earth to form a tomb. The second change sees the Wood of Xun destroyed by the Metal of Dui, hence "not planting trees," meaning not planting trees as markers. The third change produces the hexagram Cauldron, with Li representing the eye and the water from Dui's marsh flowing out, which signifies weeping. The upper nine changes to correspond with the lower nine three, with Kan and Dui combining to form "Regulation," which remains unchanged, so the mourning period is "without number." Wood is beneath the marsh, with the figure of Heaven in the center, representing the coffin. At burial, the coffin surrounds the body, the outer case surrounds the coffin, and earth surrounds the case, layer by layer, exactly "Great Excess." This is what the Great Treatise says about ancient burial practices: "Not sealing, not planting trees, mourning without number; later sages replaced this with coffins and outer cases, taking the meaning from the hexagram Great Excess."

夬《夬》自《姤》，四變《大有》。《姤》，巽為繩，結繩也。巽變成離、坤。離為文書也。兌金刻木契也。

The hexagram Guai is derived from Guo, with the fourth line changing to Dàyǒu. In Guo, Xun represents a rope, which is "binding with ropes"; when Xun changes into Li and Kun, Li represents documents. The trigram Dui (metal) carves wood, which is "carving contracts". This is what the Great Treatise says: "In ancient times, they governed by binding with ropes; later sages replaced this with written contracts. Thus, officials could govern and people could be examined. This is taken from Guai."

一：《履》，德之基；《謙》，德之柄；《復》，德之本；《恆》，德之固；《損》，德之修；《益》，德之裕；《困》，德之辯；《井》，德之地；《巽》，德之制。

The first explanation discusses which part of virtue each of the nine trigrams represents: The trigram "Xu" (Progress) is the foundation of virtue, "Qian" (Humility) is the handle of virtue, "Fu" (Return) is the origin of virtue, "Heng" (Perseverance) is the stable place of virtue, "Sun" (Loss) is the cultivation of virtue, "Yi" (Gain) is the abundance of virtue, "Kun" (Obstruction) is the discernment of virtue, "Jing" (Well) is the dwelling place of virtue, and "Xun" (Wind) is the restraint of virtue.

二：《履》和而至；《謙》尊而光；《復》小而辨於物；《恆》雜而不厭；《損》先難而後易；《益》長裕而不設；《困》窮而通；《井》居其所而遷；《巽》稱而隱。

The second explanation discusses the characteristics of these nine trigrams: The trigram "Xu" (Progress) is harmonious and can achieve its purpose; The trigram "Qian" (Humility) is modest and thus becomes more esteemed; The trigram "Fu" (Return) arises from small beginnings and can discern things; The trigram "Heng" (Perseverance) remains steadfast even in complex situations without tiring; The trigram "Sun" (Loss) starts with difficulty but becomes easy later; The trigram "Yi" (Gain) maintains long-term abundance without artificiality; The trigram "Kun" (Obstruction) remains in hardship yet its path is clear; The trigram "Jing" (Well) does not move itself but benefits others; The trigram "Xun" (Wind) measures things and remains hidden.

三：《履》以和行；《謙》以制禮；《復》以自知；《恆》以一德；《損》以遠害；《益》以興利；《困》以寡怨；《井》以辨義；《巽》以行權。

The third explanation discusses the respective uses of these nine trigrams: using the trigram "履" (Foot) to make conduct harmonious, using "谦" (Modesty) to establish propriety, using "复" (Return) for self-examination, using "恒" (Perseverance) to maintain steadfast virtue, using "损" (Loss) to avoid calamity, using "益" (Gain) to promote benefit, using "困" (Obstruction) to reduce grievances, using "井" (Well) to discern righteousness, and using "巽" (Wind) to exercise flexibility.

上經卦三三敘而九，下經卦六三叔而十八。《履》十，《謙》十五，《復》二十四，《恆》二，《損》十一，《益》十二，《困》十七，《井》十八，《巽》二十七，九卦之數，總一百三十有六。凡三求之，四百有八也。周天三百六十成數也，餘四十八，陰陽所以進退也。陽進於《乾》，六月各四十八，《復》至《乾》也。陰退於《坤》，六月亦四十八，《娠》至《坤》也。

The upper section of the Classic contains nine trigrams arranged in groups of three, and the lower section contains eighteen trigrams arranged in six groups of three. The nine trigrams in their respective sections are: The Trigram of Progress at the tenth position, The Trigram of Humility at the fifteenth, The Trigram of Return at the twenty-fourth, The Trigram of Constancy at the second, The Trigram of Loss at the eleventh, The Trigram of Gain at the twelfth, The Trigram of Obstruction at the seventeenth, The Trigram of Well at the eighteenth, and The Trigram of Wind at the twenty-seventh. In total, there are one hundred and thirty-six trigrams. When multiplied by three, this gives four hundred and eight. The full cycle of the heavens is three hundred and sixty, and the remaining forty-eight corresponds to the movement of yin and yang. Yang advances toward the Trigram of Heaven, advancing six months, which totals forty-eight, from the Trigram of Return to the Trigram of Heaven. Yin retreats toward the Trigram of Earth, retreating six months, which also totals forty-eight, from the Trigram of Encounter to the Trigram of Earth. The original text uses 'shu' for 'xu' and 'sen' for 'gou'.

天一下生地六，地二上生天七；天三左生地八，地四右生天九。

The heavenly numbers descend to produce the earthly numbers six, and the earthly numbers two ascend to produce the heavenly number seven; the heavenly number three generates the earthly number eight to the left, and the earthly number four generates the heavenly number nine to the right. These four pairs of generating numbers and forming numbers are paired up in the up-down and left-right directions, forming the basic structure of this diagram.

參，合也。配，偶也。天地之數，各相參配，錯綜往來而相生，故生成之數大備，而天地之文生焉。《繫辭》日：參伍以變，錯綜其數，通其變，遂成天地之文。此之謂也。

"San" means to come together, and "pei" means to pair. The heavenly numbers and earthly numbers each come together and pair with each other, interweaving and combining, alternating and generating each other, so that the generated numbers and completed numbers are fully complete, and thus the cultural patterns of heaven and earth are produced. The Great Treatise says: "By combining three and five, changes occur; numbers are interwoven and combined. By comprehending these changes, the cultural patterns of heaven and earth are formed." This is exactly the meaning being explained.

男女合者，上、下經惟十二位。正位《乾》、《坤》、《坎》、《離》、《咸》、《恆》、《損》、《益》八卦，分為十八位。《乾》、《坤》變《頤》、《大過》，《頤》、《大過》變《坎》、《離》，《坎》、《離》變《中孚》、《小過》，《中孚》、《小過》變《咸》、《恆》，成人倫也。

In terms of matching male and female, there are only twelve positions in the Upper and Lower Classics. The trigrams that take the correct positions are Qian, Kun, Kan, Li, Xian, Heng, Shen, and Yi, arranged separately to form eighteen positions. Qian and Kun generate Yi and Da Guo, Yi and Da Guo generate Kan and Li, Kan and Li generate Zhong Fu and Xiao Guo, Zhong Fu and Xiao Guo generate Xian and Heng, and thus the principles of human relationships are established. This successive transformation is referred to as 'eighteen changes'.

六十四卦，一陰一陽，始《乾》終《坤》。先自《乾》、《坤》一陰一陽，排六十四，次自《乾》二陽二陰，次四陽四陰，次十六陽十六陰，次三十二陽三十二陰，即成六十四卦也。故曰一陰一陽之謂道。

The sixty-four hexagrams alternate between one yin and one yang, starting with Qian (Heaven) and ending with Kun (Earth). First, they are arranged beginning with Qian and Kun, alternating one yin and one yang until all sixty-four positions are filled. Then, starting again with Qian, they are arranged in pairs of two yangs and two yins, then in groups of four yangs and four yins, then sixteen yangs and sixteen yins, and finally thirty-two yangs and thirty-two yins. Thus, the sixty-four hexagrams are arranged. Therefore, the Great Treatise says: "To alternate one yin and one yang is called the Way."

自甲午至癸亥三十日。起申至巳。先甲。黑暈。自甲子至癸巳三十日。起寅至亥。後甲。白暈。

From the day of Jiawu to the day of Guisi, a period of thirty days, beginning at Shen and ending at Si, this section is classified as "Xian Jia," marked with a black halo on the diagram. From the day of Jiazi to the day of Guisi, another period of thirty days, beginning at Yin and ending at Hai, this section is classified as "Hou Jia," marked with a white halo on the diagram. This arrangement distributes the Hexagram Statement of "Gǔ" ("Guilt") which states "Xian Jia three days, Hou Jia three days" across the sixty Jiazi cycles.

陽卦以奇為君，故一陽而二陰，陽為君，陰為民也。陰卦以偶為君，故二陽而一陰，陰為君，陽為民也。陽，一畫為君，二畫為民，其理順，故日君子之道。陰，二畫為君，一畫為民，其理逆，故曰小人之道。

In a yang trigram, the odd number line is considered the ruler, so it is one yang line paired with two yin lines, with yang as the ruler and yin as the people. In a yin trigram, the even number line is considered the ruler, so it is two yang lines paired with one yin line, with yin as the ruler and yang as the people. In a yang trigram, the single line is the ruler and the two lines are the people, which follows the natural order, so the Great Treatise calls it "the way of the superior man." In a yin trigram, the two lines are the ruler and the single line is the people, which goes against the natural order, so it is called "the way of the inferior man."

震、坎、艮，陽卦也。曷為而多陰？自坤而索也。其卦皆一陽二陰，凡五也，故曰陽卦奇。巽、離、兌，陰卦也。曷為而多陽？自乾而來也。其卦皆一陰二陽，凡四也，故日陰卦耦。

Zhen, Kan, and Gen are yang hexagrams, yet they have more yin lines. This is because they are obtained by seeking from Kun. These three hexagrams each consist of one yang line and two yin lines, totaling five strokes. Five is an odd number, so it is said "yang hexagrams are odd." Xun, Li, and Dui are yin hexagrams, yet they have more yang lines. This is because they come from Qian. These three hexagrams each consist of one yin line and two yang lines, totaling four strokes. Four is an even number, so it is said "yin hexagrams are even."

第一揲、第二揲、第三揲。第一卦於小指間，不五則九；第二卦於中指間、第三卦於食指間，皆不四則八。

To determine one line of the divination, the process involves three steps: the first, second, and third divinations. In the first step, the remaining stalks are held between the little finger, resulting in either five or nine. In the second step, they are held between the middle finger, and in the third step, between the index finger, resulting in either four or eight each time.

五四四，此係三少，計十三策，四十九策中除十三，餘三十六，即四九之數也，是為老陽。

Three throws of the yarrow stalks resulted in five, four, and four, which constitutes a "three few" combination, totaling thirteen lines. Subtracting these thirteen lines from the forty-nine, leaves thirty-six, which is four times nine. Therefore, this line is determined to be an old yang.

九八八，此係三多，計二十五策，四十九中除二十五，餘二十四，即四六之數，是為老陰。

Three throws of the yarrow stalks resulted in nine, eight, and eight, which constitutes a group of 'three multiples,' totaling twenty-five lines. Subtracting these twenty-five lines from the total of forty-nine leaves twenty-four, which is exactly four times six. Therefore, this line is determined to be old yin.

五八八，少陽。九四八，並係兩多一少，各計二十一策，四十九中除二十一，餘二十八，即四七之數也，是為少陽。九八四，少陽。

Obtaining five, eight, and eight, it is considered a minor yang. Obtaining nine, four, and eight, it is the same as the previous case, belonging to 'two many and one few,' with each total amounting to twenty-one counts; subtracting twenty-one from forty-nine leaves twenty-eight, which is four times seven, so it is determined as minor yang. Obtaining nine, eight, and four, it is also minor yang.

九四四，少陰。五八四，並係兩少一多，各計十七策，四十九中除十七，餘三十二，即四八八之數也，是為少陽。五四八，少陰。

The numbers obtained are nine, four, and four, which belong to the category of "few yin." The numbers five, eight, and four also fall into the same "two fews and one many" category, each totaling seventeen counts. Subtracting seventeen from forty-nine leaves thirty-two, which is the product of four multiplied by eight. According to this, it should be determined as "few yin" — the original text mistakenly writes it as "few yang," and "four eight eight" should be corrected to "four eight." The numbers five, four, and eight also belong to "few yin."

以三因天地十五數，得四十五。以五因天地十五數，得七十五。以七因天地十五數，得一百五。九宮數止一百五，故百六為極數。用三、五、七者，取陽數中者用之。

By multiplying three by the number of heaven and earth, which is fifteen, we get forty-five; by multiplying five by fifteen, we get seventy-five; by multiplying seven by fifteen, we get one hundred and five. The numbers in the Nine Stars system do not exceed one hundred and five, so one hundred and six is taken as the extreme number. The reason we only use three, five, and seven for multiplication is that we are selecting several middle numbers from the yang numbers to use.

乾職生覆，坎司寒化，艮司溼化，震司動化，巽司風化，離司暑化，坤職形載，兌司燥化。

The function of Qian is to generate and cover, Kan governs the transformation of cold energy, Gen governs the transformation of dampness, Zhen governs the transformation of movement, Xun governs the transformation of wind, Li governs the transformation of heat, and Kun's function is to form and carry. This diagram arranges the eight trigrams, each responsible for a specific type of energetic transformation.

坎北，震束，乾西北，艮束北，四卦皆陽也。離南，兌西，巽束南，坤西南，四卦皆陰也。故日：方以類聚。一聚於六而分乾、坎，四聚於九而分坤、兌，二聚於七而分離、巽，三聚於八而分震、艮，故日：物以群分。得朋則吉，乖類則凶，此吉凶所以生也。

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Glossary: Northeast, Southeast, Northwest, Southwest, Due East, Due South, Due West, Due North, Great Treatise Kan is located in the north, Zhen in the east, Qian in the northwest, and Gen in the northeast; these four trigrams are all yang. Li is located in the south, Dui in the west, Xun in the southeast, and Kun in the southwest; these four trigrams are all yin. Therefore, the Great Treatise says, "Things gather by their kind." One gathers to six and distinguishes Qian and Kan, four gathers to nine and distinguishes Kun and Dui, two gathers to seven and distinguishes Li and Xun, three gathers to eight and distinguishes Zhen and Gen. Therefore, the Great Treatise says, "Things separate by their group." To associate with similar things brings good fortune, while separating from similar things brings misfortune, and thus good and bad fortune arise.

子者，乾之始，而終於巳。午者，坤之始，而終於亥。陽爻二百九十二，晝數也，其數一千七百二十八。陰爻一百九十二，夜數也，其數一千一百五十二。總而言之，二千八百八十九，四求之合，萬有一千五百二十，故日：通乎晝夜之道而始。

Zi is the beginning of Qian, and it ends at Si; Wu is the beginning of Kun, and it ends at Hai. Among the sixty-four hexagrams, there are 192 yang lines, which belong to the number of day, and their total is 1728; there are 192 yin lines, which belong to the number of night, and their total is 1152. Altogether, they total 2880. Then using four to find their combined number, it becomes 11520. Therefore, the Great Treatise says: "To understand the principle of day and night." The original text "two hundred ninety-two" should be "one hundred ninety-two," "two thousand eight hundred eighty-nine" should be "two thousand eight hundred eighty," and "while beginning" should be "while knowing."

上經三十，下經三十四。

This diagram is arranged according to the "Xu Gua" (Sequence of the Hexagrams): the Upper Classic contains thirty hexagrams, and the Lower Classic contains thirty-four hexagrams, making a total of sixty-four hexagrams.

《雜卦》者，雜揉眾卦，錯綜其義，以暢無窮之用，故其義專以剛柔、升降、反覆取義，與《序卦》不同。故韓康伯云：或以同相類，或以異相明，雜六十四卦以為義是也。

The so-called "Zage" (Miscellaneous Hexagrams) combines and blends the various hexagrams, interweaving their meanings to demonstrate infinite applications. Therefore, it focuses on aspects such as hardness and softness, rising and falling, and right and wrong. This approach differs from that of the "Xugua" (Order of Hexagrams). Hence, Han Kangbo of the Jin Dynasty said that some group similar ones together, while others contrast differing ones to illuminate each other, and by combining all sixty-four hexagrams into one meaning, this is exactly what is referred to.

一玄生三方，用三乘一。三方生九州島，用三乘三。九州島生二十七部，用三乘九。二十七部生八十一家，用三乘二十七。八十一家生二百四十三表，用三乘八十一。二百四十三表生七百二十九贊，用三乘二百四十三。七百二十九贊生二萬六千二百四十四策，用三十六乘七百二十九。凡一玄為一歲，七十二策為一日，起十一月。

Yang Xiong's "Tai Xuan" is structured in layers as follows: one "Xuan" gives rise to three "Fang," which is three times one; three "Fang" give rise to nine "Zhou," which is three times three; nine "Zhou" give rise to twenty-seven "Bu," which is three times nine; twenty-seven "Bu" give rise to eighty-one "Jia," which is three times twenty-seven; eighty-one "Jia" give rise to two hundred forty-three "Biao," which is three times eighty-one; two hundred forty-three "Biao" give rise to seven hundred twenty-nine "Zan," which is three times two hundred forty-three; seven hundred twenty-nine "Zan" give rise to twenty-six thousand two hundred forty-four "Ce," which is thirty-six times seven hundred twenty-nine. In total, one "Xuan" corresponds to one whole year, and seventy-two "Ce" correspond to one day, starting from November. The original "Jiu Zhou" refers to "Jiu Zhou," and the diagram title "Wan Xuan" refers to "Tai Xuan."

右律曆之元，始於冬至，卦氣起於《中孚》。

The diagram above indicates that the calculation of the laws and calendar begins at the winter solstice, while the卦气 (gua qi) starts from the hexagram Zhongfou.

一一：元之元，日之日，乾之乾，一。二一：會之元，月之日，兌之乾，一十二。一二：元之會，日之月，乾之兌，卜十二。二二：會之會，月之月，兌之兌，一百四十四。一三：元之運，日之星，乾之離，三百六十。二三：會之運，月之星，兌之離，四千三百二十。一四：元之世，日之辰，乾之震，四千三白二十。二四：會之世，月之辰，兌之震，五萬一千八百四十。

This diagram is from Shao Yong's "Huang Ji Jing Shi," representing the full numerical table of the interactions between the yuan, hui, yun, and shi, as well as the sun, moon, stars, and the eight trigrams. Each row first lists two position numbers, followed by the corresponding pairings of yuan, hui, yun, and shi, the pairings of the sun, moon, stars, and the eight trigrams, and finally the number for that row. The first row "yi yi" refers to yuan within yuan, day within day, and Qian within Qian, with the number being one. "Er yi" refers to yuan within hui, day within moon, and Dui within Qian, with the number being twelve. "Yi er" refers to hui within yuan, day within moon, and Qian within Dui, with the number being twelve (the original text's "bu" is a misinterpretation). "Er er" refers to hui within hui, moon within moon, and Dui within Dui, with the number being one hundred forty-four. "Yi san" refers to yun within yuan, star within day, and Li within Qian, with the number being three hundred sixty. "Er san" refers to yun within hui, star within moon, and Li within Dui, with the number being four thousand three hundred twenty. "Yi si" refers to shi within yuan, chen within day, and Zhen within Qian, with the number being four thousand three hundred twenty (the original text's "bai" is a misinterpretation of "bai"). "Er si" refers to shi within hui, chen within moon, and Zhen within Dui, with the number being five thousand one hundred eighty-four.

一五：元之歲，日之石，乾之巽，一十一萬九千六百。二五：會之歲，月之石，兌之巽，一百五十五萬五千二百。一六：元之月，日之土，乾之坎，一百五十五萬五千二百。二六：會之月，月之土，兌之坎，一千八百六十六萬二千四百。一七：元之日，日之火，乾之艮，四千六百六計五萬六千。二七：會之日，月之火，兌之艮，五萬五千九百八十七萬二千。一八：元之星，日之水，乾之坤，五萬五千九百八十七萬二千。二八：會之辰，月之水，兌之坤，六十七萬一千八百四十六萬四千。

「One Five」: The first five, the beginning in the middle of the year, the stone in the middle of the day, the wind in the middle of heaven, the number is eleven million nine thousand six hundred. 「Two Five」: The second five, the gathering in the middle of the year, the stone in the middle of the month, the wind in the middle of lake, the number is one million five hundred and fifty-five thousand two hundred. 「One Six」: The first six, the beginning in the middle of the month, the soil in the middle of the day, the water in the middle of heaven, the number is one million five hundred and fifty-five thousand two hundred. 「Two Six」: The second six, the gathering in the middle of the month, the soil in the middle of the month, the water in the middle of lake, the number is eighteen million six hundred and sixty-six thousand two hundred and forty. 「One Seven」: The first seven, the beginning in the middle of the day, the fire in the middle of the day, the mountain in the middle of heaven, the number is forty-six million six hundred and fifty-five thousand six hundred (the original text mistakenly writes 'count' instead of 'ten'). 「Two Seven」: The second seven, the gathering in the middle of the day, the fire in the middle of the month, the mountain in the middle of lake, the number is five million five hundred and ninety-eight thousand seven hundred and twenty. 「One Eight」: The first eight, the beginning in the middle of the star, the water in the middle of the day, the earth in the middle of heaven, the number is five million five hundred and ninety-eight thousand seven hundred and twenty. 「Two Eight」: The second eight, the gathering in the middle of the hour, the water in the middle of the month, the earth in the middle of lake, the number is sixty-seven million one hundred and eighty-four thousand six hundred and forty.

三一：運之元，星之離，日之乾，三百六十。四一：世之元，辰之日，震之乾，四千三百二十。三二：運之會，星之月，離之兌，四千三百二十。四二：世之會，辰之月，震之兌，八萬五千一百四十。三三：運之運，星之星，離之離，一十二萬九千六百。四三：世之運，辰之星，震之離，一百五十五萬五千二百。三四：運之世，星之辰，震之震，一百五十五萬五千二百。四四：世之世，辰之辰，震之震，一千八百八十六萬二千四百。

"The Three One": The beginning of the cycle, the day of the star, the Heaven in the Fire, the number is three hundred and sixty (the original text has a misplacement in the columns "star's Fire" and "day's Heaven"). "The Four One": The beginning of the world, the day of the hour, the Heaven in the Thunder, the number is four thousand three hundred and twenty. "The Three Two": The meeting in the cycle, the month of the star, the Lake in the Fire, the number is four thousand three hundred and twenty. "The Four Two": The meeting in the world, the month of the hour, the Lake in the Thunder, the number should be fifty-one thousand eight hundred and forty (the original text says "eighty-five thousand one hundred and forty"). "The Three Three": The cycle in the cycle, the star in the star, the Fire in the Fire, the number is one hundred twenty-nine thousand six hundred. "The Four Three": The cycle in the world, the star in the hour, the Thunder in the Fire, the number is one hundred fifty-five thousand five hundred and twenty. "The Three Four": The world in the cycle, the hour in the star, the Thunder in the Fire, the number is one hundred fifty-five thousand five hundred and twenty (the original text says "Thunder's Thunder" but should be "Fire's Thunder"). "The Four Four": The world in the world, the hour in the hour, the Thunder in the Thunder, the number should be one million eight hundred and sixty-six thousand two hundred and forty.

三五：運之歲，星之石，離之巽，四千六百六十五萬六千。四五：世之歲，辰之石，震之巽，五萬九千九百八十七萬二千。三六：運之月，星之土，離之坎，五萬五千九百八十七萬二千。四六：世之月，辰之土，震之坎，六十萬一千八百四十六萬四千。三七：運之日，皋之火，離之艮，一百六十七萬九千六百一十六萬。四七：世之日，辰之火，震之艮，二千一十五萬五千三百九十二萬。三八：運之辰，星之水，離之坤，二千一十五萬五千三百九十二萬。四八：世之辰，辰之水，農之坤，二萬四千一百八十六萬四千七百四萬。

"Three and five": In the cycle of years, among the stars, in the fire trigram, the number is forty-six million six hundred and fifty-six thousand six hundred. "Four and five": In the cycle of years, among the celestial stems, in the thunder trigram, the number should be fifty-five million nine hundred and eighty-seven thousand two hundred. "Three and six": In the cycle of months, among the earthly branches, in the water trigram, the number is fifty-five million nine hundred and eighty-seven thousand two hundred. "Four and six": In the cycle of months, among the earthly branches, in the water trigram, the number should be sixty-seven million one hundred and eighty-four thousand six hundred and forty. "Three and seven": In the cycle of days, among the stars, in the mountain trigram, the number is one hundred and sixty-seven million nine hundred and sixty-one thousand six hundred. "Four and seven": In the cycle of days, among the celestial stems, in the mountain trigram, the number is twenty million one hundred and fifteen thousand five hundred and thirty-nine thousand two hundred. "Three and eight": In the cycle of days, among the stars, in the earth trigram, the number is twenty million one hundred and fifteen thousand five hundred and thirty-nine thousand two hundred. "Four and eight": In the cycle of days, among the earthly branches, in the earth trigram, the number is twenty-four million one hundred and eighty-six thousand four hundred and seventy thousand four hundred.

五一：歲之元，石之日，巽之乾，一十二萬九千六百。六一：月之元，土之日，坎之乾，一百五十五萬五千二百。五二：歲之會，石之月，巽之兌，一百五十五萬五千二百。六二：月之會，土之月，坎之兌，一千八百六十六萬二千四百。五三：歲之運，石之星，巽之離，四千六百六十五萬六千。六三：月之運，土之星，坎之離，五萬五千九百八百八十七萬二千。五四：歲之世，石之辰，巽之震，五萬五千九百八十七萬二千。六四：月之世，土之辰，坎之震，六十七萬一千八百四十六萬四千。

"Five One": The beginning of the year, the day in stone, the乾 in wind, the number is twelve million nine thousand six hundred. "Six One": The beginning of the month, the day in earth, the乾 in water, the number is one million five hundred fifty-five thousand two hundred. "Five Two": The meeting of the year, the month in stone, the兑 in wind, the number is one million five hundred fifty-five thousand two hundred. "Six Two": The meeting of the month, the month in earth, the兑 in water, the number is eighteen million six hundred sixty-six thousand two hundred forty. "Five Three": The movement of the year, the star in stone, the离 in wind, the number is four million six hundred sixty-five thousand six hundred. "Six Three": The movement of the month, the star in earth, the离 in water, the number is five million five hundred ninety-eight thousand seven hundred twenty (the original text has an addition of 'eight hundred' characters). "Five Four": The era of the year, the hour in stone, the震 in wind, the number is five million five hundred ninety-eight thousand seven hundred twenty. "Six Four": The era of the month, the hour in earth, the震 in water, the number is sixty-seven million one hundred eighty-four thousand six hundred forty.

五五：歲之歲，石之石，巽之巽，一百六十七萬九千六百一十六萬。六五：月之歲，土之石，坎之巽，二千一十五萬五千三百九十二萬。五六：歲之月，石之土，巽之坎，二千一十五萬五千三百九十二萬。六六：月之月，土之土，坎之坎，二萬四千一百八十六萬四千七百四萬。五七：歲之日，石之火，巽之艮，六萬四百六十六萬一千七百六十萬。六七：月之日，土之火，坎之艮，七十二萬五千五百九十四萬一千一百二十萬。五八：歲之辰，石之水，巽之坤，七十二萬五千五百九十四萬一千一百二十萬。六八：月之辰，土之水，坎之坤，八百七十萬七千一百二十九萬三千四百四十萬。

"Five-Five": Within the year within the year, stone within stone, wind within wind, the number is one hundred sixty-seven million nine thousand six hundred sixteen thousand. "Six-Five": Within the month within the year, earth within stone, water within wind, the number is twenty million fifteen thousand five hundred thirty-nine thousand two hundred. "Five-Six": Within the year within the month, stone within earth, wind within water, the number is twenty million fifteen thousand five hundred thirty-nine thousand two hundred. "Six-Six": Within the month within the month, earth within earth, water within water, the number is two million four hundred eighteen thousand six thousand four hundred seventy-four thousand. "Five-Seven": Within the year within the day, stone within fire, wind within mountain, the number is six million forty-six thousand six hundred seventeen thousand six hundred. "Six-Seven": Within the month within the day, earth within fire, water within mountain, the number is seventy-two million five hundred fifty-nine thousand four hundred eleven thousand two hundred. "Five-Eight": Within the year within the hour, stone within water, wind within earth, the number is seventy-two million five hundred fifty-nine thousand four hundred eleven thousand two hundred. "Six-Eight": Within the month within the hour, earth within water, water within earth, the number is eight hundred seventy million seven hundred twenty-nine thousand three hundred forty-four thousand.

七一：日之元，火之日，艮之乾，四千六百六十五萬六千。八一：辰之元，水之口，坤之乾，五萬五千九百八十七萬三千。七二：日之會，火之月，艮之兌，五萬五千九百八十七萬二千。八二：辰之會，水之月，坤之兌，六千七萬一千八百四十六萬四千。七三：日之運，火之星，艮之離，一百六十七萬九千六百一十六萬。八三：辰之運，水之星，坤之離，一千一十五萬五千三百九十二萬。七四：日之世，火之辰，艮之震，一千一十五萬五千三百九十二萬。八四：辰之世，水之辰，坤之震，二萬四千一百八十六萬四千七百四萬。

「Seven One」: The origin in the middle of the day, the day in the fire, the dry earth in the mountain, the number is four million six hundred and sixty-five thousand six hundred. 「Eight One」: The origin in the middle of the morning, the day in the water, the earth in the mountain, the number should be five million five hundred and ninety-eight thousand seven hundred and twenty. (The original text mistakenly wrote 「mouth」 instead of 「day」, and the ending 「three thousand」 should be 「two thousand」.) 「Seven Two」: The gathering in the middle of the day, the month in the fire, the mountain in the lake, the number is five million five hundred and ninety-eight thousand seven hundred and twenty. 「Eight Two」: The gathering in the middle of the morning, the month in the water, the earth in the lake, the number should be sixty-seven million one hundred and eighty-four thousand six hundred and forty. (The original text mistakenly wrote 「six million seven thousand」.) 「Seven Three」: The movement in the middle of the day, the star in the fire, the mountain in the fire, the number is one hundred and sixty-seven million nine thousand six hundred and sixteen. 「Eight Three」: The movement in the middle of the morning, the star in the water, the earth in the fire, the number should be twenty million one hundred and fifteen thousand five hundred and thirty-nine hundred and twenty. 「Seven Four」: The era in the middle of the day, the time in the fire, the mountain in the thunder, the number should be twenty million one hundred and fifteen thousand five hundred and thirty-nine hundred and twenty. 「Eight Four」: The era in the middle of the morning, the time in the water, the earth in the thunder, the number is two million four hundred and eighteen thousand six hundred and forty-seven hundred and four.

七五：日之歲，火之石，艮之巽，六萬四百六十六萬一千七百六十萬。八五：辰之歲，水之石，坤之巽，七十二萬五千五百九十四萬一千一百二十萬。七六：日之月，火之土，艮之坎，七十二萬五千五百九十四萬一千一百二十萬。八六：辰之月，水之土，坤之坎，八百七十萬七千一百二十九萬三千四百四十萬。七七：日之日，火之火，艮之艮，二百一十七萬六千七百八十二萬三千五百。八七：辰之日，水之火，坤之艮，二千六百一十一萬千三百八十八萬二千。七八：日之辰，火之水，艮之坤，二千六百一十一萬一千三百八十八萬二千。八八：辰之辰，水之水，坤之坤，三萬一千三百四十五萬六千六百五十八萬四千。

"75": In the middle of the day, stone in fire, mountain in wind, the number is six million and four hundred sixty-six thousand one hundred seventy-six thousand. "85": In the middle of the morning, stone in water, earth in wind, the number is seventy-two million five thousand five hundred ninety-four thousand one hundred twenty thousand. "76": In the middle of the month, earth in fire, mountain in water, the number is seventy-two million five thousand five hundred ninety-four thousand one hundred twenty thousand. "86": In the middle of the month, earth in water, earth in water, the number is eight hundred seventy million seven hundred twenty-nine thousand three thousand four hundred forty thousand. "77": In the middle of the day, fire in fire, mountain in mountain, the number is two hundred seventeen million six thousand seven hundred eighty-two thousand three thousand five hundred. "87": In the middle of the day, fire in water, earth in mountain, the number is twenty-six million one hundred eleven thousand one hundred thirty-eight thousand eight hundred twenty thousand (the original text lacks one 'one' character). "78": In the middle of the day, water in fire, mountain in earth, the number is twenty-six million one hundred eleven thousand one hundred thirty-eight thousand eight hundred twenty thousand. "88": In the middle of the day, water in water, earth in earth, the number is three million one hundred thirty-five thousand six hundred fifty-eight thousand four hundred. The entire table ends here, with eight columns both horizontally and vertically, making a total of sixty-four sections, exactly matching the sixty-four hexagrams.