Yao Xiang Twelfth

爻分於卦，卦之象即爻之象。卦由爻變，爻之象亦卦之變象也。《說卦》廣象，半為卦變言之。名隸於卦，而重實在爻。六十四卦，《彖》、《象》要皆以象之交易變易反易而互變其義，以定其辭。變之所在，即象之所在。所謂“辭也者，各指其所之”是也。

Yao comes from the division of a hexagram, so the image of the hexagram is the image of Yao; a hexagram is formed by the movement of Yao, so the image of Yao is also the image after the change of the hexagram. The large number of "broad images" presented in the "Commentary on the Changes" are half about the changing of hexagrams. Although they are nominally attributed to hexagrams, their actual content lies in Yao. The "Commentary on the Judgment" and "Image Commentary" of the sixty-four hexagrams are mostly based on the transformation, change, and reversal of images to derive their meanings and determine the words of the hexagram and its lines. Where there is change, there is also the image — this is exactly what the "Great Treatise" means when it says, "Words are each directed to their destination."

變不同，象亦不同。或一爻變，或二爻變，或三爻變。三爻變者，則為對象。以一卦全變，本體之象已不見，所謂伏也。若二爻或一爻變，則變其半而存其半，京氏所以有半象之說也。

The way of change differs, resulting in different images: there are cases of one line changing, two lines changing, or three lines changing. When all three lines change, the inner trigram or outer trigram becomes its opposite trigram, forming the "opposite image." If all six lines of a hexagram change, the original image disappears entirely, which is called "concealed." As for cases where only two lines or only one line change, this represents changing half and retaining half, which is the origin of Jing Fang's concept of "half image."

向來講《易》者莫明京氏半象之義，往往置之不論。焦理堂氏《易通釋》宗虞仲翔氏之說者也，乃駁其半象，不遺餘力。謂“坎之半即巽之半，坤之半即艮之半”云云，而不知京說之正謂“坎半即巽半，坤半即艮半”耳。孔子《雜卦》，“震起艮止，巽伏兌見”，即發明離坎變化，乃震艮巽兌起止伏見之作用。《虞注》：“小畜密雲不雨，謂坎象半見。”即指巽為坎之半耳。

Those who have explained the Yi Jing throughout history have failed to understand Jing Fang's concept of 'half-figures'. They often set it aside without discussion. Jiao Xun, known as Li Tang, in his work Yi Tong Shi, originally followed Yu Fan, known as Zhong Xiang, but he vigorously refuted the idea of half-figures, saying 'half of Kan is half of Xun, and half of Kun is half of Gen' — but he did not realize that Jing Fang's view was precisely 'half of Kan is half of Xun, and half of Kun is half of Gen'. Confucius in the Zage Zhuan said 'Zhen signifies movement; Gen signifies stillness', 'Xun signifies concealment; Dui signifies revelation', which is explaining the transformation of Li and Kan, and applying it to the four functions of Zhen, Gen, Xun, and Dui: movement, stillness, concealment, and revelation. Yu Fan's commentary on the Xiao Xu hexagram 'dense clouds without rain' refers to 'half of Kan being visible', meaning Xun is half of Kan.

惟半象二字，在可解不可解之間。與其謂之半象，不如名之曰爻象為簡當而易曉也。一卦六爻，本有風雷山澤水火之爻位。與八卦之正位，有其位即有其象。故僅知卦象，而不明爻象，仍未能盡象義之蘊也。

The term "half-trigram" is ambiguous, lying between something that can be explained and something that cannot. Instead of calling it "half-trigram," it would be more concise and clear to refer to it as "yao-xiang" (line image). A hexagram consists of six lines, each originally representing wind, thunder, mountain, marsh, water, and fire respectively. Combined with the proper positions of the eight trigrams mentioned earlier, each position corresponds to a specific image. Therefore, understanding only the hexagram image without grasping the line images fails to fully explain the meaning of the images.

爻象有正變之分，亦與卦同。如本卦不變，而分爻取象者，則以其位之上下而象異。如震為足，正象也，爻分震之初則為趾。乾為首，正象也，爻分乾之上則為顛，為額，或為項。而六子分乾坤之爻者，亦得推此義以取象。如艮為乾之上爻，亦有首之象。離得坤之中爻，亦取腹象。此不變之變，即廣象之義也。

The lines of a hexagram also have distinctions of 'correct' and 'changed' images, just like the hexagrams themselves. For example, if the primary hexagram remains unchanged, but each line is taken separately to form images, then the images will vary according to the position of the lines: Zhen represents the foot, which is the correct image, but when taken from the first line of Zhen, it becomes 'toe'; Qian represents the head, which is the correct image, but when taken from the top line of Qian, it becomes 'top of the head', or 'forehead', or 'neck'. Similarly, the six sons of the hexagram, having taken the lines of Qian and Kun, can also take images in this way: for instance, Gen is formed from the top line of Qian, and thus carries the image of 'head'; Li is formed from the middle line of Kun, and thus can take the image of 'abdomen'. This is the case where the primary hexagram remains unchanged, yet the image changes. This is exactly the purpose of the "Broad Images" discussed in the "Discourse on Hexagrams".

其因本卦已變，而爻即隨其變而易其象，則必以其時其位之不同，而各異其義，即各異其象。如離為目，正象也，因變巽而為多白眼。艮為山，正象也，因反為震，而變為陵。巽為雞，正象也，因反為兌，而稱鶴。其餘變化，各以類求，未可指數也。一卦六爻，初爻為足為趾；二爻為脛，為股；三四為心，為腹；上五為首，為面。比例甚多，更論爻而不論卦，可謂專以爻位取象，為爻象之本義矣。

When the primary hexagram has changed, its lines also change their images accordingly. Therefore, the meanings and images vary according to the time and position. For example, the trigram Li represents the eye, which is the standard image. But when it changes to Xun, it becomes 'many white eyes'. The trigram Gen represents a mountain, which is the standard image. But when it is reversed to Zhen, it becomes 'a hill'. Similarly, the trigram Xun represents a chicken, which is the standard image. But when it is reversed to Dui, it becomes 'a crane'. Other changes should be examined according to their categories, and there are too many to list. Regarding the human body as an image, the six lines of a hexagram correspond to different body parts: the first line corresponds to the foot and toes; the second line corresponds to the calf and thigh; the third and fourth lines correspond to the heart and abdomen; the top line and fifth line correspond to the head and face. These correspondences are numerous, and they focus solely on the lines rather than the hexagram itself. This is the true meaning of 'yao xiang' (line images).

六位成章，陰陽迭運。位虛爻實，奇偶相生。積爻成卦，數亦相因。復一坎子，震未出用，故曰“復小”。臨二丑寅，坤兌數十，故曰“臨大”。陰爻無始，陽爻無終。陰陽首尾，往復不窮。故數盡十位，而爻十二。天五地六，以定甲子。八宮六世，三四相重。飛伏隱見，變化無盡，而無不可以數稽之。故爻位與象義既明，必征之於數，而後是非可辨也。

Six yao positions are arranged in order, with yin and yang alternating. The positions are empty, while the yao are actual. Odd and even numbers generate each other. Yao accumulate to form a hexagram, and numbers arise accordingly. The hexagram "Fu" is at the Zi position, paired with the number one, belonging to Kan; at this time, the yang line of Zhen has just begun to arise but has not yet fully activated, so the "Zajiaguanzhuan" says, "Fu, small but discerning in things." The hexagram "Lin" is at the Chou and Yin positions, paired with the number two; Kun and Dui combine, and the number reaches ten, so it is said, "Lin, great." Yin yao has no beginning, yang yao has no end; yin and yang connect head to tail, alternating endlessly. Therefore, numbers only go up to ten, but yao have twelve (Kun and Qian each have six). The heavenly number five and the earthly number six are paired to establish the sixty Jiazi. Each of the eight palaces has six generations; the third and fourth lines alternate, with flying and hidden lines appearing and disappearing, changes are endless, yet nothing is beyond the scope of numbers. Therefore, after the yao positions and symbolic meanings are understood, numbers must be used for verification, so that right and wrong can be clearly discerned.

陰陽六爻，皆指乾坤。乾父坤母，六子卦皆分乾坤之爻，各得乾坤之一體。象數變化，皆不離其宗。鄭氏爻辰，即以乾坤兩卦，分十二辰。鍾度聲律，亦各以此數交錯，相生相合，而各得其應得之數。《節·彖傳》曰：“節以制度。君子以制度數，議德行。”若由後儒之說，德行與度數何涉？

Yin and Yang and the six lines of divination all ultimately point to the trigrams Qian and Kun. Qian represents the father and Kun the mother, and the six subsidiary trigrams are each derived by taking lines from Qian and Kun, each receiving a part of Qian and Kun. All the variations of images and numbers depend on this fundamental principle. Zheng Xuan's "Yao Chen" takes the twelve lines of Qian and Kun and assigns them to the twelve earthly branches. The measurements of the bells and the five tones and six laws also follow this system, interweaving and combining with each other, each receiving its proper number. The "Commentary on the Judgment" of the "Jie" hexagram says "Jie is about establishing rules and measures," and the "Great Image Commentary" says "the gentleman establishes numbers and measures, discusses virtue and conduct." If we follow the interpretations of later Confucian scholars, how can virtue and measures be related to each other?

宋人性理諸書，汗牛充棟，所謂表裡精粗無不到者，獨無度數以節之。陰陽五行，皆鑿空之談。而所謂異端者，若老子若墨子若莊列諸子，及釋家大乘經典，其言之精者，各有數度，各有法象之可征。皆所謂法言，非任意空談可擬也。故明乎八卦之象數，明乎《彖》、《象》十翼無一辭一字之不合象數，而後三代兩漢文章之度數可辨。後世之書是否合於度數者，亦皆可辨矣。

Sung dynasty writings on nature and principles are numerous, claiming to cover all aspects thoroughly, yet they lack numerical measures to restrain them. When discussing yin and yang and the Five Phases, they all make up theories out of nowhere. In contrast, those criticized by them as heretical schools, such as Laozi, Mozi, Zhuangzi, Liezi, and the Mahayana scriptures of Buddhism, contain precise statements, each with numbers, measures, and methods that can be verified, belonging to regulated speech, which cannot be compared to mere idle talk. Therefore, only by first understanding the images and numbers of the Eight Trigrams, and realizing that every word and sentence in the Commentary on the Judgment, the Image Commentary, and the Ten Wings conforms to images and numbers, can the measures of the writings of the Xia, Shang, and Zhou dynasties and the two Han dynasties be discerned. Then, whether later writings conform to measures can also be judged.

(揚子雲知《易》象數理之精，恐後人不解，乃苦心焦思作《太玄》，以明數。作《法言》，以仿《論語》。非擬經侮聖也，其意欲人之由淺入深，因《太玄》而進於《易》。因《法言》而悟《論語》之法度，用心良苦。乃後人並《太玄》不能解，何有於《易》？讀《論語註疏》，更蔑視《法言》。又以朱子綱目“莽大夫”三字作揚雄定評，後世遂存以人廢言之成見。《太玄》、《法言》乃真成覆醬瓶之物。《太玄》、《法言》不足惜，《易經》、《論語》法象數度之不明，貽人心世道之優，良足痛焉！)。

The original commentary says: Yang Xiong (style name Ziyun) deeply understood the subtle aspects of the principles, numbers, and meanings in the Book of Changes, and feared that later generations would not be able to understand them. Therefore, he painstakingly composed the Tai Xuan to explain the numbers, and the Fa Yan to imitate the Analects. He was not trying to imitate the classics or belittle the sages, but rather to guide people from the simple to the profound: using the Tai Xuan to understand the Book of Changes, and the Fa Yan to grasp the principles of the Analects. His intention was truly arduous. Who would have thought that later generations could not even understand the Tai Xuan, let alone the Book of Changes? Those who read the annotated and interpreted Analects look down upon the Fa Yan. Moreover, Zhu Xi's Comprehensive Mirror to Aid in Government used the three words "Mang Da Fu" to evaluate Yang Xiong, leading later generations to hold the prejudice of discarding the words because of the person. Thus, the Tai Xuan and Fa Yan have truly become the discarded waste paper that Liu Xin once mocked as "covering the jar with sauce." The Tai Xuan and Fa Yan themselves are not so precious, but what is truly regrettable is that the principles, images, numbers, and measurements in the Book of Changes and the Analects have become obscure, causing harm to people's hearts and the world, which is truly heartbreaking. The character "you" in "yi renxin shidao zhi you" should be read as "you" meaning "grief."

乾簡坤易，象數著明。象由微而知著，數執簡以御繁。太極由是生兩儀，生四象，生八卦，以生六十四卦。而六十四卦仍以一“是(《未濟·上六·象》曰“有孚失是”，為全經最後之一字。)”返本還原。故欲求其“是”，當求諸始。乾坤《易》之始，六爻乾坤之始，一畫開天又六爻之始。故言卦數者，必自爻數始。

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: Six at the Top = Shang Liu Eight Trigrams = Ba Gua Heavenly Qian values simplicity as its virtue, and Earthly Kun values ease as its virtue. Through these, images and numbers become clear and distinct. Images infer the significant from the subtle, while numbers control complexity through simplicity. Thus, the Taiji gives rise to the Two Principles, then the Four Symbols, then the Eight Trigrams, and further leads to the sixty-four hexagrams. Yet the sixty-four hexagrams ultimately return to their origin through the single character 'is' (是). Therefore, to seek this 'is,' one must go back to the beginning. Qian and Kun are the beginning of the Book of Changes, the six lines (yao) are the beginning of Qian and Kun, and the single stroke that 'opened the heavens' is the beginning of the six lines. Therefore, those who discuss hexagram numbers must necessarily begin with yao numbers.

先儒言卦變者多矣。虞氏以後，眾說紛紜，莫衷一是。虞《易》既無完書，其注及《周易集林》，僅於《李氏集解》中得一鱗片甲，語焉不詳。漢上朱氏，據此以定虞氏卦變圖，當時已多異議。李氏挺之，有六十四相生及反對兩圖。朱子《本義》，復有變更。陰陽重出，其為卦乃至一百二十有四。雖稱根據《彖傳》，而其舉例之十九卦，有自一卦來，兩卦三卦來者，參差不一，亦不能自圓其說。後之為圖者更多，如朱楓林等，更自鄶以下無足言矣。

Earlier scholars discussed the transformation of hexagrams extensively. Since Yu Fan, there have been many conflicting views, with no definitive conclusion. Yu Fan's commentary on the Book of Changes is no longer a complete work; his annotations and the "Zhou Yi Jilin" can only be found in fragments within Li Dingzuo's "Zhou Yi Jiejie," and they are vague and incomplete. Zhu Zhen, known as the Han Shang Master, constructed Yu's hexagram transformation diagram based on these limited materials, and at that time, it already aroused considerable controversy. Li Zhishi, who was called Tingzhi, created two diagrams: "the mutual generation of the sixty-four hexagrams" and "opposition." Zhu Xi, in his "Zhou Yi Benyi," further modified them, arranging them again in both yin and yang lines, resulting in as many as 124 hexagrams. Although he claimed to base his work on the "Tuan Zhuan," the nineteen examples he provided vary; some say they come from one hexagram, others from two or three, making them inconsistent and making it impossible for him to justify his own reasoning. Later diagram makers became even more varied, such as Zhu Sheng of the Ming dynasty, who were far inferior and hardly worth mentioning.

虞李二氏之圖，皆根本乾坤，其立論自不可磨。後儒如來氏知德，胡氏滄曉，錢氏辛楣，焦氏理堂，各有變通修正，均不能越其範圍。然皆爻變，而不盡為卦變也。夫卦者，必一卦盡變，如坤之變乾，巽之變震，斯謂之卦變可矣。若乾變姤夬同人大有小畜履，坤變剝復師比謙豫，則只一爻變。上下之乾坤，固未變焉。且占變知來，因貳以濟民行，事物萬變，烏能以六十四卦之變，應之而不窮乎？

Yu Fan and Li Zhicai both took Qian and Kun as the fundamental elements, and their theories are naturally indelible. Later scholars such as Lai Zhide, Hu Xu (who went by the courtesy name Cangxiao), Qian Daxin (who went by the courtesy name Xinei), and Jiao Xun (who went by the name Litan) each made their own modifications and corrections, but none could go beyond the scope of these two schools. However, what they discussed was actually about "yao change" rather than "guan change."the so-called "guan change" must involve all six lines of a single hexagram changing. For example, when Kun changes into Qian or when Xun changes into Zhen, this is called "guan change." As for when Qian changes into Guo, Guai, Tongren, Dayou, Xiaoxu, and Liu, or when Kun changes into Bo, Fu, Shi, Bi, Qian, and Yu, these are only changes of a single line. The Heaven and Earth trigrams within the upper and lower trigrams of the hexagram have not actually changed. Moreover, divination through change is intended to foresee the future and help people act according to auspicious or inauspicious signs. Since the changes in things are infinite, how could relying on only the sixty-four hexagrams be sufficient to cope with all situations without exhausting the possibilities?

故朱子占法，據《左》《國》所載故事為例，而又自定前十卦後十卦之別，以補其未備。無論其所謂前後十卦者，即其卦變圖百二十四卦之次序，決非古人所有。即能相合，而上下二編彖辭象辭並計，亦只四百四十八變，再加合兩卦彖辭，亦僅五百十二，烏能悉應所占之事，而定其吉凶？其無當可斷言也。

Therefore, Zhu Xi established the method of divination based on the old examples recorded in the "Zuo Zhuan" and the "Guoyu," and he himself divided the hexagrams into "the first ten hexagrams" and "the latter ten hexagrams" to make up for their shortcomings. Moreover, even if we do not consider his distinction between the first and latter ten hexagrams, the order of the 128 hexagrams in his diagram of changing hexagrams is not the original order of the ancients. Even if we suppose that all the correspondences are correct, when we combine the interpretations of the upper and lower parts of the two classics, there are only 448 kinds of changes. Adding the calculation based on the interpretations of two hexagrams together, it would not exceed 512 kinds. How could such a limited number of possibilities be sufficient to deal with all the matters of divination and determine their fortune or misfortune? It can be confidently stated that this method is not practical.

《周官》太卜所掌三《易》，自別有占法。而文周上下二編之《彖》、《象》，特其綱領。孔子《十翼》，但示人以觀象玩辭，為進德明道之本，來嘗為人言占卜之方也。“大衍”一章，明象數之根本。揲蓍求卦，以盡變通之義。引伸觸類，以盡天下之能事。亦非專為卜筮而言也。

In the "Rites of Zhou," the three books of the Yi hexagram kept by the Grand Diviner had their own separate method of divination; the commentaries on the hexagrams and images in the upper and lower volumes by King Wen and the Duke of Zhou were merely summaries of that method. Confucius composed the Ten Wings, which taught people to observe the images and play with the words, using them as the foundation for cultivating virtue and understanding the Way. He never explained the specific techniques of divination ("lai chang" should be "wei chang"). The chapter on "Great Derivation" in the "Great Treatise" discusses the fundamental principles of images and numbers; using the method of divining with yarrow stalks to obtain a hexagram was to exhaust the meaning of change and adaptability; "extending the principles and applying them to similar cases" was to exhaust all possible skills in the world — all of this was not specifically for divination.

自“掛一”，“再扐”之義不明，自唐以後，異說紛起。如劉夢得、張轅、莊綽、程伊川、朱元晦、張理、郭兼山諸家，議論不一。要皆書生之見，無當於事，無與於《易》。故歷代精於占筮者，皆屏不用，徒留為經生家聚訟之資而已(沈氏需時眇言，據天地之數由大衍求一之術，證以微積分，合而定揲四之義，與《易》象數皆能確合。俟參考儀象諸書，更試驗得實，當別為一書詳之。)。故茲編於卦變之說，概棄不錄。卦變皆由爻變，言爻變即所以言卦變也。卦變可圖，爻變則非圖所能盡也。略圖示意，閱者以意會之可耳。

Since the meanings of the divination steps "hang one to represent three" and "take two and then hang" have not been clearly explained, various interpretations have arisen since the Tang dynasty: for example, those of Liu Yuxi (courtesy name Mengde), Zhang Yuan, Zhuang Chuozhuo, Cheng Yi, Zhu Xi (courtesy name Yuanhui), Zhang Li, and Guo Zhongxiao (courtesy name Jianshan), each offering different opinions. These are mostly the views of scholars, of no practical use, and unrelated to the Book of Changes. Therefore, those who truly excel in divination have all abandoned these interpretations, leaving them only for scholars to argue over. (Shen's "Needle Time Miao Yan" uses the numbers of heaven and earth, the method of "seeking one" in the Great Derivation, and applies calculus to verify, thereby determining the meaning of "divining by four," which aligns accurately with the imagery and numbers of the Book of Changes. After consulting books on astronomical instruments and obtaining practical evidence, I will write another book to discuss this in detail.) Therefore, this compilation omits all the various interpretations regarding changes in hexagrams. Changes in hexagrams come from changes in lines. Discussing changes in lines is equivalent to discussing changes in hexagrams. Changes in hexagrams can be illustrated with diagrams, but changes in lines cannot be fully expressed in diagrams. Therefore, I will only briefly draw a diagram for illustration, and readers are expected to understand it by implication.

爻分陰陽奇偶二者而已。卦有六爻，乾坤十有二爻而已。一爻變至二三四五六爻俱變，一卦之變，六十有四，四千零九十六而已。四千九十六，亦烏足盡萬事萬物之變哉！故爻之變，有時有位，有主有應，有物有事，而數與象，猶不預焉。

The distinction of lines lies only in yin and yang, odd and even. A hexagram has six lines, and the trigrams Qian and Kun together have no more than twelve lines. From one line changing up to all six lines changing, one hexagram can produce sixty-four variations. When all sixty-four hexagrams are multiplied together, they total four thousand and ninety-six variations. That is all. Four thousand and ninety-six variations are nowhere near sufficient to exhaust all the changes of myriad things and events. Therefore, the change of lines must also be considered in terms of time and position, which one is the main and which is the responding, and whether it refers to an object or an event; yet this still does not include the factors of numbers and images.

如同一卦也，卦不變，爻亦不變。而時與位六者有一變，則利害情偽，已迥乎不同，此不變之變一也。更有爻不變而象數已變者，如七與九，皆陽也。六與八，皆陰也。七八易九六，爻之陰陽如故，而數與象，均各不同。此不變之變二也。

For example, if the same hexagram remains unchanged and none of its lines have changed, yet among the six factors—time, position, subject, responding line, matter, and event—any one of them changes, the advantage, disadvantage, truth, or falsehood will be completely different. This is the first type of "unchanging change." There is another type where the lines remain unchanged but the figures and numbers have changed: seven and nine both belong to yang, and six and eight both belong to yin. If seven and eight are exchanged for nine and six, the yin and yang of the lines remain the same, but the figures and numbers are entirely different. This is the second type of "unchanging change."

故《易》曰：動則變，變則通。動之機甚多，不必爻之動而卦始變也。朱子曰：“坤初之變為復，非頓然而變也。自小雪起，一日變一分，至冬至而始成復之一爻。”知言哉！惟其變由微而顯，由顯而著，至見於象，而陰陽始判，吉凶始見耳。僅知卦爻之變，而不知不變之變，不足以言卦，不足以言爻，並不足以言變也。

Therefore, the Book of Changes says: movement leads to change, and change leads to communication. The occasion that triggers "movement" is numerous, and it is not necessary to wait until a line moves within a hexagram before change begins. Zhu Xi said: when the first line of the Hexagram of Earth changes into the Hexagram of Return, it is not a sudden change, but a gradual change, starting from the beginning of Xiaoxue, changing by a fraction each day, until the winter solstice when it finally forms the single yang line of the Hexagram of Return. This truly hits the mark. It is precisely because change proceeds from subtle to apparent, from apparent to prominent, until it manifests in the image, that yin and yang can be distinguished, and fortune and misfortune can be seen. Knowing only the obvious change of hexagram lines and not understanding this "change without change" is insufficient for discussing hexagrams, lines, and change.

上圖略舉其例，非事物之必初上，主應之必二五。六爻皆具此六者，而六者又各有變化之不同。如今昔時也，盛衰亦時也，月建日符亦時也。位則有方位，有地位，有貴賤之位。千態萬狀，何可數限？但概之以動，察之以幾，知幾其神，而《易》始可言矣。

The diagram above is merely an example, not implying that "things" and "events" must necessarily fall on the first and top lines, nor that "subject" and "response" must necessarily be on the second and fifth lines. All six lines simultaneously possess the six elements of time, position, subject, response, thing, and event, and these six elements each have different variations. Regarding "time," present and past are time, prosperity and decline are also time, as are month builder and day symbol. Regarding "position," there is direction, status, and rank. With countless variations, how can they be counted? They can only be summarized under one word: "movement." Using the initial, subtle movement called "ji" to understand it. The Great Treatise says, "To know ji is truly divine." Only by understanding ji can one truly discuss the Book of Changes.

先天八卦，以陰陽升降，應日月之晦朔弦望，於是乎有納甲。因而重之，為六十四卦。卦有六爻，卦納乾而爻納支，於是乎有爻辰。辰者天度十二宮之次舍。而地支之十二，與天度相應者也。

The Earlier Heaven Trigrams correspond to the waxing and waning of yin and yang, matching the moon's phases of new moon, first quarter, full moon, and last quarter. This gives rise to the concept of 'Najia'. By stacking two trigrams together, sixty-four hexagrams are formed, each with six lines. Each hexagram is paired with a Heavenly Stem, and each line is paired with an Earthly Branch, leading to the concept of 'Yao Chen'. The term 'Chen' refers to the positions in the twelve divisions of the celestial circle. The twelve Earthly Branches correspond exactly to these twelve celestial divisions.

漢人言爻辰者，有鄭氏，有京氏，其說不同。鄭氏以乾陽坤陰，十二爻順逆交錯，以應十二月。而又以六十四卦之爻，合乾坤，分二十八宿之度數、星象合卦爻之象，以釋經。其書久佚，僅自《李氏集解》，及各經註疏採集其說，但存其梗概而已。有清戴氏棠，據《甘石星經》、《開元占經》等書，按六十四卦之《彖》、《象》、《繫辭》，有以星象名義，或形似相類，援鄭例而補之，名《爻辰補》。然於經義象數，均未有當，無足採焉。

In the Han dynasty, two scholars, Zheng Xuan and Jing Fang, discussed the concept of yao chen, but their views differed. Zheng Xuan regarded Qian as yang and Kun as yin, arranging the twelve lines of the two trigrams in alternating order, either forward or backward, to correspond with the twelve months of a year. He also combined the sixty-four trigrams' lines with the twenty-eight constellations, assigning degrees to them, and used celestial phenomena to match the images of the trigrams and lines, thereby interpreting the classics. His work has long been lost, and today only fragments can be reconstructed from Li Dingzuo's "Collected Explanations of the Zhou Changes" and citations in various annotations and commentaries on the classics, leaving only a general outline. In the Qing dynasty, Dai Tang, based on star and calendar texts such as the "Gan Shi Star Classic" and "Kaiyuan Treatise on Astrology," thoroughly examined the "Commentary on the Judgment," "Image Commentary," and "Great Treatise" of the sixty-four trigrams. He incorporated any lines that could correspond to celestial terms or whose shapes could be compared, following Zheng Xuan's precedent, and named his work "Yao Chen Bu" (Supplement to Yao Chen). However, from both the perspective of classical meaning and numerical symbolism, what he supplemented was not very appropriate and is not worth adopting.

京氏納辰為古今術家所遵用，證之於《彖》、《象》十翼，多能相合。有與經義相發明，為經學家所不能道者。始知黃帝五甲六子三元九宮，實探陰陰造化之秘，明天人之際。以濟世利民者，固不僅卜筮之用也。

Jing Fang's method of Nache, which has been followed by diviners throughout history, can be verified with the Commentary on the Judgment, the Image Commentary, and the Ten Wings, and in most cases they agree. Some even reveal insights that complement the classics and are not explained by scholars of the classics. From this, we realize that the system of "Wujia," "Luzi," and "San Yuan Jiugong" attributed to the Yellow Emperor indeed explores the profound mysteries of yin and yang and elucidates the relationship between heaven and humanity, aiming to benefit the world, not merely for divination purposes.

康成生於漢季，施、孟、梁丘之《易》，已多失傳。獨費氏，因其說簡約而獨存。康成亦有所不足，故採取殘缺之緯書，兼及五行律曆星象，以釋卦爻，固費《易》之所無，或亦三家之遺義也。惜其書又亡。致三代之《易》，不能盡見於今。猶幸京《易》雖亡，而八宮世應納音納甲之數，猶得貫通，得與《周易》相參證。乃學者又畏其繁瑣，目為蕪穢，必盡棄之，以自詡擴清之功，《易》道又何自明哉！

Zheng Xuan (style name Kangcheng) was born in the late Eastern Han dynasty. At that time, the schools of Shi Chou, Meng Xi, and Liang Qiu He had largely lost their teachings on the I Ching. Only the school of Fei Zhi remained because its interpretations were simple and concise. Zheng Xuan also thought that the I Ching of Fei's school had some shortcomings, so he used fragmented yijing texts, combined with the Five Phases, the system of musical scales and calendars, and celestial phenomena to explain the hexagrams and lines. These were certainly not found in Fei's I Ching, but perhaps they were the lost meanings left behind by the schools of Shi, Meng, and Liang Qiu. Unfortunately, his works later became lost, making it impossible to preserve the complete study of the I Ching from the Three Dynasties to the present. Fortunately, although the Jingshi I Ching has been lost, the system of eight palaces, Shiying, Naying, and Najia still remains intact and can be used to cross-reference with the Zhouyi. However, scholars have become tired of its complexity, considering it messy and dirty, and want to completely eliminate it, claiming they have achieved a purification. In this way, how can the principles of the I Ching be made clear?

卦納甲而爻納辰，京氏以陽順陰逆，交錯為用。以乾坤為綱，六子分乾坤之爻，以次相推。仍以本宮為體，而六爻所納之支，視其與本宮生克，以為親疏遠近利害之分。圖如下：

The trigrams are paired with the heavenly stems and the lines are paired with the earthly branches. Jing Fang used the principle of "Yang moves in order and Yin moves in reverse" to alternate and select them. Taking the trigrams Qian and Kun as the main framework, the six subordinate trigrams take the lines of Qian and Kun in sequence, proceeding downward. Still taking the original trigram as the main body, one then examines the earthly branches contained in the six lines and determines whether they are in mutual generation or mutual control with the five phases of the original trigram. Based on this, the closeness, distance, benefits, harms, good fortune, and misfortune are distinguished. The diagram is listed below.

陽卦納陽，於陽支皆順行。陰卦納陰，於陰支皆逆行。乾內納甲，外納壬，支起子，子寅辰午申戌順行。坤內納乙，外納癸，支起未，未巳卯丑亥酉逆行。陰陽交錯，以相合為用者也。

Yang trigrams take yang stems, and the paired yang branches are counted in sequence; yin trigrams take yin stems, and the paired yin branches are counted in reverse order. For the Qian trigram, the lower trigram takes Jia and the upper trigram takes Ren. The earthly branches start from Zi and proceed in sequence from the first line to the top line: Zi, Yin, Chen, Wu, Shen, Xu. For the Kun trigram, the lower trigram takes Yi and the upper trigram takes Gui. The earthly branches start from Wei and proceed in reverse order from the first line to the top line: Wei, Si, Mao, Chou, Hai, You. Yang and yin trigrams alternate, and they are used in mutual harmony.

故乾生震，震為長子。長子代父納庚，而六爻之支，與乾全同。子寅辰午申戌皆順行也。坎中男，得乾中爻，乾內中寅，坎納戊，故初爻自寅起，為戊寅，戊辰，戊午，戊申，戊戌，戊子也。艮少男，得乾之上爻。乾內三辰，艮納丙，故初爻自辰起為丙辰，丙午，丙戌，丙子，丙寅也。

Therefore, the trigram Qian generates Zhen, and Zhen is the eldest son. The eldest son acts on behalf of the father, taking the heavenly stem Geng. The earthly branches taken by the six lines are the same as those of Qian: Zi, Yin, Chen, Wu, Shen, Xu, proceeding in order. Kan is the middle son, receiving the middle line of Qian. The middle line of the lower trigram of Qian is Yin, so Kan takes the heavenly stem Wu. Thus, the first line of Kan starts with Yin, proceeding in order as Wu Yin, Wu Chen, Wu Wu, Wu Shen, Wu Xu, Wu Zi. Gen is the youngest son, receiving the top line of Qian. The third line of the lower trigram of Qian is Chen, so Gen takes the heavenly stem Bing. Thus, the first line of Gen starts with Chen, proceeding in order as Bing Chen, Bing Wu, Bing Shen, Bing Xu, Bing Zi, Bing Yin (the entry for Bing Shen is omitted in the original text).

坤生長女為巽，長女代母，而納不起於丑，而起於未，與震襲乾不同者，此男女之別，陰陽之分。女以出為歸，故自內出外。由四爻起未，五巳上卯，而反至初為丑二為亥三為酉也。離為中女，得坤中爻，故於外中五爻起未。兌為少女，得坤上爻，故於外上起未，皆未巳卯丑亥酉，與巽同例也。季彭山不知陰陽之別，妄改坤起乙丑。又有不分陰陽，不知本末，妄改乾為甲子，甲戌，甲午，甲寅，甲辰者，皆絕無意義。學者不可好奇喜新，為所誤也。

The eldest daughter of the Earth trigram is Wind, which takes the position of the mother. However, the Wind trigram does not start its branches from the Ox (Chou) but from the Sheep (Wei). This is different from the Thunder trigram, which follows the same order as the Heaven trigram. This difference reflects the distinction between male and female, yin and yang. Women's destiny is to marry and thus they move from the inner to the outer: the Wind trigram starts from the fourth line with Wei, the fifth line with Si, the top line with Mao, then turns back to the first line with Chou, the second line with Hai, and the third line with You. The Fire trigram is the middle daughter, taking the middle line of the Earth trigram, so it starts from the fifth line with Wei in the outer trigram. The Lake trigram is the youngest daughter, taking the top line of the Earth trigram, so it starts from the top line with Wei in the outer trigram. The three trigrams all follow the sequence of Wei, Si, Mao, Chou, Hai, You, similar to the Wind trigram. Ji Ben of the Ming dynasty (pen name Pengshan) did not understand the distinction between yin and yang and mistakenly changed the Earth trigram to start from Yichou. Others failed to distinguish yin and yang and the beginning and end, and arbitrarily changed the Heaven trigram to start with Jiazi, Jiaxu, Jiawu, Jiayin, and Jiachen, which are all meaningless. Scholars should not be greedy for novelty and be misled by such incorrect views.

六十四卦，八純卦外，一世至六世，皆取本宮納甲。見者為飛，不見者為伏。游魂歸魂十六卦，不取本宮為伏。分舉爻位如下：晉以艮為伏，而取艮四爻者，以游魂仍為四爻變。而晉上之離，由剝上之艮變來者也。故不以本宮不以對宮而取艮。大有下卦之離，由晉下卦之坤變來者也。歸魂為三爻，故取坤三。餘卦仿此。

Among the sixty-four hexagrams, except for the eight pure hexagrams, the hexagrams of the first to sixth generations take the stem assignment from their own palace: those that are visible on the outside are called 'Flying' (飞), and those that are hidden inside are called 'Hidden' (伏). The sixteen hexagrams of the wandering soul (游魂) and returning soul (归魂) do not take the hidden stem from their own palace. Here are the specific lines for each: The hexagram of晋 takes the trigram艮 as its hidden stem, specifically the fourth line of艮, because the wandering soul still originates from the fourth line. The trigram离 on top of晋 comes from the trigram艮 on top of剥, so it does not take the stem from its own palace or the opposite palace, but instead takes the stem from艮. The trigram离 in the lower trigram of大有 comes from the trigram坤 in the lower trigram of晋; the returning soul changes on the third line, so it takes the third line of坤. The rest of the hexagrams follow the same pattern.

鄭氏爻辰，亦以陰陽六爻，相間用事。乾辰子寅辰午申戌，其次與京氏同，而坤則為未酉亥丑卯巳與京氏異。蓋陰陽雖間一位，而皆順行。蓋以十二律相生為據也。他卦分乾坤之爻，亦分乾坤之辰，不論納甲。

Zheng Xuan's yao chen system also involves yin and yang hexagrams taking turns in succession. The six lines of Qian are assigned to Zi, Yin, Chen, Wu, Shen, and Xu in that order, which is the same as Jing Fang's system. However, the six lines of Kun are assigned to Wei, You, Hai, Chou, Mao, and Si, which differs from Jing Fang's system. Although Zheng Xuan also selects every other branch, both Qian and Kun hexagrams follow a clockwise order, whereas Jing Fang's system has Kun in a counterclockwise order. Zheng Xuan based his system on the sequence of the twelve tones in mutual generation. The other hexagrams inherit the yao assignments of Qian and Kun, and thus also inherit their corresponding chen, without relying on the Najia system.

徵者，用之見乎外者也。壽陽閻氏《爻徵廣義》，詳於鄭氏爻辰，殊於實用無征焉。六爻制用，肆應不窮，皆以五行陽干陰支為綱領，以生克刑害少壯盛休廢類別去取，以征吉凶。以其與卦爻象數，相為統系，足以推六十四卦變化往來之跡。且有與經傳互相發明者，亦初學所不可不知者也。爰取《京氏易》與《易緯》諸書之著錄者，分隸六爻，徵爻用，亦以存古義也。至推演條理，今密於古，術家所習用，更毋庸備述焉。

The term "zheng" refers to the external manifestation of "use" as a form of verification. The Yan family of Shouyang in Shanxi wrote "Yao Zheng Guangyi," which provides a detailed explanation of Zheng Xuan's theory of yao chen, but in practical application, it fails to produce verifiable results. The system of controlling and responding to the six yao (lines) is endless, and all are organized under the framework of the Five Phases, as well as the yang stems and yin branches. They are classified and selected according to the states of generation, overcoming, punishment, and harm, as well as the stages of youth, maturity, prosperity, rest, and decline. These are used to verify auspicious and inauspicious outcomes. Because this system is integrated with the imagery and numbers of the hexagrams, forming a unified whole, it can trace the trajectory of the sixty-four hexagrams' transformations. Moreover, in some cases, it can also complement the classic texts, which is something beginners should not be unaware of. Therefore, the content recorded in "Jing Shi Yi Chuan" and the various works of "Yi Wei" has been systematically assigned to the six yao, to verify the function of the yao, and also to preserve ancient meanings. As for the logical structure of the divination process, it is now more precise than in ancient times, and these are common methods used by numerological practitioners, so there is no need to elaborate on them one by one.

京氏曰：“八卦鬼為繫爻，財為制爻，天地為義爻，福德為寶爻，同氣為專爻。”此五者，今術家謂之六親(親者，族也。《易》曰“類族辨物”，先辨諸爻。)，蓋與本身為六也。相傳甚古，義簡而賅，言占者所不能廢。

Jing Fang said: Among the Eight Trigrams, "ghost" is called the tied line, "wealth" is called the controlling line, "heaven and earth" is called the meaning line, "fortune virtue" is called the treasure line, and "same nature" is called the exclusive line. These five items, today's divination experts call them "Six Relations" ("relation" refers to category. The Image Commentary of Tongren says, "The superior man uses classification of kinship to distinguish things," first distinguishing clearly each line. ) Because adding the self makes a total of six. This system is said to have a long history, with clear and comprehensive meaning, and those who interpret the hexagrams cannot abandon it.

朱子《周易本義》，以周孔之《易》為教人卜筮之用，而焦京之言卜筮者，反悉廢之，僅以六爻之動靜為占，宜其無徵驗之可言也。茲以京說為主，而以近世皆用者附之。非敢謂援古證今，亦發其凡而已。

Zhu Xi wrote The Original Meaning of the Zhou Changes, claiming that the Zhou Changes and the Analects of Confucius were meant for divination. Yet he discarded the methods established by genuine diviners like Jiao Yanshou and Jing Fang, relying solely on the movement of the six lines for divination. It's no wonder there's no verification. Here, we mainly follow Jing Fang's approach, and add the commonly used terms of recent times. I dare not say this is using ancient principles to verify current practices, but rather just providing an outline and example.

專爻一，同氣為專爻。陸績曰：同氣兄弟也，如金與金，木遇木之類。今稱兄弟。寶爻二，福德為寶爻。福德子孫也。我所生者也。如金與水，水與木是也。今稱子孫。義爻三，天地為義爻。天地父母也，生我者也。如木為水生，水為金生。今稱父母。制爻四，財為制爻。財者我所制也。如木克土，土為木之財是也。今稱妻財。繫爻五，鬼為繫爻。繫者束縛之意，制我者也。如火克金，火即金之鬼也。今稱官鬼。

This is a flat six relations chart. Originally divided into the five phases, each row lists in order the old name from Jing Fang, its explanation, the commentary by Lu Ji of the Three Kingdoms period, and the common term used by modern divination practitioners. First, the exclusive爻 (special爻), meaning "same qi is the exclusive爻": Lu Ji said that same qi refers to siblings, for example, metal meeting metal, wood meeting wood, etc. Today this is called "siblings". Second, the treasure爻 (treasure爻), meaning "fortune virtue is the treasure爻": fortune virtue refers to children, which is the aspect I generate, for example, metal generates water, water generates wood, etc. Today this is called "children". Third, the righteousness爻 (righteousness爻), meaning "heaven and earth are the righteousness爻": heaven and earth refer to parents, which is the aspect that generates me, for example, wood is generated by water, water is generated by metal, etc. Today this is called "parents". Fourth, the controlling爻 (controlling爻), meaning "wealth is the controlling爻": wealth is what I can control, for example, wood controls earth, and earth is the wealth of wood. Today this is called "wealth". Fifth, the binding爻 (binding爻), meaning "ghost is the binding爻": "binding" means restraint, referring to the aspect that controls me, for example, fire controls metal, and fire is the ghost of metal. Today this is called "official ghost".

五者與本身為六。今稱六親者，義亦近古。親者族也。類族辨物，舉一起例，凡言兄弟，則比肩者可類；言子孫，則後我者可類；言父母，則庇我者皆其類；言妻財，則奉我者皆其類；言官鬼，則制我害我者皆其類。遠近不同，則親疏自異。而為利為害，爰有重輕之別。是在察其爻之所在，而鑑別之，非可概論也。

These five elements, together with the self, make six, which is called the "Six Relations" today. The meaning is quite close to the ancient concept. "Relation" refers to a category. The phrase "classifying kinship and distinguishing objects" means using one example to establish a general rule: whenever we refer to "siblings," all those who are on the same level as me can be classified under this category; when we refer to "children," all those who come after me can be classified under this category; when we refer to "parents," all those who protect me can be classified under this category; when we refer to "wealth," all those who support me can be classified under this category; and when we refer to "official ghost," all those who restrain me or harm me can be classified under this category. The relationship may be distant or close, so the degree of intimacy varies naturally; whether it is beneficial or harmful also has different degrees of importance. This depends on which line falls in a particular position to determine the distinction, and cannot be considered in a general way.

神(神者存也。成性存存，陰陽不測，假定其名，亦猶類族辨物之意也。)也者，妙萬物而為言。過化存神，有非可以跡象求之者。六親征其實，六神徵諸虛。周流六虛，無乎不在。渺焉漠焉，將何從徵？曰陰陽之氣，布為五行，其幾甚微。《傳》曰：“本於陰陽而立卦，陰陽變化，而神寓也。”此六爻之神所由名，要非泥其名以為實者也。

The term "shen" (spirit) refers to "cun" (presence). The Great Treatise says, "Forming nature and maintaining presence," meaning that the changes of yin and yang are unpredictable, so we give it a name, just as "classifying kinds and distinguishing things" helps in identification. According to the Discourse on the Hexagrams, "shen speaks of the subtle workings of all things." The Mencius says, "Where it passes, it transforms; where it resides, it is shen," showing that some things cannot be pursued through physical traces. The Six Relations verify the tangible aspect, while the Six Spirits verify the intangible. Shen flows through the six voids, present everywhere, yet it is vast and indistinct, so how can it be verified? The answer is: the qi of yin and yang spreads out to form the Five Phases, and its initial movement is extremely subtle. The transmitted text says, "Establishing hexagrams based on yin and yang, and the subtle spirit resides within their changes"—this is the reason for the term "six yao shen." The important point is not to be rigid about the name, treating it as an actual entity.

震東方木，木之神青龍，甲乙日起青龍。離南方火，火之神朱雀，丙丁日起朱雀。兌西方金，金之神白虎，庚辛日起白虎。坎北方水，水之神玄武，壬癸日起玄武。坤艮中央土，土之神勾陳螣蛇，戊己日起勾陳騰蛇。

This is a flat chart showing the assignment of the Six Spirits, linking the trigrams, directions, the Five Phases, the names of the spirits, and the days they begin. Zhen is in the East and belongs to wood; the spirit of wood is the Azure Dragon, and on days of Jia and Yi, the sequence starts with the Azure Dragon. Li is in the South and belongs to fire; the spirit of fire is the Vermilion Bird, and on days of Bing and Ding, the sequence starts with the Vermilion Bird. Dui is in the West and belongs to metal; the spirit of metal is the White Tiger, and on days of Geng and Xin, the sequence starts with the White Tiger. Kan is in the North and belongs to water; the spirit of water is the Black Tortoise, and on days of Ren and Gui, the sequence starts with the Black Tortoise. Kun and Gen are in the center and belong to earth; the spirits of earth are Gou Chen and Tan Sha, and on days of Wu and Ji, the sequence starts with Gou Chen and Tan Sha. When divining, determine the starting spirit based on the heavenly stem of the day, then arrange the spirits sequentially on the six lines.

《傳》曰：“前朱雀而後玄武，左青龍而右白虎。”古者五行各有專官，官世其守，功德在民，民不能忘。即假人名以神號，舉其名知其用，所以便事也。吉凶神煞之名，皆此類也。必求其人以實之，愚也。必妄其名而斥之，亦詎足為智哉！六壬、太乙、遁甲之言神，舉可隅反矣。

The Book of Rites, Volume of the Rituals says: "In front is the Vermilion Bird, behind is the Black Tortoise, on the left is the Azure Dragon, and on the right is the White Tiger." In ancient times, each of the Five Phases had officials in charge, whose positions were passed down through generations. Their virtues remained in the hearts of the people, who could not forget them. Thus, they used these people's names as titles for deities. By mentioning the name, one knew what function it represented, making it convenient for affairs. All the various names of auspicious and inauspicious deities belong to this category. It is foolish to insist on finding real people to confirm their existence. Conversely, to deny all these names as mere fabrications and refute them is not necessarily wise either. The various deities mentioned in the systems of Liu Ren, Tai Yi, and Dun Jia can all be understood by applying this principle.

六屬者以五音分屬六爻，即本於納音。納音與納甲相表裡。屬之於爻，仍隨八卦之納甲以定其數也。舉例如下：

The so-called "six attributes" involve assigning the five tones, Gong, Shang, Jue, Zhi, and Yu, to the six lines of a hexagram. This practice originates from "Nayin" or sound elements. Nayin and Najia are interrelated; when assigning the five tones to the lines of a hexagram, the determination still follows the numerical assignments based on the Eight Trigrams' Najia. For example:

子午屬庚，震初爻也，庚子午。

This line is the first entry of the "six attributes" assignment table. The "six attributes" refer to distributing the five tones across the six lines of a hexagram, and its basis remains "najia" stem assignment. The Zhen hexagram is assigned the heavenly stem "Geng," its first line is paired with the earthly branch "Zi," and its fourth line is paired with the earthly branch "Wu," so the branches "Zi" and "Wu" are assigned to "Geng," written as "Gengzi" and "Gengwu." The table only lists the first line because the first line is the starting point of the hexagram's earthly branch assignment: for a yang hexagram, starting from the first line, the branches are taken in order, skipping one each time, and by the fourth line, it is exactly six positions away from the first line, forming a conflicting pair. Therefore, one heavenly stem controls two conflicting earthly branches.

卯酉屬己，離初爻也已，卯酉。

The branches of卯 and酉 belong to the heavenly stem「己」, referring to the卦 of Li (Fire). According to the method ofNajia stem assignment, the eight trigrams are assigned the ten heavenly stems. The trigrams Qian (Heaven) and Kun (Earth) are considered parents and each take two stems, while the six children trigrams each take one stem. The trigram Li (Fire) is assigned「己」. Since Li is a yin trigram, the branches are assigned in reverse order starting from the first line: first line isJimao, second line isJichou, third line isJihai, and fourth line isJiyou. Therefore, the first and fourth lines correspond to卯 and酉, written as「己卯」and「己酉」. In the table, the third column is mistakenly carved as「已」, which is a form similar to「己」.

寅申屬戊，坎初爻也，戊寅申。

The branches Yin and Shen belong to the heavenly stem Wu. This refers to the Kan hexagram. Kan is a yang hexagram, and it incorporates the stem Wu. It pairs with the Li hexagram's stem Ji, forming a pair of earth stems in the middle of the ten heavenly stems. One is located in the north, and the other in the south, corresponding to the positions of the sun and moon, as well as the middle qi. The branches incorporated into Kan hexagram start from the first line and proceed in order: the first line is Wu Yin, the second line is Wu Chen, the third line is Wu Wu, and the fourth line is Wu Shen. Therefore, the first and fourth lines contain Yin and Shen, written as 'Wu Yin' and 'Wu Shen'. Yin and Shen are in opposition, yet they are still unified under one stem.

辰戌屬丙，艮初爻也，丙辰戌。

The Earthly Branches Chen and Xu belong to the Heavenly Stem Bing. This refers to the Gen hexagram. Gen is a Yang hexagram, and it receives the stem Bing. Its reception of the branches also starts from the first line and proceeds in order, selecting every other branch: first line Bingchen, second line Bingwu, third line Bingshen, fourth line Bingxu. Therefore, the first and fourth lines correspond to Chen and Xu, written as "Bingchen" and "Bingxu". Chen and Xu are two of the four earthly repositories (si ku), both representing earth. This aligns with the nature of Gen, which represents mountain, stopping, and earth.

巳亥屬丁，兌初爻也，丁巳亥。

The branches Si and Hai belong to the heavenly stem Ding, referring to the Dui hexagram. Dui is a yin hexagram, and its heavenly stem is Ding. The earthly branches are arranged from the first line in reverse order: the first line is Ding Si, the second line is Ding Mao, the third line is Ding Chou, and the fourth line is Ding Hai. Therefore, the first and fourth lines have Si and Hai, written as "Ding Si" and "Ding Hai." Since it is called "six belonging," there should be six entries, but here only five hexagrams are listed: Zhen, Li, Kan, Gen, and Dui. The missing one is Xun, which takes "Xin." The first line is Xin Chou and the fourth line is Xin Wei, written as "Chou Wei belong to Xin." This entry is missing in the transmitted text.

不言乾坤，六子之爻，皆乾坤之爻也。《說卦》“神也者”一章，不言乾坤，非特六子之用，皆乾坤之用。而所謂神者，即乾坤之陰陽不測，周流六虛者也。納音之說似淺而實深。精微之理，非可以跡象求之。

The upper trigrams only list Zhen, Li, Kan, Gen, and Dui but do not mention Qian and Kun, because the lines of the six subordinate trigrams originally come from the lines of the Qian and Kun trigrams. By discussing the six subordinate trigrams, Qian and Kun are already included. The passage in "Shuo Gua" that says "The 'spirit' is what speaks of the subtle workings of all things" also does not mention Qian and Kun throughout, using the same method. What is discussed in that passage is not only about the functions of the six subordinate trigrams; in fact, it is about the functions of Qian and Kun throughout. The term "spirit" refers to the function of the two energies of Qian and Kun, yin and yang, which change mysteriously and flow through the six lines' empty positions. The concept of "Nayin" may seem superficial, but it is actually very profound. The subtle principles within it cannot be understood merely by superficial appearances or numerical patterns.

謂之音者，乾坤爻辰左行右行。間辰六位，即六律六呂，相生之所本，故以分屬六爻，各納其辰，而謂之納音。今術家占筮推演及風角堪輿諸家，均不能廢納音以為言，而莫知其所由來。因備六爻所屬，並列《內經》及揚子雲、抱朴子諸家之圖於後，庶閱者可悉其始末矣。

It is called "sound" because the yao chen of the Qian trigram move left in a clockwise direction, while those of the Kun trigram move right in a counterclockwise direction. The two sides alternate and are separated by six positions, which is the basis for the mutual generation of the twelve laws of the "six laws" and "six lü." These twelve laws are distributed among the six yao, with each yao taking in one chen, hence it is called "Nayin." Now, those who practice divination and those who study wind angles and geomancy all rely on Nayin to establish their theories, yet no one can clearly explain its origin. Therefore, Hang氏 here lists the respective chen for each of the six yao, and also appends the diagrams from the Huangdi Neijing, Yang Xiong, and Ge Hong, so that readers may clearly understand the origin and development of this theory.

納音始於黃帝，今《內經》所載最詳。京氏六十律與甲子分配，自是古法。蓋以一律納五音，十二律納六十音。《內經》五音，始於金，傳火傳木傳水傳土。陽律陰呂，隔八相生。葛稚川曰：“一言得之者，宮與土（所屬者即一言而得）。三言得之者，徵與火（如戊去庚三位，故曰三言。下仿此）。五言得之者，羽與水。七言得之者，商與金。九言得之者，角與木。故子午九，丑未八，寅申七，卯酉六，辰戌五，巳亥四也。”

The method of Nayin sound elements originated in the time of the Yellow Emperor. The most detailed surviving account today is found in the "Huangdi Neijing" (Yellow Emperor's Inner Canon). Jing Fang paired the sixty tones with the sixty Jiazi (Heavenly Stems and Earthly Branches), which was originally an ancient method. His approach was that one tone governed five musical tones, and twelve tones could thus produce sixty musical tones. The five musical tones arranged in the "Huangdi Neijing" start with metal, then pass on to fire, wood, water, and finally earth. Among the twelve tones, the yang ones are called "Lu" and the yin ones are called "Lv," and they generate each other by being separated by eight positions. Ge Hong wrote in the "Baopuzi" that one syllable produces "Gong" and earth (since one syllable is the first sound, it is called one syllable); three syllables produce "Zhi" and fire (for example, from Wu to Geng, there are three positions in between, so it is called three syllables, and so on). Five syllables produce "Yu" and water; seven syllables produce "Shang" and metal; nine syllables produce "Jue" and wood. Therefore, the numbers for Zi and Wu are nine, Chou and Wei are eight, Yin and Shen are seven, Mao and You are six, Chen and Xu are five, and Si and Hai are four.

揚子雲《太玄》以火土木金水為序，與《內經》不同。甲子乙丑金者，言甲乙子午其數九，乙庚丑未其數八，甲乙子丑積數三十四，以五除之餘四，故為金。

Yang Xiong's "Tai Xuan" arranges the Five Phases in the order of fire, earth, wood, metal, and water, differing from the "Neijing" which starts with metal. As for the Nayin sound element of "Jiazi Yichou" being assigned to metal, it is calculated as follows: Jia and Ji are paired with Zi and Wu, their number being nine; Yi and Geng are paired with Chou and Wei, their number being eight. The numbers of the four characters Jia, Yi, Zi, and Chou are added together to total thirty-four. When divided by five, the remainder is four, which corresponds to metal in the Five Phases, hence the Nayin sound element of Jiazi Yichou is metal. (In the original edition, it reads 'Jia Yi Zi Wu' and 'Yi Geng Chou Wei', but the 'Jia Yi' in the first instance should be 'Jia Ji' as indicated by the following text, which is a transmission error.)

餘仿此數，列右圖。按：甲己子午九，乙庚辛未八，丙辛寅申七，丁壬卯酉六，戊癸辰戌五，巳亥四（己亥對宮亥空為虛，己與虛對為孤，己亥者孤虛之數也。）。

The other groups are calculated in the same way. The original book by Hang氏 includes a diagram on the right, but the transmitted version has lost it. Hang氏 himself explained: Jia and Ji are paired with Zi and Wu to make nine, Yi and Geng are paired with Chou and Wei to make eight (the original edition says 'Xinwei', which should be 'Chouwei' instead), Bing and Xin are paired with Yin and Shen to make seven, Ding and Ren are paired with Mao and You to make six, Wu and Gui are paired with Chen and Xu to make five, while Si and Hai are only paired with four and do not have another heavenly stem. Why is this so? Because the palace opposite Ji is Hai, and since the position of Hai is empty, it is called 'Xu' (empty). Ji facing 'Xu' becomes 'Gu' (solitary), so 'Jihai' is exactly the number of 'Gu Xu', which is the only one missing.

黃梨洲先生《象數論》所評議者，頗多未當。其謂甲子乙丑金者，甲九子九，乙八丑八，積三十四，以五除之餘四故為金。其數則是，其術則非也。故於丙寅丁卯，丙七寅七丁六卯六積二十六，以五陰之餘一故為火，便不成文矣。金四為一當為水，何以為火？而猶曰餘準此將無一能合者矣。

Huang Zongxi in his work "Yixue Xiangshu Lun" has many inappropriate comments on the concept of nayin. He said that Jiazi and Yichou belong to metal because Jia gets nine, Zi gets nine, Yi gets eight, and Chou gets eight, adding up to thirty-four, which when divided by five leaves a remainder of four, thus belonging to metal. Although the calculation is correct, the method he used is wrong. Therefore, when he comes to Bingyin and Dingmao, his reasoning becomes inconsistent: Bing gets seven, Yin gets seven, Ding gets six, and Mao gets six, adding up to twenty-six, which when divided by five leaves a remainder of one, and he concludes it belongs to fire. This reasoning is completely invalid. If a remainder of four can be considered metal, then according to the same principle, a remainder of one should be considered water, so why does he say it is fire? He also says "the rest can be inferred in the same way," but if this is the case, there is no way to make the reasoning consistent.

蓋納音得數之算法，當以大衍為本。以大衍之數五十去一，除去甲己子午之積數，餘則以五除之，得一則屬水，水生木，其納音為木。丙寅丁卯之為火，當以積數二十六，除大衍五十去一，餘二十三，以五除之餘三，屬木，木生火，故納音為火。甲子乙丑之積三十四，以除大衍去一餘五，五屬土，土生金。非三十四餘五餘四之謂也。

The calculation of the nayin sound element should be based on the fundamental principle of "Da Yan" or the Great Derivation. Take the number of Da Yan, which is fifty, subtract one to get forty-nine. Then subtract the accumulated number of categories such as Jia and Ji, Zi and Wu. The remainder is divided by five. If the result is one, it belongs to water, as water generates wood, and thus the nayin sound element is wood. For Bing Yin and Ding Mao, which are assigned to fire, the calculation is as follows: the accumulated number is twenty-six. Subtract this from forty-nine, leaving twenty-three. Divide this by five, resulting in a remainder of three. Three corresponds to wood in the Five Phases, and since wood generates fire, the nayin sound element is fire. For Jia Zi and Yi Chou, the accumulated number is thirty-four. Again, subtract this from forty-nine, leaving fourteen. Divide by five, resulting in a remainder of four. Four corresponds to fire in the Five Phases, and since fire generates earth, the nayin sound element is earth. The key lies in "first subtracting Da Yan and then determining the generated element," rather than directly dividing thirty-four by five as Huang did, and discussing the remainder of five and four.

納音納甲，與天干地支，皆始於黃帝。蓋自伏羲畫卦，利用宜民，至神農黃帝，文明日進，變化益繁。非單純八卦之象數所能濟用，故益之以陰陽五行。天五地六，迎日推歷，布算測地，以盡八卦之用。所謂“窮則變，變則通，通則久”。

The systems of Na Yin and Na Jia, along with the Heavenly Stems and Earthly Branches themselves, originated in the time of the Yellow Emperor. Since Fuxi drew the trigrams and taught the people to make full use of resources for a better life, civilization has gradually advanced, and the complexity of things has increased day by day. The simple images and numbers in the Eight Trigrams alone were no longer sufficient to cope with these changes. Therefore, the concept of Yin and Yang and the Five Phases were added beyond the Eight Trigrams. Taking "Heavenly Five" and "Earthly Six" as the main framework, they followed the sun's shadow to determine the calendar, used counting rods for calculations, and measured the terrain, thus fully developing the functions of the Eight Trigrams. This is exactly what the Great Treatise says: "When things reach their limit, they change; when they change, they become unblocked; when they become unblocked, they can endure for a long time."

納甲取先天，法象乎日月，仰以觀於天文也。納音以先天合後天，取數於陰陽十二消息，以布五行，俯以察於地理也。故京孟之《易》，悉本於此。朱元升《三易備遺》推衍納音最詳，巳亥數伏，一六相合，以為即《歸藏》之數，非無見也。

"Na Jia" derives the Earlier Heaven hexagram positions, based on the rising and setting and waxing and waning of the sun and moon, corresponding to the "looking up to observe the celestial phenomena" mentioned in the "Great Treatise." "Na Yin" combines Earlier Heaven and Later Heaven, taking numbers from the twelve yin and yang message hexagrams, then arranging the Five Phases accordingly, corresponding to "looking down to examine the terrestrial features." Therefore, the Yi studies of Jing Fang and Meng Xi all rest upon this foundation. Zhu Yuansheng of the Song dynasty wrote "San Yi Bei Yi," elaborating on Na Yin most thoroughly. He pointed out that the numbers of the branches Si and Hai are concealed and not apparent, and that one and six exactly correspond, believing this to be the numerical system of the "Guizang" Yi. This view is not without merit.