On the Pairing of Heavenly Stems and Earthly Branches

论配支干

支干之義.多所配合.今略論方位及配所.幹不獨立.支不虛設.要須配合.以定歲月日時而用.如君臣夫婦.必配合以相成.總而言之.從甲至癸.爲陽.爲干.爲日.從寅至丑.爲陰.爲支.爲辰.別而言之.干則甲丙戊庚壬爲陽.乙丁己辛癸爲陰.支則寅辰午申戌子爲陽.卯巳未酉亥丑爲陰.陽則爲剛.爲君.爲夫.爲上.爲外.爲表.爲動.爲進.爲起.爲仰.爲前.爲左.爲德.爲施.爲開.陰則爲柔.爲臣.爲妻.爲妾.爲財.爲下.爲內.爲裏.爲止.爲退.爲伏.爲俯.爲後.爲右.爲刑.爲藏.爲閉.陰陽所擬.例多且略.大綱如此.甲乙寅卯.木也.位在東方.丙丁巳午.火也.位在南方.戊己辰戌丑未.土也.位在中央.分王四季.寄治丙丁.庚辛申酉.金也.位在西方.壬癸亥子.水也.位在北方.甲爲干首.子爲支初.相配者.太陽之氣.動於黄泉之下.在建子之月.黄鐘之律.爲氣之源.在子.故以子爲先.萬物湊出.於建寅之月.皆以見形.甲屬此月.故以甲爲先.而配子.見者爲陽.故從干.未見者爲陰.故從支.所以用甲子相配.爲六旬之始.干既有十.支有十二.輪轉相配.終於癸亥.故有六十日.十日一旬.故有六旬.一旬盡一甲癸.便以甲配子盡干.至癸酉便盡干.餘支有戌亥.又起甲配戌.盡干.至癸未.餘支有申酉.又起甲配申.盡干.至癸巳.餘支有午未.又起甲配午.盡干.至癸卯.餘支有辰巳.又起甲配辰.盡干.至癸丑.餘支有寅卯.又起甲配寅.盡干.至癸亥.十干有十二支相配.周畢.還從甲子起.故六甲輪轉.止六十日.十日一旬.一旬之内.二支無配偶者.爲之孤.所對衝者.爲之虚.卜筮所云空亡.以支孤無干.故名爲空亡.亡者.无也.无干故亡.所對者全虛.故云空也.算法.横下十二支.位於四方.縱下八干.位於四方.下戊己.位於中央.若甲子旬.取甲干以配子支.如此次第相配.至戊辰.位在中央.土爲四行主.不可移.故取辰支.巳支.入中央.配戊己.餘悉以干就支.至戌亥.无干配之.單故爲孤.辰巳之位.支干竝无.故名爲虛.其空亡之辰.從五行言之.如甲子旬.无戌亥.水土半空亡.以戌是土.亥是水也.不全無亥子.故云半也.甲戌旬.無申酉.爲金全空亡.以金二支竝无也.甲申旬.無午未.爲火土半空亡.以巳午不全无也.甲午旬.無辰巳.亦然.甲辰旬.無寅卯.亦云木全空亡.甲寅旬.無子丑.亦水土半空亡.竝以二支不俱無也.兵書云.陽生甲子.不足戌亥.仍爲天門.陰生甲午.不足辰巳.仍爲地戶.陽界甲寅.不足子丑.仍爲鬼門.陰界甲申.不足午未.仍爲人門.陽盛甲辰.卯爲之隔.陰興甲戌.酉爲之隔.此竝是六甲之空支也.春秋元命苞云.地不足東南.右動終而入虛門.此明甲子.孤在戌亥.虛在辰巳也.一干一支爲一日者.以周天三百六十五度四分度之一日.日行一度.故正用一干一支.以主一日也.三旬爲一月者.月日行十三度四分度之一.三旬而周天也.十二月爲一歲者.四時時有三月.生殺之功.備遍十二支也.一歲合三百六十日者.六六三十六.六甲之數也.六甲閒兩月之日者.以陰陽奇偶備也.陽者爲奇.陰者爲偶.萬物庶類.吉凶之理.以此彰矣.其支干相配.歲月日時竝然.立歲之元.起於上元甲子.立月之元.起甲巳之歲.十一月甲子.立日之元.六旬起自甲子.立時之元.冬夏二至後.得甲巳之日.夜半起甲子.四事皆以甲子爲首也.其上配九星.下配九州者.黃帝兵決云.甲子從北斗魁第一星起.順數至庚午.在第七剛星.至辛未.還從第六星.逆數至丙子.又從第一星.順數盡六甲.其下配九州者.史書云.甲齊.乙東夷.丙楚.丁南夷.戊魏.己韓.庚秦.辛西夷.壬燕.癸北夷.漢書五行志云.甲乙.海外.日月不治.丙丁.江淮海岱.戊己.中州河濟.庚辛.華山以西.壬癸.常山以北.子.周.丑.翟.寅.楚.卯.鄭.辰.邯鄲.巳.衛.午.秦.未.中山.宋.申.齊.酉.魯.戌.越.亥.燕.龍首經曰.子.齊.青州.丑.吳.越.揚州.寅.燕.幽州.卯.宋.豫州.辰.晉.兗州.巳.楚.荆州.午.周.三河.未.秦.雍州.申.蜀.益州.酉.梁州.戌.徐州.亥.衛.并州.若地辰之位.史漢近之.星次而論.龍首爲當.其配人身.甲乙爲頭.丙丁爲胸脇.戊己爲心腹.庚辛爲股.壬癸爲手足.則子爲頭.丑亥爲胸臂.寅戌爲手.卯酉爲腰脇.辰申爲尻肱.巳未爲脛.午爲足.此皆初爲首.末爲足.配五藏也.干以甲乙爲肝.丙丁爲心.戊己爲脾.庚辛爲肺.壬癸爲腎也.支以寅卯爲肝.巳午爲心.辰戌丑未爲脾.申酉爲肺.亥子爲腎.此皆從五行配之.又干以甲乙爲皮毛.丙丁爲爪筋.戊己爲肉.庚辛爲骨.壬癸爲血脈也.支以寅卯爲皮毛.巳午爲爪筋.辰戊丑未爲肉.申酉爲骨.亥子爲血脈也.木生在地上.故爲皮毛.火有猛毅.故爲爪筋.土有持載.故以爲肉.金性堅剛.故爲骨.水本流潤.故是血脈.竝支干所配.故以備釋.

On the Pairing of Heavenly Stems and Earthly Branches

Overall Paraphrased Meaning
The system of Heavenly Stems and Earthly Branches is profoundly rich in meaning, primarily applied through their mutual pairing. Heavenly Stems cannot stand alone, nor are Earthly Branches arbitrarily assigned; they must be matched to define years, months, days, and hours for practical use 🌄. This is akin to the relationship between a ruler and subjects or a husband and wife, where mutual cooperation is essential for fulfillment.

From a macro perspective: the sequence from Jia to Gui represents Yang, Heavenly Stems, and the sun; the sequence from Yin to Chou represents Yin, Earthly Branches, and time. In detail: among the Heavenly Stems, Jia, Bing, Wu, Geng, and Ren are Yang, while Yi, Ding, Ji, Xin, and Gui are Yin; among the Earthly Branches, Yin, Chen, Wu, Shen, Xu, and Zi are Yang, while Mao, Si, Wei, You, Hai, and Chou are Yin.

Yang symbolizes strength, the ruler, the husband, the upper position, the external, the surface, movement, progress, initiation, upward direction, forward, left, virtue, giving, and openness; Yin symbolizes gentleness, the subject, the wife, the concubine, wealth, humility, the internal, the interior, stillness, retreat, concealment, submission, backward direction, right, punishment, storage, and closure. The phenomena represented by Yin and Yang are vast, and the above serves only as an outline.

The correspondence between the Five Elements and the Stems and Branches is as follows:

• Jia, Yi, Yin, Mao belong to Wood 🌳, located in the East;
• Bing, Ding, Si, Wu belong to Fire 🔥, located in the South;
• Wu, Ji, Chen, Xu, Chou, Wei belong to Earth ⛰, located in the Center, governing the four seasons, and are placed between Bing and Ding;
• Geng, Xin, Shen, You belong to Metal ⚔️, located in the West;
• Ren, Gui, Hai, Zi belong to Water 🌊, located in the North.

Jia is the first Heavenly Stem, and Zi is the first Earthly Branch. Their pairing symbolizes the surging energy of the sun beneath the Yellow Springs. The month of Jianzi (the 11th lunar month) corresponds to the Huangzhong pitch pipe, the source of energy, hence Zi is the starting point. All things take form in the month of Jianyin (the 1st lunar month), and Jia belongs to this month, making it the beginning of the Heavenly Stems, paired with Zi. The visible belongs to Yang and follows the Heavenly Stems; the hidden belongs to Yin and follows the Earthly Branches. Thus, the Jia-Zi pairing serves as the starting point of the 60-year cycle.

There are ten Heavenly Stems and twelve Earthly Branches, rotating in pairing until Guihai, totaling 60 pairs, known as the "Sexagenary Cycle." Every ten pairs form a decade, totaling six decades. In each decade, one pair of Stems and Branches is fully cycled (e.g., Jiazi to Guiyou), leaving two Earthly Branches without a matching Heavenly Stem, called "orphaned"; their opposing Branches are called "void." In divination, this is referred to as "Kongwang" (空亡), meaning "empty and void"—"wang" (亡) signifies "none." The opposing positions are entirely empty, hence "empty."

The calculation method is as follows: arrange the twelve Branches horizontally in the four directions, and arrange the eight Stems (excluding Wu and Ji) vertically in the four directions, placing Wu and Ji in the center. For example, in the Jiazi decade, Jia is paired with Zi, and the pairing continues in sequence. When reaching Wuchen, Wu and Ji belong to Earth in the center, serving as the masters of the four elements and cannot be moved. Thus, the Branches Chen and Si enter the center to pair with Wu and Ji. The remaining Heavenly Stems are arranged according to the Earthly Branches, and when reaching Xu and Hai, no Stems are left to pair, making them "orphaned"; the positions of Chen and Si have neither Branches nor Stems, making them "void."

From the perspective of the Five Elements, the voids are as follows:

• Jiazi decade lacks Xu and Hai; Xu is Earth, Hai is Water, hence "half void of Water and Earth";
• Jiaxu decade lacks Shen and You; Metal Branches are entirely absent, hence "full void of Metal";
• Jiashen decade lacks Wu and Wei; Fire and Earth are partially absent, hence "half void of Fire and Earth";
• Jiawu decade lacks Chen and Si, similarly;
• Jiachen decade lacks Yin and Mao, hence "full void of Wood";
• Jiayin decade lacks Zi and Chou, hence "half void of Water and Earth."

Military texts state: "Yang is born in Jiazi, lacking Xu and Hai, yet it is the Gate of Heaven; Yin is born in Jiawu, lacking Chen and Si, yet it is the Gate of Earth; Yang's boundary is Jiayin, lacking Zi and Chou, yet it is the Gate of Ghosts; Yin's boundary is Jiashen, lacking Wu and Wei, yet it is the Gate of Humans; Yang peaks in Jiachen, with Mao as its barrier; Yin peaks in Jiaxu, with You as its barrier." These are the void Branches within the Six Jia cycles.

The Chunqiu Yuanming Bao states: "The Earth is incomplete in the southeast, moving rightward to end in the void gate," indicating that in the Jiazi decade, Xu and Hai are orphaned, and Chen and Si are void.

Using one Stem-Branch pair to represent a day is because the celestial sphere has 365¼ degrees, and the sun moves one degree per day, hence one Stem-Branch pair governs a day; three decades form a month because the moon moves 13¼ degrees per day, completing a near-full celestial cycle in thirty days; twelve months form a year because each of the four seasons has three months, and the functions of growth and decline span all twelve Branches; a year totals 360 days, symbolizing the six times six—thirty-six—cycles of the Six Jia. The two-month gap between the Six Jia cycles ensures the inclusion of both odd and even—Yang as odd, Yin as even. The principles of fortune and misfortune for all things are revealed through this.

The pairing of Stems and Branches applies similarly to years, months, days, and hours:

• The year cycle begins from the first year of the Shangyuan period, Jiazi;
• The month cycle begins from the 11th month of the year of Jiasi, with Jiazi;
• The day cycle begins from the six-decade Jiazi;
• The hour cycle begins from the midnight of Jiazi following the winter or summer solstice on a Jiasi day.
  All four cycles start with Jiazi.

Stems and Branches can also correspond to the Nine Stars and the Nine Provinces:

• According to the Huangdi Bingjue: Starting from the first star of the Big Dipper with Jiazi, count forward; by Gengwu, it reaches the seventh star, then Xinwei returns to the sixth star and counts backward; by Bingzi, it starts over forward, covering the Six Jia cycles;
• Multiple theories exist for correspondence with the Nine Provinces: For example, the Book of Han: Treatise on the Five Elements states that Jia and Yi belong to regions beyond the seas, Bing and Ding to the Yangtze-Huai River and Mount Tai regions, Wu and Ji to the Central Plains and the Yellow River-Ji River regions, Geng and Xin to regions west of Mount Hua, and Ren and Gui to regions north of Mount Heng;
• Earthly Branches correspond to regions: Zi to Zhou, Chou to Di, Yin to Chu, Mao to Zheng, Chen to Handan, Si to Wei, Wu to Qin, Wei to Zhongshan/Song, Shen to Qi, You to Lu, Xu to Yue, Hai to Yan;
• The Longshou Jing provides a detailed breakdown: Zi to Qi and Qingzhou, Chou to Wu-Yue and Yangzhou, Yin to Yan and Youzhou, Mao to Song and Yuzhou, Chen to Jin and Yanzhou, Si to Chu and Jingzhou, Wu to Zhou and Sanhe, Wei to Qin and Yongzhou, Shen to Shu and Yizhou, You to Liangzhou, Xu to Xuzhou, Hai to Wei and Bingzhou. In terms of geographical方位, the Longshou Jing is more appropriate.

Stems and Branches correspond to the human body:

• Heavenly Stems: Jia and Yi to the head, Bing and Ding to the chest and ribs, Wu and Ji to the heart and abdomen, Geng and Xin to the thighs, Ren and Gui to the hands and feet;
• Earthly Branches: Zi to the head, Chou and Hai to the chest and arms, Yin and Xu to the hands, Mao and You to the waist and ribs, Chen and Shen to the buttocks and upper arms, Si and Wei to the shins, Wu to the feet—from head to feet, assigned in sequence.

Correspondence to the five organs:

• Heavenly Stems: Jia and Yi to the liver, Bing and Ding to the heart, Wu and Ji to the spleen, Geng and Xin to the lungs, Ren and Gui to the kidneys;
• Earthly Branches: Yin and Mao to the liver, Si and Wu to the heart, Chen, Xu, Chou, Wei to the spleen, Shen and You to the lungs, Hai and Zi to the kidneys.

Further correspondence to the body based on Five Elements characteristics:

• Heavenly Stems: Jia and Yi to the skin and hair, Bing and Ding to the claws and tendons, Wu and Ji to the flesh, Geng and Xin to the bones, Ren and Gui to the blood vessels;
• Earthly Branches: Yin and Mao to the skin and hair, Si and Wu to the claws and tendons, Chen, Xu, Chou, Wei to the flesh, Shen and You to the bones, Hai and Zi to the blood vessels.

The rationale is as follows:

• Wood grows above ground, hence corresponding to skin and hair;
• Fire is fierce and resolute, hence corresponding to claws and tendons;
• Earth supports and carries, hence corresponding to flesh;
• Metal is hard and rigid, hence corresponding to bones;
• Water flows and moistens, hence corresponding to blood vessels.

The above provides a fundamental explanation of the Stem-Branch correspondence system, covering its essence and application framework.

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🧠 In-Depth Understanding

Core Concepts 💡

• Yin-Yang Pairing: The Stem-Branch system is fundamentally a dynamic pairing system of Yin-Yang and the Five Elements, emphasizing that "lone Yin cannot birth, lone Yang cannot grow"—mutual pairing is essential to form an effective spatiotemporal framework.
• Principle of Void (Kongwang): Reveals "void points" in spatiotemporal energy, which are both deficiencies and opportunities for transformation, akin to unallocated resources or dormant nodes in modern systems.
• Holographic Correspondence: Maps Heavenly Stems and Earthly Branches to celestial phenomena, geography, the human body, and organs, reflecting the holographic thinking of "heaven-human correspondence" in classical Chinese philosophy.

Modern Interpretation 🌟

• Systems Thinking: The Stem-Branch system is an ancient coding system, using 60 sets of codes to record changes in time, space, and energy states, similar to modern binary coding in computers but more multidimensional and symbolic.
• Modern Significance of Void (Kongwang): Can be understood as "buffer zones" or "transition interfaces" within cycles, indicating areas temporarily lacking energy support, requiring cautious decision-making or active adjustment.
• Principle of Bodily Correspondence: Unlike modern anatomy, this is a functional and energetic mapping, reflecting the holistic view of "external correspondence and internal connection" in traditional Chinese medicine.

Practical Value ⚡

• Time Management: Understanding Stem-Branch cycles can help identify personal energy fluctuation cycles and合理安排 important tasks.
• Decision-Making Reference: The concept of Kongwang提醒 us to be especially cautious in certain time periods or areas, avoiding rash actions.
• Health and Wellness: The correspondence between Stems/Branches and organs provides a basis for temporal medicine in traditional wellness, such as deep sleep during the Yin period (3-5 a.m.) when the lung meridian is active.

Philosophical Reflection 🤔

• Relativity and Completeness: The pairing of Yin-Yang and Stems/Branches shows the universe as a relative yet complete system, where everything has its counterpart and correspondence.
• Dialectic of Visible and Hidden: "The visible is Yang, the unseen is Yin" reveals the relationship between表象 and essence, appearance and concealment, reminding us to consider the influence of unseen energies.

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📚 Related Knowledge

Related Concepts

• Sexagenary Cycle (六十甲子): The least common multiple cycle system of Heavenly Stems and Earthly Branches.
• Kongwang (空亡): Also known as "decade void," the state where certain Earthly Branches lack a matching Heavenly Stem in a specific decade.
• Jianyue (建月): The fixed correspondence of Earthly Branches to lunar months (e.g., the first month is Jianyin).
• Nayin Wuxing (纳音五行): The deeper Five Elements attributes generated by Stem-Branch combinations.

Further Reading

• Sanming Tonghui: On the origin and development of Stems and Branches.
• Yuanhai Ziping: Chapters on Stem-Branch pairing.
• Wuxing Jingji: Detailed explanation of Kongwang.
• Huangji Jingshi: Theory of cosmic cycles.

Modern Research

• Qin Lunshi's Practical Studies on Eight Characters: Modern interpretation of Kongwang.
• Li Shunxiang's Mysteries of the Four Pillars: Practical methods for interpreting Kongwang.
• Western scholars' mathematical modeling research on the Stem-Branch system.