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支干数者，凡有二种。一通数，二别数。今先辩通数，后论别数。
通数者，十干、十二支也。干有十者，应天地之大数也。《易·系辞》言：天数五，地数五。天地之数，不过于十，故以干极于十。十主日，十日为一旬也。
支十二者。《礼·稽命征》言：布政十二，尊卑有序。《援神契》言：三三参行，四四相扶。天有四时之气，以三月成一时，故言三三参行，四四相扶。天地人谓之三才，是为三者，物生之常数，因而各生三，本三而末九，所以十二。《元命苞》言：数成于三，故合于三。三月，阳极于九，故一时九十日也。支象于月，十二月为一岁也。此辨通数。
别数者，支数，则子数九，丑八，寅七，卯六，辰五，巳四，午九，未八，申七，酉六，戌五，亥四。《太玄经》云：子午九者，阳起于子，讫于午；阴起于午，讫于子。故子午对冲，而阴阳二气之所起也。寅为阳始，申为阴始，从所起而左数，至所始而定数。故自子数至申，数九；自午数至寅，亦九。所以子午九也。丑未为对冲，自丑数至申，数八；自未数至寅，亦八。所以丑未八也。寅申为对冲，自寅数至申，数七；自申数至寅，亦七。所以寅申七也。卯酉为对冲，自卯数至申，数六；自酉数至寅，亦六。所以卯酉六也。辰戌为对冲，自辰数至申，数五；自戌数至寅，亦五。所以辰戌五也。巳亥为对冲，自巳数至申，数四；自亥数至寅，亦四。所以巳亥四也。
又云：阳数极于九。子午为天地之经，故取阳之极数。自丑未巳下，各减一，从八至四，理自可知。
干数者：甲九，乙八，丙七，丁六，戊五，己九，庚八，辛七，壬六，癸五。《太玄经》云：甲己九者，甲起甲子，从子故九，己为甲配，故与甲俱九。乙起乙丑，从丑故八，乙配于庚，与庚俱八。丙起丙寅，从寅故七，辛配于丙，与丙俱七。丁起丁卯，从卯故六，丁配于壬，与壬俱六。戊起戊辰，从辰故五，癸配于戊，与戊俱五。
支有十二，以对冲同数，故自九至四。干唯有十，以配合同数，故自九至五。
又云：支从地，故数毕于阴，以四偶也。干从天，故数毕于阳，以五奇也。五则止于五气，四则极于四时。上不过九者，阳之极数也。
五行及支干之数，相则倍之，王则十而倍之，休则如本，因死半之。以此四而孳，数乃无极。此并从气增减，气盛则多，气衰则少也。
The numerical system of the Heavenly Stems and Earthly Branches consists of two types: General Numerology and Special Numerology. 🌿 We will first analyze the General Numerology and then explore the Special Numerology.
General Numerology refers to the basic numerical framework of the Ten Heavenly Stems and Twelve Earthly Branches. The reason the Heavenly Stems are "ten" corresponds to the core numerology of heaven and earth. The Book of Changes: Appended Judgments states: "The number of heaven is five, and the number of earth is also five." 🌌 The sum of the numbers of heaven and earth is ten, so the number of Heavenly Stems is limited to "ten." The Ten Heavenly Stems represent the cycle of the "sun," with ten days forming a xun (a ten-day period).
The Earthly Branches are "twelve" in number, originating from rituals and natural laws. The Book of Rites: Lifeline Divination states: "The calendar divides the year into twelve months to administer governance, reflecting the order of hierarchy." The Yuanshen Qi states: "Three and three are mutually complementary, four and four support each other." Heaven has the energy of four seasons, with three months in each season, hence the phrase "three and three operate together, four and four support each other." 🌏 Heaven, earth, and humanity are collectively called the "Three Powers," which is the fundamental constant for the generation of all things. From this, each derives three, with the root being three and the end being nine, thus totaling twelve. The Yuanming Bao states: "Numerology is completed in 'three,' thus aligning with three." Each season has three months, and the peak of yang energy is nine (3×3), so a season consists of ninety days. The Earthly Branches symbolize the moon, with twelve months making a year. The above forms the basis of General Numerology.
Special Numerology refers to the individual numbering systems of the Earthly Branches and Heavenly Stems:
The Taixuan Jing explains the numerology of the Earthly Branches: "Zi and Wu are numbered nine because yang energy begins at Zi and peaks at Wu; yin energy begins at Wu and peaks at Zi. Zi and Wu are opposing directions, representing the starting points of yin and yang energies. Yin is the beginning of yang, and Shen is the beginning of yin. Counting leftward from the starting point to the beginning of yin or yang determines the number. Thus, counting from Zi to Shen totals nine positions; counting from Wu to Yin also totals nine positions, so both Zi and Wu are numbered nine." Similarly:
The numerical extremes of yin and yang are nine. Zi and Wu represent the warp and weft of heaven and earth, so they take the peak yang number nine. From Chou and Wei downward, the numbers decrease by one, from eight to four, aligning with numerical logic.
The numbering principle for the Heavenly Stems is similar: Jia starts from Jiazi, and Zi is numbered nine, so Jia is nine; Ji pairs with Jia, so it is also nine. Yi starts from Yichou, and Chou is numbered eight, so Yi is eight; Geng pairs with Yi, so it is also eight. The rest follow the same pattern.
The numerology of the Earthly Branches is based on "opposing branches sharing the same number," so the range is from nine to four. The Heavenly Stems are based on "matching stems sharing the same number," so the range is from nine to five. The Earthly Branches belong to earth, and their numbers end with the yin number four (even). The Heavenly Stems belong to heaven, and their numbers end with the yang number five (odd). Five symbolizes the five energies (Five Elements), and four symbolizes the four seasons. Numbers do not exceed nine, as nine is the extreme number of yang.
The numerology of the Five Elements and the Stems and Branches doubles in the "Xiang" (flourishing) state, multiplies tenfold in the "Wang" (peak) state, remains unchanged in the "Xiu" (resting) state, and halves in the "Si" (death) state. Following this pattern, numerical changes are infinite. All of this is based on the rise and fall of energy—increasing when energy is abundant and decreasing when energy is weak.
This numerical system is essentially an ancient, precise phenomenological mathematical model:
The ancient numerical system reveals the quantitative thinking of Chinese philosophy—transforming abstract philosophical concepts into calculable models. This "numerical philosophy" unifies the Three Powers (heaven, earth, and humanity) within a mathematical framework, reflecting the ancient pursuit of cosmic unity. This mode of thinking shares surprising similarities with modern systems science.
Contemporary scholars have discovered that the numerology of the Stems and Branches:
Note: The numerical system in this chapter is a foundational tool for advanced astrological analysis. It is recommended to master its application through practical case calculations.
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