Heavenly stems and earthly branches: the twenty-two characters a chart is spelled with

The stems are the short wheel. Ten characters, two to each of the five elements, the first of each pair yang and the second yin, in the fixed order Wood, Fire, Earth, Metal, Water. In a chart the stem is the top character of every pillar, and the stem of your day pillar is the one the whole reading is organized around: the day master, the character that is you.

The first Chinese dictionary, Xu Shen's Shuowen Jiezi of AD 100, defines them as weather. Jia is "the first of the east, the yang breath beginning to stir"; yi is "spring plants pushing up bent and crooked"; bing is "the south, everything formed and bright"; and so on round the year to gui, "winter, water and earth level, everything measurable." Then, entry by entry, Xu Shen does something no English page seems to have noticed: he lays the ten stems onto a human body from the top down. Jia is like the head, yi the neck, bing the shoulders, ding the heart, wu the ribs, ji the belly, geng the navel, xin the thighs, ren the shins, gui the feet. Ten stems, one standing person. The table keeps the body column, because once you have seen it you cannot unsee the day master as the heart of the thing.

Two of the ten are odd men out, and the oddness is old. Wu and ji, the Earth pair, are the only stems the Shuowen defines by position rather than season: both are simply "the central palace." Sima Qian, writing his Shiji two centuries earlier, explains the stems on a tour of the compass, one wind at a time, hanging jia and yi on the east wind, bing and ding on the south, geng and xin on the west, ren and gui on the north, with a gloss for each: ren "is to bear, the yang breath bearing and nourishing everything below," gui "is to measure, everything now measurable." The tour has no stop at the center. Wu and ji never come up. Earth in this system is not a direction you can face; it is the ground the other four stand on, which is exactly how a bazi reading treats it.

Sima Qian also does not call them stems. His word for the ten is "the ten mothers," and for the twelve "the twelve children," and the treatise signs off with the ten mothers, the twelve children and the pitch-pipes all tuned together since high antiquity. The words we translate as stem and branch, the trunk and the limbs of one tree, are a later gloss, and the section on their history below says how much later.

The branches are the long wheel, and they do more jobs. Each one is a month of the traditional calendar, with yin as the first month and zi, the month of the winter solstice, as the eleventh. Each is a two-hour block of the day, zi centered on midnight and wu on noon, which is the shichen system and has its own page. Each, since about the second century BC, carries a zodiac animal. And each hides one to three stems, which is the part a reading actually uses and the part the next section is about. The polarity alternates down the twelve like the stems, and the element of a branch is the element of its main hidden stem.

Read the last column and notice what is not in it. The Shuowen defines every one of the twelve branches as a month and a state of the crops: mao is "to push through; the second month, everything breaks the soil"; chen is "to shake; the third month, thunder, and the farmers go out"; you is "done; the eighth month, millet ripe enough for wine." In all twelve entries there is exactly one animal. It is the snake, under si, and it is there for a reason that has nothing to do with a zodiac: the character 巳 is a drawing of one, and Xu Shen says so. No rat under zi, no ox under chou, no dragon under chen. The dictionary that fixed the meaning of these characters in AD 100 did not know they had animals, because in the sense that matters they did not yet. The animals were bolted on by the second century BC, on the evidence of a set of Qin bamboo slips found in Gansu. The zodiac is real and old; it is simply younger than the branches it rides on.

Here is the piece of the alphabet that the English pages leave out, and it is the piece the arithmetic runs on. A branch is not one element; it is a container. The Song-dynasty manual Yuanhai Ziping, the founding text of the day-master method, puts it in a line: the stem is heaven, the branch is earth, and what the branch hides is the human. Then it gives the contents of all twelve in a rhyme that every student of the art once knew by heart, and that our engine's table is checked against every time this page is built:

In plain English: zi holds gui alone; chou holds gui, xin and ji; yin holds jia with bing and wu; mao holds yi alone; chen holds yi, wu and gui; si holds geng, bing and wu; wu holds ding and ji; wei holds yi, ji and ding; shen holds geng, ren and wu; you holds xin alone; xu holds xin, ding and wu; hai holds ren and jia. The pattern is not random. The four branches at the cardinal points, zi, mao, wu and you, are pure or nearly so: one element at full strength. The four at the corners, chen, wei, xu and chou, are the Earth branches, and each keeps a residue of the season just ended (the yi inside chen is the last of spring's Wood) plus a third stem the tradition says is stored there, the way a granary holds last year's grain. The remaining four, yin, si, shen and hai, are the growth branches where a season opens, and each carries the element of the season it opens plus the stem of the element said to be born there, so Fire is already inside the first month of spring.

Which is why a chart with, say, no Fire stem at all can still be a Fire-heavy chart: the Fire is in the branches, hidden, and a reader counts it. Our calculator weighs the main hidden stem at six tenths of the branch and the two minor ones at three tenths and one tenth, which is the modern mainland convention rather than anything in the Song text; the text only says what is inside, not how much of it counts. That is the honest limit of the rhyme. It is also why two calculators fed the same birth can call the same person strong and weak, a disagreement the conventions page measures on eight of them.

The twenty-two are among the oldest characters still in daily use anywhere on earth, and the way to feel that is to notice what they were doing before they had names. The Shang kings at Anyang, around 1200 BC, cracked ox shoulder blades and turtle shells to ask their ancestors questions, and every question was dated. The dates are stem-branch pairs. In the translations that Columbia's Sources of Chinese Tradition prints, a diviner named Gu makes his cracks "on yiwei (day 32)," a diviner named Zheng "on renzi (day 49)" and again "on guichou (day 50)," and the questions they ask are whether "Father Yi" or "Grandfather Ding" is the ancestor harming the king. The sixty-day cycle is not being invented on those bones. It is being used as casually as a Tuesday, and Zhang He, in a 2020 comparative study of the Chinese and Mesoamerican cycles, notes that a complete run of all sixty pairs appears "neatly aligned" in the inscriptions by 1200 BC.

Look at those ancestors' names again. Father Yi. Grandfather Ding. The Shang royal house named its dead by stems: Pan Geng, who moved the capital to Anyang; Wu Ding, the king whose reign the oracle bones begin in; Di Xin, the last of the line. Zhang He's list runs to seven kings and the observation that "only the names of the heavenly stems were chosen to bestow upon people." Not one Shang king is named for a branch. The ten were the half that belonged to people, and the reason is probably the plainest one: ten stems made a ten-day week. The Shuowen entry for that week is three characters long, "ten days make a xun," and one of the standard divinations on the bones, cracked on the last day of one xun about the next, is three characters that David Keightley renders "In the next ten days there will be no disasters." Long before anyone put a stem on a branch, the stems were the days you lived through.

The names came a thousand years later. "The system was not clearly named until about 200 BCE," Zhang He writes, when people began calling the ten gan and the twelve zhi. The gloss that stuck is Cai Yong's, from his second-century handbook Duduan, which the Ming manual Sanming Tonghui quotes at the head of its chapter on origins: gan is a trunk, there are ten of them and they are also called the ten mothers, today's jia through gui; zhi is a branch, there are twelve of them and they are also called the twelve children. One tree, a trunk and its limbs; and behind it Sima Qian's older and stranger image of mothers and children, which the Ming author keeps, because the ten do generate the sixty and the twelve are what they generate it on.

Where the twelve came from in the first place nobody knows, and it is worth saying so plainly rather than picking a pretty story. Guo Moruo, the great twentieth-century reader of the oracle bones, suggested that the ten stems were simply ten fingers and that the twelve branches had been borrowed from the Babylonian zodiac; Zhang He points out that the Babylonian constellations were not formalized at twelve stations until 700 BC, five centuries after the branches appear complete on the bones, and files the idea under speculation. So will we.

The two wheels turn together, one notch each: jia-zi, yi-chou, bing-yin, and so on. Because both advance at once, a stem in an odd position can only ever land on a branch in an odd position, so the yang stems meet only the yang branches and the yin only the yin. Half the grid of 120 possible pairs is never visited. The sequence closes after sixty steps, comes back to jia-zi, and starts again, which is why a Chinese sixtieth birthday is the one that matters: your birth year has just been called by its full name for the first time since you arrived. The sixty pairs, the old names the Erya gave them, and the way a day pillar is counted through them without ever resetting are the next page in this series. For now, the decoder above will tell you what your own eight are made of, and the calculator will cast them if you do not have them yet.