A lookup is four finite tables, not a reading
Element lookup in BaZi means mapping characters to elements. The mapping is finite: ten stems, twelve branches, and the hidden stems inside each branch. Anyone can hold all of it in their head, and every published table that disagrees with the ones below is wrong in a way that can be demonstrated rather than argued about.
What the mapping does not do is decide strength. Two charts can carry identical counts and opposite readings, because counting visible characters ignores the season, the roots, and which hidden stems are actually in charge. The tables come first; the judgement about weight comes after, and it is a separate procedure.
The ten stems
Each stem is one element at one polarity. The polarity alternates down the list, which is why the yang stems are all odd-numbered in the traditional ordering.
| Stem | Element | Polarity | Direction |
|---|---|---|---|
| 甲 | Wood 木 | yang | east |
| 乙 | Wood 木 | yin | east |
| 丙 | Fire 火 | yang | south |
| 丁 | Fire 火 | yin | south |
| 戊 | Earth 土 | yang | centre |
| 己 | Earth 土 | yin | centre |
| 庚 | Metal 金 | yang | west |
| 辛 | Metal 金 | yin | west |
| 壬 | Water 水 | yang | north |
| 癸 | Water 水 | yin | north |
The twelve branches, with the trap built in
Branches alternate polarity by position: 子 寅 辰 午 申 戌 are yang, the other six are yin. That assignment is positional and does not follow the hidden stems inside.
子 is the case that catches people. It is a yang branch that contains only 癸, a yin stem. So a chart with 子 in it holds yang water at the branch level and yin water at the hidden-stem level, and a reading that treats 子 as simply yin water will be one polarity off in every ten-god calculation that touches it.
| Branch | Element | Polarity | Zodiac | Hours | Hidden stems |
|---|---|---|---|---|---|
| 子 | Water 水 | yang | rat | 23:00–01:00 | 癸 |
| 丑 | Earth 土 | yin | ox | 01:00–03:00 | 己 癸 辛 |
| 寅 | Wood 木 | yang | tiger | 03:00–05:00 | 甲 丙 戊 |
| 卯 | Wood 木 | yin | rabbit | 05:00–07:00 | 乙 |
| 辰 | Earth 土 | yang | dragon | 07:00–09:00 | 戊 乙 癸 |
| 巳 | Fire 火 | yin | snake | 09:00–11:00 | 丙 庚 戊 |
| 午 | Fire 火 | yang | horse | 11:00–13:00 | 丁 己 |
| 未 | Earth 土 | yin | goat | 13:00–15:00 | 己 丁 乙 |
| 申 | Metal 金 | yang | monkey | 15:00–17:00 | 庚 壬 戊 |
| 酉 | Metal 金 | yin | rooster | 17:00–19:00 | 辛 |
| 戌 | Earth 土 | yang | dog | 19:00–21:00 | 戊 辛 丁 |
| 亥 | Water 水 | yin | pig | 21:00–23:00 | 壬 甲 |
The season decides more than the count does
The month branch sets the season, and the season sets which element is 旺, 相, 休, 囚 or 死. This is the oldest weighting rule in the system and it outranks any tally of visible characters.
A chart born in 亥 month is a winter chart. Water is 旺, wood is 相, metal is 休, earth is 囚, fire is 死 — regardless of how many fire characters appear on the surface. A single 丙 in a winter chart is not the same fact as a single 丙 in a summer chart, and no counter that treats them as one unit will get there.
| Season | 旺 (dominant) | 相 (next) | 休 (resting) | 囚 (trapped) | 死 (spent) |
|---|---|---|---|---|---|
| Spring 春 | Wood 木 | Fire 火 | Water 水 | Metal 金 | Earth 土 |
| Summer 夏 | Fire 火 | Earth 土 | Wood 木 | Water 水 | Metal 金 |
| Autumn 秋 | Metal 金 | Water 水 | Earth 土 | Fire 火 | Wood 木 |
| Winter 冬 | Water 水 | Wood 木 | Metal 金 | Earth 土 | Fire 火 |
Hidden stems have an order, and the order decides
The hidden stems inside a branch are not equal. The first is the 本氣 — the branch's own element. The second and third are 中氣 and 餘氣, phases carried over from elsewhere in the cycle. 寅 holds 甲 丙 戊 with 甲 as 本氣; 巳 holds 丙 庚 戊 with 丙; 申 holds 庚 壬 戊 with 庚; 亥 holds 壬 甲 with 壬.
Which hidden stem governs the month depends on where inside the solar term the birth falls. The 人元司令 tables run 寅 month as 戊 for the opening days, then 丙, then 甲 for the longest stretch; 卯 month runs 甲 then 乙. Published tables disagree about the day counts and agree about the order, so a birth within a few days of a 節 can be assigned a different ruling stem by two readers who are each following a table correctly.
This is the reason a month reading is a claim about a hidden stem rather than about a branch. My month branch is 七殺 is shorthand for the ruling hidden stem of my month branch is 七殺, and near a boundary it may have been a different stem a few days earlier. Saying so costs one clause and makes the reading checkable.
A stem with a root is not the same as a stem on the page
通根 means a stem is supported by its own element somewhere beneath it, either directly in the branch or through a hidden stem of the same element. 透干 is the reverse direction: a hidden stem that also appears on the stem layer, which the tradition treats as the hidden quality becoming visible and therefore easier to act on.
In 庚午 丁亥 乙酉 辛巳 every stem is rooted, which is why the single visible 乙 is not a floating character. 丁 roots in 午, its 祿. 辛 roots in 酉, its 祿. 庚 roots through 酉, its 羊刃. 乙 roots in 亥 through the 甲 hidden there. Four stems, four roots, and the tally that reported one wood missed the fact that the wood is standing on something.
Now imagine the same eight characters with the stems rearranged onto branches of unrelated elements. The counts would be identical and the chart would read differently, because a root is a structural fact and a count is a tally. No counter can tell the two apart, which is the whole argument for doing this by hand instead.
One chart, two counts, one of them wrong
Take 庚午 丁亥 乙酉 辛巳. Count the visible characters by element and you get metal three (庚 辛 酉), fire three (丁 午 巳), wood one (乙), water one (亥), earth none. That is the answer a counter gives, and the headline it produces is usually a missing earth.
Now open the hidden stems. 午 holds 己, which is earth. 巳 holds 戊, which is also earth. So earth is not missing at all — it is present twice, both times inside branches whose surface element is fire. The chart has no earth on the stem or branch layer and two earth stems underneath it.
The season adds a third correction. Born in 亥 month, water is 旺 and wood is 相, so the single 乙 is not a weak character in a hostile chart; it is a wood Day Master in its supporting season, with 亥 holding 壬 and 甲 behind it. Three readings of the same eight characters, and only the one that includes hidden stems and season survives contact with the rules.
What the lookup cannot answer
It cannot name the useful element. That is 用神, and it depends on a method — 扶抑, 調候, 通關, or 病藥 — which different schools rank differently. Two readers can agree on every count above and disagree about which element the chart needs, because they are answering a different question.
It cannot treat a missing element as a need. Charts are not buckets with holes. A chart strong in an element can still be harmed by more of it, and a chart with none of an element can be perfectly functional without it. The lookup tells you what is on the board. What to do about it is a separate argument, and the tables will not settle it.