Hidden Stems: What Each Earthly Branch Holds Inside
A branch is not a single element. Inside each of the twelve earthly branches sit one to three heavenly stems, called hidden stems, and the tradition shares a thirty-day month out among them. This is why a chart can contain an element that no visible character shows.
Why a branch holds stems
Each branch stands for a whole month, and a month is never one pure thing. The first days still carry some of the month before, the middle may hold a trace of what is coming, and only then does the month's own character take over. The tradition expresses this by placing stems inside each branch. In Chinese they are called 藏干, the stored stems; in Korean they are 지장간 (地藏干), the stems stored in the earth.
The haru engine lists them in time order, as parts of a thirty-day month:
- Residual qi (餘氣, 여기): the lingering stem from the month before, first in line.
- Middle qi (中氣, 중기): a short middle layer, present in nine of the twelve branches.
- Main qi (正氣, 정기): the branch's own stem, which always has the most days and matches the branch's element.
The full table
Each row adds up to 30 days. A dash means the branch has no middle stem.
| Branch | Residual (days) | Middle (days) | Main (days) | Branch element |
|---|---|---|---|---|
| 子 Rat | 壬 Water (10) | - | 癸 Water (20) | Water |
| 丑 Ox | 癸 Water (9) | 辛 Metal (3) | 己 Earth (18) | Earth |
| 寅 Tiger | 戊 Earth (7) | 丙 Fire (7) | 甲 Wood (16) | Wood |
| 卯 Rabbit | 甲 Wood (10) | - | 乙 Wood (20) | Wood |
| 辰 Dragon | 乙 Wood (9) | 癸 Water (3) | 戊 Earth (18) | Earth |
| 巳 Snake | 戊 Earth (7) | 庚 Metal (7) | 丙 Fire (16) | Fire |
| 午 Horse | 丙 Fire (10) | 己 Earth (9) | 丁 Fire (11) | Fire |
| 未 Goat | 丁 Fire (9) | 乙 Wood (3) | 己 Earth (18) | Earth |
| 申 Monkey | 戊 Earth (7) | 壬 Water (7) | 庚 Metal (16) | Metal |
| 酉 Rooster | 庚 Metal (10) | - | 辛 Metal (20) | Metal |
| 戌 Dog | 辛 Metal (9) | 丁 Fire (3) | 戊 Earth (18) | Earth |
| 亥 Pig | 戊 Earth (7) | 甲 Wood (7) | 壬 Water (16) | Water |
Three families of branches
The table falls into three neat groups with the same day pattern.
The four season-opening branches 寅, 巳, 申 and 亥 all split 7, 7 and 16, and all begin with 戊 for 7 days. Their middle stem is the element whose three-harmony group begins there: 寅 holds 丙 Fire, and 寅 is the first of the Fire trio 寅午戌; 巳 holds 庚 Metal, first of 巳酉丑; 申 holds 壬 Water, first of 申子辰; 亥 holds 甲 Wood, first of 亥卯未.
The four mid-season branches are 子, 卯, 午 and 酉. Three of them, 子, 卯 and 酉, hold just two stems of one element, 10 and 20 days, which is why the tradition calls them the purest branches. 午 is the exception, with 丙 10, 己 9 and 丁 11.
The four Earth branches 辰, 未, 戌 and 丑 all split 9, 3 and 18. Their residual stem is the main stem of the month just before: 辰 opens with 乙 from 卯, 未 with 丁 from 午, 戌 with 辛 from 酉 and 丑 with 癸 from 子. Their small 3-day middle stem is the element whose three-harmony group ends there: 癸 Water in 辰, 乙 Wood in 未, 丁 Fire in 戌 and 辛 Metal in 丑. The tradition calls these branches storehouses for that reason.
How the engine counts them
When the haru engine measures the elements of a chart, each visible stem counts 1. Each branch counts 1 in total, shared among its hidden stems by days out of 30, so 18 days of 己 adds 0.6 to Earth. The month branch counts double, because it is the season the person was born into. The totals are then turned into percentages.
Example A from the engine's test set is Seoul, 15 May 1990, 14:30, with the pillars 庚午 (year), 辛巳 (month), 庚辰 (day) and 癸未 (hour). No visible character is Wood, so the surface count for Wood is 0. Yet two branches hide 乙 Wood: 辰 for 9 days, worth 0.3, and 未 for 3 days, worth 0.1. With four stems, three ordinary branches and one doubled month branch, the total weight is 9, and 0.4 out of 9 is the 4.4% Wood the engine reports.
Metal shows the opposite effect. Three visible stems are Metal (庚, 辛, 庚), and the month branch 巳 hides 庚 for 7 days, counted twice. That lifts Metal to 38.5%, the largest share in the chart. When a hidden stem also appears on top of a pillar, as 庚 does here, the tradition says the stem shows through (透出) and reads it as especially active.
| Element | Visible characters | Weighted share | Where the hidden part comes from |
|---|---|---|---|
| Wood | 0 | 4.4% | 乙 in 辰 (9 days) and in 未 (3 days) |
| Fire | 2 | 23% | 丙 and 丁 in 午, 丙 in the month branch 巳, 丁 in 未 |
| Earth | 2 | 21.9% | 己 in 午 and 未, 戊 in 巳 and 辰 |
| Metal | 3 | 38.5% | 庚 in the month branch 巳 (7 days, doubled) |
| Water | 1 | 12.2% | 癸 in 辰 (3 days) |
Different books, slightly different days
Classical manuals do not all agree on the exact day counts, and some schools leave out a middle stem that others include. The haru engine uses one fixed table, the one shown above, so its numbers are consistent from chart to chart. If you compare with another source and see a day or two of difference, that is a difference of school, not an error in either.
Questions
Do hidden stems count as much as visible ones?
No. In the haru engine a visible stem counts 1, while a whole branch counts 1 shared among its hidden stems by days, except the month branch, which counts 2.
Why does 午 contain Earth when it is a Fire branch?
Its middle stem is 己 Earth for 9 days. Its residual 丙 and main 丁 are both Fire, so Fire still makes up 21 of its 30 days.
Why can an element be 'missing' but still have a percentage?
The missing list looks only at visible characters. The percentage includes hidden stems, so an element can be absent on the surface yet present underneath.
Which hidden stem matters most?
The main stem, which always has the most days. The tradition reads residual and middle stems as quieter background layers.
Read next
Traditional Four Pillars (myeongni) and yin-yang five-element interpretation. Not a medical diagnosis or advice.