What is the Sixty Stem-Branch Cycle?
The sixty stem-branch cycle is the calendar-symbol system at the foundation of Sanmei-gaku. It combines the ten heavenly stems and twelve earthly branches in order, producing sixty named pairs used for years, months, and days.
Contents
Stems as qualities, branches as coordinates
The ten heavenly stems express qualities of qi: the Five Elements divided into Yin and Yang. Jia and Yi are Wood, Bing and Ding are Fire, Wu and Ji are Earth, Geng and Xin are Metal, and Ren and Gui are Water.
The twelve earthly branches express coordinates of time, direction, month, and season. Rat marks north and midnight, Rabbit marks east and dawn, Horse marks south and noon, and Rooster marks west and evening.
When a chart is calculated, each pillar contains one stem and one branch. Together they show both the quality of qi and its position in time and season.
The ten stems express qualities of energy: the five elements refined by yin and yang.
The twelve branches act as coordinates of time, season, month, and direction.
| Stem | Element | Yin/Yang | Image | Quality |
|---|---|---|---|---|
| 甲 | Wood | Yang | Tall tree | Straight growth; beginning |
| 乙 | Wood | Yin | Grass and flowers | Flexible spread; connection |
| 丙 | Fire | Yang | Sun | Brightly illuminates; appears outwardly |
| 丁 | Fire | Yin | Lamp flame | Burns inwardly; refines sensitivity |
| 戊 | Earth | Yang | Mountain | Receives broadly; protects |
| 己 | Earth | Yin | Cultivated field | Cultivates; orders; stores |
| 庚 | Metal | Yang | Ore and blade | Tempers; cuts open |
| 辛 | Metal | Yin | Gemstone | Polishes; selects; refines |
| 壬 | Water | Yang | Sea and great river | Flows; expands; crosses boundaries |
| 癸 | Water | Yin | Rain and dew | Permeates; moistens; waits |
The five elements also map to directions: Wood east, Fire south, Earth center, Metal west, and Water north.
The branch side also forms directional zones. Ox, Dragon, Goat, and Dog also carry Earth as seasonal transition points.
| Element | Direction | Season | Stems | Branch Zone | Meaning |
|---|---|---|---|---|---|
| Wood | East | Spring | Jia / Yi | Tiger / Rabbit / Dragon | Sprouting, growth, beginnings. Overlaps with Rabbit, east, and morning symbolism. |
| Fire | South | Summer | Bing / Ding | Snake / Horse / Goat | Brightness, diffusion, expression. Overlaps with Horse, south, and noon symbolism. |
| Earth | Center | Seasonal transitions | Wu / Ji | Ox / Dragon / Goat / Dog | Receiving, adjustment, roots. Works as the center that connects the four directions. |
| Metal | West | Autumn | Geng / Xin | Monkey / Rooster / Dog | Harvest, ordering, selection. Overlaps with Rooster, west, and dusk symbolism. |
| Water | North | Winter | Ren / Gui | Boar / Rat / Ox | Accumulation, introspection, flow. Overlaps with Rat, north, and midnight symbolism. |
Branches as time, month, direction, and season
The twelve branches divide one day into twelve two-hour periods. The Rabbit hour is roughly 5:00 to 7:00, centred around 6:00, when light begins to appear.
The same branches also mark months and seasons. Rabbit month is roughly March, when winter has passed and spring warmth begins to extend.
They also mark directions: north and winter around Rat, east and spring around Rabbit, south and summer around Horse, and west and autumn around Rooster.
Traditional timekeeping divides the day into 12 branches, each about two hours. The same sequence also maps onto compass directions.
Branch months follow the same seasonal logic. Rabbit month roughly corresponds to March, when light and warmth begin to expand.
| Branch | Time | Center | Direction | Month | Meaning |
|---|---|---|---|---|---|
| 子Rat | 23:00-1:00 | 00:00 | North | Rat month (around December; Great Snow to before Minor Cold) | Midnight. At the depth of winter solstice, yang qi begins to form within. |
| 丑Ox | 1:00-3:00 | 02:00 | NNE | Ox month (around January; Minor Cold to before Beginning of Spring) | Before dawn. At the depth of cold, strength is stored for what comes next. |
| 寅Tiger | 3:00-5:00 | 04:00 | ENE | Tiger month (around February; Beginning of Spring to before Awakening of Insects) | Pre-dawn. Spring begins and dormant force starts moving outward. |
| 卯Rabbit | 5:00-7:00 | 06:00 | East | Rabbit month (around March; Awakening of Insects to before Clear and Bright) | Dawn. Light arrives and warmth after winter begins to extend. |
| 辰Dragon | 7:00-9:00 | 08:00 | ESE | Dragon month (around April; Clear and Bright to before Beginning of Summer) | Morning. In moist earth, what has grown begins to take form. |
| 巳Snake | 9:00-11:00 | 10:00 | SSE | Snake month (around May; Beginning of Summer to before Grain in Ear) | Late morning. Heat rises and activity becomes clear. |
| 午Horse | 11:00-13:00 | 12:00 | South | Horse month (around June; Grain in Ear to before Minor Heat) | Noon. Yang force opens outward at its brightest. |
| 未Goat | 13:00-15:00 | 14:00 | SSW | Goat month (around July; Minor Heat to before Beginning of Autumn) | Afternoon. Holding the heat of fullness, it turns toward ripening and adjustment. |
| 申Monkey | 15:00-17:00 | 16:00 | WSW | Monkey month (around August; Beginning of Autumn to before White Dew) | Before evening. Light tilts and what has ripened begins to be gathered. |
| 酉Rooster | 17:00-19:00 | 18:00 | West | Rooster month (around September; White Dew to before Cold Dew) | Dusk. Harvesting, selecting, and sharpening outlines. |
| 戌Dog | 19:00-21:00 | 20:00 | WNW | Dog month (around October; Cold Dew to before Beginning of Winter) | Entry into night. Protecting what has ended and preparing for inner return. |
| 亥Boar | 21:00-23:00 | 22:00 | NNW | Boar month (around November; Beginning of Winter to before Great Snow) | Night. Outer activity closes and returns inward like water. |
Month ranges are approximate and based on solar terms; exact boundaries vary slightly by year.
Why there are sixty combinations
The cycle begins with Jia-Rat, then Yi-Ox, Bing-Tiger, and so on. The stems and branches advance together one step at a time.
Because the stems cycle in ten and the branches cycle in twelve, both return to the starting point after sixty steps. This is why the system has sixty combinations rather than 120 free pairings.
Yang stems meet Yang branches and Yin stems meet Yin branches because odd-numbered stems continue to meet odd-numbered branches, while even-numbered stems meet even-numbered branches.
| Step | Pair | Polarity | Logic |
|---|---|---|---|
| 1 | 甲子 | Yang + Yang | Stems and branches advance at the same pace |
| 2 | 乙丑 | Yin + Yin | Stems and branches advance at the same pace |
| 3 | 丙寅 | Yang + Yang | Stems and branches advance at the same pace |
| 4 | 丁卯 | Yin + Yin | Stems and branches advance at the same pace |
| 5 | 戊辰 | Yang + Yang | Stems and branches advance at the same pace |
| 6 | 己巳 | Yin + Yin | Stems and branches advance at the same pace |
| 7 | 庚午 | Yang + Yang | Stems and branches advance at the same pace |
| 8 | 辛未 | Yin + Yin | Stems and branches advance at the same pace |
| 9 | 壬申 | Yang + Yang | Stems and branches advance at the same pace |
| 10 | 癸酉 | Yin + Yin | Stems and branches advance at the same pace |
| 11 | 甲戌 | Yang + Yang | Stems return to Jia/Yi while branches continue to Dog/Boar |
| 12 | 乙亥 | Yin + Yin | Stems return to Jia/Yi while branches continue to Dog/Boar |
The least common multiple of 10 and 12 is 60, so both cycles return to Jia-Rat together after 60 steps.
The full list and Tenchusatsu groups
The sixty combinations are divided into groups of ten. Each group leaves two branches without a matching stem, which creates the Tenchusatsu group.
Seeing the list by groups makes it easier to understand why, for example, one set belongs to Dog-Boar Tenchusatsu while the next belongs to Monkey-Rooster Tenchusatsu.
The list is also useful for understanding kanreki, the return to the same yearly stem-branch pair after sixty years.
| Tenchusatsu Group | No. | Void Branches | Stem-Branch Pairs |
|---|---|---|---|
| Dog-Boar Tenchusatsu | 1-10 | Dog / Boar | 1.甲子2.乙丑3.丙寅4.丁卯5.戊辰6.己巳7.庚午8.辛未9.壬申10.癸酉 |
| Monkey-Rooster Tenchusatsu | 11-20 | Monkey / Rooster | 11.甲戌12.乙亥13.丙子14.丁丑15.戊寅16.己卯17.庚辰18.辛巳19.壬午20.癸未 |
| Horse-Goat Tenchusatsu | 21-30 | Horse / Goat | 21.甲申22.乙酉23.丙戌24.丁亥25.戊子26.己丑27.庚寅28.辛卯29.壬辰30.癸巳 |
| Dragon-Snake Tenchusatsu | 31-40 | Dragon / Snake | 31.甲午32.乙未33.丙申34.丁酉35.戊戌36.己亥37.庚子38.辛丑39.壬寅40.癸卯 |
| Tiger-Rabbit Tenchusatsu | 41-50 | Tiger / Rabbit | 41.甲辰42.乙巳43.丙午44.丁未45.戊申46.己酉47.庚戌48.辛亥49.壬子50.癸丑 |
| Rat-Ox Tenchusatsu | 51-60 | Rat / Ox | 51.甲寅52.乙卯53.丙辰54.丁巳55.戊午56.己未57.庚申58.辛酉59.壬戌60.癸亥 |
Each row is one Tenchusatsu group. The void branches change every ten stem-branch pairs.
How it is used in a chart
A Sanmei-gaku chart assigns one stem-branch pair to the year pillar, one to the month pillar, and one to the day pillar. The day stem becomes the Day Master, the central reference point for many readings.
The day pillar's number in the sixty-cycle is also used to determine the person's Tenchusatsu group.
The sixty cycle is therefore a shared language for reading elemental balance, hidden stems, phase relationships, timing cycles, and Tenchusatsu.
FAQ
Is the stem-branch cycle only for years?
No. It is used for years, months, and days. Sanmei-gaku reads the year, month, and day pillars as a three-pillar chart.
Why is it not 120 combinations?
Because stems and branches advance together in order. Ten and twelve return to the starting point after sixty steps.
How do I find my day pillar?
It is calculated from the birth date using the stem-branch calendar. FATE DECODER calculates it automatically.
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