Stem combinations (天干五合)
Five pairs of stems combine: 甲–己, 乙–庚, 丙–辛, 丁–壬, 戊–癸. In each pair a yang stem meets the yin stem it controls (or is controlled by), five places apart in the list. The traditional elements they can transform into are earth, metal, water, wood and fire respectively. San Ming Tong Hui explains combination as the harmony of yin and yang, using the image of marriage:
夫合者，乃和谐之义，如阳见阳，二阳相竞则为克，阴见阴，二阴不足则为克，唯阴见阳，阳见阴为合，亦如男女相合而成夫妇之道。“Combination means harmony. When yang meets yang, the two compete, and that is control; when yin meets yin, the two are insufficient, and that is also control. Only yin meeting yang, or yang meeting yin, makes a combination — like man and woman joining in marriage.”— San Ming Tong Hui 《三命通會》, 卷二 · 论十干合. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
A combination binds the two stems, so they act less freely. Whether the pair actually transforms into a new element is a stricter question. The Di Tian Sui discusses “true transformation” in its chapter on following and transforming, requiring that the combining stems be adjacent, that the transformed element be supported by the month, and that nothing in the chart obstruct it:
化得真者只論化，化神還有幾般話。“Where the transformation is true, discuss only the transformation; and of the transformed spirit there is still more to say.”— Di Tian Sui (Drops from Heaven’s Marrow) 《滴天髓》, 從化論－真. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
Most combinations in real charts are binding rather than transforming.
The three harmonies (三合)
Four groups of three branches, each four places apart, form an elemental “frame”: 申子辰 water, 亥卯未 wood, 寅午戌 fire and 巳酉丑 metal. Each group joins the element’s Birth, Peak and Tomb branches. San Ming Tong Hui explains the water frame:
如申子辰，申乃子之母，辰乃子之子，申乃水生，子乃水旺。“Take Shen-Zi-Chen: Shen is the mother of Zi and Chen is the child of Zi; in Shen water is born, in Zi water is at its peak.”— San Ming Tong Hui 《三命通會》, 卷二 · 论支元三合. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
and insists that all three must be present:
若三字缺一则化不成局，不可以三合化局论。“If one of the three characters is missing, the transformation does not form a frame, and it cannot be treated as a three-harmony frame.”— San Ming Tong Hui 《三命通會》, 卷二 · 论支元三合. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
Many later practitioners accept “half harmonies” of two branches, especially when the middle (peak) branch is present, as a weaker version. That is a modern extension; the classical line above is strict.
The directional groups (三会)
The three branches of each season — 寅卯辰 east/wood, 巳午未 south/fire, 申酉戌 west/metal, 亥子丑 north/water — form directional groups, usually considered even stronger than the harmonies. The Di Tian Sui warns not to confuse the two kinds of group:
方是方兮局是局，方要得方莫混局。“A direction is a direction and a frame is a frame; a direction should be a pure direction, not mixed with a frame.”— Di Tian Sui (Drops from Heaven’s Marrow) 《滴天髓》, 方局論. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
The six combinations (六合)
Six pairs of branches combine: 子–丑, 寅–亥, 卯–戌, 辰–酉, 巳–申, 午–未. San Ming Tong Hui derives them from yin-yang numerology:
夫合者，和也，乃阴阳相和，其气自合。“Combination means harmony: yin and yang in accord, their energies naturally join.”— San Ming Tong Hui 《三命通會》, 卷二 · 论支元六合. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
It explains why 子 pairs with 丑 rather than with 亥 by counting “yang numbers”: 子 is the first yang and 丑 the second yin, one plus two makes three. 午 and 未 also make three (午 the first yang, 未 the second yin); the other four pairs all sum to nine, the extreme of yang numbers. Six combinations bind branches and, in some readings, transform them; like stem combinations, they are usually read as ties rather than full transformations.
Clashes (六冲)
Branches directly opposite each other on the twelve-branch circle clash: 子–午, 丑–未, 寅–申, 卯–酉, 辰–戌, 巳–亥. San Ming Tong Hui relates this to the stems, where the seventh stem counting from oneself is the controlling “killing” stem:
地支取七位为冲，犹天干取七位为煞之义。如子午对冲，子至午七数，甲逢庚为煞，甲至庚七数。“Among the branches, the seventh position is the clash, just as among the stems the seventh position is the “killing”. Zi and Wu face each other in clash: from Zi to Wu is seven counts; Jia meeting Geng is the killing: from Jia to Geng is seven counts.”— San Ming Tong Hui 《三命通會》, 卷二 · 论冲击. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
The Di Tian Sui distinguishes clashes among stems and among branches, and says branch clashes are the more urgent:
天戰猶自可，地戰急如火。“A battle in the heavens can still be tolerated; a battle on the earth is as urgent as fire.”— Di Tian Sui (Drops from Heaven’s Marrow) 《滴天髓》, 戰合論. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
As explained on the earthly branches page, the effect of a clash depends on the branches: the growth branches 寅 申 巳 亥 suffer from it, while the storage branches 辰 戌 丑 未 are “opened”. San Ming Tong Hui says the same about the storehouses:
若戌丑辰未四库所藏为十干财官、印绶等物，尤喜冲激“As for Xu, Chou, Chen and Wei, the four storehouses, what they store are the Wealth, Officer, Resource and other things of the ten stems; they especially welcome being clashed.”— San Ming Tong Hui 《三命通會》, 卷二 · 论冲击. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
Other relationships
Classical texts also discuss punishments (刑), harms (害) and breaks (破). They are less consistent across sources and much debated, and the Di Tian Sui itself treats them as secondary to clashes:
支神祇以沖為重，刑與害兮動不動。“Among the branch spirits, only the clash is weighty; punishments and harms may or may not move anything.”— Di Tian Sui (Drops from Heaven’s Marrow) 《滴天髓》, 地支論. Original text: Wikisource · also on ctext.org (different edition). Translation: bazimethod.
A quick reference
| Relationship | Members | Traditional result |
|---|---|---|
| Stem combinations | 甲己 · 乙庚 · 丙辛 · 丁壬 · 戊癸 | Earth · Metal · Water · Wood · Fire |
| Three harmonies | 申子辰 · 亥卯未 · 寅午戌 · 巳酉丑 | Water · Wood · Fire · Metal |
| Directional groups | 寅卯辰 · 巳午未 · 申酉戌 · 亥子丑 | Wood · Fire · Metal · Water |
| Six combinations | 子丑 · 寅亥 · 卯戌 · 辰酉 · 巳申 · 午未 | Earth · Wood · Fire · Metal · Water · (Fire/Earth) |
| Six clashes | 子午 · 丑未 · 寅申 · 卯酉 · 辰戌 · 巳亥 | Opposites on the circle |
The results listed for the six combinations follow the common modern table; sources differ on 午未 in particular, which is given as fire, earth or simply “sun and moon”. Treat that column as conventional rather than settled.
Why position matters
Almost all authors agree that interactions between neighbouring pillars are stronger than interactions across the chart. A 子–午 clash between the day and hour branches is felt more than the same clash between the year and hour. Combinations that involve the month branch are especially important, because the month carries the season. When the texts disagree, it is usually about how much weight distance and position should carry.
Reading interactions in practice
When you look at a chart, check in this order: are there stem combinations between adjacent stems? Is there a complete directional group or three harmony in the branches? Are there clashes, and do they hit growth, peak or storage branches? Do the luck pillar and the year bring the missing third branch of a harmony, or clash a natal branch? Combinations and clashes with the luck pillars and years are a large part of how practitioners describe changes over time. Our calculator does not yet mark interactions automatically; we plan to add this, with each rule labelled by its source.
Keep learning
Classical quotations are copied from the public-domain texts on Wikisource; links let you check every line. English translations are our own. Traditional Bazi statements are reported as tradition, not as fact.