Branch Alliances
What Are Three Harmonies (San He) and Directional Trines (San Hui) in Ba Zi?
While a Six-Harmony (Liu He) is a one-on-one pairing, a Three-Harmony trine (San He) unites the Birth, Peak, and Vault branches of an element into a powerhouse coalition—capable of reshaping your chart's dominant momentum.
TianJiGe Editorial TeamUpdated

In Ba Zi, branch alliances rank by strength from Directional Trines (San Hui, e.g., Yin-Mao-Chen East Wood) down to Three-Harmony Trines (San He: Shen-Zi-Chen Water, Yin-Wu-Xu Fire, Si-You-Chou Metal, Hai-Mao-Wei Wood), Growth Half-Trines, Six Harmonies, and Vault Half-Trines. Every San He trine revolves around its central Cardinal Peak branch (Zi, Wu, Mao, or You), and whether completing a trine brings breakthroughs or pressure depends on whether the resulting element serves your Useful God.
The lifecycle anatomy of a Three-Harmony trine: Birth + Peak + Vault
Each of the four Three-Harmony (San He) trines unites the three critical milestones of an element's Twelve-Life-Stage cycle—its **Birth (Chang Sheng)**, **Peak (Di Wang / Hub)**, and **Vault (Mu Ku)**:
**Shen–Zi–Chen Water Trine** (Born in Shen, Peaks in Zi, Stored in Chen); **Hai–Mao–Wei Wood Trine** (Born in Hai, Peaks in Mao, Stored in Wei); **Yin–Wu–Xu Fire Trine** (Born in Yin, Peaks in Wu, Stored in Xu); **Si–You–Chou Metal Trine** (Born in Si, Peaks in You, Stored in Chou).
Comparing San Hui, San He, Half-Trines (Ban He), and Arching Trines (Gong He)
**Directional Trine (San Hui)**: Three consecutive seasonal months (such as Yin–Mao–Chen spring Wood)—the purest, heaviest elemental force.
**Full Three-Harmony (San He)**: All three trine branches present, channeling cross-seasonal resources toward the central Peak element.
**Half-Trine (Ban He)**: Two of the three branches present, including the central Peak branch (Zi, Wu, Mao, or You). A **Growth Half-Trine** (Birth + Peak, like Shen–Zi or Yin–Wu) is significantly stronger than a **Vault Half-Trine** (Peak + Vault, like Zi–Chen).
**Arching Trine (Gong He)**: When the Birth and Vault branches appear without the central Peak (like Shen–Chen without Zi), holding latent energy until a transit year supplies the missing hub.
What happens when a Luck or Annual Pillar completes a Three-Harmony trine
When a transit supplies the third branch to complete a San He trine in your chart, collaborations, multi-party deals, or marriage milestones frequently crystallize—bringing windfalls if the element is your Useful God, or calling for boundary discipline if it amplifies an Unfavorable God.
How to Get Started
- 1Check your four natal branches (plus Luck and Annual branches) for complete San He or San Hui sets.
- 2If two branches appear, check whether the central Cardinal branch (Zi, Wu, Mao, or You) is present to form a true Half-Trine.
- 3Verify whether the combined element protrudes in the Heavenly Stems.
- 4Evaluate whether the resulting elemental surge supports or pressures your Day Master.
Common Mistakes
- Judging business or marriage compatibility solely by birth-year zodiac trines while ignoring the Day Pillars.
- Confusing a weak Arching pair (missing Zi/Wu/Mao/You) with a full Three-Harmony trine.
- Forgetting that a heavy clash directly against the central Peak branch can break up a trine.
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FAQ
A Growth Half-Trine (Birth + Peak) is noticeably stronger because the Birth branch actively generates and feeds the Peak branch.
It occurs when the first and last branches of a trine (such as Yin and Xu) sit in the chart without the middle Peak branch (Wu)—acting like an arch waiting for a Horse (Wu) year to drop the keystone into place.
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