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Relations · Three Harmony (San He)

Three Harmony (San He): every pair, derived

The trines frame three branches into an element: four groups, equally spaced on the wheel, each with a cardinal middle. That no Earth trine exists is a checkable structural fact. This page lists all four with the geometry.

Computed facts (engine-verified + build-time assertions)

This page is generated from engine vv0.14.0; the pairs follow convention R35 on the methodology page, and the generator refuses to render if any cross-check fails. Audit item by item.

Trines4 (three branches each)
Geometryeach trine sits at wheel seats {0, 4, 8} with a cardinal middle (Zi/Wu/Mao/You) — build-time assertion
No Earth trineno Earth trine exists: the four tomb branches Chen-Xu-Chou-Wei all clash one another, so no equilateral triangle of Earth
SourceBRANCH_TRINE (engine constant, with English names)

The complete table

One row per pair or group: members, nature and a one-step derivation. Nothing omitted — the table is the full set.

TrineElementOne-step derivation
申 Shen · 子 Zi · 辰 ChenWaterthree branches at equal distance (+4, +8) with the cardinal middle at 子 Zi
亥 Hai · 卯 Mao · 未 WeiWoodthree branches at equal distance (+4, +8) with the cardinal middle at 卯 Mao
寅 Yin · 午 Wu · 戌 XuFirethree branches at equal distance (+4, +8) with the cardinal middle at 午 Wu
巳 Si · 酉 You · 丑 ChouMetalthree branches at equal distance (+4, +8) with the cardinal middle at 酉 You

Scan your own four pillars

Enter your birth moment (time optional). The page finds every hit of this relation among the six pairwise combinations of your four pillars.

A note on what this page deliberately does not do: the popular versions of this material assign a fixed personality to each term — one character per branch, one destiny per stage. This site rejects that framing. What is published here is a structural position: which element sits where, on what kind of ground, with which tenants inside. The same term reads differently under a different month command, and no meaningful judgement exists without the other characters of the chart. Where the tradition offers a reading it is labelled as the tradition's; this site's own contribution is that every number and term on this page is computed, versioned and checkable against the methodology page.

Frequently asked

Why is there no Earth trine?
A trine needs three branches at equal wheel distance (0, 4, 8). The four Earth branches Chen-Xu-Chou-Wei clash one another pairwise and cannot form an equilateral triangle — a checkable structural fact, not a school choice.
What is the middle god?
The middle branch of each trine (Zi of Shen-Zi-Chen, Mao of Hai-Mao-Wei, Wu of Yin-Wu-Xu, You of Si-You-Chou) — exactly the four cardinal branches. It anchors the frame: the half-combination and bow-pair dispute turns on whether it is present (see the half page).
What if only two of the three branches appear?
That is exactly the half-combination versus bow-pair question — all 12 two-branch picks are listed on the half page, 8 half combinations and 4 bow pairs separately marked, so you choose your reading openly.

The other seven relation pages

Heavenly Stem Combination →  ·  Heavenly Stem Clash →  ·  Six Harmony (Liu He) →  ·  Six Clash (Liu Chong) →  ·  Six Harm (Liu Hai) →  ·  Punishment (Xing) →  ·  Half Combination (Ban He) →

Reference index

Every enumerable component of ba zi has its own page here. Each page is computed by the same engine and can be checked item by item — none of it is a personality table.