Two related rules cover most of traditional zodiac compatibility. The six harmonies pair branches off; the three harmonies group them into seasonal triangles. Both come out of the same system that generates the five elements.
Liu He — the six harmonies
Six pairs: Zi–Chou, Yin–Hai, Mao–Xu, Chen–You, Si–Shen, Wu–Wei. Historically these derive from the same pairing as the heavenly stem five combinations, which is why they are considered the tighter of the two rules.
Each pair is also understood as a stem-and-branch combination that resolves to a single element — Rat and Ox together are said to settle into Earth, for example. That is why these pairs read as "combining" rather than merely "compatible".
San He — the three harmonies
Four triangles, each naming a phase of the year rather than a fixed relationship:
| Triangle | Phase |
|---|---|
| Hai–Mao–Wei | Growth — wood, spring |
| Yin–Wu–Xu | Peak — fire, summer |
| Si–You–Chou | Decline — metal, autumn |
| Shen–Zi–Chen | Storage — water, winter |
Reading them as seasonal phases rather than as scores explains something the score versions do not: harmony here is about two people being at compatible stages, not about being similar.
Note that the four triangles are four branches apart — which is exactly why they form a triangle on a twelve-point circle. The geometry is the rule.
Using both rules together
In practice a reader checks the six harmonies first, because a direct pair is stronger than a shared triangle. If neither applies, the three-harmony group is the fallback. Both failing is not a negative result — most pairs sit in the neutral middle, and that is normal rather than ominous.
How much weight to give them
Because both rules use only the year branch, they say nothing about the other seven characters in either chart. They are a reasonable first pass on a compatibility question and an unreliable final answer.
Why most pairs are neutral
Twelve branches, six pairs, four triangles — the arithmetic leaves most combinations unaffected by either rule. That is the normal case, not an ominous one.
It is worth saying plainly because compatibility tables rarely mention it, and the omission pushes readers toward treating "no harmony found" as a negative result.
Harmony is not sameness
The seasonal reading makes this clear: a triangle gathers the branch that begins a season with the one that peaks and the one that stores it. Those are different stages, not similar ones.
Compatibility here is about being at stages that fit, which is a different claim from being alike.