Reference · 66 pairings audited

The mechanisms behind zodiac compatibility

Almost every English page about Chinese zodiac compatibility hands out a verdict without saying where it came from. The tradition it is drawing on is not a mood board. It is a short, closed set of positional rules on a wheel of twelve, and once you know the rules you can check any claim yourself in about ten seconds. This page states the rules, does the arithmetic of the whole wheel, and then takes ten claims that circulate widely and sorts them into the ones the tables support, the ones that are folk verse wearing a table's clothes, and the ones that were made up.

The single most useful number is this one. There are 66 possible pairings of two different signs. 30 of them carry one of the four main relational marks, and 3 more appear only in the punishment lists, which leaves 33 pairings, exactly 50 percent of the wheel, with no traditional mark of any kind. A site that publishes a confident verdict for all 66 is not reading a tradition. It is filling in a grid.

The five relations

Four of these are derived from seat position, so they can be computed rather than looked up. The fifth is a listed overlay.

Relation	Rule	Covers	How tradition reads it
Trine sān hé · 三合	Signs four seats apart. Three of them form a triangle on the wheel.	4 triangles 12 pairings	The strongest positive mark. Natural allies who want the same things.
Secret friend liù hé · 六合	A mirror pairing across the wheel. Every sign has exactly one, and never more.	one per sign 6 pairings	A private alliance rather than a public one. Rated as high as a trine.
Clash liù chōng · 六冲	The sign directly opposite, six seats away.	one per sign 6 pairings	The hardest negative mark, and the one old matchmakers checked first.
Harm liù hài · 六害	Your clash partner’s secret friend. The relation is its own inverse.	one per sign 6 pairings	Slow friction rather than open conflict. Quieter than a clash and longer.
Punishment xíng · 相刑	Three fixed groups, listed rather than derived from seat position.	3 groups 7 pairings	An overlay, not a verdict. It can fall on a pair the other tables call good.

The arithmetic of the wheel

Twelve signs make 66 pairings of two different signs. Every one of them falls into exactly one of five buckets, and the buckets add up, which is a useful thing to be able to check:

12 trine pairings, from 4 triangles of three
6 secret-friend pairings, one per sign
6 clashes, one per sign, across the wheel
6 harm pairings, one per sign
36 with no main-relation mark, read through fixed elements instead
66 total

The punishment overlay sits on top of this count rather than inside it. It falls on 7 pairings, and it cuts across every other verdict: some of the 7 are already graded well by the main tables, which is why the overlay is read as a caution and not as a verdict of its own. 3 of them fall on otherwise unmarked pairs, and that detail is what makes the 50 percent figure 33 rather than 36. Most pages that quote a count here quote the wrong one.

Ten claims, checked

Each claim below circulates widely in English. The right-hand column is what the branch tables actually contain.

“Rat and Horse are the worst possible match.”

Mechanism-backed

A real clash. The Rat holds seat 1 and the Horse seat 7, six apart, directly opposite. Tradition does flag the clashes hardest. It calls them a caution, not a prohibition.

“Rat and Ox are unusually well matched.”

Mechanism-backed

A secret-friend pairing, one of the six. Nothing to do with the animals getting along; it is a fixed positional alliance in the branch tables.

“Your best matches are the signs four years apart from you.”

Mechanism-backed

That is the trine rule, and it is the one piece of the system the English web usually gets right. Four seats apart, 4 triangles, 12 pairs in total.

“Dragon and Dog are doomed.”

Mechanism-backed, overstated

A clash, yes. "Doomed" is not in the tables, which mark a position and offer no prediction about any particular couple.

“Goat and Rat should never marry.”

Folk rhyme, not a table

The pair is a genuine harm listing. The "never marry" force comes from a folk rhyme of marriages to avoid, which says the Goat and the Rat, once joined, are soon done. Old verse, honestly labeled, not a classical table.

“Tiger and Monkey clash because they are opposites in personality.”

Right answer, wrong reason

They are opposite in seat position, which is what produces the clash. Personality is the gloss written afterward, not the input. This pair also carries a punishment flag, which most pages miss entirely.

“Compatibility depends on your element, so a Metal Rat differs from a Water Rat.”

Two layers confused

There are two different elements in play. The element in "Metal Rat" comes from the year’s heavenly stem and rotates on a sixty-year cycle. The element the compatibility tables use is the branch’s own fixed element, which never changes: the Rat is always Water. The trine, clash, and harm relations run on branch position and are not affected by the stem at all.

“Same-sign couples are ideal.”

Not in the tables

The branch system has no entry for a sign paired with itself, which is why this site’s pair census counts 66 pairings rather than 78. The only classical footnote is the self-punishment list, which names four signs and is a caution about self-sameness.

“Dragon and Dog are 30% compatible.”

No basis at all

The tradition contains no numbers. Every relation is categorical: a pair either appears in a listing or it does not. Percentage scores are invented downstream, and no two sites that publish them agree.

“Every pairing has a traditional verdict.”

False, and this is the big one

Of the 66 pairings, 18 carry a positive mark, 12 carry a negative one, and 3 more show up only in the punishment lists. That leaves 33, exactly 50 percent of the wheel, in no listing whatsoever; those are read through fixed elements instead. Most confident verdicts you will read online are about pairs the tables never mention.

How each relation is derived

Number the seats 1 to 12 in cycle order, starting with the Rat. Then:

Trines are the four groups whose seats share the same remainder when divided by four. That is all the rule is, and it produces the four familiar triangles, each associated with one element:

Water · Rat, Dragon, Monkey (seats 1, 5, 9)
Metal · Ox, Snake, Rooster (seats 2, 6, 10)
Fire · Tiger, Horse, Dog (seats 3, 7, 11)
Wood · Rabbit, Goat, Pig (seats 4, 8, 12)

Clashes are the sign six seats away, which on a twelve-seat wheel means directly opposite. Six pairs, and every sign has exactly one.

Secret friends are a reflection. Fold the wheel along the line that runs between the Rat and the Ox, and every sign lands on its secret friend, with the Rat and the Ox, sitting either side of the fold, paired with each other. In arithmetic that is the same as saying the two branch numbers add to fifteen for five of the pairs, with Rat and Ox the exception on the fold itself. The six pairs are Rat and Ox, Tiger and Pig, Rabbit and Dog, Dragon and Rooster, Snake and Monkey, Horse and Goat.

Harms are the interesting one, because they look arbitrary in the classical tables and are not. Take a sign, find its clash partner, then find that partner's secret friend. The sign you land on is your harm. Run that on all twelve and you reproduce the classical six-harm listing exactly, and because the operation is its own inverse, doing it twice returns you to where you started. Our engine derives the harms this way and asserts that property in its test suite rather than storing the table by hand.

Punishments resist derivation. They are three named groups, carried as a list: 7 pairings are flagged, and they cut across the other verdicts.

The six harms and their rhyme

The harms are the least understood relation in English, partly because their force in popular culture comes from a folk rhyme of marriages to avoid rather than from the tables. The rhyme is genuine oral tradition and worth reading as exactly that. It is verse, not doctrine, and it is where a lot of the "never marry" phrasing online originally comes from.

Harm pairing	The rhyme's line, in English
Ox and Horse	From of old, the white horse fears the black ox.
Rat and Goat	The Goat and the Rat, once joined, are soon done.
Tiger and Snake	The snake that meets the tiger is cut as if by a blade.
Rabbit and Dragon	The dragon that meets the rabbit departs into the clouds.
Monkey and Pig	The pig that meets the monkey never sees it through.
Rooster and Dog	The golden rooster and the jade dog meet in tears.

What the tables do not do

Four honest limits, because a reference page that only lists what a system contains is only half useful.

They produce no numbers. Not scores, not percentages, not rankings within a category. A pair is in a listing or it is not.

They do not cover half the wheel. 33 of 66 pairings carry no mark at all. Reading those through fixed elements, as this site does, is a reasonable and traditional extension, but it is an extension, and we say so on every one of those pages.

They describe positions, not people. The animal glosses everyone enjoys, the Rat's memory and the Pig's open door, were written to explain relations that were already fixed by seat number. The geometry came first.

They are not evidence about anyone. No study has shown that a birth year shapes character or predicts a relationship. This is heritage worth knowing precisely and reading honestly, which is a different and better reason to know it than believing it.

Every pairing on this site names the rule that produced its verdict, and you can check any of them against the full 66-pair table. The exact year boundaries that decide which sign a birthday belongs to are a separate and surprisingly contested question, handled in our year-boundaries dataset and on the Li Chun page.

Sources

Chinese zodiac, for the compatibility system and its layers.
Earthly Branches, for the twelve-branch cycle, each branch's fixed element and yin-yang polarity, and the double-hours.
Wu Xing, for the five elements and the generating and controlling cycles used to read unmarked pairings.
The counts, pair lists, trine groupings, and harm derivation on this page are computed at build time from the same module that generates all 66 pairing pages, so the numbers here and the verdicts there cannot disagree.