Four elements,
three tempos.

The grid

Four elements times three modes is twelve, and the zodiac fills every cell once. Fire has a cardinal, a fixed and a mutable sign; so does every other element. No two signs share both properties. Knowing a sign's element and mode tells you which sign it is.

The four elements

The elements come from Greek natural philosophy, where they were an account of what matter is made of. Astrology kept them after chemistry stopped needing them, as a description of four registers a person can operate in. Signs sharing an element sit 120° apart — a trine — which is the closest thing the wheel has to a shared native language.

Fire — Aries, Leo, Sagittarius

Heat, initiative, self-assertion. Fire is the element that acts before it has all the information, and its characteristic error is treating momentum as evidence. It warms a room and it does not check the ground first.

Earth — Taurus, Virgo, Capricorn

Substance, endurance, consequence. Earth is the element that asks what a thing actually costs, who does the work and by when. Its characteristic error is confusing what is durable with what is right.

Air — Gemini, Libra, Aquarius

Distance, pattern, exchange. Air is the element that steps back from a situation it is standing in and describes it. Its characteristic error is mistaking having named a feeling for having had one.

Water — Cancer, Scorpio, Pisces

Depth, memory, permeability. Water registers the emotional temperature of a room as information and is usually right about it. Its characteristic error is being unable to tell which of the feelings currently present belong to it.

The three modes

The modes — also called qualities or quadruplicities — describe tempo rather than substance. They are tied directly to the solar year: each season has a sign that opens it, one that sits in the middle of it, and one that hands it over. Signs sharing a mode sit 90° or 180° apart, which is why they grind against each other.

Cardinal — Aries, Cancer, Libra, Capricorn

Starts. Each cardinal sign begins at a solstice or an equinox — the four hinges of the solar year — and each initiates in its own element. The cardinal difficulty is the middle of anything.

Fixed — Taurus, Leo, Scorpio, Aquarius

Holds. The fixed signs occupy the settled middle of each season, and they behave like it: enormous staying power, and a reversing gear that has to be installed by hand.

Mutable — Gemini, Virgo, Sagittarius, Pisces

Adapts. The mutable signs fall at the end of each season, where one is turning into the next, and they are fluent in changed circumstances — sometimes before the circumstances have changed.

Why this is one fact and not two

Here is the part that matters, and it is the reason this page exists rather than being a paragraph on another one. Element and mode are both functions of the distance between two signs. Two signs four apart necessarily share an element. Two signs three apart necessarily share a mode. Neither is free information once you know the angle.

Any compatibility model that scores element, mode and distance as three separate terms is therefore counting one thing three times. The consequence is not subtle: the scores compress into a narrow flattering band, hard pairings become unreachable, and two different friends return the same number. That is precisely what the first version of this site's engine did, and rebuilding it around the angle alone is the single largest change this tool has had.

Polarity, the fourth property

There is one more division, usually mentioned and rarely used. The signs alternate between two polarities — traditionally masculine and feminine, more usefully described as outward-facing and inward-facing. Fire and air signs are outward; earth and water signs are inward. Signs of the same polarity are an even number of signs apart, which is why every soft aspect joins same-polarity signs and the semi-sextile and quincunx do not.