Zodiac sign compatibility: what the grid actually measures
A compatibility grid measures one thing exactly, and that thing is not two people. It measures the angle between the starts of two signs. The zodiac is a circle cut into twelve blocks of 30°, so any two signs stand 0°, 30°, 60°, 90°, 120°, 150° or 180° apart, and every familiar verdict — the easy pairs, the difficult ones, the pairs said to be blind to each other — follows from which of those seven numbers applies. The structure is real. What it is a structure of is the arithmetic of a divided circle.
Seven distances, and nothing else
Number the signs from Aries as zero. The distance between any two is 30° times the number of steps between them, counted the short way round, which leaves seven cases. The tradition named five of them, conjunction and sextile and square and trine and opposition, and treated the remaining two, the 30° and the 150°, as aversion: signs that do not behold one another.
Three further properties fall out of the same count. Modality cycles with a period of three, so signs three or six steps apart always share one, cardinal with cardinal, fixed with fixed, mutable with mutable. Polarity alternates at every step, so an even number of steps preserves it and an odd number reverses it. Element cycles with a period of four.
The classical sorting follows entirely from that. The even distances, 0° and 60° and 120° and 180°, keep polarity and were read as signs that can see each other. The square keeps modality but not polarity, and was counted among the hard aspects. The 30° and the 150° keep nothing at all.
Fire with air, earth with water: the same rule stated twice
Element affinity is usually taught as a separate doctrine. Fire and air are said to feed one another, earth and water to shape one another, and the two families not to mix. Laid against the count, it is not a second rule.
Same element means four steps: the trine at 120°. Complementary element, fire with air or earth with water, means two steps or six: the sextile at 60° and the opposition at 180°. Every remaining pairing, fire with earth, fire with water, air with earth, air with water, falls at one, three or five steps, which is 30°, 90° or 150°.
That is why the grid is so smooth. It does not accumulate observations about people born in April and people born in October. It renders the parity of a difference between two integers, and anyone with the twelve names and a pencil could reconstruct the whole table from scratch.
What the grid discards
Comparing whole signs rounds every position down to the start of its block, and a sun does not sit at the start of its sign. Take the trine, the cell the grids treat as the most fortunate. If one sun stands anywhere in Aries and the other anywhere in Leo, the true separation lies somewhere between 90° and 150°. Measured in degrees the pair may be a square, and the table will still call it a trine. A window 60° wide is thrown away so that the grid fits on a page.
The hour is discarded too. A sun sign is a function of a date, so comparing two of them compares two birthdays at a resolution of about a month and returns one of 144 cells for every pair of people who have ever lived. The moon and the ascendant move far faster, which is why two people who share a sun sign routinely share nothing else; /blog/three-placements sets out how far apart two births on one date can stand.
Whatever older synastry was, it was not this. Comparisons were made between whole charts, in degrees, with an orb allowed on either side. The twelve-by-twelve table is the shape left over once the degrees are gone.
What a synastry reading requires, and what this site computes
Synastry in the sense the tradition means compares two complete charts: each person's moon, Venus and Mars as the classical significators of affection and desire, the houses of one chart that the other's planets fall into, and the aspects, measured in degrees, between the two sets of positions. Some practitioners then derive a third chart from the pair.
This site computes three positions for a single birth and no others, as /method states. It produces no synastry, gives no compatibility score, and sells neither. What remains is smaller and honest: the three placements can be computed for one person at a time, free and with the degree shown, and two sets of results can be read side by side. Nothing is being measured between two charts there. Two descriptions are simply standing next to each other.
What compatibility talk is actually good for
It survives because it lends vocabulary to a conversation that is hard to open. To say that one person needs an empty evening after company and the other does not is a difficult sentence. To say that one moon is in Gemini and the other in Virgo is an easy one, and it lands close enough to be worth the exchange that follows.
The value lies there rather than in adjudication. Read afterwards, a square describes two things standing at right angles, which is a decent picture of a difference that keeps recurring. Read in advance, the same cell forecloses a person who has not yet been met.
The tradition offers images to think against, not verdicts about a life. No arrangement of the sky has ever ended a relationship, and the arithmetic beneath the grid is the arithmetic of a circle divided into twelve parts, which knew nothing about either party when it was drawn.