Aspects

An aspect is a relationship of angle. Two bodies are placed at their own ecliptic longitudes, the difference between those longitudes is measured, and if the difference is close enough to one of a small set of named angles, the tradition treats the two as standing in a particular relation. Nothing about the measurement is interpretive: the angle between two directions is a fact about where the bodies are. What the relation was held to mean is the part that belongs to a tradition and a period.

The four figures, and where they come from

Ptolemy names four, and derives them from the circle. Chapter 13 of the first book lists opposition at 180 degrees, trine at 120, quartile at 90 and sextile at 60, each described both as a fraction of the right angle and as a count of signs ^{1 bk. I ch. 13}. The derivation is explicitly musical:

if we take the two fractions and the two superparticulars most important in music, and if the fractions one-half and one-third be applied to opposition, composed of two right angles, the half makes the quartile and the third the sextile and trine

The same chapter divides the four in two, on a structural ground: “trine and sextile are called harmonious because they are composed of signs of the same kind, either entirely of feminine or entirely of masculine signs; while quartile and opposition are disharmonious because they are composed of signs of opposite kinds.”

That explains why the set is closed. The figures are the angles at which two signs share a quality, and the number of them follows from the twelve-fold division of the circle having exactly those symmetries.

Signs that see nothing of each other

The complement of the doctrine matters as much as the doctrine. Signs that stand in none of these relations are, in the Hellenistic material, in aversion: adjacent signs, and signs five apart, share neither element nor modality and were held to have no line of sight between them ². A body can therefore sit thirty degrees from another and be, in the system’s own terms, further from it than a body sitting a hundred and twenty degrees away.

This is the piece most often lost. Later astrology filled the gaps with additional angles, the best known being the set Kepler proposed, and those later figures occupy precisely the intervals the older scheme treated as blind. Whether to draw them is a choice between two systems, and mixing them silently inverts the logic of both. This site’s chart tool draws the five and reports aversion.

Orbs are a convention, and the numbers are visible

An exact 120 degrees between two bodies is vanishingly rare. Every practical system therefore allows a tolerance, the orb, within which the figure still counts. The tolerance is where the arithmetic stops and the convention starts.

Two consequences follow, and both are visible in the tool. Because the allowance is a convention, two pieces of software applying different allowances will disagree about whether an aspect exists at all, without either being wrong about where the bodies are. And because the allowance is symmetric around an exact angle, an aspect has a strength as well as a presence: how near the exact figure a pair sits is a real number, and it is the only part of this apparatus that is not stipulated.

What a figure was held to mean

Later writers built a great deal on top of that division, and the elaboration is a history: what a square was said to do differs between the Hellenistic material, the medieval Arabic and Latin traditions, and twentieth-century psychological astrology, which reinterpreted the whole harmonious-and-disharmonious axis as one of ease and friction inside a person ³. The angle stayed the same throughout. The reading of it did not, which is the ordinary condition of everything in this subject and the reason this site reports the angle and attributes the reading.