The semi-square is an aspect of forty-five degrees, formed when two planets stand an eighth of the circle apart, half a square. It is a minor aspect, but one of the hard or challenging kind, and it shares the frictional character of the square in a lesser key. Given a narrow orb, it is read in the tradition as a source of irritation, minor obstacle, and low-level tension that prods toward action, the small abrasive counterpart of the ninety-degree square. It was among the aspects introduced by Kepler in his expansion of the classical set beyond the five Ptolemaic figures. With the sesqui-quadrate it forms a pair of eighth-division hard aspects. These are the interpretive conventions of the astrological tradition for this angular relation, one of the minor hard aspects that add finer degrees of challenge to the major square and opposition.
The semi-square, like the semi-sextile, is formed by bisecting a Ptolemaic aspect, in this case the ninety-degree square, and it belongs to a small family with the sesqui-quadrate that together mark the quarter-points falling between conjunction, square and opposition. Both are sometimes called the eighth-harmonic aspects, since forty-five degrees is 360 divided by eight, and the family is generally treated as older than the fifth-harmonic aspects Kepler popularised in his Harmonices Mundi of 1619, appearing in earlier medieval and Renaissance aspect doctrine as a subdivision of the square rather than as a harmonic construction in its own right. The traditional orb is narrow, typically one to three degrees, and the semi-square is usually read as a lesser version of the tension the full square carries, friction that can be worked through rather than a fixed obstruction.