The sesqui-quadrate, also called the sesquiquadrate or trioctile, is an aspect of one hundred and thirty-five degrees, formed when two planets stand three-eighths of the circle apart, a square plus a semi-square. It is a minor aspect of the hard or challenging kind, sharing the frictional character of the square, and it is given a narrow orb. The tradition reads it as a relation of accumulated tension and agitation that seeks release, akin to the semi-square with which it is paired as the two eighth-division hard aspects. Like the semi-square it was introduced by Kepler in his expansion of the aspects beyond the classical five. These are the interpretive conventions of the astrological tradition for this angular relation, one of the minor hard aspects that supplement the major square and opposition with further shadings of challenge between planets.
The sesqui-quadrate, one and a half squares, completes the eighth-harmonic family together with the semi-square, and both mark the forty-five degree points that fall between the major aspects rather than coinciding with them. It is generally counted, along with the biquintile, among the aspects Kepler treated in his Harmonices Mundi of 1619, where he set out a theory of aspects grounded in the geometry of constructible polygons rather than in the older, purely traditional five. Where the semi-square is usually read as a minor friction, the sesqui-quadrate, standing closer to the full ninety-degree square and to the opposition, is generally given a sharper reading, a pressure that forces an adjustment rather than merely announcing one, and it is often paired with the semi-square in a chart as evidence of a recurring pattern of strain across a planet's aspects.