Semi-square

A semi-square, also called the octile or semiquartile, is the aspect of forty-five degrees, half a square. It belongs to the family of aspects generated by repeatedly halving the circle, the eighth division, and is counted among the minor aspects that entered general use through the seventeenth century harmonic reform associated chiefly with Johannes Kepler, though the semi-square itself, unlike the quintile, biquintile and sesqui-quadrate, is not always named among the specific angles Kepler introduced in the Harmonices Mundi, and is better described as belonging to the same eightfold, repeated-halving family as the square and sesqui-quadrate that the harmonic astrologers who followed Kepler put into regular use. Its glyph is not a dedicated astrological mark but the ordinary mathematical sign for an angle, an acute angle drawn open to the right, borrowed wholesale from geometry in the way the trine and square glyphs are borrowed from plain geometric shapes. It is read as a lesser square, friction and irritation rather than outright obstruction, and is usually given a narrow orb on account of its comparative weakness. The narrow orb is itself part of the same harmonic logic: the further an aspect's angle sits from the small set of divisions, halves, thirds, fourths, that dominate the classical scheme, the less tolerance later astrologers have generally allowed for it to drift from exact before its effect is judged too weak to count.