Biquintile

The biquintile is an aspect of one hundred and forty-four degrees, formed by taking two-fifths of the circle, twice the seventy-two-degree quintile. Both are minor aspects derived from dividing the circle by five, a division not among the classical Ptolemaic set but introduced by Kepler, who valued the fivefold aspects highly. Given a narrow orb, the biquintile is read in the tradition as a relation of talent, creativity, and a distinctive, self-directed skill, the fifth-harmonic quality of style, artistry, and the shaping power of the will, sharing the character of the quintile in a doubled form. These are the interpretive conventions of the astrological tradition for this angular relation, one of the subtler aspects that supplement the major figures with the creative fivefold shadings Kepler added to the astrologer's vocabulary of angles.

The biquintile, twice the quintile's thirty-six-degree unit at one hundred and forty-four degrees, belongs to the fifth-harmonic family that Kepler introduced in his Harmonices Mundi of 1619, where he connected the geometry of the regular pentagon to musical consonance and to what he took to be a corresponding astrological effect. Kepler regarded the quintile and its multiples as aspects of a different order from the traditional five, tied to individual creative or technical talent rather than to the broader temperamental and circumstantial matters the Ptolemaic aspects govern, and that reading has persisted in the harmonic astrology that developed from his work in the twentieth century, particularly in the writing of John Addey. The orb given to it is narrow, and it remains one of the aspects used chiefly by astrologers working explicitly within the harmonic tradition rather than in general practice.

A hundred and forty four degrees is two fifths of the circle. The biquintile is therefore the quintile's partner in the fifth harmonic, standing to it as the sesqui-quadrate stands to the semi-square, and it comes from the same source: Kepler's attempt to derive aspects from the regular figures inscribable in a circle and from the musical ratios those figures express.

It is the least used aspect in common circulation, and the reasons are practical. Five does not divide twelve, so it cannot be found by sign and has no traditional standing to inherit. Its orb is narrow, commonly one to two degrees, so it appears in few charts. And it sits close enough to the trine at a hundred and twenty degrees and to the opposition at a hundred and eighty that a reader working with generous orbs elsewhere will often have accounted for the same pair of planets already.

What is said about it follows from the quintile rather than from anything observed independently: facility, pattern-making, a talent that shows as style. Writers in the harmonic school treat the fifth harmonic as a whole and read the quintile and biquintile together rather than separately, which is the more defensible approach, since the case for either rests on the case for the division by five. The geometry is exact and can be stated without qualification. The meaning is an inference from number symbolism, roughly four centuries old at most, and it should be presented that way rather than as inherited doctrine.

The biquintile derives, like the quintile, from the fivefold division of the circle at the centre of Kepler's harmonic scheme, published in the Harmonices Mundi of 1619, where the two aspects appear together as products of the same reasoning, that the pentagon's constructibility with compass and straightedge, and its correspondence to a consonant musical interval, made a hundred and forty-four degrees as legitimate an aspect angle as any of the four Ptolemy had already recognised. It has no settled glyph in the way the sextile or the sesqui-quadrate do; it is written with the letters BQ, or with a mark derived from the quintile sign, and it was not among the aspects given a dedicated codepoint when astrological symbols were added to the Unicode Standard, so its appearance still varies between astrology programs and publishers rather than following one fixed convention.

The pentagon and pentagram that the fivefold family carries with it have made the quintile and biquintile a natural pairing in harmonic astrology ever since Kepler first proposed them, and the two aspects are still generally discussed together in modern textbooks rather than treated as separate topics, much as the semi-square and sesqui-quadrate are usually presented as one eightfold pair rather than two unrelated angles.