Quintile

The five aspects Ptolemy admits, conjunction, sextile, square, trine, opposition, are the ones the twelve signs can generate. Divide the circle by one, six, four, three and two and every result is a whole number of signs. That is not a coincidence; it is the reason those five and no others.

Johannes Kepler thought the reasoning was backwards. In the Harmony of the World of 1619 he argued that aspects work because certain angular ratios are harmonious in the same way musical intervals are, and that the sign-based derivation was an accident of an inherited scheme rather than a cause. If the ratios do the work, then divisions the signs cannot produce should also count. He proposed the quintile at seventy-two degrees and its double the biquintile at a hundred and forty-four, the semi-square at forty-five, and the sesquiquadrate at a hundred and thirty-five.

This is a genuinely awkward fact about the history. Kepler is the figure most often cited to show that serious astronomers once took astrology seriously, and the thing he actually contributed to astrology is the set of aspects traditional astrologers are most likely to throw out. He was also, in the same work, dismissive of most of the rest of the practice.

The argument was extended in the twentieth century by John Addey, whose Harmonics in Astrology of 1976 treated the whole aspect doctrine as a special case of dividing the circle by successive integers, generating septiles, noviles and beyond. Addey's scheme is internally consistent and produces an unbounded number of aspects, which is either its strength or the reduction that refutes it depending on who is describing it.

Positions currently held. Traditional and Hellenistic-revival practitioners generally use the Ptolemaic five and nothing else, on the grounds that the others cannot be sign relations. Mainstream modern astrology uses the five plus the quincunx, and often the semi-square and sesquiquadrate. Harmonic astrologers use as many divisions as the chart will support. The quintile family sits on the boundary, admitted by many and treated by others as arithmetic with a delineation attached to it after the fact.

Seventy two degrees is a fifth of the circle, and the quintile is the aspect that fifth produces. It has no place in Hellenistic or medieval doctrine, which recognised only the divisions by one, two, three, four and six. It was proposed by Johannes Kepler, who was looking for aspects on the basis of the regular polygons that can be inscribed in a circle and the musical ratios those divisions correspond to, and who added the quintile, the biquintile and several others on that reasoning.

The justification matters because it is a different kind of justification. The classical aspects were defended by their relation to the signs: a trine joins signs of one element, a square joins signs of one mode. The quintile joins nothing in particular, because five does not divide twelve. Two planets seventy two degrees apart may stand in signs that are in aversion to one another, so a quintile can exist between planets that traditional doctrine says cannot see each other at all. Kepler was not troubled by this, having already set aside the sign-based account.

Modern usage keeps the quintile on a narrow orb, typically one to two degrees, and associates it with craft, style and a facility that is developed rather than given. That association is a twentieth century accretion, not something Kepler stated, and it circulates chiefly through the harmonic school. The honest summary is that the quintile is a real division of the circle with a short and traceable history, and that most of the meaning attached to it is younger than the aspect itself.

Kepler added the quintile and the related fivefold divisions to the classical five aspects in the Harmonices Mundi of 1619, arguing from the consonant musical ratios he believed corresponded to the regular polygons that geometry allows to be constructed, the pentagon among them, rather than from the sign-based logic of the older Ptolemaic scheme. Despite being among the best documented of the minor aspects in terms of who introduced it and when, the quintile was never given a dedicated codepoint of its own in the Unicode Standard; it is noted in chart work by the letter Q, by the digit five, or by a stylised mark that varies from one program or publisher to the next, unlike the sextile, semi-sextile, quincunx and sesqui-quadrate, which did receive purpose-built astrological glyphs.

Because five does not divide evenly into the twelve signs of the zodiac, a quintile always links two signs of unrelated element and mode, a geometric fact later commentators have read as part of why the aspect's effects are felt as individual talent rather than as a shared temperament between the bodies involved. Kepler himself was explicit that he was breaking with the older, sign-based way of judging which angles mattered, arguing in the Harmonices Mundi that the ear and the compass, not the twelve signs, ought to settle the question, a genuinely new principle for choosing aspects rather than simply a new angle added to an old list.