House Division
This site’s chart tool can divide a birth chart into houses under seven different systems: whole sign, equal, Porphyry, Alcabitius, Campanus, Regiomontanus and Placidus. Switch from one to another for the same birth data and the house cusps move, sometimes by tens of degrees, and a planet can change house entirely. The natural response is to ask which of the seven is correct. That question has no answer, because the seven systems are seven different computations. Each one divides a different object into twelve, and the differences between their results are differences between the objects.
This entry covers only how the twelve houses are divided. What named, dated sources held each of the resulting twelve places to signify is a separate and more delicate question, covered house by house from First House through Twelfth House.
Twelve houses, seven different objects
Whole sign takes the sign containing the Ascendant and makes it the first house entire: the following signs become the following houses, unmodified, so that a house and a sign are, in this system, the same twelve-part division under two names. Equal measures twelve arcs of thirty degrees from the Ascendant’s own degree rather than from the start of its sign, so cusp one sits exactly on the Ascendant and the Midheaven falls somewhere inside a house rather than defining a cusp of its own.
The five remaining systems all use the Midheaven as well as the Ascendant, and four of them need more besides: the local sidereal time, the true obliquity of the ecliptic for the date, and the birth’s geographic latitude, because each is dividing an object that exists only relative to a place on Earth.
Porphyry trisects the ecliptic arcs between the four angles, Ascendant to Midheaven and Ascendant to Imum Coeli, into three equal parts each; it needs only the Ascendant and Midheaven and nothing about place or time of day. Alcabitius trisects the Ascendant degree’s own diurnal and nocturnal semi-arcs, measured in right ascension rather than ecliptic degrees, and projects the trisection points back onto the ecliptic. Campanus divides the prime vertical, the great circle running through the zenith, the horizon’s east point, the nadir and the horizon’s west point, into twelve equal arcs and projects each division point through the horizon’s north and south points onto the ecliptic. Regiomontanus performs the same projection but divides the celestial equator rather than the prime vertical. Placidus trisects each ecliptic degree’s own semi-arc by time, rather than trisecting one fixed arc belonging to the Ascendant: cusp eleven is the point that has completed one third, in time, of the interval from its own rising to its own culmination, and that point’s semi-arc depends on its own declination, which depends on where the cusp itself falls. There is no formula for that. It has to be solved by starting from a guess and correcting it until it stops moving.
None of this is a matter of one system approximating another more or less well. Whole sign answers which sign the Ascendant occupies. Placidus answers a question about time. Campanus answers a question about the local horizon. Seven different questions, asked of the same birth data, produce seven different, equally well-defined answers.
Correction
Commonly saidA chart's house cusps, once computed and labelled Placidus, were computed by the Placidus method.
Not always, and the reason is a documented defect in widely used astrological software. Placidus solves for a point on a semi-arc that a given ecliptic degree must complete; above roughly the polar circles, a wide band of ecliptic degrees never rises at all, has no semi-arc, and gives Placidus nothing to solve. Swiss Ephemeris, the calculation library most chart programs are built on, handles this case by silently substituting Porphyry cusps and reporting the substitution only through a return code that most calling code never checks. A chart displayed as Placidus, at a high enough latitude, can therefore be showing Porphyry cusps under the wrong name, and neither the practitioner reading it nor the client receiving it has any way to see that from the output alone.
The better design is failure reported by name, stating which system was requested and whether it was the one delivered. This site’s own implementation returns no cusps and a stated reason, because the alternative is documented software behaviour.
Where the quadrant systems fail
A system that divides time, or a great circle running through the poles of the local horizon, runs into geometry with no answer once the latitude gets high enough. Placidus is worst affected: it fails wherever the relevant ecliptic degree’s own declination puts it beyond the point where it rises or sets at all, a true absence of a solution, and that failure begins at the polar circles and covers a growing share of every day beyond them. Regiomontanus and Campanus stay numerically finite everywhere short of the poles themselves, but at high latitude their twelve cusps can come out of ecliptic order, houses no longer following one another the short way round the circle, which is its own kind of wrong answer even though every individual cusp is a real number. Alcabitius is the best-behaved of the four, by direct measurement: because the Ascendant itself always stands on the horizon, its own semi-arc can never be undefined the way an arbitrary ecliptic degree’s can, and this site’s own test suite finds it failing exactly as often as Porphyry and Campanus and markedly less often than Placidus, at every high latitude sampled. Porphyry, needing only the Ascendant and Midheaven, is undefined only in the rare case where the Ascendant’s position relative to the Midheaven becomes so distorted that the relationship between the two angles itself breaks down.
Where the systems came from
Whole sign is the system the surviving Hellenistic handbooks assume, from Dorotheus of Sidon in the first century onward 1, and it is why this site’s chart tool defaults to it. Its disappearance and return are part of the same story told in full at Sect: a body of English-language practitioners working from the 1990s onward, retranslating the Hellenistic manuals directly, restored whole sign to a central place in the technique they teach, arguing that a chart’s houses cannot be read correctly without it 2. That account is a practitioner-scholar synthesis, comprehensive and well referenced against the primary texts, and it is cited here on that footing.
Quadrant division did not disappear once and return once. It multiplied. The medieval and early modern astrological literature carries several distinct quadrant constructions side by side, without the tradition ever converging on one 3, and Alcabitius, Campanus, Regiomontanus and Placidus are four different, still-current answers to the unsettled question of how a quadrant should be divided.
Gap in the evidence
It is often repeated that Placidus became the default of the English-speaking world for a reason that has nothing to do with astronomy: that a small number of published tables of houses, computed by the Placidus method, dominated the nineteenth-century English print market, and that the software written in the twentieth century then defaulted to whatever practitioners already had in hand from those tables. That is a plausible account of publishing history and it may well be correct, but it is a claim about print runs and market share, not about astronomy or textual transmission, and no source in this site’s pool establishes it to the standard this site requires before printing it as fact. It is recorded here as an open historical question.
A dispute the tradition has not settled
Contested
At issueWhich house system should a chart use?
The traditional revival’s position is that whole sign is what the earliest surviving handbooks assume, and is the ancestral one, temporarily lost and now restored 2; see Sect for the identical argument made about a chart’s day and night division.
Much of contemporary Western practice keeps some quadrant system instead, on the position that a house cast from the actual place and moment of birth, using the local horizon and meridian, carries information that a division ignoring them cannot. Which quadrant system, though, is a second and unresolved argument inside that position: Alcabitius, Campanus, Regiomontanus and Placidus each divide a different object, none has produced an argument that persuaded holders of the others, and the medieval and early modern literature already shows several running side by side 3.
Practitioners today hold all of these positions, and this site does not choose among them.
A single birth chart, run through all seven systems, places a given planet in different houses under at least two of them for most birth data, and the doctrine attached to a house, what it governs and what a planet placed there is held to do, is read against whichever house that computation happens to put the planet in. A chart factor with seven defensible answers is a chart factor with no single claim in it for anyone to read or to test, and it belongs to the same argument made at greater length about a chart’s dignities: see Essential Dignity for the fivefold scheme’s own internal disagreements, and Testing Astrology for what a chart built from factors like these leaves over for an empirical test to test.
References
- Dorotheus of Sidon, trans. Benjamin N. Dykes. Carmen Astrologicum: The ʿUmar al-Tabarī Translation: Cazimi Press, 2019 (composed c. 75 CE). ISBN 9781934586501 recordprimary source
Second updated edition. A practitioner translation, cited alongside rather than instead of Pingree's 1976 Teubner critical edition. The Greek original is lost; the text survives through a Middle Persian intermediary into Arabic, which is itself part of why the Dorothean material needs careful reading.
- Chris Brennan. Hellenistic Astrology: The Study of Fate and Fortune: Amor Fati Publications, 2017. ISBN 9780998588902 recordscholarly
A practitioner-scholar synthesis: comprehensive and well referenced, but not peer-reviewed philology. This site cites it with that characterisation.
- Nicholas Campion. A History of Western Astrology, Volume II: The Medieval and Modern Worlds: Continuum, 2009. ISBN 9781441181299 recordscholarly
The companion volume, and the one that carries everything after the fifth century: its own description runs from the collapse of classical astrology to popular astrology in the twentieth century and its standing in the twenty-first. Volume I stops in the ancient and classical world, so a claim about the Renaissance, the Victorian press, the newspaper column or twentieth-century psychological astrology belongs here and not there. Listed by Bloomsbury Academic since Bloomsbury acquired Continuum in 2011; the 2009 printing is Continuum, and the ISBN is unchanged.