It is difficult to ascertain exactly when the concept of house division began, but there is some evidence that the most primitive form of house division may have been influenced by the Egyptian divisions of the ecliptic and date back to between the 3^rd and 2^nd centuries BC -- when horoscopic astrology was being developed in Alexandria during the Hellenistic period. The Egyptians imagined the path of the Sun-god along the sky as symbolic of his birth, life, death and rebirth. At sunrise in the east, the sun-god is born and develops to reach maturity when he is directly overhead at noon. As he ages, he begins to descend overhead to die over the western horizon at sunset. From there, the sun continued his journey through the underworld or duat, through the nadir of the heavens at which point he transforms into a developing infant to be born again at sunrise. The sky therefore, was divided into four quadrants called cardines in Latin, which were points of intersection where the ecliptic cut the horizon and meridian. This influence may explain why the birthchart reflects the Egyptian convention of orienting their maps in a southerly direction, since East is typically placed on the left.

There are different house system classifications, depending upon how one differentiates them. One way is to separate the Quadrant systems from the Non-quadrant systems. Another classification system incorporates three categories:1) the Ecliptic-based methods which include the Equal-House, the Whole Sign Houses, and the Porphyry systems; 2) the Time-based methods which comprise the Alcabitius, the Classical, the Natural Hours, the Placidus, the Koch, and the Topocentric systems; 3) the Space-based methods which include the Campanus, the Regiomontanus, and the Morinus systems. In this paper, one house system from each of the three different categories above will be described and illustrated and the differences between them examined. These will be the: the Porphyry, the Alcabitius, and the Regiomontanus systems.

The Ascendant and Midheaven

The earliest house systems merely fixed the relationship of the Zodiac to the conceived geometric house circles by means of what the Greeks called the horoscopus, or ascendant. The ascendant is defined as the degree of the zodiac which is rising over the horizon in the eastern arc at the moment of a person's birth or of an event fixed in time. This point usually constitutes the cusp of the first house in most house systems.

In what is thought to be the earliest method of house division -- first described by Ptolemy -- the ascending ecliptic Zodiac degree was calculated to form the first house cusp, and 30 degrees were added to each of the remaining 11 house cusps. Most of the early astrologers did not calculate the Midheaven, the point on the ecliptic that intersects the meridian. It was only about a century or two after the initial horoscopes that some astrologers began calculating this point, not as the cusp of the 10^th house, but as a sensitive point on the chart usually falling somewhere in the 9^th or 10^th houses for charts in the Mediterranean latitudes. This system, known as the Equal House or the Sign-House method, is an example of an ecliptic-based mode of dividing the chart into houses, since the divisions are made directly on that line. Other systems of house division are analogous in terms of the way they calculate the Ascendant and Midheaven points, but they vary greatly in the manner in which they chose to divide the intermediate house cusps -- often choosing other great circles to divide and projecting those arcs onto the ecliptic.

Ecliptic-Based Systems: Porphyry Method of House Division

After the Equal House system, Porphyry is one of the earliest and simplest methods of house division as well as being the first of the quadrant systems. The first appearance of a description and explanation of this method is made by Vettius Valens (150-175 AD) in Book III, Chapter 2 of his Anthology entitled "The Authentic Degrees of the Angles". Valens attributes this method to an otherwise unknown astrologer named Orion. Holden believes this author to have written before Valens and points to the fact that he could have been the true originator of the system and not Porphyry himself, since Porphyry describes the system 150 to 175 years after Valens does.

Although the method may have originated with an earlier astrologer or mathematician, it was named after Porphyry (233-c.304), the Greek philosopher and student of Plotinus. Porphyry is best known for his work Introduction to Ptolemy's Tetrabiblos, which is essentially an encyclopedic dictionary of astrological terms and techniques. In chapter 43 entitled "Determination of the Angular, Cadent, and Succedent Houses to the Degree," Porphyry how the cusps are derived by trisecting the semi-arc between the Ascendant and Midheaven.

After the Ascendant and Midheaven ecliptic positions have been calculated, the semi-arc between them is computed by subtracting one from the other. This semi-arc -- which represents one quadrant of the chart -- is then divided by 3 to determine the arc of each of the intermediate houses. This constant is then added to the Midheaven to yield the cusp of the 11^th house, to the 11^th to yield the cusp of the 12^th, and to the 12^th to confirm the Ascendant degree. The cusps of the 4^th and 7^th houses will be 180 degrees from the Ascendant and Midheaven respectively and opposite in Zodical sign. The same quadrant arc division process is applied to the northeastern, northwestern, and southwestern quadrants of the chart to yield the cusps of houses 2, 3, 5, 6, 8, and 9. Because this process yields the same constant in each quadrant arc division, house cusps 11 and 5; 3 and 9; 2 and 8; and 6 and 12 will be 180 degrees apart. Also houses 11 and 3, 9 and 5 will be 120 degrees apart; houses 12 and 2, 8 and 6 will be 60 degrees apart.

Time-Based Systems: Alcabitius Method of House Division

The Alcabitius (sometimes spelled Alchabitius or Alcibitius) method of house division first appears in a treatise written by Rhetorius, the Egyptian (505 AD) entitled From the Treasury of Antiochus, an Explanation and Narration of the Whole Art of Astrology. The treatise is a compilation of the works of Antiochus and Porphyry, with excerpts from Vettius Valens, and describes a modified version of the Alcabitius method, which includes Ptolemy's convention of starting the houses 5 degrees before the actual calculated cusps to account for optical distortion at the horizon. Munkasey calls the Alcabitius method with the 5 degree compensation as the Classical Method of house division and names the version without Ptolemy's compensation as the Alcabitius Declination House System. North also describes this method and calls it the Standard Method of House calculation. But all three are essentially variations of the method that Rhetorius describes 400 years before the birth of the Arabic astrologer who would popularize it and lend his name to it.

The system was attributed to Abu al-Saqr al-Qabisi Abd al-Aziz ibn Uthman (d. 967) thankfully also known as Alcabitius, the author of the Introduction to the Art of Judgements of the Stars (c. 916-967). Although this system was presented by various other Arabic writers of the time, Alcabitius' text was translated into Latin by John Seville in the 12^th century and by Erhard Ratdolt in Venice in 1503, thus helping to popularize the method and make Alcabitius the "author" of the most widespread method of erecting house cusps in the early middle ages. Holden says the method is a "logical development from the Porphyry system" since that method trisects the semi-arc of the ecliptic while this one trisects the diurnal arc and projects it onto the ecliptic by means of hour circles.

The Alcabitius method is probably one of the more difficult methods to explain without a diagram. In the diagram on the right, the horizon is the great circle that runs horizontally along the middle of the celestial sphere. Where the ecliptic and the horizon intersect, is the Ascendant. Diurnal circles are small circles that parallel the equator circling the poles at different latitudes. In the diagram, only one diurnal circle is shown running parallel to the equator. This is the diurnal circle of the ascendant which starts at the ascendant and circles back to it. The diurnal arc of the ascendant is that portion of the circle that is visible above the horizon. In the Alcabitius method, this arc is trisected and those points become the starting points for hour circles -- which are great circles circling through the north and south poles. These circles are shown on the diagram intersecting the ecliptic at the arrows. The points where these circles cross the ecliptic become the house cusps.

Space-Based Systems: Regiomontanus Method of House Division

The man known to us as Regiomontanus, was born Johann Muller in 1436 in southern Germany and educated in the University of Vienna as a mathematician and astronomer. With the help of Martin Bylica, and because he found fault with the Campanus method of house division -- which was a century older but never really caught on because it was too complex and no tables were available -- Regiomontanus calculated a set of tables using his own method which were published in 1490. The result was that the Regiomontanus system supplanted Alcabitius as the standard method of house division in the middle ages. According to Holden:

It has been a cliché in the 20^th century that the Placidus system later became the 19^th and 20^th century standard because it was the only one for which affordable tables were readily available. This is partly true, but the same thing could be said for the initial success of the Regiomontanus system. Had the first published book of house and auxiliary tables been according to the Campanus system, there is little doubt that it would have become the standard of the time.

Generally speaking, in the Regiomontanus system of house division, the celestial equator is divided into 30 degree arcs starting at the Aries point. These points are then projected onto the ecliptic using house circles. In the diagram to the right, the horizon is the great circle that runs horizontally along the middle of the celestial sphere. The ecliptic is the line that runs almost vertically through the celestial sphere. Where the two intersect is the ascendant. The line that runs diagonally, cutting through the ecliptic and the horizon is the equator. The dots on the equator mark the 30 degree divisions of this circle. House circles are great circles whose poles are the North and South poles of the horizon (here the right and left points of the horizon plane). These circles cut the celestial sphere like slices of an orange on its side. On the diagram, the intersections of these circles on the ecliptic are marked by arrows. These mark the cusps of the houses which are indicated by the dotted lines. The projections then, are from the equator to the ecliptic. In the Campanus method, a similar system of projections is used to intersect the ecliptic, however the great circle that is divided is the prime vertical, not the equator.

Porphyry, Alcabitius, & Regiomontanus Compared

Among astrology students, one of the most frequent questions asked is: "Which house system works best?" The typical responses are that "It depends on what type of astrology you are practicing" or "All systems work well for different areas of astrology" or better yet, "I've always used Placidus and it works well for me." The truth of the matter is that all house division methods --with the exception of the Topocentric method -- were derived theoretically, without any empirical verification or comparative testing. Historically, the popularity of certain house systems were either the result of their simplicity, because tables were not needed and charts could be calculated easily by hand; or like the Placidus system, because they were so mathematically complex that publishers could establish a monopoly on specific House Tables. Lorenz makes this point:

Much criticism of astrology centers on the "arbitrariness" of house division. The matter of division, if houses have meaning at all, is certainly not arbitrary since the differences between methods are sizable. Criticism is properly focused however on failure of astrologers to weigh the differences of the various methods against empirical findings."

In the following section of the paper the three systems covered will be compared empirically. Wheels comparing the house cusps of 6 popular methods at different latitudes may be found in Appendix C. To compare the Porphyry, Alcabitius and Regiomontanus methods, two horary charts were selected as test cases. The criteria for choosing these charts were: 1) horary charts were preferred to natal charts because the focus for delineation is much more narrow and because changes in house cusps produce changes in the significators for the particular question asked 2) existing charts which have already been delineated and whose outcome is known were preferred as they provide an objective context upon which to make a comparative judgment and 3) charts whose intermediate house cusps were either in late or early degrees were preferred since these were more likely to produce a change in sign using different systems and therefore to produce different significators for the subjects involved.

Test Case 1: Will Tim get custody of his kids?

Aug. 7, 1973 10:01 am PDT, Los Angeles, CA. 34N04, 118W15

Porphyry House System

According to March and McEvers, the querent was a friend of Tim's. With 2° of Leo on the 11^th house cusp, Tim is signified by the sun which is posited in its own sign in this house. Tim's children are to be mapped under the ruler of the 3^rd house, which is the 5^th from the 11^th. Porphyry has 2° Sagittarius on this cusp and Jupiter, its ruler, in retrograde motion, is located 4° from the cusp of the 5^th house (the 7^th from the 11^th). Tim's legal standing is mapped 9 houses from the 11^th, by the 7^th house cusp and by Mars, its significator posited in that same house. Tim's significator is strong and applying to a trine with Mars -- the children -- within 12°. The moon echoes a favorable judgment as it trines both the sun and Mars and sextiles Jupiter. We know from McEvers and March that Tim did receive custody of his children three weeks after the question was posed. Let's now look at how the case changes under the Alcabitius method of house division.

Alcabitius House System

In this system, the signs on the relevant house cusps -- cusps 11, 3 and 7 do not change at all. The sun is still significator for Tim, Mars still rules the legal situation, and the children are still depicted by Jupiter. The only departure from the Porphyry method affected by this system, is that the Moon is placed 8' farther away from the 3^rd house -- which depicts Tim's children -- instead of inside of it. Jupiter also moves farther from the beginning of the 5^th house cusp (relative to the Porphyry placement), which depicts Tim's ex-wife. This may be significant as we may see Jupiter's retrograde motion away from the 5^th house as indicative of the children's move away from their mother and return to their father (5^th being the 7^th from the 11^th).

Regiomontanus House System

In the this system, the significators for Tim and for the legal situation do not change; but the children's significator changes from Jupiter to Mars as the cusp moves back to 28° of Scorpio. Jupiter becomes co-ruler of the children since Sagittarius is intercepted within the 3^rd house. Because Mars also rules the legal situation, this change reflects well the fact that the children's fate is directly tied to the courts. The moon has also moved fully into the 3^rd house and Jupiter, co-ruler of the children, has just moved beyond the domain of the 7^th house, depicting Tim's wife. If we consider Pluto as modern ruler for the children, we find that it is exactly on the cusp of Tim's 3^rd house -- which is his ex-wife's legal house -- about to square Saturn, her significator. The now late degrees on the 3^rd house, better reflect the change that the children are about to experience with the custody judgment.

Interestingly, McEvers and March map all person's referred to by name by the 7^th house and therefore Tim's children by the 11^th, and the legal case by the 3^rd. As we have seen, the significators turn out to be the same and their applying aspects therefore reveal the same outcome.

Test Case 2: Where are Rachel's eyeglasses?

Sept. 15, 1992 7:21 am EDT, Bridgeport, CT. 41N10 73W12

Porphyry House System

Rachel was the querent for test case #2. Rachel had misplaced her rather expensive eyeglasses and was desperate to find them. Using Porphyry, the ruler for Rachel is Venus located in the 1^st house and strong in its own sign. The ruler of the 2^nd house of her possessions is Mars located on the MC in Cancer and in fall. The Moon, indicator of the question, is appropriately posited in Taurus and 1° from the cusp of the 8^th house, which Louis indicates is a place "where valuables may be kept". There are no applying aspects between Mars and Venus in this chart but the Moon is applying to a sextile to Mars within 1° 01' of arc. Mars at the MC would suggest that the eyeglasses should be highly visible which was not the case here. Louis tells us that Rachel found her eyeglasses 2 days later at the bottom of her purse.

Alcabitius House System

Using Alcabitius, the matter changes little. As with the above test case, compared to the Porphyry method, the intermediate house cusps in Alcabitius retract about 2° in the Southeast and Northwest sectors and advance by the same amount in the Southwest and Northeast sectors. Because the question is located in the 2^nd house in the Northeast sector, the sign on that cusp does not change from that showing in the Porphyry method. The only difference here is that the moon has receded farther away from the 8^th house cusp by 2° relative to its position in the Porphyry chart.

Regiomontanus House System

As in test case 1, the Regiomontanus system differs the most between the three methods. Here Libra is the sign on both the 1^st house signifying Rachel and the 2^nd house, depicting her movable possessions. Venus therefore is the significator for both Rachel and her eyeglasses and it is posited in the 1^st house at 18° of the same sign. Louis quoting Lilly says that if the ruler of the 2^nd lies in the 1^st "you may judge the thing is in that part of the house which he himself [the querent] most frequents, or wherein he doth most abide, or is conversant, or where himself layeth up his own commodities." Translation: the thing is right under one's nose. Having the eyeglasses, which are an item that affects one's appearance and which are symetrical in design, depicted by Venus in the 1^st in Libra seems far more revealing than having Mars reflect the same in the other two systems. This test case also seems to point toward Regiomontanus as the best method to depict the situation symbolically.

This analysis raises some important implications for further research. The first is that locating test charts for this type of analysis may be difficult as was the case here. Since late or early degrees on the intermediate house cusps tend to correlate with early or late degrees rising, the charts selected had to violate the stricture against considering charts with early or late degrees as non-radical. Therefore, large populations of horary charts would have to be searched for those meeting these strict criteria. Also, the other popular house systems should be examined in a similar way. Second, it may be argued that since only horary charts are being used, one can only determine which system works better for horary and not necessarily for natal or event astrology. This is a matter for empirical testing and it is my hope that other systems may be extensively tested within the different domains of astrology in a systematic way.

Notes

[1] Jim Tester. A History of Western Astrology. p. 25.

[2] Deborah Houlding. The Traditional Astrologer Magazine. Issue 10.

[3] See Appendix A for astronomical definitions.

[4] James Herschel Holden. A History of Horoscopic Astrology. p.14.

[5] Holden. p.18.

[6] A designation given by Holden.

[7] Holden. p. 50.

[8] Holden. p. 62.

[9] See Appendix B for the Porphyry formula.

[10] See Appendix B for Ascendant & Midheaven formulas.

[11] Holden. p.85.

[12] Michael Munkasey. "An Astrological House Formulary". 

[13] J. D. North. Horoscopes and History. p.4.

[14] Holden. p. 124.

[15] See Appendix B for the Alcabitius formula.

[16] Holden. p. 149.

[17] North. p.29.

[18] Holden. p.150.

[19] See Appendix B for the Regiomontanus formula.

[20] Howard Sasportas. The Twelve Houses. p.383.

[21] Lorenz. p.20.

[22] Lorenz. p.20.

[23] The test chart #1 was selected from March and McEvers' The Only Way to Learn about Horary and Electional Astrology Vol. VI and test case #2 was selected from Anthony Louis' Horary Astrology Plain & Simple.

[24] McEvers and March employ the Koch system which produces intermediate house cusps closer to those of the Porphyry system for this test case.

[25] Louis. p.178.

[26] Louis. p. 178.

Appendix A

Astronomical Terms Defined

Definitions reprinted from Michael Munkasey's "An Astrological House Formulary"

CELESTIAL EQUATOR: A great circle denoted by an extension of the Earth's equator infinitely projected into space. This is the circle along which the measurement of right ascension is made

ECLIPTIC

ECLIPTIC That great circle of the celestial sphere which the Sun traces, when seen from the Earth, in its yearly travels against the backdrop of the sky.

ECLIPTIC PLANE or SYSTEM 

ECLIPTIC PLANE or SYSTEM: The mathematical plane which contains the Solar System, with the Sun as its center and its planets at the center of their motions. A sphere of space using the ecliptic as its equator

GREAT CIRCLE:

GREAT CIRCLE: A circle contained within the celestial sphere which has as its center the center point of the celestial sphere.

HORIZON: A great circle, for which there are actually four associated terms:Visible, Rational, Sensible, and Celestial. In the way that we use these terms, the Visible Horizon is our view of where the earth and the sky meet off in the distance from where we stand on or near the earth. The Celestial Horizon is the horizon we use mathematically as our starting point to calculate houses and sensitive points, and it is the visible horizon as if that horizon were starting at the center of the earth (as opposed to where we are located on or near the surface of the earth) and was extended infinitely into space.

HOUR CIRCLE:

HOUR CIRCLE: A great circle which is perpendicular to the Celestial Equator and which passes through a particular body in space.

HOUSE CIRCLE: A great circle which has as its poles the North and South points of the Horizon, and which is perpendicular to the Prime Vertical.

MERIDIAN: A great circle of the Horizon system which passes through the Zenith, the nadir, and the North and South points of the horizon.

OBLIQUITY:

OBLIQUITY: The angle in space formed between the ecliptic and the celestial equator. Presently it is about twenty-three and a half degrees and decreasing slowly with time.

PERPENDICULAR: Ninety degrees. Circles which meet at ninety degree angles.

POLE: When describing three or four dimensional space (using time as a fourth dimension) a pole is a mathematical point that is ninety degrees everywhere from a circle. For instance, the earth's North or South Poles are ninety degrees from all points on the earth's equator.

PRIME VERTICAL: A great circle which passes through the Zenith, the Nadir, and the East and West points of the horizon. It is ninety degrees from the meridian, and vice-versa.

VERTICAL CIRCLE: A great circle which is perpendicular to the horizon and passes through the Zenith and the Nadir.

ZENITH: The North Pole of the horizon system. The point in the horizon system which is over your head. Opposed to the nadir.

ZODIAC: A small portion of the celestial sphere which is about eight degrees on either side of the ecliptic circle.

Appendix B

Formulas for Ascendant and Midheaven

Formulas for Porphyry, Alcabitius and Regiomontanus House Systems

Formulas adapted from Michael Munkasey's "An Astrological House Formulary"

and from Bruce Scofield's "Astrological Chart Calculations"

Ascendant

ASC = ARCCOT (- ( (TAN f x SIN e) + (SIN RAMC x COS e) ) ÷ COS RAMC)

Midheaven

MC = ARCTAN ( TAN (RAMC) ÷ COS e )

Where e is the obliquity of the earth and RAMC is the right ascension of the MC or Local Sidereal Time x 15.

Porphyry House System

1. Compute the RAMC, MC, and ASC in the normal manner.

2. Determine the number of zodiacal degrees between the ASC and MC:

L = ASC - MC

3. Compute the house cusp intervals as follows:

L ÷ 3 = F

4. Compute the individual house cusps as follows:

C10 = MC C4 = C10 +180°

C11 = MC+ F

C12 = C11+ F C6 = C12+180°

C1 = ASC C7 = C1+180°

C2 = ASC + F C8 = C2 +180°

C3 = C2 + F C9 = C3 + 180°

Alcabitius Declination House System

1. Compute the RAMC, MC, and ASC in the normal manner.

2. Determine the number of zodiacal degrees between the ASC and MC:

L = ASC - MC

3. Determine the Diurnal and Nocturnal Semi-arcs:

D = ARCTAN ( TAN L x COS e )

P = 180o - D

4. Determine these intermediate working values:

F = D ÷ 3 J = P ÷ 3

G = F x 2 K = J x 2

5. Compute the house cusp intervals as follows:

H11 = ARCTAN ( TAN F ÷ COS e )

H12 = ARCTAN ( TAN G ÷ COS e )

H2 = ARCTAN ( TAN K ÷ COS e )

H3 = ARCTAN ( TAN J ÷ COS e )

6. Compute the individual house cusps as follows:

C10 = MC C4 = 180o + C10

C11 = MC + H11 C5 = 180o + C11

C12 = MC + H12 C6 = 180o + C12

C1 = ASC C7 = 180o + C1

C2 = MC + H2 C8 = 180o + C2

C3 = MC + H3 C9 = 180o + C3

The Regiomontanus House System

1. Compute the RAMC, MC, and ASC in the normal manner. Use the MC as the cusp of the tenth house and the ASC as the cusp of the first house.

2. Determine the following house cusp intervals:

H11 = 30o H2 = 120o

H12 = 60o H3 = 150o

3. Set the equatorial intervals:

F11 = RAMC + H11 F2 = RAMC + H2

F12 = RAMC + H12 F3 = RAMC + H3

4. Compute the house poles:

P11 = ARCTAN ( TAN f x SIN H11 ) P2 = ARCTAN ( SIN f x SIN H2 )

P12 = ARCTAN ( TAN f x SIN H12 ) P3 = ARCTAN ( SIN f x SIN H3 )

5. Compute the first intermediate values:

M11 = ARCTAN ( TAN P11 ÷ COS F11 )

M12 = ARCTAN ( TAN P12 ÷ COS F12 )

M2 = ARCTAN ( TAN P2 ÷ COS F2 )

M3 = ARCTAN ( TAN P3 ÷ COS F3)

6. Compute the intermediate house cusps:

R11 = ARCTAN ( ( TAN F11 x COS M11 ) ÷ COS ( M11 + e) )

R12 = ARCTAN ( ( TAN F12 x COS M12 ) ÷ COS ( M12 + e) )

R2 = ARCTAN ( ( TAN F2 x COS M2 ) ÷ COS ( M2 + e) )

R3 = ARCTAN ( ( TAN F3 x COS M3 ) ÷ COS ( M3 + e) )

7. Compute the individual house cusps as follows:

C10 = MC C4 = 180o + C10

C11 = R11 C5 = 180o + C11

C12 = R12 C6 = 180o + C12

C1 = ASC C7 = 180o + C1

C2 = R2 C8 = 180o + C2

C3 = R3 C9 = 180o + C3

 

Sources

Scofield, Bruce. Astrological Chart Calculations:An Outline of Conventions and Methodology. Kepler College Teaching Handout. 2001.

Holden, James Herschel. A History of Horoscopic Astrology. American Federation of Astrologers. Tempe, AZ. 1996.

Houlding, Deborah. "The Origin of House Meanings". The Traditional Astrologer Magazine. Issue 10. 1994. www.astrology-world.com/articles/houseorigin.html

Lorenz, Dona Marie. Tools of Astrology: Houses. Eomega Grove Press. Topanga. CA. 1973.

Louis, Anthony. Horary Astrology Plain and Simple. Llewellyn Publications. St. Paul, MN. 1998.

Munkasey, Michael P. "An Astrological House Formulary". www.geocosmic.org/HouseArticle.html.

North, J. D. Horoscopes and History. The Warburg Institute. University of London. 1986.

Sasportas, Howard. The Twelve Houses. Thorsons. London. 1998.

Tester, Jim. A History of Western Astrology. The Boydell Press. Woodbridge, Suffolk. 1987.

HOME