The house system that has been named after Porphyri is the oldest known example of a quadrant system.
The MC is in these systems the cusp of the 10th house and the ascendant the cusp of the first house.
You will find the succeeding and falling houses by dividing the ecliptical length of each of the quadrants in equals parts. So you will use only the ecliptic for the calculations of the intermediate cusps; therefore this system is one of the ecliptical house systems.
It is possible to define position circles for Porphyri; these will pass through the aforementioned points at the ecliptic and through the poles of the ecliptic. But you need to calculate the cusps to find these circles which makes the use of position circles doubtful.
In 1979 I already published a short description of the system of Porphyri in the dutch periodical Spica [Kampherbeek, 1979].
History
Porphyri was a philosopher who lived from 234 until 305 CE. He was a neo-Platonist and a student of Plotinus.
The house system that was named after him however, was not made by him. It was used earlier by Vettius Valens and others a long time before Porphyri lived.
About a century before Porphyri, Vettius Valends describes in book III of the Anthology a division of the quadrants in three equal parts [Valens, 1994, p. 33-35]. This results in more or less advantageous places for the activity of a planet. Robert Schmidt, who translated this text, notifies us that these indications of activity (chrēmatistrikoi topoi) differ from the common meaning of houses. Therefore he does not see this text as a definition of a house system. [Valens, 1994, p. 35]. However, Valens does give a complete technical description of the system. It appears to me to be less relevant what the meanings of the houses are. As Cris Brennan indicates the measure of activity is an important alternative way to define the meanings of the houses. [Brennan, 2017, Hellenistic astrology p. 333-335].
Besides the description by Valens we know multiple horoscopes that use the system of Porphyri and are from a period far earlier, e.g. 76 CE. [Knappich, 1978, p. 14].
Deborah Houlding also mentions that this system was much older and was already used by Antiochus, long before Porphyri. [Houlding, 2006, p. 107]
We can conclude safely that Porphyri was not the inventor of the system that was named after him. According to Max Duval, it was due to Luca Gaurico that this system was attributed to Porphyri. [Duval, 1984, p. 20]. Probably the attribution to Porphyri was also due to Porphyri himself, describing a different system that did divide the quadrants but also used an additional span of 5 degrees.
The Porphyri system has been reinvented several times, among others by A. M. Grimm who named it the “Neuen Manier” (New way) and obviously did not know about the existence of the Porphyri system. [Wiesel, 1930, p. 26-30]
Arguments pro and contra
Bruce Scofield performed a test with his own horoscope. He noted the transits to the cusps of different systems and concluded that the system of Porphyri yielded the best results. [Scofield, 1993].
Max Duval mentions that the calculation according to Porphyri results in segments that exist partially above and partially under the horizon, both for day and for night houses. [Duval, 1984, p. 21]
Ralph William Holden considers it a disadvantage that the segments that result from position circles are unequal in size. [Holden, 1977, p. 65-67]
The objections by Duval and Holden are only relevant if you divide the cusps with real position circles that pass through the poles of the ecliptic. You can also define Porphyri perfectly without using position circles, these circles do not serve any purpose.
Calculation
Our location is Enschede in the Netherlands (52º13′ North and 6º54′ East). Date and time November 2, 2016 (Gregorian calendar), 21:17:30 UT. The sidereal time will be 0:35:23.6, the obliquity 23°26′13.56586091”. The MC is 9.62989868323 (9°37′48” Aries) and the ascendant 123,507983345667 (3°30’28” Leo)
The distance between MC and ascendant
123.507983345667 - 9.62989868323 = 113.878084662437
The fraction for the fourth quadrant is this distance divided by 3
113.878084662437 / 3 = 37.959361554145
The distance between ascendant and IC
189.62989868323 - 123.507983345667 = 66.121915337563
The fraction for the first quadrant is this distance divided by 3
66.121915337563 / 3 = 22.040638445854
Both fractions will always be 60 degrees if combined.
cusp 11 = MC + fraction fourth quadrant
9.62989868323 + 37.959361554145 = 47.589260237375
In degrees and minutes 17°35’21” Taurus
cusp 12 = cusp 11 + fraction fourth quadrant:
47.589260237375 + 37.959361554145 = 85.54862179152
In degrees and minutes 25°32’55” Gemini
cups 2 = Asc + fraction first quadrant
123.507983345667 + 22.040638445854 = 145.548621791521
In degrees and minutes 25°32’55” Leo
cups 3 = cusp 2 + fraction first quadrant
145.548621791521 + 22.040638445854 = 167.589260237375
In degrees and minutes 17°35’21” Virgo
The remaining cusps are the opposites of the calculated cusps.
There is always an exact triangle between cusps 11 and 3 and an exact sextile between cusps 12 and 2. This is always so in the Porphyri system. This is because you divide two parts by three whereby these two parts are 180 degrees combined. So you end up with one third or two third of 180 degrees for two fractions combined.
References
- Duval, Max – La domification et les transits. Paris, 1984.
- Holden, Ralph William – The elements of house division. Romford, 1977.
- Houlding, Deborah – The Houses: Temples of the Sky. Bournemouth, 2006, 2nd edition.
- Kampherbeek, Jan – Eclipticale huizen. In Spica vol. 3 no. 2/3. Enschede, june/september 1979.
- Scofield, Bruce – Why I use Porphyry Houses. In The Ascendant, Connecticut, Fall/Winter 1992/1993.
- Valens, Vettius – Anthology, Book II (concl.), & Book III. Transl. Robert Schmidt, ed. Robert Hand. Project Hindsight, Greek Track, Volume VIII. Berkeley Springs, WV, 1994.
- Wiesel, Erich – Das Astrologische Häuser-Problem. München-Planegg, 1930.
Image: http://wiki.astro.com/astrowiki/de/Datei:Porphyrius.jpg