For the house system that has been named after Porphyri, a variant exists where the cusps are not situated at the start of the houses by, more or less, in the center.
I was not able to find an official name for this system; I will just call it Porphyri-center.
This system is hardly mentioned in the literature. The only reference I could find was Max Duval. [Duval, 1984, p. 21].
According to Duval this is a hindu system (“domification hindoue”).
The calculation is based upon the same principle as for Porphyri, but now you calculate the center for each house and use this as the cusp. The original cusps according to Porphyri are situated more or less in the center of the houses. Not exactly, because the houses can have different sizes.
Our only source is Duval and he remarks that the centers of this system are not really situated at the center of the houses, just as we described before. This is the cases for the angular houses that are constructed of house-‘halfs’ of different sizes.
The basic principle is simple: calculate the distance between MC and Ascendant and divide the result by 6. This is the size of half a house in the fourth quadrant. Add the longitude of such a half house starting from the MC. The result is cusp 11. Add two more halfs and the result is cusp 12. And another time two halfs added gives you cusp 1.
For the first quadrant you use the same calculation, but now you calculate the house-“halfs” by dividing the distance between Ascendant and IC by 6.
Adding a half to the longitude of the Ascendant gives you cusp 2.
Adding two more halfs cusp 3.
And again two other halfs cusp 4.
Cusps on the western half of the horoscope do form oppositions with the cusps on the eastern half.
Angular cusps will never be the same as MC, Ascendant, IC or Descendant.
A special effect is that cusps cusp 11 and 4 are always separated by 150°, cusps 12 and 3 always by 90°
and cusps 1 and 2 always by a distance of 30°.
Our default example uses the following data:
Location Enschede 52º 13′ North and 6º 54′ East. November 2, 2016 (Gregorian calendar), 21:17:30 UT.
Sidereal time 0:35:23.6 and angle of the ecliptic E 23° 26′ 13.56586091”.
MC is 9.62989868323 or 9°37′48” Aries and the Ascendant 123.507983345667 or 3°30’28” Leo.
The distance between Ascendant and MC
123.507983345667 - 9.62989868323 = 113.87808466243
one sixth of this result
113.87808466243 / 6 = 18.97968077707
|This is therefore one sixth portion of the fourth quadrant.
MC + 1/6 part of quadrant 4, this is 9.62989868323 + 18.97968077707 = 28.6095794603 or 28°36'34" Aries
cusp 11 + 2 x 1/6 part of quadrant 4, this is 28.6095794603 + 37.95936155414 = 66.56894101444 or 6°34'08" Gemini
cusp 12 + 2 x 1/6 part of quadrant 4, this is 66.56894101444 + 37.95936155414 = 104.52830256858 or 14°31'42" Cancer
The distance between IC and Ascendant
189.62989868323 - 123.507983345667 = 66.121915337563
One sixth of this result
66.121915337563 / 6 = 11.020319222927
This is therefore one sixth portion of the first quadrant.
Ascendant + 1/6 part of quadrant 1, this is 123.507983345667 + 11.020319222927 = 134.528302568594 or 14°31'42" Leo
cusp 2 + 2 x 1/6 part of quadrant 1, this is is 134.528302568594 + 22.040638445854 = 156.568941014448 or 6°34'08" Virgo
cusp 3 + 2 x 1/6 part of quadrant 1, this is is 156.568941014448 + 22.040638445854 = 178.609579460302 or 28°36'34" Virgo
Cusps 5 up until 10 are always in opposition with cusps 11 up until 4.
- Duval, Max – La domification et les transits. Paris, 1984.