Chris
Thanks very much for a fascinating and illuminating article. The hypothesis for the attribution of the elements to the signs of the zodiac makes me want to use them, as it had always seemed to me be based just on unconvincing seasonal ideas.
The scheme of angular triads and a coherent rationale for the triplicity rulers is also very impressive. The diagrams showing this and the sect-mates brings to mind Taoist symbols, as used in Tai-chi etc, yang fading into yin and vv.
Just one thing about the classical scheme that still bothers me (as it perhaps did others wiser than me like Ptolemy, Lilly and Morin, because they changed it - well, Morin changed the whole system): the water triplicity is not symmetrical with the rest, and awkwardly has Venus as day ruler although it already has that role in the Earth tripliclity, and Moon as cooperating ruler although the Sun was not chosen for the that in the Air triplicity. It would seem logical to use each planet twice in the scheme, and the luminaries once, as in the rulerships. This is highlighted by your commentary on the symmetry of the diagram:
It is notable that in every instance the cooperating triplicity lord happens to be the next closest planet in the diagram among planets of the same sect. For example, the Sun and Jupiter are the main triplicity lords for fire, and Saturn is the cooperating lord because he is the next closest planet to them. Saturn and Mercury are the main triplicity lords for air, and Jupiter is the cooperating lord because he is the next closest planet to them. The Moon and Venus are the primary triplicity lords for earth, and Mars is the cooperating lord because he is the next closest planet to one of them. Finally, Mars and Venus are the main lords for water, and the Moon is the cooperating lord because she is the next closest planet.
From your diagrams and commentary it's clear that the Fire and Air rulers follow an anticlockwise sequence around the angles: cadent (Sun)> succedent> cadent // same cadent (Saturn)> pivot > back to previous succedent.
This starts the same for Water: cadent (Moon)> succedent> cadent,
then starts again in the same cadent as before, but then goes clockwise instead of anticlockwise, and doesn't include the pivot. This leads to Venus being used twice as a day ruler, and Mercury only once, while Moon is used twice though Sun isn't.
You mention how Mercury is assigned to the ascendant pivot because it can be both diurnal and nocturnal, yet in the Sect-Mates diagram it only appears as diurnal, because there's nothing in H7. If we put a nocturnal (occidental) Mercury in H7, the whole system would be completely symmetrical, and the Water triplicity could be Mars (night)> Mercury (day)>Venus (coop) (i.e. cadent>pivot> back to succedent, as for Air)
The diurnal triplicities would begin with a light (as ruler of the primary sect of each), and the nocturnal ones with a malefic; the 5 planets would each be used twice and the lights once, and only in leading roles.
I know one isn't supposed to tamper too readily with what's handed down, but it's your fault for triggering off these ideas! I'm wondering if it could help to sort out which version of the terms is most coherent, as that still seems to be a bit of a mess.
Thanks again for the great article, it really helps to have visual diagrams to understand rather than just tables to learn parrot-fashion.
I've got a few ideas about the Oktotopos (Oktotropos?) which I looked into recently, and will try to put together tomorrow if time.
Graham