hmm, I always saw the Greater Hexagram Ritual as more concerned with planetary energies and the Lesser Hexagram Ritual as concerning zodiacal elements. After all quite different hexagrams are used.
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That was Crowley's view point, the Golden Dawn magicians do not agree. The angelic correspondences are seen as the four worlds of Qabalah or YHVH. Many people agree with Crowley and many do not. I personally don't but go with works for you.
I can't really follow this system as I can't see how these archangels can represent the four worlds. For one, Atzilut is unattainable in it of itself and can only be experience when dressed in the Forms of the lower worlds. Some kabbalists ascribed the highest ranking holy archangels to Beri'ah, but even then they need to "lower" themselves to Yetzirah in order to interact with us on the astral plane or the mundis imaginalis. So how does Raphael come to be associated with Atzilut, etc. ? Even in the G.D. systems and other occult western schools the world of Atzilut is represented by the divine names and not angelic forms. Would you mind clarifying this point?