Astrological Magical Foci & Potent Magic

I have a question pertaining to the optional Astrological Magical Foci and Potent Magic described on pages 36-37 of "The Mysteries, Revised".

It states that these may be taken by any Magus, without any prerequisite Virtue or Mystery membership. It then goes on to say that all spells casting using these Foci or Potent Magic count as "Astrological spells".

What, exactly, does this mean? The chapter on Hermetic Astrology develops spells which require Planetary Magic or its successor, Celestial Magic. Spells which use, for example, a Minor Magical Focus in an Astrological House are affected in what way? Do they merely require that the local Astrological Time be determined, as per the general-purpose spells presented in the chapter, or is there something more?

What about long-term study or enchantments which use the Foci? For instance, the Astrological House of Frates with its emphasis on partnership and/or friendship could easily represent a bonus to working on a Familiar. Does this require a detailed horoscope for the season? That's a product of Celestial Magic, which, again, is not something that is stated as a requirement for the Astrological Focus. The enchantment isn't an Astrological enchantment per se, so it shouldn't fluctuate in intensity. What does happen?

Additionally, does a Magus with this type of Focus or working in this type of Potent Magic gain a benefit from all of the listed Astrological Correspondences (pages 56-57) for their particular Virtue (House for Minor; Sign or Planetary for Major)?

ah well, ... nothing.
I think there was a time when it mattered, but the distinction got lost, and the term never got edited out.

You can imagine any number of cases where an "Astrological" quality of a spell distinguishes it from other spells, but there are no such rules in TMRE.

not actually affected, no. A Potency in a House has no interaction with Celestial Magic, or astrological time...

any magus can cast a Horoscope using Artes Liberales ... it's what you know to do with the horoscope that matters.
Celestial Magic, frinstance, lets you use the horoscope in new ways. (Potent Magic doesn't)

Yes: Potent Magic (Sign: Aries) governs spells of the 3 Decans, and covers adventure, zeal, dishonor, misfortune, nobility, leadership, propaganda and scandal.

Magical Foucs (House: Frates) covers all of family, communication, and speech.

The idea is that the areas governed are not tied to specific TeFo combinations (like normal Potency or Focus), but to narrow or broader themes.

It helps to look sympathetically at them in the light of conventional Major/Minor Focus and to be careful to be neither too restrictive nor too generous - care may be needed, depending on troupe and players.

Thank you. This is more-or-less what I had thought, myself.

Astrological Foci are, however, potentially much broader than traditional Foci, and some of their applications, while legitimate, could seemingly cover many actions. The Pietas House, for example, with its emphasis on study could arguably apply to the learning (not casting) of any spell from a Lab Text.

Does anyone have an idea how common Astrological Foci are in the Order? Logically, anyone could have it, and since it can be taught by anyone who has it (Major or Minor, as applicable) to another, regardless of their respective "signs" it would be something that could proliferate quickly.

... A Magical Focus only provides a bonus to spells determined by the existing guidelines - a Focus does not of itself provide new guidelines.

Since, AFIK, there are no guidelines for spells to boost Learning (it is generally considered outside Hermetic magic, presumably in part for game balance), the Pietas house is more limited here than you suggest...

not particularly common, I think.
Not every magus has a Focus anyway, and there are a great many conventional foci before you even begin to consider the astrologically inclined ones...

(Note: Virtues cannot in general be taught - I presume by "Taught" you actually mean "any magus can be initiated into a virtue known by a mystagogue"? Even though a Virtue is "common" you still need an Initiation Script to pass it on, and some sort of Cult Lore applicable to that particular script.)

(The process by which Apprentices gain Virtues and Flaws is not covered in TMRE: the parens specifically does not "initiate" the apprentice unless they are in one of the 4 Mystery Houses (or a Mystery Cult) and then only for the Mystery aspect of business.
For now, you must assume that Apprentices have their innate strengths and weaknesses "drawn forth" along with a degree of "like father like son" osmotic change.
However, an Apprentice may well turn out to have an Astrological twist to their V/F...)

Looking at the rules presented in "The Mysteries, Revised", one would think that Mystagogues would also be more common. The process for carrying out many Initiation Scripts is no more exhaustive than the creation of some enchanted items, and one would think that a Parens would Initiate his Filius along the way--not just in the Mystery Houses.

Mysteries are arguably opposed to the Bonisagus tradition, which emphasises the collection and dissemination of arcane knowledge. The Code of Hermes may respect the right of others to preserve their own Mysteries, however, the Seekers of House Bonisagus would probably be exactly the type to search out ancient secrets, learn them (via the creation of new Mystery Scripts), and work on ways to teach them to others in the Order. Alchemy, Astrology, and Numerology are all disciplines which really belong in general circulation in the Order, though the highest levels of them might still be restricted to a small group.