For a Gifted Elementalist, do they need to take the Minor versions of (Type) Techniques in order to open up more?
For example... Say you had Theurgical Summoning from being an Apostle of Appolonius. It seems to suggest that you can't use it for Philosophical or Medicinal Summoning.
What if a Gifted Character just learned (learned through teaching, not initiated) the Art of Summoning from an unGifted Magus with the Major virtue and both minor virtues? It's only one Art. Would he automatically gain the additional Minor Virtues to use all 3 times?
What if the unGifted teacher didn't have any, just the first one, Theurgical Summoning, or only one of the two Minor virtues?
I think I'd treat this as three different Supernatural Abilities. So the Gifted character could learn Theurgical Summoning, Philosophical Summoning, or Medicinal Summoning from the teacher with all three Virtues, and his scores in all of them would just combine together after he learned them.
I don't think that's Rules As Written, but yeah, that's how I do it. In RAW, what gets called an Art or an Ability usually has nothing to do with whether or not it uses the Art or Ability experience scale.
So every rule that has some effect on an Art, everything that modifies the Art Score, every Total calculated using the Art Score treats the Difficult Art the same as it would treat a normal Art.
The only exception is when you are spending XP to increase the Art Score. To increase the Difficult Art Score you use the Difficult Art Experience Point Table (which happens to look the same as the Ability Experience Point Table).
Maybe Elementalist Hedge Arts can be, but they do need explicit text to enable this.
I don't have my books in front of me, but I don't believe that there is any general rule (in the RAW) that enables an Art to be learnt as if it was a Supernatural Ability. I could well be wrong though.
It may well also be that Elementalist Hedge Arts explicitly make themselves an exception to the normal rules.
By the core rules, any and all supernatural abilities may be learned by teaching, but there is a penalty based on the number and scores of all abilities possessed, explicitly including the Arts. What Opening the Gift does is open every art at score 0 in a single season whilst possibly destroying the other abilities, and attune you to hermetic magic such that hermetic Art scores and hermetic ability scores don't count against each other. What a mystery initiation does is allow you, at the cost of time, effort and likely flaws, to ignore the penalty for having other supernatural abilities. Opening the Gift can thus be regarded as an Initiation script known to all magi, at least as far as system and possibly setting is concerned.
As such, whilst you could teach hermetic Arts to anyone with the Gift, it'd be deathly slow process, and take at least two seasons to get a single Technique/Form combination. Potentially useful, but not usually worth the effort. Likewise you could develop initiation scripts to allow nonGifted people to learn the Arts but again it probably isn't worth the time or effort for a magus.
While you may be correct about the rest of the post, it's noted that, like Vitkir, unGifted initiations into the Hermetic Arts are not possible, nor for the Parma Magica. Why, I have no idea, not that it'd be worth much anyway in the case of Hermetic Arts, considering how many there are.
Yes the penalty to the source quality explicitly includes Scores in Arts. The issue however is that the rules only talk about actually learning Supernatural Abilities in this way. Arts are not Abilities.
Well, yes and no. The words Arts and Abilities (and Methods and and and) are used more or less interchangably at times. The former is, in the core, because of the XP difference and historical reasons. With the advent of accellerated abilities and difficult arts, the difference is muddied. Aside from Magi themselves calling them Arts rather than mere skills, there is no difference from the point of view of systems or theme. They function the same way, save that Abilities can't be learned from Vis and Arts can't be practised, and even then you could make arguments for exceptions to those too.
Where does it say that in Hedge Magic? (I'm not doubting you; I just can't find it.) The closest I can find is a note about unGifted not being able to learn Hermetic Arts, and Vitkir requiring the Gift but nothing mentioned about initiations and their impossibility, though certainly it implies their nonexistance as yet in canon.