Spell Mastery + Specialties

While it would be nice that your Mastery of a spell might be better in certain circumstances, I am with KevinShultz in saying that in such a case you should not gain an extra Mastery type, merely that your effective Mastery score is +1 in terms of reducing botch dice, adding to the casting score, and any already existing Mastery type whose effect is dependent on the Mastery score.

Tangential thought - In raccoonmask's example, how do you define 'heretic'? What happens if your Flambeau was a believer in Catharism?

More on topic thought - Because there are so many Ars Magic books where rules are distributed, and since I don't have access to the books at the moment (and not all books at that), does anyone have a comprehensive list of all the ways to study/increase score in Mastery of a Spell?

A cheeky House Rule: Spell Masteries are abilities for each spell, and only apply when their specialty is applicable rather than the specialty adding a point. All Spell Masteries have the implicit Specialty (When Casting the [Named] spell).

Normally the means of learning something (at least from what I remember of the ArM5 main book) is:
Adventuring Experience
Book Learning
Practice
Training
Teaching

My understanding is that Spell Mastery can't be learned by Training, as you don't use it in normal living occupation.
And that Book Learning gives you XP towards the next level in Mastery, but the Mastery type you choose doesn't have to be one that the book's author wrote about.

Take the hypothetical example: My Tremere character with Flawless Magic and Apt Student who has one level of Mastery in "Pilum of Fire" spell, is wanting to impress a Flambeau when next they meet. So he asks his Tremere parens to teach him more Mastery fro this spell
Lets say the parens, also with Flawless Magic and Good Teacher and 5 or 6 levels of Mastery in "Pilum of Flame", agrees to one on one instruction for a Season.
Assuming the parens has, say, Com of 1 and an effective Teaching skill of 6, so the Quality he supplies is 1 + 6 + 3 + 6 = 16
My character's Apt Student adds +5 -> 21, then Flawless Magic doubles that to be a source Quality of 42 XP
So one Season of Teaching by my parens would improve my Spell Mastery from 1 to 3 with 3XP short of gaining level 4. (assuming the parens has at least 4 levels of Mastery)
Did I calculate that correctly?
Remembering the Book Learning, can I learn Mastery types that the parens did not have for this spell?

And you can't have Virtues such as Affinity with [Ability] or Learn form Mistakes [Ability] when it comes to Spell Mastery?

Not quite - Good Teacher adds 5 rather than 3 when directly teaching a student (3 is when writing a book). So you've got an extra 4 xp, and can reach level 4.

XP Total would be 1 (Com) + 6 (Ability) + 3 (Formula constant) + 6 (single Student bonus) + 5 (Adept Student) + 5 (Good Teacher) = 26 * 2 (Flawless Magic) = 52xp

It could be higher, depending on Teaching specialization and up to +3 for a Teaching specialization bonus for the Lab, or up to an additional +8 XP after doubling.

that is a lot of experience - could you split it amongst the appropriate areas of study and not just apply it to the mastery ?

The above example covers teaching the deeper applications (mastery) of pilum of fire - so could the student learn the skill of teaching or gain insights into ignem

the student will gain a lot (double) because of the major virtue Flawless Magic doubling the Study total and because of the niche knowledge the teacher has. Although this is a lot there have to be a lot of specific boxes to tick. So should there be flexibility in what is actually being learnt?

This is starting to boil down to what can be learnt through any sort of study. Is it solely the skill being delivered or can you collect pointers on anything related to the subject?

Can you learn read and write latin by reading a summae on Creo?

If you want to learn how to teach then your teacher teaches the teach skill (sorry) However just being in any class you could pick up on how the teacher delivers the lesson - rather than listening to the content you observe the delivery method

The flipside is that you only get what it says on the tin - making life and bookkeeping easier

If you study subject X, then you get XP in X and not in any other ability or art - barring special virtues like Secondary Insight.

If you concentrate on some other aspect than what is actually being taught you could get XP in that other aspect instead. (Note: instead, not also)
For example sitting through a bunch of lectures concentrating on how the lecturer is presenting the material rather than on what he is trying to teach.
Doing it this way would only get you Exposure experience though - 2XP per season and no more.
Basically you learn a little bit just by being exposed to the subject matter all season. Note though that you can't get Exposure XP and some other type of XP during a single season.

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Since the specific product mentions has 3 Magi there with Spell Mastery, and only one of them has specialties listed, I'd notch it down to an error. Plus, one gets quite a bit from Spell Mastery that I don't think adding a specialty is needed.

Yes. Note my comment (from 3.5 years ago) that "it could always be that an author erred and it wasn't caught." Technically core book absolutely does allow for those specialties, though.

There is some allowance for learning multiple subjects in Art & Academe - see the box "Academic Learning and Experience Points" on page 96. In summary, it is possible sometimes to learn both a specific Academic Ability and Latin or Teaching in a season, or Latin and Artes Liberales, but you have to put at least half of the xp into the primary subject.