I'd like to comment on this, because it is an interesting topic of discussion, I would like to stress before I begin that I will be approaching this academically and do not intend to make personal attack on anyone. If you believe that I fail at this and that I do make a personal attack please let me know so I can apologise and alter how I behave in future. Also feel free to disagree, conversations are boring when people don’t.
I'd also like to clarify the following, I also came from older editions where the intent was a far more subtle magic and was written clearly as such, however this is 5th edition and I will be focusing on it as its own entity, so any input from older editions will be superseded by 5th. In fact I wasn’t even aware it may have changed until I read this thread, so I will be having to actively ignore my own previous assumptions on this matter.
To begin, lets examine the first paragraph in perceiving magic. It starts with the statements that 'magic is rarely subtle' and 'any form of magic (examples) changes the world around it', both imply that magic is noticeable but do not implicitly state as such. It then goes on to state 'sometimes its obvious through a magicians gestures or incantations', followed by a fluff bit saying magicians are sometimes called twitchy fingers. This sentence annoys me, it feels like it ends to soon, like someone was about to follow up with some kind of sometimes it not example but got distracted by the twitchy fingers example and forgot to finish their sentence. Regardless of how poor I feel the sentence is, it once again implies that magic is in one way or another, noticeable, I could write a few paragraphs on how much I hate the idea of spotting 'twitchy fingers' but its not needed for this discussion.
The next sentence is 'spirits sometimes cause the air to shimmer, even from astral space', and here we have the first instance of an otherwise invisible effect being noticed, also worth noting is that the spirit is making itself noticed by altering the equivalent material space it would be in and it doesn’t make mention of in requiring effect on the observer to be observed. This is probably the first really usable sentence going forward, it give some solid information without being too vague, not enough to go on by itself, but useful none the less. The final sentence, 'people have reported feeling chills, dread, or other unnatural sensations they can’t quite put their finger on when magic is in the area', is another useful one, it lets us know that perception of magic goes beyond the normal 5 senses, dread can be felt in response to and as an indicator of magic that would be otherwise imperceptible. The second half is also invaluable to us, 'when magic is in the area', this lets us know that effect on observer is not necessarily needed, its not perfect since the term area is about a vague as it gets but its still a solid step towards an answer.
To sum up the first paragraph on its own, the intent feels very clear that magic is potentially noticeable even when it isn’t obvious, it isn’t automatically noticed and details beyond the presence of a magical effect do not exist, but it does make the distinct impression that all magic can be noticed. However, it seems an easy inference that magic that is noticed might not even be noticed as magic, you could feel a chill from magic and adjust the AC in response, see a shimmer in the air and clean your glasses to make it go away, noticing magic and recognising that you have seem to be two different things.
On the the second paragraph and the fun part, rules. Lets focus on magic with a skill involved first, 'Noticing magic is a simple Perception + Intuition [Mental] Test with a threshold equal to the Skill Rating of the being performing it minus the Force of the magic' now this is straightforward, and easy, to notice magic you just make a perception test against a threshold, the one hiccup is the term 'performing', but we'll get back to that later. Now for when a skill isn’t involved 'or 6 – Force if there’s no skill involved (minimum 1 in either case).' again, straightforward and easy, and give us the clarifier that there is a minimum in both cases, solidifying that while magic can be noticed it is not automatic.
The paragraph goes on to give some examples and state that a magical skill can give the observer bonuses, and honestly I feel that these examples are terrible. The first example gives us no new information to use as it is just an implementation of the math, it gives us no indication of what was seen or felt or heard or what, just that it was spotted on that roll. The second one does give us some more though, it states that a test is made when you walk through the ward, and it says that two things that could be used as an identifier is either a tingle or seeing some markings. Annoyingly those markings are not explained, if they are just real markings carved in to something then they shouldn’t be detected with a perceiving magic test, that’s just a straight up normal perception test that even a drone could do, and the test would happen before going through the ward. I really don’t like these examples. The part where having a magical skill is interesting though, and complicates the earlier idea that you might not know you're noticing magic, does it mean that you're 'magically attuned' or whatever and as such more sensitive to this kind of thing or does it mean that you are better at separating false alarms from the real deal? The latter definitely debunks the idea that you can notice magic without realizing it.
After that paragraph it seems an easy thing, if skill is involved use x formula, if skill is not involved use y, for x roll perception vs (skill rating of being performing the skill-force), for y roll perception vs (6-force). This however, is not the case, otherwise we wouldn’t all be here, so lets throw an oft used example in to that equation.
Improved invisibility on a mage walking trough a security checkpoint, it is a magical effect that involves a skill, so we use x formula. Here in is the rub as presented by others so far, in that the calculation for the threshold requires the skill of the magician performing the spell, that the mage is no longer 'performing' the spell, and therefore the magic cannot be detected due to the formula not being completed.
Now, a critical problem here is that this is a formula to perceive magic, and there is nothing so far in the perceiving magic section to suggest that there is any magic that can not possibly be perceived, so there must be a solution here somewhere.
The solution as proposed by some other posters, is that it simply uses y formula instead. I do not like this for a few reasons, number one is that the rules clearly state that formula y is for when no skill is involved and in this case there very much so is, a skill was used to cast the spell. Number two is that it allows for no way for a magic user to increase their ability to go undetected outside lower force, which kinda sucks.
So now we are left with the problem, we are feeding this use case in to the rules and not getting a proper result, we are in effect getting an error as up until the calculation of the threshold it is rather straight forward, then we end up expecting a number where there isn’t one. This outcome should not, as the rules are presented to us, result in the magic not being possibly detectable, but to simply throw it in to the other option despite it being the wrong option is also not what the outcome of this rule should be.
If I had to pinpoint where the wording of this rule is wrong, it would be the word 'performing'. I just did a word search of the SR5 CRB and there was not a definition of what constitutes performing magic entails. Some have assumed that it is the act of casting, which is a fair assumption that I too may have come to had I not been reading the rule with a critical eye, however with this rule in mind I feel that that is not the case. I think that performing magic begins when a spell is cast and ends when the spells effect ends for the purpose of this rule, to my knowledge of the English language this is an appropriate use of the word performing, this use make the above example of improved invisibility flow through the rule properly, and there is nothing in the perceiving magic section that contradicts this interpretation.
Now, you may be thinking, how is the mage 'performing magic' in the case of improved invisibility, its effectually a fire and forget spell, but its not, it is sustained and therefore the mage is still having input on it even if it is passive. Just look at other illusion spells as an example, such as trid phantasm, you create a bunch of illusions that you continue to control past the casting of the spell, in that case I feel it is painfully clear that you are still 'performing magic' with active input. Now admittedly this brings up questions of what happens when you put it in a sustaining focus, since its sustaining it instead of you and whether it still uses the skill formula or the non skill formula, but I'd rather not get in to that yet as it isn’t really directly relevant to the discussion at hand.
The final paragraph is fairly unnecessary for us, just pointing out the obvious that things like an exploding fireball need not be rolled for in this way.
To conclude my reading of the perceiving magic section, I would say that the rules for detecting magic can most definitely be applied to things such as sustained or quickened spells, and that they use the first formula as opposed to the second. They can be detected without the need for the observer to be affected by the thing to be detected, and that even when they are detected they aren’t necessarily understood as the detection of magic, let alone pinpointed in their detection. That said, the rule remains vague on things such as range and what modifiers would apply to the test.
I hope you found my ramblings useful, and invite any critique or comment you may have, especially on the point of how this approach will interact with sustaining foci and any houserules you would apply, I for example would probably let a spec in magic reduce the chances of magic being detected for that type, though I am unsure as to how much it would change it. Also sorry for the length, believe it or not this is the cut down version.
