Could you please provide some sources about that? I am asking about the categories listed in the DMG in the Starting Equipment equipment table, and for calculating price of enchantment items and such stuff.
Is there some rule of thumb to determine if some setting is “High magic” or “Low magic”?
While magic is somewhat commonplace in the Forgotten Realms, this is really the baseline level of magic in Dungeons & Dragons 5th edition. The Forgotten Realms is defined in the rulebooks as a standard D&D campaign setting.
This is not to say that you can't run a campaign in the Forgotten Realms which is high-magic; the DMG explicitly tells DMs they may freely change the parameters of prewritten campaign settings. But by default, and canonically, 5e-era Faerûn is a world of standard magic.
The term "high magic campaign" is not strictly defined in the D&D 5e core rulebooks, except to state that magic items are more readily available to player characters than standard (Dungeon Master's Guide p.38, Xanathar's Guide to Everything p.126). In a low magic campaign, by the same token, they are rarer than standard.
The standard campaign is the default D&D experience as described by the core rules. Dungeon Master's Guide p.9, "The Big Picture", defines the Forgotten Realms as one such campaign setting:
This book, the Player's Handbook, and the Monster Manual present the default assumptions for how the worlds of D&D work. Among the established settings of D&D, the Forgotten Realms, Greyhawk, Dragonlance, and Mystara don't stray very far from those assumptions. Settings such as Dark Sun, Eberron, Ravenloft, Spelljammer, and Planescape venture further from that baseline.
D&D's standard level of magic in particular is defined in Dungeon Master's Guide, p. 23, "Magic in Your World", making particular reference to the Forgotten Realms:
People everywhere know about magic, and most people see evidence of it at some point in their lives. ... In the city of Waterdeep in the Forgotten Realms setting, the Watchful Order of Magists and Protectors is a guild of wizards. These arcanists wish to make wizardry more accessible so the order's members can profit from selling their services.
Eberron is then cited as an example of a world where magic items are more common than standard:
Some D&D settings have more magic in them than others. ... in the world of Eberron, magic is as commonplace as any other commodity. ... spellcasters of low-level spells are common ... authorities and common folk are more likely to have access to and use the results of such spells. Buying commonplace magic isn't only possible, but also less expensive.
A formal definition of a "high magic" campaign can be found in the D&D 3.0 Dungeon Master's Guide (2000), p.164:
High Magic: Spellcasters and magic treasures are twice as common as presented in these rules, if not more so. Most characters have a level or two of wizard or sorcerer. Even a shopkeeper might be at least a 1st-level spellcaster. Magic items are bought and sold in clearly marked shops like any other commodity. Spells are used to light homes, keep people warm, and communicate. The function they serve is as commonplace as modern-day technology is in the real world.
By this definition, Eberron is probably high magic in terms of magic items, though author Keith Baker avoids this terminology, as he considers the ready availability of high-level magic, which Eberron lacks, to be a defining trait of high magic setting. We see here that there is some subjectivity in the term's definition.
The terms "high magic" and "low magic" were infrequently used in WotC D&D products after this point, and even the 3.5 DMG omits these definitions. In the preview article Warforged, Shifters, Changelings, and Kalashtar in Your D&D Game (2005), Stephen Schubert states that magically created humanoid life forms may be commonplace in a high-magic setting:
Because warforged are examples of magical creation at its peak, they're perfect for high-magic games. However, they could also be ancient relics of a bygone civilization that have recently been uncovered by adventurers.
In the Cityscape interview (2006), Ari Marmell describes high magic as something notably beyond the normal paradigm, though potentially local to a single place in an otherwise standard world:
Similarly, the book does indeed take some time to address certain high-magic or other unusual cities. (For instance, the notion of flying or planar cities is addressed in brief.)
No, not in general.
To begin with, the 5e Dungeon Master's Guide defines the Forgotten Realms as a standard D&D world, as mentioned above.
The Forgotten Realms Sword Coast Adventurer's Guide does not describe spellcasting classes as any more common than in baseline D&D. There are "a few" sorcerers in larger cities, and the are only slightly more common in some cultures (SCAG p.136); this concurs with the Player's Handbook which notes that sorcerers are rare. Wizards who advance in level find themselves with few peers.
Magic items are not described as any more common, cheaper, or readily available than standard D&D.
For more historic detail, the magic level of the Realms was canonically described in the D&D 3.0 Forgotten Realms Campaign Setting, p. 92, "Magic in Society":
Wielders of arcane magic—also known as the Art—are rare in most Heartlands societies. No more than one person in a hundred or so is likely to have any ability as a wizard or sorcerer.
The text goes on to describe that in the most concentrated places of magic, such as among high elves, the rate of arcane spellcasters is up to ten times higher, but that's still around 10% of the population, which is far below D&D 3.0's formal definition.
Even the World of Greyhawk, which sets the D&D 3e baseline for what is standard magic, has several high-level and epic spellcasters (the Circle of Eight, Mordenkainen, Gwydiesin of the Cranes) and several high-magic elements (the vanishing city of Rauxes, a shop in the Free City that straight-up sells any magic item, a nation-state run by a literal demigod, the Tomb of Horrors, Overking Ivid V's pit fiend ally freely casting wish, and numerous powerful artifacts).
The rarity of magic items, another defining factor in high-magic, is addressed on page 94 of the 3e Forgotten Realms Campaign Setting:
Magic is not technology. Wizards and clerics do not manufacture levitating elevators or mass-produce magic portals for simple convenience or crude commerce. ...
Nearly all Faerûnians, no matter how humble, have seen minor magic gimmicks at some point in their lives. Fewer actually own such treasures, but it's not unheard of for well-off merchants or low nobles to save their money for minor trinkets such as a pot that can make itself hot, or a broom that can sweep itself.
In a high-magic world, magic items are as commonplace as modern technology, so most people would have a magic cooking pot. In 3e-era Faerûn, they are rare enough that only the richest might own one.
Further, magic items are described in this book as primarily obtained by looting ancient sources, as well as produced at great expense by temples or the Red Wizards. This isn't the "bought and sold in clearly marked shops like any other commodity" of D&D's "high magic"; magic items are found or commissioned specially, and adventuring magic items are rare.
Magic of Faerûn p.136 says that hundreds of magic items are made each year; not quite the thousands or millions one might expect if it were as commonplace as modern day technology. Page 64 of that book notes that the open market is largely full of superstitious charms instead of real magic items, with the few real sellers operating secretively or on the black market:
Unfortunately, in open-market stalls, a spellcaster won't find the more special items. She's more likely to find herself rubbing elbows with young men and women seeking objects whose effects rely more on the power of suggestion and superstition than any real magic, such as a ring of love's eternal hope or a pendant of fertility.
Magic items aren't widely sold openly, in clearly marked shops; according to Magic of Faerûn p.65, Risa's Shop in Baldur's Gate is specifically unmarked, operates secretively, and is available by invite only. Shalush Myrkeer secretly operates a secret auction once per year in a warehouse upon the full moon.
Races of Faerûn does describe certain magic items as "common items" among certain races, but the definition of that term on page 5 is merely an item regionally available at a 10% discount due to it being more prevalent than usual. The average shield dwarf still can't afford to buy a +1 keen battleaxe; it costs 7,479 gp instead of 8,310 gp, but that's still beyond most NPC fighters' budgets, so it would be a misnomer to say these items are really common, and inaccurate to infer that magic items are generally common in the Forgotten Realms. It's not the same definition of "common item" used in 5e's Xanathar's Guide, which instead represents very minor effects like automatically-mending clothing or an orb that tells which way is north.
What's more, this was all 3e era—the canonical 4e and 5e Forgotten Realms transitional cataclysms are likely to have reduced the setting's magic even further since then. Notably, the Spellplague weakened some items and violently reduced the number of spellcasters:
Most permanent magic items, such as artifacts, were left intact at the end of the Spellplague but charged magical items were either destroyed, warped, or simply ceased to function. ...
The blue flames also infected portals and planar gates, spreading even further across Toril. Almost every part of Faerûn was affected by the Spellplague and certain areas were eliminated entirely, while others were created anew. Thousands of spellcasters were either destroyed or went insane due to the collapse of the Weave after Mystra's death. In Cormyr, a third of the War Wizards were either killed or driven mad. Those who survived lost their ability to use arcane magic.
The Forgotten Realms is a magical world with some exceptional elements, but it is not high-magic by the standards of Dungeons & Dragons. In D&D 5e this is even more true, since Forgotten Realms now increasingly defines the standard level of magic for Dungeons & Dragons, and historic changes have significantly reduced the amount of high-level magic in the world.
The primary question here, to me, is, what exactly constitutes “high magic”? D&D itself supplies a definition—but I don’t think it’s a good one, it doesn’t capture, to me, what people mean when they say high magic. That is because it is defining “high magic” as being “high” relative to the norms of D&D—which are already, I would say, very “high magic.”
And unfortunately, this is not a term you can just look up in a dictionary. If you do a search on it, you’ll get details about the ceremonial magic of pagan, occult, and neo-pagan beliefs, not anything about fantasy. If you search harder to try to force things to be talking about fantasy literature and works, you’ll get redirected to “high fantasy,” rather than “high magic”—and D&D is undoubtedly that, but it’s not the same thing. High fantasy and low fantasy are the subject of a fair amount of critical and academic discussion, so there are more useful definitions and terminology around them, so we can be more confident in that statement. (For the record, “high fantasy” is, per Wikipedia, typified by a “secondary world” distinct from the “primary” one of the person reading the novel or otherwise consuming the work—Lord of the Rings being the quintessential example, but D&D and the Forgotten Realms also being mentioned in the same article.)
Anyway, the key thing with “high magic” is that magic is dominant—it is everywhere, or it is so powerful that its effects—even if not its effectors—are felt by everyone in it. It’s noted that 99% of people in Forgotten Realms residents don’t have any magic ability—sure. But 1% isn’t a small portion of the population; fewer than 1% of the United States is a plumber, but you wouldn’t say the US is a “low plumbing” country. Likewise, 99% of the people in the Forgotten Realms may have no ability with magic, but every one of them stands pretty good odds of knowing somebody who does—everyone who knows a hundred people during their lifetimes is expected to have met somebody who can do it.
Moreover, they know magic is out there. Their little hamlet may have no practitioners, but they know that if they go into the big city, they can find one. They know that magic is real and works; they know that it has caused significant historical events that impact their lives. This is not Lord of the Rings where when they say “wizard” they mean “wise person” and who mostly think Gandalf can do no more than set off fireworks. A gold ring undamaged by a fireplace, a sword that’s particularly hard—but not impossible—to break, these are items of wonder and astonishment in Lord of the Rings. They would not be in the Forgotten Realms.
Finally, even more than the life of the average person living in the Forgotten Realms, we have to remember that the Forgotten Realms is the setting of a role-playing game. The intent of the setting isn’t to follow the life of a random peasant farmer, it’s to follow the lives of adventurers. And adventurers’ lives are not 99% magic-free. In fact, adventurers in the Forgotten Realms will—if by some stroke of ill luck they have no spellcasters among their own number, and by great fortune avoid any enemies who have their own—still find magic items as a matter of course within their first few levels. Gameplay in Dungeons & Dragons in general—but really, in the Forgotten Realms in particular, with its host of extremely powerful mages and other magic-inclined movers and shakers—relies on, often revolves around, the use of magic and/or magic items. Consider that the 3rd-edition supplement Races of Faerûn saw fit to define the “common magic items” utilized by the denizens of each of the races and ethnicities described therein. Any setting that has “common magic items” is, I think, safely considered “high magic.”
First of all, Forgotten Realms is what you make of it. Since you seem to be asking to determine how much magic items cost and how available they are, it is really up to you; pick according to your own campaign's needs. Yet, it is worth noting that the overall lore since the introduction of the setting in AD&D 1e aligns with the description provided in the answer by @Kryan.
If you are asking the level for the "official" Forgotten Realms, I can refer you to unofficial tweets (April 21, 2019) by Ed Greenwood, the creator (and long-time major contributor) of the setting. Considering the extensive use of magic by his character Elminster, and the importance of the role of magic and the goddess Mystra in his novels, we would expect him to define the setting as high-magic. His answer is more nuanced (as always) than a flat yes/no, as he states that it depends on location and time.
Q: As per 5e rules for buying an item as a downtime activity, you actually have to roll to see what items appear(better rolls, rarer items) and if a player seeks a specific one they must roll particularly high depending on rarity. There is also a bonus to represent how high/low magic the setting is, from -10 if it's super low magic to +10 if it's super high magic. What would be a reasonable bonus(if any) to add for Waterdeep in this step? ...
Ed Greenwood: Any large crossroads trading city in the Realms that attracts a lot of money will be trending towards "super high magic." As the Realms heads into the 1500s DR, I'd put Waterdeep at a +7 bonus in harsh winter height, up to +9 at end of summer when some folk want to leave and make one last "big sale" to tide them through the winter lean trading times.
The rest of the tweets are also interesting as Ed Greenwood goes on to discuss how the actual machinery runs: who are the sellers, why do they want to sell, how the auctions are run, where to find them, etc.
Yet, he finishes with a warning that is similar to what I mentioned in the beginning of this answer:
Ed Greenwood: And remember: the rules are guidelines/suggestions. When I DM, magic items are never determined by dice rolls; I place what I think best fits the campaign (often 'custom' items), and the hunt and the negotiations are roleplayed.
Regarding other settings, it is difficult to set a clear guidance that fits all, as fantasy, by definition, is very open to people's imagination. For example, Eberron could be considered high magic due to common-place use of magic in daily life (magic as science), yet it has been characterised as "wide magic" by its creator Keith Baker (here) and magic item availabilities are not necessarily what you would expect from a high magic setting (read here):
I don't generally see #Eberron as bleak or traditional high magic; we generally describe it as "wide magic." Effects like teleportation are rare, but lower level magic has been incorporated into everyday life.
On the other hand, Matthew Mercer, the DM of the Critical Role campaigns, sees Tal'Dorei as a medium-to-high magic setting (here):
Q: Would you define Tal'Dorei as a "High Magic" setting?
Mercer: I’d consider Tal’Dorei medium-to-high magic, sure.
I would argue that Forgotten Realms is at least as high magic as Tal'Dorei. So, again, set the bar according to your own gaming preferences.
