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Let me start off by firmly stating: I love Shin Megami Tensei III: Nocturne.
While it wasn't the game that introduced me to the MegaTen world (the original NAPlaystation Persona was), it was the first game that captured my love for the series as a whole.
As I've spent more time with the series (and it's spin-offs) over recent years, I've come to the conclusion that Nocturne is the "odd man out" of the SMT universe, despite being such a critical success and fan favorite.
Officially released in Japan nine years after Shin Megami Tensei II, Nocturne was a drastic departure from everything that made the MegaTen series what it is. In many ways (both good and bad) Nocturne drastically changed the formula and created a new standard that MegaTen fans would compare future SMT releases to; much in the same way Persona 3 redefined an entire era of JRPGs.
But, as Persona 3 seemingly became the future model for the Persona series, the new formula established in Nocturne was promptly dropped as both Strange Journey and Shin Megami Tensei IV became strict returns to form.
In trying to understand the series arc as a whole, I found it near impossible to place Nocturne on both the continuity line, and on my list of favorites. While I still attest Nocturne is a phenomenal game made by an incredible team of people, these are the reasons why I believe Nocturne shouldn't be considered a mainline Shin Megami Tensei game:
No Demon Summoning App.
This is at the very heart and core of what is considered not only Shin Megami Tensei but MegaTen at all.
For the uninitiated, the MegaTen (or "Megami Tensei") series came from a novel by Aya Nishitani. In short, the novel is about a computer programming high school student who opens a portal to Makai (think "The Underworld"). This is the basis for the cyberpunk storyline (ie. digital devil story).
Shin Megami Tensei refined the idea: a highly intelligent computer programmer (Steven) is creating a new teleportation technology that goes awry, unleashing demons from the Makai realm. In response to the dangerous demons that are beginning to break through to our realm, he designs the Demon Summoning App: a computer program that allows users to converse with and capture demons.
Shin Megami Tensei II doesn't do much to expand on the idea but being a direct sequel to Shin Megami Tensei, it uses the same Demon Summoning App as a means of plot. Both Strange Journey and Shin Megami Tensei IV also use the Demon Summoning App as a central plot device.
In Strange Journey, the human characters can't even see the demons until they receive the App from a third party, and in Shin Megami Tensei IV Steven himself shows up and approves of the protagonist's usage of it.
Nocturne is the only SMT game that doesn't use any kind of Demon Summoning App whatsoever. No means or measure is communicated at all to express how or even why the protagonist of Nocturne recruits demons; which leads me into my next point:
The protagonist of Nocturne isn't human.
The Shin Megami Tensei series is a very humanistic journey; each game asking questions about morality, law and order, compassion, kindness, brutality, control, right and wrong... Nocturne tries (keyword: tries) to ask those same questions but from the perspective of a demon.
At the beginning of Nocturne, a young boy gives the protagonist the power to become a demon. This unfortunately changes the nature of right and wrong as the other human characters he interacts with (himself as well) question his humanity until he finally accepts the status of "demi-fiend" (half demon).
While it is an interesting plot choice, it ultimately takes the "digital" out of "digital devil story" and makes the humanistic choices somewhat unrelatable and far-fetched.
As a side note, Nocturne is the only mainline entry that doesn't let the protagonist equip or use weapons and guns.
No Law or Chaos path.
In every other SMT game, there are three story paths: Law, Chaos, and Neutral. Instead of this tried and true mechanic, Nocturne opts for multiple "reasons" that create a multi-tier'd story, if you could call it that. The truth is, Nocturne doesn't really have a story; only more of an atmosphere.
The main character wanders the wasteland listening to everyone's stories, and simply picks one to agree with. None of the "reasons" have an actual ending (save one; the pseudo-Neutral path) nor do most of the reasons have a complete story arc. The most you can do is answer predetermined dialog choices for one reason or another. It's more about world building; never once in Nocturne did I ever feel like I was creating "my" story.
What's worse is that every one of the characters which represent the respective "reasons" are entirely unlikable. They are vague caricatures which can be summed up with various stereotypical tropes: "The Pretty Girl", "The Weak Willed Boy", "The Caring Teacher", "The Controlling Badguy", etc.
I admit it's an interesting perspective, "a man struggling to define his own humanity amidst humanity's worst, clawing for control"; but it pales in comparison to the series familiar Law and Chaos heroes.
In previous (and future) SMT titles, both the Law and Chaos paths are represented directly by characters. Not just NPCs you interact with on occasion (as in Nocturne), but characters who travel with you and constantly give you opportunity to understand and explore the different paths.
Moreover, they are both likable. They react to each story situation in a believable way according to their alignment. Both perspectives (law and chaos) become acutely relatable and you struggle knowing that choosing one path will ultimately alienate (and lead to confronting) one of your two "companions". While Nocturne's "reason" system was an interesting departure from the series, I strongly affirm the series' law and chaos hero scenario is much more emotionally engaging.
There were originally no fiends in Nocturne.
This is a big deal in series continuity and lore.
The "fiends" were originally special demons that were only in certain dungeons with extremely rare encounter rates in previous SMT games. Because of the absolute rarity of their appearance, combined with their ridiculous difficulty (often considered harder then any other enemy, including final bosses), they became something like "urban legends" of the series.
However, when Nocturne first released, they were entirely omitted from the game. Due to fan outrage, Atlus decided to add them back into the game, along with a new dungeon and an entirely new ending pertaining specifically to the fiends. Despite series fashion, the fiends were not added in as random encounters; you could encounter them at predetermined points along the story.
The new version complete with fiends (originally titled "Shin Megami Tensei III: Maniax") would be the only version to reach Western shores. Most Western players don't even realize one of the highest and most iconic points of the game (the fiends) were not originally included.
The universe breaking retconn.
The new dungeon (entitled "Kalpa") included new story scenes in the Nocturne/Maniax re-release. I can only guess that in an effort to please series fans, they tried to link Nocturne with SMT I & II; but only very loosely, and broke the universe continuity at the same time.
Shin Megami Tensei I and II were continuations of the same story; II was a direct and related sequel to I. Both took place in the same post-apocalyptic Tokyo. From the beginning, Nocturne didn't take place in the same Tokyo; it was obviously a different story.
One of the Kalpa story sequences makes a vague reference that a Nocturne character is actually the reincarnated protagonist from Shin Megami Tensei II. It's speculated that due to his actions in SMT II, he is unable to rest, eternally damned to die be reborn.
However, in a separate Kalpa story sequence, it's explained to the protagonist that the world in which he operates is actually one of a multitude of worlds which are constantly in a series of death and rebirth.
If the Nocturne world is one of many, why is Tokyo the only setting? Are all worlds the same Earth, making it a multiverse? Why is a character from a different Tokyo in this Tokyo? It just doesn't work.
On the flip-side, it's opened the door for every new SMT series game to take place in the same Tokyo while simultaneously becoming it's own unrelated game. Fortunately, Atlus decided not to take that route and opted to maintain universe continuity in both Strange Journey and SMT IV.
It's because of these reasons I feel that Shin Megami Tensei III: Nocturne shouldn't be considered a mainline Shin Megami Tensei game. There are additional reasons I could include (drastically different style of music, missing more iconic demons from SMT I & II, fantasy setting divergent from series norm, lack of any cyberpunk elements, "cubist" art direction, conflicting series themes, introducing entirely new convoluted and unnecessary concepts to the universe)...
I still feel Nocturne is a great game and should be experienced by everyone; it's just not a "true" Shin Megami Tensei game (pun intended).