Interdependence in a Series

Alright, now we're finally getting around to what I wanted to talk about with the start of my reaction to the Tor article last week.

To recap, I talked about endings in novels and the necessity for a book to have a self-contained story. Then I talked about how everything in a novel is dependent on what you say elsewhere in that novel. Main idea I'm getting at here is that everything is interconnected.

Obvious, I know.

Now we come to this question though: Does each novel absolutely have to stand alone?

The way I see it, there are at least three distinct ways to deal with a large, multi-book series. A series can be comprised of independent elements, interdependent elements, or codependent elements.

In a series made up of independent elements, each novel stands on its own as a more-or-less complete story. Each book, however, also includes elements that contribute to the overarching story that is being told across the series.
The best example of this in recent memory is probably Harry Potter. At its core, each book covers the span of one year and features its own distinct plotline, independent of the overarching series. For the most part, you can read each book without much introduction or surrounding context and come out of it with a solid understanding of what happened. Yes, some of the later ones begin to contribute more to the larger story and thus require a little bit of context, but they're still structured to tell a story with a distinct beginning, middle, and end. You might think, "Hey, don't all stories do that?" Well... we'll see.
(By the way, from what I know about it, The Wheel of Time largely behaves this way as well. Each book in the series presents a specific problem and the characters spend their time trying to deal with that problem while others arise and further world/character/story development takes place around this main event. Thus, it is very episodic in nature -- which is another way of describing this style of storytelling. However, I have not yet read The Wheel of Time, so I can't comment further on its use of this technique with any authority. Once I have, however, I may return to this discussion.)

In a series made up of interdependent elements, each novel has a relatively clear arc, but the plotline is a bit less distinct. In addition, there is a lot more "bleed through" between the individual books. It's clear very early on that the story won't end with the first book. Thus, although each book has a noticeably-contained plot, none of the books are expected to stand on their own. The resolution of one book sets the stage for the beginning of the next book, constantly building the series toward the giant, cataclysmic climax at the end of the series.
The best example of this from recent fiction has been Brandon Sanderson's work. While Mistborn is his only series that has been completed, The Way of Kings sets the stage for this kind of story even better than The Final Empire did. There's definitely a climax to each of his books, but it's very clear that that ending is nowhere near The End for the series. Heck, even the end of Hero of Ages started setting the stage for a sequel trilogy (which Sanderson has said is coming at some point.)
(Again, from what I know about the series, the later books from The Wheel of Time might fit well into this category. And again, once I have gotten around to reading the series, I will have more to comment on this.)

In a series made up of codependent elements, the entire series should be treated as one novel. There is so much "bleed through" in each book that you can't even take a break between each one. You have to keep reading from one into the next into the next in order to keep track of what's going on and where everyone is. There's no definite story arc in any book (though there are major events that occur, they aren't always at the predictable points in the three-act structure), and there's no clear end in sight until you actually reach The End. This makes the series much more difficult (as in "requiring more mental effort") to read, but also much more immersive, as the story is often hidden beneath layers of world-building and character development.
The absolute epitome of this style of story-telling is George R. R. Martin's A Song of Ice and Fire. I can never tell where the next turn of the story is going to take me, and I don't care because I'm so absorbed in the characters' lives and emotions and the rich conflicts and settings that he weaves together throughout the series. Yes, there are memorable, major events that occur throughout the series, and many of these are often situated near the end of each book, but it's not structured or told in a way that makes us feel like we're getting a big "action set piece" at the end of each book.
Another reasonable example of this from recent memory is J.R.R. Tolkien's The Lord of the Rings. This isn't as apparent as Martin because you are constantly aware of an eventual goal, instead of being swept away in the immersion. However, the simple fact is that no one part of The Lord of the Rings can stand alone. It's basically one book broken up for the ease of publishing.
That's probably the most important element of a codependent series, it's essentially one book that's been separated into multiple parts for one reason or another.

Alright. That's done with now. I'm going to let my thoughts settle and get back to you with another topic later.