An offhand comment I made a previous post about how I felt that Hedwig's theme could be to the Harry Potter films what the James Bond theme was to that franchise made me think a bit more about that subject. Sequels are interesting creatures; they have to be familiar enough to satisfy the audience that liked the first one but different enough to prevent that same audience from feeling acute déjà vu. The same challenge faces the composer of a sequel; how much material from the first film ought to be included in the new one, and how much should be new material.
There are different methods of handling this; sometimes the composer will work more towards creating musical continuity throughout a series, other times it pays more to slightly expand upon the original but ultimately write a very similar score, still other times it is most effective to come up with a distinctive musical sound for each film. Of course, the composer may also choose to completely jettison any thematic material from the original and write a wholly new score, but that usually only happens when it is a different composer scoring the sequel. The choice that the composer makes is one based on their own styles, but also on the relationships of the films to one another. Is the sequel continuing the story from the original, or is it presenting a new adventure for its hero?
The Star Wars and Lord of the Rings trilogies, for example, are designed to tell a story over the course of three films, and so thematic continuity between the films is essential to carry the threads through. Themes and lietmotives are introduced and reprised throughout each series as part of the storytelling process (it is always interesting to point out to people that the Gondor theme that dominates The Return of the King actually appears in the Council of Elrond scene in The Fellowship of the Ring). Hearing each of these scores for the first time is interesting not only from the point of view of the new material, but also how the familiar material is integrated into the new score. Analyzing how thematic material is developed in scores of this type is one of the things I find most interesting about listening to film music, but it is not the only way to score a film franchise.
You can have something like the Indiana Jones or the James Bond films, where the only real continuity between each entry is that of the main character. The only musical constant between the different Indy pictures is the Raiders March and brief references to Raiders of the Lost Ark in each of the sequels (yes, I know that technically Indiana Jones and the Temple of Doom is a prequel, but it is a sequel for all intents and purposes). Each Bond film had a title song that yielded the materia primoris for the score, with the James Bond theme (and, in the case of the Barry scored ones, the 007 theme as well) providing all the continuity necessary for the films. The Rambo films also fall into this category.
When I first heard the score for Harry Potter and the Philosopher's Stone, I liked it well enough but was wondering exactly what it was doing. When I finally saw the film, I found that the score was doing something that Williams had not done for a while, in fact, not since Superman. He was musically defining a mythology, and in the case of Superman the impression was so indelible that when he was unavailable to score the sequel, Ken Thorne was brought in to arrange his music for Superman II. Even future unrelated Superman projects (such as Smallville) referenced his theme. Philosopher's Stone works very well in the film, although it is sometimes a bit overbearing for Columbus' literal approach. Like Superman II, Williams wasn't around to handle all of the scoring details on Chamber of Secrets, although he remained a presence throughout the process (rumor has it that he even got more involved during the recording stage). Unlike Superman II, Williams composed new music for the project, and unlike Thorne's brass bastardization of Williams' epic material, in this case the recordings William Ross conducted did the music some justice. However, there are several moments when the music directly reprises Philosopher's Stone, and I feel that had Williams had more time that the score would have had much more original material in it.
Prisoner of Azkaban is a different case altogether. Williams was back, and in fine form, and instead of bringing the rich tapestry of thematic material that was developed in the first two films, he jettisoned everything except Hedwig's theme and a brief quote of the playful theme loosely associated with flying. There are several new themes in the score, but one, "Double Trouble" (which several analysts have erroneously reported appears only in the first half of the film; it is actually referenced in several cues towards the end of the movie) is effectively the theme for the new film. There were some complaints initially that Williams didn't carry over as much material as some would have liked, but viewing the film reveals that this works beautifully. "Double Trouble" and itsvariations give the film its own distinctive flavor, enhanced by the period instrumentation.
This also (perhaps inadvertently) set the stage for the changing of the guard with regards to the composer. Shortly after the release of Prisoner of Azkaban, it was revealed that Williams would not be returning for Goblet of Fire, but that instead Patrick Doyle had been announced to take up the composer's quill. There was some speculation for some time as to whether or not Doyle would reprise any of Williams' material, with many rightfully commenting that Hedwig's theme had become synonymous with Harry Potter. Of course, the speculation is over now; Goblet of Fire sounds different from the previous three films, which is to be expected, but it isn't such a break in musical continuity because Doyle did use (a heavily reworked) Hedwig's theme. Watching the film unfold, one can also point out that the score works differently in the film than Williams' did; where Williams relied more on thematic development, Doyle instead uses his score to set mood. There are several themes in Doyle's score, but they are not as distinct as Williams'. This is not a bad thing at all, although it's subtlety does make the score somewhat less accessible on album than Williams' three were.
I think that this works. With the exception of Chamber of Secrets, each Harry Potter film has a very characteristic sound unique to each one. Over time, one finds the books presenting an overarching storyline, but each book is different from the others, mostly because the age that the protagonists are defines J.K. Rowling's narrative for each one, and so they develop over time. The celeste theme for Harry's family heard in Philosopher's Stone would have been too innocent for Prisoner of Azkaban, and so Williams came up with the more mature and introspective recorder and strings "A Window to the Past." The playful mischief of "Double Trouble" likewise would not have fit the much darker and grimmer Goblet of Fire either.