A sequel score is a strange animal. The composer has to reference the original thematic material (unless a different composer scored the previous work), but at the same time build upon that as a basis and add new themes, and possibly develop old ones. John Williams has provided astounding scores for plenty of sequels, including the yardstick by which most sequel scores are now judged, The Empire Strikes Back (which actually redefined how people thought of the Star Wars movies musically - the Imperial March is one of the most recognized movie themes since John Barry's James Bond theme*). As a result, the composer has the luxury of being able to write in a world where they had already created the musical landscape. On the other hand, they have to keep it fresh and engaging, which is not always an easy task.
The Harry Potter scores are particularly interesting because Williams could not devote as much time to the second film as he did the first. Employing the services of arranger/conductor William Ross to "adapt" the score, Williams penned a few new themes, but much of the actual scoring adapts material from Philosopher's Stone. While the new music is really good, Chamber of Secrets didn't have enough of an original voice to be as satisfying a sequel score as I would have liked.
So, along comes Prisoner of Azkaban, for which Williams composed the complete score. Whether at Alfonso Cuarón's request or as a response to the darker, more mature entry in the series, other than Hedwig's theme (which remains central to the score) Williams used almost none of the material he wrote for the first two films. I think that this caused some film music fans to be somewhat disappointed by the score, but having revisited the score for the first time in a while, I can't emphasize how much I feel this was the right move.
Not that the music from Philosopher's Stone or Chamber of Secrets is at all bad, mind you. It's just that the first film is more of a child's memory of that story and the second film did not have the advantage of Williams' full attention. The music had a very clear palette, one which Williams is quite at home in (I have compared the structure and mythic underpinnings of the Philosopher's Stone score to that of Superman: The Movie more than once). The former film introduced us to the world and the music therefore is quite iconic; the latter film is more story oriented and the music is more of the same.
Not so with Prisoner of Azkaban for two reasons. The first is that the tone of the film is very different, not just darker but also more European, more quirky, told with a kind of Roald Dahl humor that is not present in the Americanized franchise entries the first two films were. The second is that the children are now older and dealing with different sorts of pressures, which Cuarón is eager to explore (he got Rowling's approval because she felt that his previous film, the steamy Y tu mamá también, showed an impressive grasp of youth outlook).
As a result, the score is at both more serious and more playful. Haunting compositions abound in this score, as well as grand material for the Buckbeak (forming the basis for the beautiful cue "Buckbeak's Flight" and the finale which doesn't appear on the record), but that is offset by a tongue in cheek aspect that keeps the music from becoming maudlin. Isolated set-pieces such as clankerous (my word, go make up your own) jazz cue for "The Knight Bus," the frolicking cue for "The Snowball Fight" and the grand "Aunt Marge's Waltz" are instant classics, as well as some smaller moments - my favorite of which is the pretty flute solo that accompanies a bluebird twittering about the Hogwarts' campus... only to fly too close to the Whomping Willow.
Williams replaced the music-box theme for family used in the first two films with a much more dramatic piece that bears a certain similarity to his theme from The Witches of Eastwick, one which delves deeper than the previous piece could have. While the family motif in Philosopher's Stone and Chamber of Secrets was charming and could be used in a heartwarming manner (it is featured prominently in the finales of both pictures), the new theme is mournful, speaking of the loss inherent in Harry's history.
"Double Trouble" is a fantastic counterpoint to this; serving as a theme for Hogwarts itself it is heard in many arrangements, most of them touching upon a Medieval sound that was unheard in the previous two scores except as source music for the Diagon Alley sequences. This beautifully brings to the forefront a character of the castle that did not come through either musically or cinematically in the previous entries, and that is the fusion of the ancient and the modern. Hogwarts is thousands of years old, but you know some Muggleborn or half-blood is walking around with a walkman on (I know I would). However, the motif can also sound ominous; it is the basis for the intense "Quidditch Year Three" cue (of course, the album for Chamber of Secrets inconveniently left off the "Quidditch Year Two" cue, which featured some really cool bombastic stuff too). This theme pretty much replaces the "Harry's Wondrous World" material from the first two films.
Danger appears with Williams' trademark magniloquence with booming music for the action sequences ("The Werewolf Scene" is a knockout), a ticking clock for the time-travel episode and a delightfully old-fashioned three note stinger for Sirius Black. There is also that damn autoharp theme for the Maurauder's Map that never appears on the damn album, damn it.
The result was that Williams had composed what to my sensibilities was his best genre score since Steven Spielberg's otherwise lackluster Hook in 1991 (yes, I am including the Star Wars prequels in that assessment). The initial critical reaction was that the score was dense and interesting, but because it wasn't as familiar as people were expecting, it left some people cold. It would appear, however, that most critics have come around, since the score was nominated for an Academy Award and it made several "Best of" lists from many sources, including FSM.
* Fuck Monty Norman, we all know the truth.