> I've never picked up on a theme for either Sirius or Pettigrew. Don't know
> what you're talking about there.
Pettigrew's Theme is played on the harpsichord. It contains nine notes, but the first six are the same. Unfortunately it never appears on album at all, but it's played many times in the film with reference to Pettigrew.
The Sirius/Grim theme contains four notes. It doesn't appear on album much either, but you can hear it at 1:35 in "Quidditch, Third Year". The immediate start to that same track hints at the theme, as well. It is heard in the film as Harry and Mr. Weasley discuss Sirius Black and when Sirius steps out from behind the door in the Shrieking Shack.
> Buckbeak's music never appears again after the initial scene of Harry flying > on his back, therefore it's not a theme (a theme, by its very nature, is
That's not true. It appears again when Harry and Hermione fly on Buckbeak to save Sirius from the tower at the end of the film. There is also a very brief hint to it in the film after Harry and Hermione go back in time. Hermione realizes that Dumbledore wants them to save Buckbeak too, and Buckbeak's Theme is reprised very lightly and briefly.
> Double Trouble appears in so many places in the score I couldn't tell you
> what it symbolizes.
It's just the main theme of the score, probably intented to represent the somewhat playful darkness of the film.
> Neither Hedwig's Theme nor the Nimbus/Flying theme show up enough to
> really count.
Hedwig's Theme appears in "Lumos", "Secrets of the Castle", "Mischief Managed", and "A Window to the Past". There's the scene in which the season changes to winter, which is not on album. The theme is also played seconds before Lupin changes into a werewolf. "The Whomping Willow and the Snowball Fight" is based around a variation of Hedwig's Theme. But you're right about the Nimbus/Flying theme.
> Aunt Marge's Waltz, The Knight Bus, Buckbeak's flight, The Whomping
> Willow/Snowball Fight, Quidditch Third Year (which bears no relation to
> the quidditch music in the first two movies), The Werewolf Scene, Saving
> Buckbeak, Forward to Time Past. The score is more heavily tilted toward
> the non-thematic elements.
It seems like these are non-thematic, but some of those are based around variations of the other themes. "Quidditch, Third Year" contains variations of the Double Trouble theme, while "The Whomping Willow" contains Hedwig's theme variations. But the others ones you mentioned, as far as I know, do not contain themes. I wouldn't be surprised if they are based around variations of themes, though.