Which part? There are only four pieces with enough theme to hum to.
So I'm going to guess either Sander Cohen's little piano piece, or the waltz from the second track.
Cohen's Masterpiece is Tchaikovsky? I was under the impression that Gary Schyman composed all of the music in the game (sans the music with vocals and one piece you hear at the very beginning, which is in turn excepted by "Rise Rapture Rise").
They threw in some non-thematic Bioshock ambiance between Tchaikovsky and Cohen. It's nothing important, or even with a name. The "Part 1" is actually two other pieces from the soundtrack stapled together, and have nothing to do with Sander, or Fort Frolic.