Frankenstein created a monster, but he had less success creating music.
Compared to films today, Frankenstein has very little in the way of a score. You'd think that there'd be a big dramatic orchestral oomph during the scene where the peasants chase the monster down in the windmill, for example, but there isn't. When the peasants are gathering to start their search, there's music—but it's just the dissonant church bells, calling them together.
Bernard Kaun was a regular composer for Universal horror pictures, and he did provide some music, including the intro composition for the creepy title sequence, with it's floating eyes that have nothing in particular to do with the film. His score is suspenseful, minor key, ominous orchestra backing. It's nice enough, but there's nothing particularly special about it.
In fact, the notable thing about the music in Frankenstein is really that there isn't any. The quiet gives an added eerie kick to James Whale's stark, carefully composed visuals. The monster will come on you in silence—there's no dramatic soundtrack to cue you to watch out.