The licensed music in Bioshock is from crooners circa the 30s, 40s, and 50s (gotta love Wikipedia)
Totally agree with you about the music's awesomeness, it's a big part of why it's so atmospheric and sucks you in 
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"The superior man is the providence of the inferior. He is eyes for the blind, strength for the weak, and a shield for the defenseless. He stands erect by bending above the fallen. He rises by lifting others."
- Robert G. Ingersoll