It turns out that the ability to identify the pitch of a musical note without needing a reference note to compare to is more common than previously believed. This ability is called "perfect pitch" or "absolute pitch", as opposed to "relative pitch".
Using a testing technique adapted from studies involving infant hearing, researchers at the University of Rochester's Eastman School of Music and Department of Brain and Cognitive Sciences were able to test for perfect pitch in a random sample of people, including people with no musical training whatsoever. In the past, these tests were performed only on people with musical training who could identify notes by name. For more on this study, follow this link.