John Sloboda, "Explaining exceptionally high and exceptionally low achievement in music: elite performers, savants, and the self-defined 'tone deaf'" talked about how 4 to 5 percent of the population may indeed be unable to perceive pitch (cognitive amusia), up to 15% of college-aged populations call themselves "tone deaf." His studies reveal that these people who claim to be tone deaf have "perceptual skills indistinguishable from normals, and that the key deficits appear to be in the area of planning and monitoring of singing behaviour." Even the simple inclusion of accompaniment helps these people of "low musical achievement" to improve their performances.
The National Institute of Health has done research on tone deafness, as reported by Dennis Drayna, Jennifer Jones, Carmen Brewer and Chris Zalewski "Genetics and phenotypes in tune-deafness." They found that tone deafness is a complex genetic trait, such that members of a family may all have difficulties with pitch perception, but the amount of "deafness" varies greatly and there is no strict segregation between pitch perceivers and nonperceivers. They also found that people with amusia also have other aural perception difficulties, including speech. And people who do poorly on auditory tests often have attention deficits.
Isabelle Peretz, the coiner of the term "congenital amusia," gave a paper entitled, "The Genetics of Congenital Amusia (or tone-deafness): Family Aggregation." She confirmed that amusia is a pitch problem, not a rhythm problem, and agreed with the previous study on the strong genetic component. She identified 10 large amusic families with 40% of the first-degree relatives suffering from tone deafness, whereas only 3% of the relatives in the control families were tone deaf.
Timothy D. Griffiths et al, is attempting to identify a single gene that explains congenital amusia: "Could a congenital disorder of musical perception ever be explained by a single gene? Relating neuronal organization to a complex behavioural phenotype." More interestingly, they explain the physical causes of these perceptual deficits:
Pitch-direction analysis is likely to depend on a right-lateralized network including the secondary auditory cortices and inferior frontal cortex (Stewart et al., 2006). Recent voxel-based-morphometry data acquired in collaboration with the Montreal group (Hyde et al., 2006) demonstrate either an increase in grey-matter density or a decrease in white-matter density in right inferior frontal cortex. In either event, such deficits could be produced by single genes. An increase in grey-matter density could be caused by heterotopic cortex due to a neuronal migration disorder (which can be due to an autosomal dominant or x-linked recessive single-gene disorder). A decrease in white-matter density might reflect a disorder of axonal guidance which could be plausibly related to a single gene such as that for a cell-adhesion molecule.
So, don't assume you are tone deaf if you can't sing well; and if you are tone deaf, blame it on your parents.