With the aid of the Distorted Tunes Test a group of British adults could be established whose melodic aptitude was below a certain level and whom we called tune deaf. They are only a fraction of those popularly called tone deaf. The Distorted Tunes Test is only slightly correlated with pitch discrimination, short term tonal memory or number memory. In children ability to pass the Distorted Tunes Test develops at greatly varying speeds and to a varying degree, reaching stability in adolescence. Tune deafness has a familial distribution and segregates in a way suggesting an autosomal dominant trait with imperfect penetrance. Some degree of positive assortative mating has been established. Some people, unfamiliar with the British melodies which form the basis of the test, pass it. This indicates the existence of a partly innate and partly acquired competence to judge what is acceptable and what is not, within the tradition of Western popular or classical music. This seems to indicate the existence of some deep structure of tonality, comparable with Chomsky's deep language structure. Asians who have not been much exposed to this kind of music find the task very difficult.