This part of the paper is concerned with the relationship between the subjectively estimated 'unpleasantness' and the purely objective cause-the degree of non-linearity distortion. A formula, described as the 'distortion criterion', is setup in terms of the distortion spectrum, and is justified in several different ways. It survives two critical tests, one of which is the deriving of equal criteria from sine-wave signals which have been clipped once only, or twice symmetrically by diodes, thus conforming to the subjective assessment (established in Part 1), that such wave-forms sound equally unpleasant. The form of the criterion brings out the importance of a quantity related to the signal/noise ratio; experimental evidence as to the level at which this ratio becomes significant is, however, inconclusive.