Psychophysical phenomena such as categorical perception and the perceptual magnet effect indicate that our auditory perceptual spaces are warped for some stimuli. This paper investigates the effects of two different kinds of training on auditory perceptual space. It is first shown that categorization training using nonspeech stimuli, in which subjects learn to identify stimuli within a particular frequency range as members of the same category, can lead to a decrease in sensitivity to stimuli in that category. This phenomenon is an example of acquired similarity and apparently has not been previously demonstrated for a category-relevant dimension. Discrimination training with the same set of stimuli was shown to have the opposite effect: subjects became more sensitive to differences in the stimuli presented during training. Further experiments investigated some of the conditions that are necessary to generate the acquired similarity found in the first experiment. The results of these experiments are used to evaluate two neural network models of the perceptual magnet effect. These models, in combination with our experimental results, are used to generate an experimentally testable prediction concerning changes in the brain's auditory maps under different training conditions.