This study compared the influence of musical and psychoacoustical training on auditory pitch discrimination abilities. In a first experiment, pitch discrimination thresholds for pure and complex tones were measured in 30 classical musicians and 30 non-musicians, none of whom had prior psychoacoustical training. The non-musicians' mean thresholds were more than six times larger than those of the classical musicians initially, and still about four times larger after 2h of training using an adaptive two-interval forced-choice procedure; this difference is two to three times larger than suggested by previous studies. The musicians' thresholds were close to those measured in earlier psychoacoustical studies using highly trained listeners, and showed little improvement with training; this suggests that classical musical training can lead to optimal or nearly optimal pitch discrimination performance. A second experiment was performed to determine how much additional training was required for the non-musicians to obtain thresholds as low as those of the classical musicians from experiment 1. Eight new non-musicians with no prior training practiced the frequency discrimination task for a total of 14 h. It took between 4 and 8h of training for their thresholds to become as small as those measured in the classical musicians from experiment 1. These findings supplement and qualify earlier data in the literature regarding the respective influence of musical and psychoacoustical training on pitch discrimination performance.