In this paper, the auditory model developed by Dau, Kollmeier, and Kohlrausch [(1997). J. Acoust. Soc. Am. 102, 2892–2905] was used to simulate the perceptual similarity between complex sounds. As complex sounds, a set of piano recordings was used, whose perceptual similarity has recently been measured by Osses, Kohlrausch, and Chaigne [(2019). J. Acoust. Soc. Am. 146, 1024–1035] using a three-alternative forced-choice discrimination task in noise. To simulate this discrimination task, the auditory model required a new back-end stage, the central processor, which is preceded by several processing stages that are to a greater or lesser extent inspired by physiological aspects of the normal-hearing system. Therefore, a comprehensive review of the model parameters as used in the literature is given, indicating the fixed set of parameter values that is used in all simulations. Due to the perceptual relevance of the piano note onsets, this review includes an in-depth description of the auditory adaptation stage, the adaptation loops. A moderate to high correlation was found between the simulation results and existing experimental data.