Although cognitive music psychology has a long tradition of expert–novice comparisons, experimental training studies are rare. Studies on the learning progress of trained novices in hearing harmonic relationships are still largely lacking. This paper presents a simple training concept using the example of tone/triad similarity ratings, demonstrating the gradual progress of non-musicians compared to musical experts: In a feedback-based “rapid learning” paradigm, participants had to decide for single tones and chords whether paired sounds matched each other well. Before and after the training sessions, they provided similarity judgments for a complete set of sound pairs. From these similarity matrices, individual relational sound maps, intended to display mental representations, were calculated by means of non-metric multidimensional scaling (NMDS), and were compared to an expert model through procrustean transformation. Approximately half of the novices showed substantial learning success, with some participants even reaching the level of professional musicians. Results speak for a fundamental ability to quickly train an understanding of harmony, show inter-individual differences in learning success, and demonstrate the suitability of the scaling method used for learning research in music and other domains. Results are discussed in the context of the “giftedness” debate.