Contemporary music presents intrinsic difficulties (nontraditional use of sonorous material) and extrinsic difficulties (limited exposure) that impact the listener’s cognitive processes. The objective of this study was to observe and analyze how listeners who are not trained in atonal music attribute structural stability to rhythmic events in a piece of atonal music. The study was carried out among listeners with varying degrees of musical training: (a) musically trained listeners (music conservatory students aged 25–26 years), above all in tonal music, (b) listeners (University of Alicante students—Faculty of Education, aged 19–22 years) with generic music experience (Esteve-Faubel, Valero, & Stephens, 2009; Esteve-Faubel, Stephens, & Molina Valero, 2013), and (c) adolescents (second year of compulsory secondary education, aged 13–14 years) with limited training and musical experience. The results obtained were in line with the predictions of atonal prolongational theory (Lerdahl, 1997) and with those obtained from experienced listeners of atonal music (Dibben, 1999). The listener’s time to adapt to a new atonal language degree is inversely proportional to prior exposure to various styles of music. This underscores the importance of a latent period to facilitate adaptation for those listeners without atonal music experience. The effect of tonal reminiscences was also observed among those listeners with little training. Following this initial study, we recommend expanding the study to include other atonal musical pieces, thereby facilitating a deeper understanding of how the auditory adaptation period functions among listeners with limited experience. This would involve an analysis of other predominant parameters (timbre, motivic importance, register, dynamics, and dissonance) and an observation of their interaction with and influence on listeners exposed to atonal music.