Previous work investigating how non-musicians and expert musicians process local (musical intervals) and global information (melodic contour) in a local-global task (LGT) shed light on a processing style developed by expert musicians that prioritizes local compared to global temporal information (https://doi.org/10.1038/s41598-020-72423-7). The goal of the present work was to further address the mechanisms underlying this perceptual reorganization, in particular how it relates to auditory streaming capacities. To this end, we here considered listeners spanning a wider range of musical expertise: in addition to non-musicians (N=10) and expert musicians (N=8), a group of amateur musicians was recruited (N=8), represented by individuals with occasional solo instrumental practice but no prior theoretical training. All participants performed the LGT, as well as an interleaved melody recognition task (IMRT) taken from previous works on auditory streaming that requires the parsing of information along the frequency dimension. In the LGT, results supported previous evidence of a global advantage for non-musicians and a local advantage for expert musicians, and revealed a trend towards a local advantage for amateur musicians. In the IMRT, expert musicians outperformed both non-musicians and amateur musicians, who both had comparable poorer performance. A working memory test and a questionnaire surveying the level of musical expertise of the participants were also conducted. Taken together, our results suggest that, on the one hand, amateur musicians develop a trend to favor local compared to global information, similar to expert musicians, which is associated with their development of working memory; on the other hand, their performance for segregating a target melodic stream from another stream along the frequency dimension remains as poor as that of non-musicians. Overall, our data suggest that the perceptual reorganization of auditory information associated with musical learning takes place as a sequential reconfiguration: compared to the early change of processing style observed on the temporal dimension, the development of processing skills specific to the frequency dimension would require a higher degree of auditory expertise, that we suggest could be associated with collective musical practice.