The Journal of Neuroscience concludes that people gain benefits from even limited musical training:

The people who had studied music, even if only for a few years, had more robust neural processing of the different test sounds. Most importantly, though, the adults with music training were more effective at pulling out the fundamental frequency, or lowest frequency sound, of the test noises.

The research was described at Scientific American in a story written by Christie Wilcox. She suggests that the findings are something to consider as schools lose funding.

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