Music therapy means a lot of different things depending on who's doing the therapy, but it is generally supported empirically in terms of promoting psychological well-being. Learning an instrument and practicing music in general is also beneficial to mental health.
Music Therapy Schools:
Finding a Music Therapist:
Fagen, T. (1982). Music Therapy in the Treatment of Anxiety and Fear in Terminal Pediatric Patients. Music Therapy, 2(1), 13–23, https://doi.org/10.1093/mt/2.1.13
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MacDonald, R. (2013). Music, health and well-being: a review. International Journal of Qualitative Studies on Health and Well-Being. https://www.tandfonline.com/doi/full/10.3402/qhw.v8i0.20635
Perkins, R. and Williamon, A. (2013). Learning to make music in older adulthood: A mixed-methods exploration of impacts on wellbeing. Psychology of Music, 42(4), 550 - 567 https://doi.org/10.1177/0305735613483668
Roden, I., Zepf, F., Kreutz, G., Grube, D., and Bongard, S. (2016) Effects of music and natural science training on aggressive behavior. Learning and Instruction, 45, 85-92, https://doi.org/10.1016/j.learninstruc.2016.07.002.
Seinfeld, S., Figueroa, H., Ortiz-Gil, J., and Sanchez-Vives, M.
Effects of music learning and piano practice on cognitive function, mood and quality of life in older adults. Frontiers in Psychology,
Whipple, J. (2004). Music intervention for children and adolescents with autism: a meta-analysis. Journal of Music Therapy, 41(2), 90-106. https://www.ncbi.nlm.nih.gov/pubmed/15307805