Music study enhances teamwork skills and discipline. Music training and performance requires, among many other things, practice and performing with an ensemble.
Each of these endeavors requires a significant degree of self discipline -- to stick with the (often boring) practice regimen, to train your fingers, eyes, mind and mouth to all work together and to play precisely in the ensemble with others. The ensemble, whether it's the band or orchestra, relies on each musician to prepare his own part making each musician responsible to every other musician in the group. The music educators feel strongly this sort of training has an impact on all the other non-musical aspects on their students' lives -- forever.
Creating music requires a great deal of focus on many things simultaneously: pitch and rhythm reading and interpretation, fine motor skills, listening, etc. Aristotle said, “We are what we repeatedly do. Excellence, therefore, is not an act, but a habit.”Undisciplined rehearsals yield undisciplined performances. Practice lacking in disciplined fundamentals yields poor musicianship. We are what we do. Music students are often high achievers academically. They have the personal discipline and focus needed to study for long periods of time. The work ethic developed during personal practice, lessons, and rehearsals becomes a part of their character. And this strength of character brings successes in every future challenge they engage in.
If you would like other benefits of music, this article lists many.