| I have two degrees in music and have dealt with the composition departments in all the schools I've attended. It's an interesting thing to think about, but truthfully, the only reason you would need a degree in music composition would be to enable you to teach music composition in some college.... and at that point you'd probably need a PhD to get the gig.
Most music composition courses, after you completed the usual theory and form and analysis classes, will be involved with some kind of experimental music (read non commerical) and is on the cutting edge of compositional philosophy. Expect to write in 12 tone style, free form, electronic (not dance) music. It's all extremely interesting and I love it dearly, but I have to say in all candor that it really doesn't have much to do with anything except trying to impress other academic composers with some kind of new sound or new compositional technique.
If you don't have to work for a living, or you have some kind of support system that can carry you until you have the doctorate, and you are clever and inventive in the medium of academic music, then go for it.... you'll have a blast.
If, however, you need to see some money for your life efforts, you might think about another line of work. My signature line is from my hero, Charles E. Ives. He found a way to become a very rich man AND compose the music he wanted to. It is informative to read a bio on his life.
Good luck with your choices. I'm sure other people will have different opinions. That's what makes it all so good.
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Never confuse beauty with things that put your mind at ease. -Charles E. Ives
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