Though I've never carefully went through and tried to type all the classical composers, Schubert is beta or alpha being basically "the 1800s Paul McCartney" as I've heard him called before, and Liszt is one of the most beta people in existence along with Wagner and Strauss.
Then, I can't even figure out what gamma would refer to other than soulless corporate schlock. Mendelssohn is perfectly likely to be gamma, as are most of those other people. Mendelssohn was the guy who made Bach popular after many centuries of Bach being a nobody, and tried to lock Wagner out of composing because he didn't like Wagner's music which caused Wagner to start being sort of mildly Antisemitic despite the fact he didn't think all Jews were like that. If we're just going to say bad composers are gamma that doesn't help the "gammas have bad music and they're all corporate drones" image. (Though I don't think self-typed gammas here are corporate drones with bad taste in music.) But, people tend to really hate gamma even more than beta because of the corporate drone image, and music in general seeming like an Fe/Ni or Fe/Si affair doesn't help that.