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I'm not sure if controversial is the right term to describe him but Sorabji was an eccentric for sure both personality wise and in regards to his music. I find it completely incomprehensible but he has his hardcore admirers.

I know she doesn't necessarily generate the same talk and attention as others on this list, but I feel like I should mention her anyway just on principle: Galina Ustvolskaya. She had a pretty unusual style even for the avant-garde. She didn't start any riots or hate any Jews, but she was a weird one for sure. There were certainly those among her contemporaries who disliked her and her music. Of course, that's true of a lot of composers so that alone may not say much. Like I said, I'm mentioning her on principle. I just like trying to spell her name! :P

I dare say Schoenberg was arguably the most Controversial of all-time. One of the reasons for his "atonality" (a term he disliked) was so "people could talk about German music for the next hundred years." I think he succeeded

I don't believe Stravinsky was THAT controversial. The riot was mainly due to Ninjinsky's choreography and had less to do with the music. I believe the current most controversial composer is probably John Adams, due to the fake BS outrage over the MET's production of his Klinghoffer opera.

Short answer: any avant-gardist ranging from 1910-1960. Slightly longer answer: 1) Arnold Schoenberg. 2) Richard Wagner. 3) Igor Stravinsky. 4) Ludwig van Beethoven. 5) Gustav Mahler. 6) John Cage. 7) Pierre Boulez. 8) Karl Stockhausen. 9) Brian Ferneyhough. 10) The Beatles. Bonus answer: Antonio Salieri. Another bonus answer: any female composer of any era before 1980.

Surprised Stravinsky didn't make it. I think any composer that has a premiere of a new work causing a riot should get on the list.