The Vienna-born American composer Arnold Schoenberg (1874–1951), now considered one of the great masters of the twentieth century, was derided for having thrown out the rules of composition—for working outside the confines of traditional harmony.

In his youth, he was a fan of Wagner’s compositions, seeing each of his major operas repeatedly. A series of Schoenberg’s early works reflect the Wagnerian influence. But just after the turn of the century, Schoenberg set out on his own path. The result was the 1909 composition Three Pieces for piano, which some music historians argue is the single most important composition of the twentieth century. The work is atonal, which is to say it is organized without reference to key. Schoenberg abandoned the techniques of musical expression as they had been understood for hundreds of years. This was no small moment for the music world, and many reacted with vocal and vehement criticism. (Of the outcry Schoenberg remarked in 1947 that it was as if “I had fallen into an ocean of boiling water.”)

But he had his followers, too, among them his students. Though he was essentially self-taught as a composer, he became one of the most influential teachers of his time. It’s interesting to note, however, that his teaching approach was grounded in the traditional practices of tonal harmony. He later brought order to the chaos of atonalism by developing a 12-tone serialism, showing how entire compositions could be organized around an ordained sequence of 12 notes. However, he never taught the method and rarely lectured or wrote about it.