Atonality is a musical technique, which means that there's no tonal centre, making it, sometimes, especially at first, sound random and unharmonious.
Although first pieces of music that used atonality could be found in the 19th century, like Liszt's "Bagatelle sans tonalité" (1885), it has become popular only in the early 20th century, when it was frequently used by Austrian and German composers.
Arnold Schönberg
Arnold Schoenberg (Born in 1874) was a Jewish Austrian and American composer, music theorist, teacher, writer, and also painter. His earliest compositions were in the late-Romantic style, but then he felt it was the limit of tonality, and started experimenting with free atonality. One of his most famous works, melodrama "Pierrot lunaire", was written using free atonality.
Twelve-Tone Technique
Schoenberg saw a downside in free atonality: its freedom led to the possible presence of musical material that could suggest a tonal centre. Thus, he developed the twelve-tone technique, which would strictly avoid it, by not letting any of the 12 notes dominate. The most famous work by Schoenberg that uses it is the "Variations for Orchestra".
Schönberg's Opinion Regarding his Earlier Works
Unlike some of the other composers who explored atonality, Schoenberg didn't deprecate his earlier works. In 1923 he wrote:
"For the present, it matters more to me if people understand my older works (...) They are the natural forerunners of my later works, and only those who understand and comprehend these will be able to gain an understanding of the later works that goes beyond a fashionable bare minimum. I do not attach so much importance to being a musical bogey-man as to being a natural continuer of properly-understood good old tradition!"
Second Viennese School
The Second Viennese School was the group of composers, that included Schoenberg and his students, notably Alban Berg and Anton Webern, who went from the late-Romantic style to free atonality, and then to the serial twelve-tone technique .
Alban Berg
Austrian Alban Berg combined Romanticism with the twelve-tone technique. Despite his rather small oeuvre, he is considered an important figure in the 20th's century music for his expressive style.
Anton Webern
Austrian Anton Webern was one of the most radical composers to use atonality, and yet his music is also expressive.
Kurt Weill
Some composers, like German-born American Kurt Weill, followed other styles. Ferruccio Busoni had accepted him as one of the five master students in composition. Kurt Weill's most famous work, "Mack the Knife", had later become a jazz standard.
Paul Hindemith
Music of German and American composer Paul Hindemith could seem atonal, but even though it freely uses chromatic scale, it has a tonal centre. During the 1920s, he wrote "Kammermusik" (8 chamber music compositions) that was a reminiscent of Bach's "Brandenburg Concertos".
Degenerate Music
Later with the rise of Nazis, some music was considered "degenerate". Schoenberg's works were criticised as he was Jewish. Germany's Minister of Propaganda Joseph Goebbels publicly denounced Hindemith as an "atonal noisemaker".
