The 20th Century in classical (also called serious) music became very individualized and diverse including:
neo-classic, reverting back to the symmetry of Classic form
neo-romantic, reverting back to Romantic style: lush harmonies, lyrical melodies
avant garde, newly conceived individualized styles including a-tonal music
Some avant garde composers experimented with leaving out some of the elements of music that were previously used such as melody, harmony, or form. This style was beginning to be seen during the 20th Century and continued into the 21st Century. It was called minimalism.
Following World War I Classical and Romantic styles were coming back but with the use of more extended harmonies in chord structure. Some composers who used neo-classical and neo-romantic forms were Igor Stravinsky and Sergei Prokofiev.
There were also composers who created their own styles. In Vienna Arnold Schoenberg developed atonality, music with no tonal center. He started this 12-tone technique, also called serial music.
When I was in college studying music, Aaron Copeland, who wrote in the neo-classic format, came to speak. He called Serial Music ”intellectual music that looked good on paper but was not comfortable to listen to.”
As you start learning to play this type of music you will find that this style begins with 12 unrelated notes called a tone row on which the compositions are based. Actual melodies are not meant to be singable. Other elements such as rhythm and form stand out and are considered more important. The chord and arpeggiated intervals may be disjunctive (dissonant) but often very exciting rhythmically. Dissonance added to the mood of this type of music.
Think of the very upsetting and unsettling things that were happening during this time period that was reflected in the music: the Korean War, World War I and World War II when so many people were injured and killed. These events had a profound effect on all disciplines which includes music.
Alban Berg and Alton Webern followed Schoenberg in composing their pieces in the atonal style followed by Lucian Berio, Pierre Boulez and Stravinsky, who also explored 12-tone technique.
Electroacoustic music was a new experimental style at this time in history. Imagine being there. You may have been very interested in using synthesizers, tape, and the beginning of computer technology. You might have enjoyed meeting John Cage, Milton Babbitt, Varese, Berio and Boulez. They are some of the composers who used this technique. Unconventional things were used as instruments. Here is one of John Cage's pieces using what is known as a prepared piano, using nuts and bolts inside the piano for effect.
In France this type of music was called musique concrete.
There were other composers who include taped sounds on stage in performance along with live instruments. While you imagine being there at this time in history, you probably attended many musical happenings. People would get together to jam: improvise pieces created on the spot.
At the earlier part of the 20th century there was much controversy between classical music and jazz. University music schools did not consider jazz to be important in the curriculum. Some people looked at jazz as a phase that would pass. Later on during the 20th century there was a closer connection between classical music and jazz. Gunther Schuller called this overlap in style third stream music.
Here is an example of this type of music:
Sergei Prokofiev, a Russian composer, and the American Jewish composers George Gershwin, Leonard Bernstein and Aaron Copeland wrote for piano as well as orchestral music during the 20th century.
It has been said that George Gershwin wrote his classical/jazz piece, Rhapsody in Blue, as a concerto for piano and orchestra, while riding on a train. Jazz bands as well as classical orchestras played it. Here is an example of this exciting composition. Listen for the resemblance to the sounds of a train as it starts, stops and travels the countryside. It became a very popular piece and is still played often today. The famous Leonard Bernstein, pianist, composer, and conductor, is the piano soloist in this orchestral performance of Gershwin's piece.