Jazz. <em>Jazz.</em>
The surge of Jazz music was emphasised in America during the twentieth century.
One reason is that during WWII, Hitler had an infatuation over 'tonal' and 'German' sounding music. Specifically, Beethoven and Wagner. Jazz music was banned as it was seen as a lower form of music.
Due to this, composers at the time, strove away from writing music that would sound like Wagner's or Beethoven's. I'm not really sure how to word it, but those two composers had this particular sound.
Anyway, composers started to use 'weird' harmonies. Things that would eventually become the sound of the 'modern' period in classical music.
Another factor involved in advancing American classical music is the entwining of classical music and African folk songs / music. Gershwin, a super important composer, is kind of like the defining bridge between Classical music and Jazz. He had spent around two years, living in an African American community, where he was able to use rhythms and harmonies in African music and use it in his own compositions. Think like his piano preludes or Rhapsody in Blue.
Hope that helps