If there is one song that would represent the entirety 20th century music, it would be "Tomorrow Never Knows" by the Beatles. Seriously, much as you can probably hum Beethoven's "Fifth" or "Spring" from Vivaldi's "Four Seasons," Tomorrow Never Knows is the vehicle in which entire genres of recorded music have been delivered. You've got trance. You've got hip hop. You've got sampling. The Beatles already did the power-pop thing earlier on that same album, so I won't include that, but man, that song must have launched a million imaginations.
Not that the Beatles need another accolade, but this song truly represents the dawn of the recorded age: using the studio as an instrument.
And from here, I go into the weekend with a song without a chorus to ponder!