To a large extent, modern music is in the ear of the beholder, but there are various characteristics that your average audience would agree on as constituting this genre - undetectable (and certainly un-hummable) melodies, confusing rhythms, unexpected sounds emanating from traditional instruments.
In every generation, a composer comes to symbolize this uncomfortable, severe modernity. Once upon a time, it was Beethoven (decades after his death, critics were still railing against his "wrong chords" and "incomprehensible wildness"). Later, it was Brahms (his First Symphony was accused of being ugly and melody-free).
