The dissonant intervals that were introduced by modern composers in the late 1800s and early 1900 by composers such as Rachmaninov, Revel, Debussy, and Varèse were hardly "pure".
The most amazing feelings often wash over me, in fact, while listening to these incredible composers...after a while the "atonal" notes will suddenly "snap" into place while my brain is somehow making sense of the music without my help.
It is truly a sublime moment when this magic occurs, and I'll often laugh out loud as the sudden transition from melodic confusion to understanding occurs.