I was going to mention that in my comment, but forgot. If you define "classical" as composed, academic music, then much of its 20th century output is just as dissonant as jazz, sometimes more so.

Are you referring to atonal music using composition systems such as the Scheonerg method? In that case, even if most of it sounds dissonant, it's still composed through a systematic approach, meaning notes/harmony are carefully choosen and left little room for 'out-of-box' improvisation