One of the unfortunate bromides in discussions of jazz vs. classical music is to present jazz as the improviser's art over against Western art music aka classical music. Richard Taruskin's sprawling Oxford History of Western Music would disabuse anyone of such a stereotype if a person were to read the first two or three volumes of that roughly 3,600 expanse. Improvisation was a crucial element of composition and performance throughout what we'd now think of as the Baroque era, which might be more accurately described as eras of figured bass or thoroughbass. Well, Ramsey over at his ArtsJournal blog has noted that ...
Improvisation in music did not begin with jazz. Bach and Chopin were noted improvisers, as was Beethoven. One of the great Beethoven stories is about the flamboyant pianist Daniel Steibelt (seen right) challenging Beethoven (seen left) to an improvisation contest, in effect a musical duel. Steibelt played first. When it was Beethoven’s turn, he used a few notes of Steibelt’s score, turned the page upside down, mocked his opponent’s first notes and built a brilliant improvisation. In that early nineteenth century cutting contest, Steibelt was humiliated. The younger man announced that he would leave Vienna, never to return as long as Beethoven lived there. Beethoven died in Vienna in 1827. Steibelt, as promised, stayed away.
That Beethoven began to write out cadenzas because he didn't trust the judgment of performing musicians, and those who venerated Beethoven and his music followed suit, and that these historical moments fused with German Idealism to create a musical and pedagogical culture in which improvisation was eventually steamed out of what's now thought of as classical music seems unfortunate. Taruskin asked somewhat rhetorically if we were "really" better off having a literate art music tradition that eschewed improvisation or not. I'd say we're not better off and that if we go back to an era or cultural relationship between composer and performer closer to Haydn and Mozart (who didn't feel obliged to write out cadenzas so much) that would be good.
That ... might also depend upon a few established styles but that's another topic.
So for anyone trying to assess music history we should know better than to imagine that what's colloquially known as "classical music" didn't, doesn't or has not had a place for improvisation. Look at a score from Heinrich Schutz' Little Sacred Concert Pieces and you'll find out that it's really, really bare bones.
But for those who imagine classical music basically starts maybe as far back as Vivaldi, Bach and Handel and then goes up to where ever they decide, a lot of traditions in which improvisation was essential and inseparable from what we think of as classical music in the broadest possible sense of the term just get ignored.
It's not at all surprising to me that when people talk of possible paths of reproachment between Western art music and popular styles they do so not from the vantage point of 19th century canons and canonization but from the perspective of Baroque music.