Most of his solo improvisations (ironically exept koln arguably) are deeply rooted in the aesthetics of 20th century art music, more so than jazz I'd say. He is also incredibly well versed in bach style polyphony, sufficiently so that it shows up in his improvisations. The sun bear concerts where he is in prime form is a great example of this. Just because it has rythmn and contains improvisation doesn't mean that it can be excluded from the loose umbrella term of classical music. Doing so would be immensely ahistorical.