if anything, jazz is merely an extension of classical music.
as the symphony because the vehicle of choice, classical music became monolithic and plodding. wagner, liszt, tchaikovsky...those post-romantic composers were using these bloated sets of instrumentation because it was a competition to see what could be new and bigger and better.
jazz is a return to baroque era small chamber ensemble music. with modern instrumentation, a drumset, a syncopated beat, use of the 7th chord (which COMPLETELY changes the theoretical game) and the higher extensions, with an american bent towards featuring the individual soloist. what it isn't, is any different than classical music.
bach, vivaldi, paganini, mozart, etc...they didnt just do huge orchestral works. so much of it's devoted to smaller ensembles and soloists. and yes, baroque music heavily leaned on improvisation over theoretical structres...the very exact thing that jazz is.
what's different? probably 350 years and the difference between aristocratic central europeans and african americans in the early 1900's. it is absolutely, in no way whatsoever, the "antithesis" of classical music.
edited to add that early jazz was heavily influenced by sousa and military marches, which is more of a branch of european classical music than say, blues.
Grand Potentate
have you already listened to Danzón No. 2 from Arturo Márquez by Gustavo Dudamel?
