Nahre Sol provides a concise explanation of this phenomenon. Until the 19th century improvisation was expected from musicians of "classical" music. From cadenzas in Mozart to repeats in Baroque dance suites musicians and audiences alike expected and eagerly anticipated the performer's flights of fancy.
I'm pleased to report young musicians day are much more open to improvising in classical music than are musicians of my generation.
I'd be pleased to show you how to improvise in both the Baroque and Classical style. Just ask.
Nahre Sol spends too little time explaining her practice time breakdown: Composition, improvisation, repertoire, technique, study.
You've got to learn your instrument. Then, you practice, practice, practice. And then, when you finally get up there on the bandstand, forget all that and just wail.
I'm a professional pianist and music educator in West Toronto Ontario. I'm also a devoted percussionist and drum teacher.