Yes, wmt1 is right, Vienna is rich with musical events especially of those categories you have mentioned and most of them starts somewhat about the beginning of autumn. Probably, you know there is even such a live music venue as Musik Quartier, very special place for many musicians - you may take a look at their website to check concert dates : https://www.musikquartier.at/en/konzertkalender/
By the way, along with classic music - Vivaldi, Chopin, Brahms, there are more modern arrangements and compositions - for example, film scores and... exactly in September, Musik Quartier will welcome those who loves Joe Hisaishi scores for Hayao Miyazaki movies.
You can also read about this concert here:
https://simplemusic.world/09-09-miyazaki
I've just listened to Simple Music Ensemble once - it was this summer and they played awesome, really.
Anyway, there are lots of other musical venues in Vienna, Musik Quartier is just one of most popular and worth visiting.