What kind of headphones are the best for listening to jazz and classical music?

I am looking for closed back and wireless headphones. I cannot use any outside resources to research because every post on every site I find that explains what headphones are the best for music are always about EDM or other bass-heavy music genres. Not that there's anything wrong with that, but I want to know what closed back wireless headphones offer good balance, and not just amplify the base 10 times more than ideal, and call it a ''base monster'' or something. Please understand that my frustration is towards certain people who promote themselves as experts, and not any listeners of any kind of music. I trust the community here to make a good suggestion for me. To be more specific, I would be very happy if the headphones were:
  • closed back (as I will be in public spaces when using them)
  • wireless (I work with my hands and cables sadly get in the way)
  • around or less than 500 dolars
  • I have no big preference over noise cancellation, looks, portability; I just want to have good sound (and my understanding as a newbie is that that is hard to achieve in closed back designs)
thank you in advance and sorry for my english as it is not my first language :)
100% upvoted

Not trying to be discouraging but two of your three criteria almost guarantee issues with your preference in music in the current market (closed and wireless). You might be better off looking at IEM's/earbuds and some wire management solutions. If you are OK with some wires an ES100 is a small bluetooth receiver that could be used with a variety of portable headphones as well as the aforementioned IEM's/earbuds. It's small enough to be secured to your collar or larger headphones.
Dec 4, 2019
I got myself a pair of hd6xxs while Drop's supply lasted. I decided to wait for Drop's wireless headphones as they are apparently working on a new collab. Thanks for the comment :)
Those new wireless may be a really solid option from what I know of their development. They will probably still be a bit lacking on the soundstage front for large orchestral pieces but I think they could really excel in the audio quality front as compared to the more mainstream focused tunings (overly boosted bass, less than ideal clarity/resolution).