As the title suggests, I am looking for the next step up from the AKG Q701, which I have owned now for about 3 years. In terms of musical preferences, I mainly listen to classical and instrumental music, but I also listen to fair amounts of contemporary rock and pop music.
As much as I enjoy the Q701, I do not enjoy listening to rock and pop music with them, even though they do excel with classical. After searching through various forums, it seems like the Hifiman HE-500 is a contender for being an upgrade, while many other opinions I have read state that the only true upgrade from the Q701 is the Sennheiser HD800 (which is way out of budget for now).
With a budget of around ~$600-$700, what headphone would be a viable upgrade from the Q701?
Key aspects of the headphone I am looking for include airiness, soundstage, instrument separation, natural timbre, and a balanced, neutral presentation.
Bonus points: Suggest an amp/dac to pair with the upgraded headphone, as I have sold my Matrix M-Stage I used with the Q701.
Thanks for taking the time to read this and I appreciate any advice or suggestions.