Since you're looking in the under $500 range, here's my recommendations. I've tried all the common recommendations you'll see.
Ollo S4X are by far the best I've ever used in this price range for this purpose. Very flat frequency response, super fast transient response (even with kick and bass), amazing clarity in the lows, mids, and highs (i.e. for the first time I was able to hear the separation between bass guitar and synth bass in headphones), great soundstage / stereo separation, great support from Slovenia, serviceable parts, etc. They're also semi-open-back, meaning you won't hear as much of the acoustic string sound through the headphones as you will with the HD600 or other open back models. Also important to note is that they are 32ohm, meaning they can be easily powered to loud volumes from your phone/laptop/etc. AX3's headphone output is 35ohm which is higher than ideal for a 32ohm headphone but unless you're really into headphones and have other very expensive headphones and top tier headphone amps, you won't notice any downsides. I have an RNHP and it really is something special, but with these headphones the audible differences between RNHP and AX3's headphone amp are minuscule.
Second place is Sennheiser HD600 (not HD650 or HD6XX which have a more rolled off high end which can be less fatiguing for music listening but is not a good choice if your goal is accuracy). HD600 is a step down from the S4X in every area except weight, it's lighter and slightly more comfortable for long sessions. Although I still frequently wear the S4X for hours at a time without problems. It's also much higher impedance which makes it more "compatible" with AX3's headphone amp (again, not a big deal), but the sound from a phone or laptop headphone amp will suffer.
Everything else I've tried in this price range doesn't even come close to the HD600, let alone the S4X.
