Sorry to move the conversation briefly away from MQA but I wanted to offer a few comments for @ETEXAG about closed-back headphones under $500.
The Focal Elegia is, potentially, an excellent option if you can find one on sale for your price. Its MSRP is higher but Adorama and other vendors have been offering it for as little as $400 recently. Rumor has it that the Elegia is being discontinued. I’ve only tried it a couple of times, for about 45 minutes in total, and I liked it very much - a nice, fairly neutral, and clean, clear sound with decent bass and not the congestion of other closed-back headphones. Others with more experience than me aren’t fond of the Elegia so do plenty of research and try it for yourself first, if you can.
Some here seem to like the Shure 1540. I’ve not heard it so I can’t help, sorry. The same thing applies to the Meze 99 Classics, which also seems to be well regarded.
If you don’t mind buying used, the Mr. Speakers/Dan Clark Audio (same company but with a name change in the last year or so) Aeon Closed, first or second options might be worth trying, as might the Audeze LCD2-Closed, although I’ve not heard the latter or the second iteration of the Aeon. I wasn’t fond of the first Aeon, finding it a bit too congested and warm for my tastes, but that’s a matter of preference and opinion and not objective reality.
Again, used, you might also like the Massdrop/Drop Fostex TR-X00 or TH-X00 series of headphones. They’re not ideally comfortable for all listeners, and they don’t pretend to be neutral (like the Elegia) but they’re fun, with a v-shaped signature, lots of slam and glorious, rich, deep bass if that’s something you want. They come in three versions: Mahogany, as the cheapest, is said to have a sound that’s between the Purpleheart ones (which are bassier but have wonky treble) and the Ebony (which have great bass but a smoother, more coherent treble). The TR version has removable cables; the TH hasn’t. Again, they’re only available used now. I have the Ebony version and love it; it’s not the most resolving headphone but it’s a lot of fun and great if you like electronic music. It’s not fully sealed, though (it’s partially vented), so it won’t provide quite the isolation of other closed-back headphones.
If you want to buy new and you could stretch to $600, you might consider the Fostex 610, but be sure to read reviews of it carefully, I’m not sure it was as well received as the Drop TR-X00 series.
These Fostex headphones use a particular kind of propriety dynamic driver that is quite popular and can be found in other brands’ headphones. (Fostex also has a planar, closed back headphone, the RP Series, which were highly popular for people wanting to get into modding). The other manufacturers that make closed-back headphones using the Fostex dynamic driver include Denon and E-MU (although Denon now seems to be making its own proprietary driver).
I’d encourage you to look into the E-MU Teak as an excellent option. See what @ProfFalkin has to say about it. He’s far more more an authority than I am. See here, for instance.
I hope this helps as a starting point!