[bigj5e]

Looking for a closed-back (no semi-open and certainly not open), circumaural (over-the-ear) pair of headphones that can be driven by an mp3 player. But here's the catch:
 
I enjoy listening to music as much as every "audiophile" out there and have an extremely discerning set of ears (I am a music teacher and critic) but an integral part of my listening experience is to feel "hugged" by what I hear, some perhaps call it feeling "stuffy" or feeling the "warmth" provided by music (technically speaking the "warmth" is probably provided by the bass). By no means do I wish to convey I can tolerate distortion of any level or sacrifice hearing and feeling the full impact of every single instrument or bass. If they're not there then what exactly is 'listening'? But whether I listen to Saint-Saens' "Organ" symphony, Grieg's "In the Hall of the Mountain King", Strauss's "Alpine Symphony", or a piano piece from Chopin/Ravel or a Paganini caprice, the magic is captured when sound produces its own space and you get absorbed into it. If my words are resonating with you, you know the exquisite-ness of what I am talking about.
 
I primarily listen to classical but depart to jazz here and there.
 
Having used as many quotation marks as Bennett Brauer (I hope you get the reference

), can anyone offer suggestions to achieve this luxury? Up to $400 is ideal but feel free to suggest whatever is out there, be it a $40 pair or a $4000 pair. (I used to call myself an audiophile until I saw the price tag that goes along with a high-end pair of headphones

)

 

[GREQ]

I'll just throw this out there - Beyerdynamic DT770 (32 ohm version)
It's not ideal for classical, but it'll get the job done better than almost any other headphone under $400
 
Another option is a professionally modified Fostex T50RP MKII.
Ideally they should be run through an amp, but they're sensitive enough to be thoroughly enjoyed through most portable devices. 
While it isn't strictly 'closed-back' they're usually damped a lot and most vents closed to the point where it isolates better than many true closed-back models.