[ubs28]

After listening to various headphones, it seems that the headphones that sound the best with bad recordings are the ones that aren't necessary rated among the top headphones or speakers. If the recording is good, then the great headphones do sound really great. 
 
So to me it seems that there exist no best headphones because it all depends on what you are listening to. And cheaper headphones or speakers can sound alot better on bad recordings.

 

[JeWorms]

  And cheaper headphones or speakers can sound alot better on bad recordings.

 
Indeed， but most average recording will sound better on great headphones IMO. BTW, what will you define a recording as bad?

 

[ThickGlasses]

   
Indeed， but most average recording will sound better on great headphones IMO. BTW, what will you define a recording as bad?

I would imagine that he means a FLAC file as opposed to a variable bitrate MP3 file.

 

[ubs28]

   
Indeed， but most average recording will sound better on great headphones IMO. BTW, what will you define a recording as bad?

 
I would say a sound quality that is very flawed in terms of soundstage, frequency response, distortion and so on. It doesn't sound natural due to the inherit recording or conversion (like low quality mp3). 
 
A good recording sounds very natural and accurate.

 

[Thujone]

The bitrate does not determine whether something is a bad recording or not. If it was recorded/mastered poorly, it doesn't matter what bitrate you rip it off the CD, it will still sound poor. Of course, compressing the files more and more cause other issues.
 
Some tracks have such horrible mastering done that they sound extremely grainy on revealing headphones. No dynamic range, tons of distortion, etc.

 

[GL1TCH3D]

The bitrate does not determine whether something is a bad recording or not. If it was recorded/mastered poorly, it doesn't matter what bitrate you rip it off the CD, it will still sound poor. Of course, compressing the files more and more cause other issues.

Some tracks have such horrible mastering done that they sound extremely grainy on revealing headphones. No dynamic range, tons of distortion, etc.

There you go.
Of course even a well mastered song still won't sound good at low bitrates. Usually headphones that have a thicker, richer sound will gloss over poor recordings/bitrates a lot better while ultra clear headphones like HD800 will just punch every detail missing or badly mastered into your school

 

[Buyer no 1]

A good headphone is a headphone that gives you basis for deciding, by listening, whether the recording is good or bad.