Flat Headphones?

ue TF10 is tuned electrically flat. The original LCD 2 and HE400 are pretty flat as well

 

Your best bet would be to get something with very effortless extension to both the lowest bass and uppermost treble, with minimum distortion across the spectrum, and EQ it to flat from there.

From my personal experiences, headphones that get close to sounding pretty neutral without EQ are: HD650, HE-X, HE-560, LCD2.2 (pre fazor). Of course all of those have faults that will need EQ to address certain problem areas. 650 is humped in the mid-bass, while rolls off in the lowest bass and upper treble. HE-X rolls off in the upper treble, HE-560 needs some gain at 2khz and reduction at 4khz, while the Audezes-- well, you don't know what kind of sound you're going to get with differing units it seems-- but the one I auditioned was very neutral from bass to midrange, but needed some added presence in the upper treble.

Given inherent technical prowess, and price/performance, I think the 560 is the best to EQ out of all of these, while the HD650 or even 600 would be best if you don't want to mess with EQ all that much.

 

Tascam TH-02 aka Teac CT-H02 measures pretty much like what you are looking for.

http://www.innerfidelity.com/images/TeacCTH02.pdf

 

Flat on a HATS rig != flat on a solid plate rig != flat speakers on the listening position.

The wrongest sound comes from flat on a HATS rig, it has a 12+ dB dip @ ~3.5 KHz.

 

Speakers are never flat, even studiomonitors, when they are put into a room. In a normal room listening 10 - 20 % is direct sound and the rest of it reflections.
Moving your head a few cm the freq changes that what you hear, not to mention how our hearing drops in sensitivity at lower volumes. A lot of research been done by Dolby, Audyssey, etc about this, yet I am unaware of a similar technology for headphones.

 

Good nearfield monitors measure reasonably flat in a proper setting, don't take my word, see measurements taken by Ultrabike here, noaudiophile and others in casual settings.

 

They will measure flat if they are calibrated for that particular space they are in, yes. How they will sound is another thing... there is no standard to get headphones to measure flat, like there is for speakers. Take any pair of good speakers and put them in various spaces and and it is possible for too calibrate them too measure and sound flat if listening at the volume they where calibrated at. As far as I know there is no standard like that for headphones, nor music mixing on stereo speakers. The standard only applies for flims, as far as I know.