I really don't know much about headphone science, etc., but I wonder if it has to do with the impedance curve of the headphone?
I have the HD 650 and Beyer DT 1990, and neither are good at low volume, both also have impedance curves that are all over the map. Same with the HD 660.
The Oppo PM-3 are really good at low volume, and their impedance curve is practically flat. The RS2i also have a relatively flat impedance and are allegedly good at low volumes.
My guess (again, without really knowing what the heck I'm talking about) is the lower power used for low volumes isn't enough to overcome the mismatched impedances, causing the drivers to react differently at different frequencies, ultimately making the headphone just sound off.
Or maybe it's all just a coincidence. I'd happily be proven wrong.
what I get measuring the HD650's impedance at 3 different volume levels. green, purple(hardly visible) and yellow the quietest measurement. I started around 85dB SPL at 1khz which feels pretty loud to me after midnight^_^. I reduced by more than 10dB each time to be sure to get at least that subjective half loudness. the third measurement was at about 61dB SPL.
I'd be very tempted to suggest that we're not seeing any relevant change in the overall impedance curve. the added noise I get as I lower the volume is more likely to be my rig having to calculate the impedance based on smaller and smaller voltages and variations between the reference and the other channel. this logically makes any noises in the circuit show more and more influence as I turn the volume down. I have cheap gears so I could surely improve things with better input gain setting, but I didn't want to touch anything so that the 3 measurements would show the same conditions except for the volume level. choices were made
about the frequency response, I did measure that at various levels last year with the pads removed(so they don't screw up the results) and the headphone firmly held in place on the mic, but I don't know if I recorded that somewhere, at least it's not in my HD650 folder on this computer. so you'll have to trust me on this one, but the frequency response also doesn't change in any relevant way, at least on my horrible horrible O2, oh no how can you listen to music with that? ^_^
I'd expect possible changes on both the impedance curve and the FR if for example the airflow was miserable so at high level the driver couldn't move as it wants because of the stronger air resistance. another hypothesis would be if the coil got really hot at high level, to the point that the impedance curve would be affected, and with it the FR(at least measurably so).
the last option I can think of that would be strictly caused by the headphone side of things, is simply that the driver distorts like crazy at high volume level because we're asking it to go past its nominal excursion.
none of those ideas seem to fit our situation. the hd650 doesn't have crap drivers. and people find that low volume listening isn't as good. so unless they happen to enjoy the low freq distortions at higher volume(which isn't excluded TBH), I'd be tempted to suspect the human error and some psycho acoustic mess with a given signature.
I have no idea about distortions as even a "dreadful" 1%THD is already 40dB below signal, so it's hard for me to make sure I'm not measuring ambient noise(even less with the computer ON).
and obviously the same issue exists when trying to look for other non linear behaviors. impedance and FR variations are pretty much the limit of what I feel confident to test.