There are merits to both approaches. An averaging approach eliminates the scenario where an outlier position that’s measured doesn’t reflect “normal” on-head behavior; a single-position measurement avoids the “fuzzing” of positional details together. IMO it would be more ideal to have a plot of the average, variation at some given confidence for the number of placements used, and “worst-case” for each frequency. Keith Howard does something similar to that with the confidence limits on Headphonetestlab.co.uk
although personally I’d prefer to plot variation vs. frequency relative to the mean.
It’s hard to say that you’re wrong, publicly - particularly with how contentious this hobby is. That doesn’t excuse us from doing it, but with the amount of hostility that’s thrown around, particularly at controversial figures like Amir, I can see how it’s hard to let go of defensiveness and be honest about errors (and I say that as someone who’s had the frustrating experience of trying to convince Amir that he’s in error).
One thing to keep in mind with this concept is that, for almost anyone in this hobby, there are a least some descriptors that you think are absolute hooey - it might be “slam”, it might be “detail”, it might br “PRaT”, or the “airiness” of a cable, or how much “cleaner” a ziplocked baggie of pebbles makes things, but all of us are drawing a line somewhere, and that means we all have some bar that things have to clear. For Dr. Olive, that’s “have some evidence that it’s a quantifiable phenomenon that’s affecting listener preferences”, nearest I can tell - and with his work having shown that, at minimum, frequency response is the overwhelming majority of what’s impacting listener preference in headphones, you can see why he’d be skeptical of any supposedly separate factors.
You can, of course, record the waveform of a song or section of it playing through a headphone, using an ear simulator. From there, you can analyze it via a few methods - several of them are built into Paul Kane’s lovely DeltaWave application. You will see differences between the original and the recorded reproduction, of course - some of them are due to environmental noise that the microphone will capture (which cannot be kept constant), some are due to inevitable issues with aligning the waveforms, and some, of course, are due to the linear and nonlinear distortions of the headphones themselves.
I will note that generally music produces less significant nonlinear distortion than sine waves for a given peak level, due to its higher crest factor (music is, almost always, quieter than sine waves).
For the linear distortions…well, that’s frequency response - and it behaves the same regardless of the input.
Speed and bandwidth are inherently connected - you can see the “speed” of a headphone by looking at its high-frequency extension, and with 20khz bandlimited content, there is a maximum “speed” to any signal in your recording.
CSD waterfall graphs have the double disadvantage of being very sensitive to parameterization and not giving additional information about minimum phase systems vs. magnitude frequency response. Some dialogue and plots here.
Well, pressure is definitely pertinent to what we hear - it’s the P in SPL! A headphone which is incapable of generating sufficient air displacement is going to have a proportionately reduced low frequency response, although when it is tightly coupled to the head, the displacement required for a given eardrum pressure becomes constant below the point where waves are very long relative to the volume’s dimensions.
Also, as an aside, the HE400SE, to my knowledge, has the same diaphragm size as the HE6 - the magnet arrays and trace patterns are different though.
As @Resolve said, this can be - and is - done, but there’s nothing interesting to see here outside of impedance interactions, and those tend to be a lot less interesting for headphones (which are fairly predictable loads dominated by their DC resistance) than for multi-way speakers (which have the added fun of crossovers, and much lower coil resistance).