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Headphone sound is not approximate to ipsilateral incident sound - either in acoustics, or perception. The small, closed volume of earpads means that for much of the audio band, the driver is directly coupled to the eardrum, and above that you move into something more analogous to the modal range of a listening room - only at the very highest frequencies do you see something like conventional room sound propagation in headphones.With headphones sound is coming from the side, totally different result so not usable.
Subjectively, headphone sound is also not localized to the sides outside the head - if it were, we would require radically different target curves to achieve accurate timbre, and they would be very bright ones indeed by the standards of what we use presently. Rather, headphone sound is "in-head localized", outside of edge cases like head tracking+hrtf synthesis or well-matched HRTF binaural recordings.
Outside of the Harman target, there is no per se "headphone target" compensation for HATS, just the HRTFs of the HATS under different circumstances. However, this is ultimately neither more or less reasonable than the situation with speakers - after all, a speaker that measures flat with an omni mic in an anechoic room will measure like the free field HRTF of the HATS if you used that to measure it in said room. The "references" we have are either grounded in tests of subjective preference (e.g. the Toole and Olive experiments in speaker preference) or simply referenced to sound pressure under some acoustic circumstance, likely in an anechoic chamber or a facsimile thereof.The challenge for HATS users is to create (I assume HATS manufacturers by now will provide a correction file for this use case) an 'average' correction for headphones.
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The problem is there is no 'reference' headphone like there are reference speakers. Large, small drivers, angled or not, pads etc. differ from headphone to headphone so that's the biggest issue.
I'd generally argue that, to translate the headphone case to the world of speaker-philes, it's best to consider all measurements to be "in-room" - there is no analogue to the anechoic free field condition for headphones, because headphones are inherently designed as a system with the head and ear, and their behavior depends on that pairing. This is basically congruent with Olive's research, which indicated that people want, generally, about the same response at the eardrum from speakers and headphones (with a tad more bass and treble from speakers).
Please note that the chain of causation doesn't necessarily go this way - "good" speakers that are anechoically flat do slope downwards in real rooms, but it's not clear to me that it isn't this aspect that makes them "good". Part of Olive, Welti, & McMullin 2013 including equalizing a pair of Revel speakers flat, in room, at the listening position (with an omni mic), then measuring them with a 43AG and equalizing a set of headphones to the same response. When users were then allowed to adjust the response, they applied similar adjustments to both - and these adjustments do resemble the way that the Revels naturally slope in-room, but my argument would be that people tend to like the directivity characteristics which produce this in-room response in part because it results in this power response...That would be the room correction. The reason for adding that to the correction is because speakers in a room that radiate a 'flat' response from their position(s) in the room will be changed due to room modes, reflections and distance (small effect) to the listener.
That 'change' in general will be a downward slope from higher frequencies and some 'boost' of lower frequencies.