Thanks for your answer. 
The Griesinger procedure is this video?
Yep, that would be the one, though he got a newer Windows app made around 2019-2020 that’s presented in the latest video on that channel.
I created a website that tries to let you do this exact thing! - cabinaudio.com
The point of it is to stretch out the soundstage, changing your spatial perception of what you’re listening to.
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Can you explain how this works theoretically? I’m not sure what your methodology is based on and why the “higher pitched” sounds are supposed to sound “higher elevation”, and what EQ settings are supposed to be used to achieve those results. And even if those results could be managed with the sample sounds, how that affects tonality of normal stereo music recordings and voices.
All really great questions. I’ll give a shot at answering them, and please let me know any follow up questions you have.
How does this work theoretically?
The main idea is that we want to create separation of instruments, a large soundstage, and consistent imaging. We do this by changing the frequency response of the sound with EQ.
This works because the primary cues in localization are frequency response, ITD (interaural time difference), and ILD (interaural level difference). When we change the frequency response, we change the localization.
Because the frequency response of the sample sounds resemble the frequency response of individual sounds in music, the localization of the sample sounds is similar to the localization of instruments in the music. The sample sounds make it easy to hear how EQ changes this localization, which lets us effectively change the soundstage/imaging.
It’s definitely not perfect and we’re looking for ways to improve it.
What is your methodology based on?
Our methodology is based on the idea of using your own perception of sound to tune headphones. Originally, we tried to use perception of loudness to do this, but it never worked. Loudness is a very unreliable perception because our brain is constantly trying to subtract our HRTF from what we’re hearing. Eventually we came up with the idea to use your spatial perception of sound instead, with the hopes of improving soundstage, imaging, and separation of instruments directly.
Why do “higher pitched” sounds sound “higher elevation”?
This is a psychological/evolutionary bias our hearing system has - since we wanted to create spatial separation, we rolled with it.
Why auditory pitch and spatial elevation get high together: Shape of human ear may have evolved to mirror acoustics in natural world | ScienceDaily (Why auditory pitch and spatial elevation get high together: Shape of human ear may have evolved to mirror acoustics in natural world | ScienceDaily)
What EQ changes achieve these results?
Generally, intense V-shaped curves make lower pitched instruments sound lower and higher pitched instruments sound higher. This might be because they literally make bass-heavy sounds more bass-heavy, and treble-heavy sounds more treble-heavy, exaggerating the psychological bias for low pitches to sound lower and high pitches to sound higher. Additionally, dips and peaks that match our HRTF can create these results. Of course, you’ll notice a problem with this: if we replicate the HRTF at one elevation, then all of the instruments will sound like they are at that elevation! Well, that’s exactly the problem with small speakers and headphones: your HRTF causes all of the instruments to coalesce at the driver. Our idea is that if you undo the HRTF, you can spread out the image again, which might require strange looking peaks and dips.
How does this affect tonality?
We’re honestly not that sure. But it’s important to remember is that our brain is constantly subtracting our HRTF from what we hear. This means tonality is what we hear minus our HRTF. In other words, it’s spatially conditioned. Our brain is used to adapting what we hear based on where it thinks it’s coming from. However, in headphones, there is no ITD to match panning, the sound is spread over a much wider set of angles than in speakers (which matters b/c of HRTF), and there is no sense of distance. I’m not saying that we fix tonality, but tonality in headphones is a confusing concept in the first place because direction in headphones is unrealistic.
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I happened to come across Genelec’s Aural ID, which seems to be a system for calculating your HRTF based on a 3D scan of your head: https://www.genelec.com/aural-id
What do we know about this? When will this be available?