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Height is sensed by comb filtering caused by the outer ear at the ear canal entrance from frequencies in the 6-12 khz range. Greatest sensation of height is around 11 khz. You wouldn't expect it to be recorded. However I think some coincident microphone techniques like say Blumlein and XY may record something that is heard as height. Because you have two diaphragms that are offset vertically by an inch or so. This would cause objects higher or lower than the microphones to have interchannel comb filtering which might evoke some vague height sensations even though they are probably inaccurate vs real height differences.I am skeptical about height information being recorded in the first place and then reproduced.
It seems definitional that height information requires vertically differentiated microphones and, during playback, vertically differentiated speakers. In a two channel chain, there isn't an opportunity for this.
Hence, advent of multi-channel systems and Dolby Atmos, which specifically allocates channels for height information and includes additional speakers to reproduce it.