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There is good research done in this area by two of our signal processing luminaries in peer reviewed Journal of AES:There is a debate among so-called audiophiles who claim they can hear phase distortion right below Nyquist, where it is greatest. But frankly, I doubt that a human can hear above 20 kHz (I certainly can't, I'm far from it). Therefore, phase distortion at the DAC's output is very probably of very little concern.
On the Audibility of Midrange Phase Distortion in Audio Systems
Authors: Lipshitz, Stanley P.; Pocock, Mark; Vanderkooy, John
They are different though. We have research that shows even copious amount of phase distortion/shift is inaudible. To wit, here is the report from Clark: Measuring Audible Effects of Time Delays in Listening RoomsI might also ask why someone cares about THD+N being at ridiculous and very probably inaudible low levels while not worrying about phase distortion. It makes no sense to me. I think if phase distortion is of no concern then THD+N at e.g. -90 dB is of no concern, too, and Amir would not need to make THD+N measurements any more .