Can someone explain why it is the group delay but not phase delay that is more important to human hearing?
Ok, let’s do it in a few steps. First, let’s look at sound traveling through the air. The “phase delay” is nothing but the fact that sound travels at a finite speed: There is a time delay between a sound wave leaving a source and reaching destination. [And while we could look at it as an acoustic energy “phonon” (a “wave bundle” with its front and end) and measure the delay as the time for this phonon to reach the destination…] But it is often simpler to remember that sound is a moving wave [V=Vo cos(ωt-kx+φo)], therefore the time delay between the source and destination is simply the difference between this wave’s phase at the source and destination φ (normalized to [divided by] this wave frequency ω). So again, the “phase delay” is just the propagation delay of a sound wave.
Now, the “group delay” represents a rather different phenomenon — the fact that waves of different frequency can have different velocities. Which means that such different-frequency waves — while leaving the source at the same time (and with the same phase) — would arrive to some destination with a slight delay in respect to each other. Or, with a slight phase variation between them. This is the “group delay” — waves (signals, tones) of different frequency would arrive with a delay that depends on (“is a function of”) their frequency. Mathematically, in differential form it’s δφ(ω
)/δω
. [And this is where the term came from - a delay between waves of different frequency traveling within a “group“ of waves of some bandwidth.]
So far it was sound waves traveling in some medium. However, the same principle — of (a) a delay of a signal/wave traversing some “component“ and (b) this delay being a function of frequency — applies to all physical systems. And just like acoustic waves, to electromagnetic waves (representing sound) as well. And this “group delay” phenomenon — the dependency of the speed (thus arrival phase) on frequency — is especially pronounced in physical resonators and filters (though can be present in other elements — like amplifiers — as well).
Finally, the same effects — the delay, and the delay variation with frequency — also exist in the digital signal processing domain. Digital signal processing started by emulating physical/analog processes and circuits — resonators and filters — but grew into the development of more sophisticated systems with [digital] filtering properties far surpassing those of their physical equivalents. Yet these digital filters still would have both the phase and group delay characteristics — defined the same way as above (for physical systems). Only, as now calculated digitally, they can be rather exotic (eg, "non-minimal-phase" [ie not "physical" or "casual"] — designed “in reverse” to compensate for group delays and other non-linearities of the physical domain.)
As for “which of the two is more important for human hearing” — from the above, a simple phase delay — whether due to wave propagation or in a filter — simply delays the sound by a small fixed amount of time. Which most definitely is unnoticeable for a simple “point source and point listener“ topology. It can probably affect stereo (or multichannel) reproduction, but is easily compensated by a fixed signal-processing delay… Meanwhile, a strong group-delay might lead to, I do not know, appearance of spatial separation of a bass-drum and cymbals in a single drum kit. Or, more probably, some loss of sound clarity… depending on how strong the delay is.