Aldavis, in my opinion that author makes a mistake in assuming an anechoic environment for the sake of simplicity. I believe the room's influence to be the dominant factor in determining the perceived low-frequency characteristics, assuming competent speaker system design.
Apparently the author is aware that by the time we even hear a low frequency tone, we're well past any sort of "first-arrival" time window and into the time region where the frequency response is totally dominated by the room response. I quote him here:
"A 40Hz bass fundamental cannot be fast or slow - it is simply a 40Hz (transient) tone, and our hearing is depressingly bad at even hearing such frequencies until they have been present for several cycles."
Why he then proceeds to focus on the first less-than-a-cycle, which he pretty much just told us is virtually inaudible (or audible only insofar as it makes up part of the first several cycles), I do not understand.
Also, I've never seen a setup like his "Figure 1 - Typical Listening Room Setup". That looks somewhat contrived to me, probably to better make his point; but I certainly wouldn't call it "Typical".
I'm sure it's possible to come up with a positioning scheme and crossover frequency and slope that gives some sort of worst-case scenario, but consider this: The lowpass driver will be phase-lagging the highpass driver by 180 degrees for a second-order crossover, and 360 degrees for a fourth-order crossover. So the argument might well be made that the subs should be placed either 1/2 wavelength closer to the listener than the mains at the crossover frequency, or 1 wavelength closer to the listener, depending on the crossover type. I wouldn't make that argument personally, but my point is that placing the subs the exact same distance away as the mains doesn't time-align them anyway, because there is still the issue of a frequency-dependent time delay (a phase lag).
I think that if you can get the in-room frequency response in the bass region correct (and not just for one microphone location), you've already fixed all the major problems. At that point timing might become an audible issue, if the initial setup was something like Figure 1.
Duke
Apparently the author is aware that by the time we even hear a low frequency tone, we're well past any sort of "first-arrival" time window and into the time region where the frequency response is totally dominated by the room response. I quote him here:
"A 40Hz bass fundamental cannot be fast or slow - it is simply a 40Hz (transient) tone, and our hearing is depressingly bad at even hearing such frequencies until they have been present for several cycles."
Why he then proceeds to focus on the first less-than-a-cycle, which he pretty much just told us is virtually inaudible (or audible only insofar as it makes up part of the first several cycles), I do not understand.
Also, I've never seen a setup like his "Figure 1 - Typical Listening Room Setup". That looks somewhat contrived to me, probably to better make his point; but I certainly wouldn't call it "Typical".
I'm sure it's possible to come up with a positioning scheme and crossover frequency and slope that gives some sort of worst-case scenario, but consider this: The lowpass driver will be phase-lagging the highpass driver by 180 degrees for a second-order crossover, and 360 degrees for a fourth-order crossover. So the argument might well be made that the subs should be placed either 1/2 wavelength closer to the listener than the mains at the crossover frequency, or 1 wavelength closer to the listener, depending on the crossover type. I wouldn't make that argument personally, but my point is that placing the subs the exact same distance away as the mains doesn't time-align them anyway, because there is still the issue of a frequency-dependent time delay (a phase lag).
I think that if you can get the in-room frequency response in the bass region correct (and not just for one microphone location), you've already fixed all the major problems. At that point timing might become an audible issue, if the initial setup was something like Figure 1.
Duke