If you've got access to it, the paper is called ""On the Audibility of midrange phase distortion .....(something)....". My university probably lets me access this stuff but i've never really tried. Here's a good substitute, though:
Human Hearing - Phase Distortion Audibility Part 2 — Reviews and News from Audioholics
Right, but I overall don't pay much attention to it. My point was, on the heirarchy of important stuff, where does step response sit?
As far as vertical off-axis response, any time you have a crossover(IE two drivers operating in the same frequency band with Center to Center spacing larger than 1/4 wavelength), you've sacrificed some. The more overlap in the crossover, the more sacrifice in vertical off-axis response. A 6db/octave crossover will have the least phase distortion, but the most overlap.
As far as horizontal off-axis response (and this applies to vertical as well), it depends on the width of a driver operating at a given frequency.
Even a 4" driver has narrowing dispersion at 2khz. So a shallow slope on it will make its narrowing dispersion play up higher. But also, to get a shallow slope on a tweeter, you'll need 2X, and more likely 3x the crossover point. So not only are you making the 4" driver play higher due to a shallow slope, you're rolling it off much higher. You're probably asking a 4" driver to play up to ~5-6khz as its -3db point, and much higher on a whole. And to add to that yet again, the higher crossover point sacrifices center to center spacing, which is another blow to the vertical off-axis response.
And then add that the 4" driver is playing much lower because it too, needs a shallow slope. Chances are in a 3-way (and more likely 4-way or even 5-way), there's a lot of bandpass gain. So actually, with shallow slopes necessary for phase coherence, you have a lot of drivers contributing in the same frequency region. So at 2khz, it's not just a 4 inch mid, and a 1" tweeter that's 8-10db down, but there's also a lot of bleeding in of the midbass driver, which you can repeat all of the above with respect to off-axis response. Let's say it's an 8" midrange driver crossed over at 500hz. That's also only around 12db down at 2khz. It's contributing, however slightly, to more on-axis response than off-axis response on a whole. Now add one more factor in. An 8" midbass driver that's only 12db down at 2khz, needs to not be breaking up. So you probably have to use a softer cone material that's probably hurting overall detail at 2khz
And at the end of it all, that's
assuming your crossover was 500hz. That's really low -3db point for a 4" midrange driver, and that also means it's getting significant energy as low as 2-3 octaves below that. Think of how much 125hz energy it's getting. It might be 18db down on paper, but the power demands at these frequencies are equal to the power demands at 1khz in real source material.
And all of the above, is assuming these drivers are perfectly flat to even get these ideal slopes. How many 4" drivers are perfectly flat, without a vent, down to 65hz? Only ones with really low sensitivity....otherwise you won't be getting that "perfect phase" you wanted