Sloped baffle

Reversing the polarity of a mid in a 3-way or a tweeter in a 2-way is just a result of correcting for the phase shift of the crossover. The exception being 4th order. It's about getting the drivers to sum correctly. If they were 180 degrees out of phase, they cancel around the crossover point. In fact, one of the best ways to confirm the drivers are in phase is measuring the reverse null.

Now, if you want to talk about absolute phase and the half a millisecond @ 2000 Hz between cycles and whether that's audible, that's a different story. I don't know the audibility threshold up there but down around 100 Hz, it's around 30 milliseconds and several cycles for our ears to respond. Less for the trailing edge.

http://www.audioholics.com/room-acoustics/human-hearing-phase-distortion-audibility-part-2

That's bound to be misunderstood. Related articles in links.

The 30 milliseconds I mentioned previously came from a U-tubed Earl Geddes seminar on multiple subwoofers in a small room.

Remember, all these are opinions of folks based on their perceptions, with most of them marketing something (though Geddes does not sell subs). You were not there for the experiments. It is all self-reporting. So time aligned, phase aligned, time and phase coherent, one sub, two subs, many subs....take it all for what it is: "Self-reported" opinions based on experiments where the experimenter was the only one observing.

You have to try the products yourself, or hear them in a good setup, to form your own conclusions. And still you won't know if it is the "main feature" the manufacturer is touting that is dominating the sound, or other details of the product.

Remember, we listen to music, not features.

Sometimes I feel that in audio, buyers and enthusiasts would rather talk features than simply sit and listen to see if it sounds like music.

I think that Kiddman makes good points here. There are so many interactions and variables in the design of loudspeakers that it's got to be very hard to isolate which factor results in a speaker that you ultimately love.

To wit: you couldn't have two more different small speakers than, say, GMA Chromas and Harbeth P3ESR's. "Leaky" plywood cabinet vs. synthetic stone cabinet. Metal dome tweet vs. cloth tweet. "Complex" crossover vs. "simple" 1st-order crossover. Inverted driver polarity (!) vs. not. "Radial" cone material vs. paper-composite. Flat face baffle vs. slanted baffle. And the list goes on and on.

Now, then, various audiophiles swear by one or the other of these speakers. But who can really say whether it's the cabinet material, driver material, crossover topology, phase/time coherence or (most likely) some combination of all of the above that gives the results that you get? And THEN, factor in the room and the associated equipment and the tastes and hearing of the listener and you have more variables than anyone can deal with.

So, yeah: I can see that you might become fixated on the theoretical merits of time coherence and then fall in love with a non-time-coherent speaker, anyway.

Reminds me of the joke about the unmarried scientist who feeds his theoretical preferences in women to a computer and then cross-references it to a database of women in his city. One day he approaches his lab assistant and says, "Well, it seems I have actually found the woman of my dreams. She meets every one of my requirements."
"Then why the glum face?" asks the assistant.
"I just don't like her," he sighs.

Ng... thanks for the phase coherence article. The article seems to be based on scientific controlled studies and tests. Rather than paraphrase the conclusions, I copied them here:

"So what conclusions regarding the audibility of phase distortion can we draw from the all of the above?

'Given the data provided by the above cited references we can conclude that phase distortion is indeed audible, though generally speaking, only very subtly so and only under certain specific test conditions and perception circumstances.

'The degree of subtly depends upon the nature of the test signal, the dB SPL level at which the signal is perceived, the acoustic environment in which the signal was recorded and/or played back as well as the Q & fo of any filter networks in the signal stream. Certain combinations of conditions can render it utterly inaudible.

'Room acoustics further masks whatever cues that the hearing process may depend upon to detect the presence of phase distortion."

And here's my personal bottom line. Phase coherence is just one of many variables that is taken into account when designing a speaker system ... and there are many. As many folks have said, trust your ears and audition as many speakers as you can. But ... if I was asked to buy speakers based on their phase coherence characteristics as a stand-alone factor, I personally would not.

Thanks again Ng.... Good article. It puts the issue into context.

Bruce