Does Time alignment and Phase coherency make for a better loudspeaker?

@mijostyn lets say we have two wide band speakers.
And we time align them in the 10-20kHz region.

One has a 12dB/octave HPF slope at 2.5 kHz.
The other has a 24 dB/octave slope also at 2.5 kHz.

The phase between those two will look different in the DC to ~5kHz region.

Then lets say we have time aligned a woofer and sub at 120 Hz.
The sub is in a bandpass box, and the woofer in a sealed.
as the frequency goes towards DC the two will deviate in phase from each other.

We could address both of the phase in the first case, and the group delay in the second case with a DSP to correct the phase, or at least in the tweeter case, some XO magic can be done to better align them in phase in the ~2.5 kHz region. (I cannot do it in solder, but many can).

Usually the time alignment is done, in a “minimum phase” sense… and it is done somewhere where the phase is not swinging wildly from say, group delay.

So they are tied at the elbow, but they’re distinctly different once we talk about more than a single frequency. At any given frequency they are effectively able to give the same correction.

mijostyn  Right you are!  My custom built listening room has highly damped side walls and ceiling with all 3/4" cherry plywood walls (besides the SR HFTs & internal wall bass traps of activated charcoal chambers, etc.) and is only 19' X 15' X 10'.   

My family room is also nearly all wood but drywall finished 30' X 18' X 19'.  It has very significant reverb.  Talking comprehension across the room is especially difficult although listening to music and speech from long wall TV with separate audio is quite clear (speakers close to the wooden floor).  I wouldn't want to trade rooms for music listening.  My wife and I have to speak very loudly to be heard across the room.  The live room with high ceilings seem to blanket sound at a distance.

@holmz , no argument from me. I would just like to state for the record that slow phase shifts are likely to be less noticeable than abrupt ones. It is really what happens at the cut off frequency that counts. I avoid your scenario almost entirely by using one way main speakers. All I have to worry about is the subwoofer crossover and one phase shift. IMHO the best crossover is no crossover. This is not an endorsement of dynamic "full range" drivers. The crossover is the lesser of two evils and those drivers are really not full range. Most of them have a 6 dB/oct mechanical crossover to a whizzer cone. The only real full range driver I am aware of is an ESL and even they have to have some wizardry performed with their transformers to make it work.   

@fleschler , sounds very nice. I like cherry very much. Echos are very disruptive.

To be precise the phase alignment in question is not in the recording, amplification, but in a multi element speaker where the speaker element placing and crossover design affect the time alignment of the output.

Mr. Dunlavy was an RF engineer, reportedly, and in the RF world everything is objective and measured. I heard his speakers in the early 90s in a hifi show in Miami FL. They sounded better than most offerings there. Too big and too expensive for me back then.

You can use squarewaves to measure the timealignment of speakers. Time alignment is one of many factors in sound quality, and a pretty obvious one.

Following this logic single element speakers would be better but they have their own issues.

If this is the case ,tilling back your speakers, hummmm...I remember going to a rock concert once ,this was like 40 years ago. I noticed the speakers in the front were filled up...So when I went home I filled back my Advents and yeah I liked the sound ,they sounded different.