so that sine waves are back in "phase" if you will pardon the term.
I know what you mean, in and out of phase just seems to sound right, and any use of the term polarity with a modifier seems to sound clunky and incorrect.
Both Hi and Lo signals are shifted 45 degrees at X/O, so the woofer/tweeter discrepancy is 90 degrees (for first order).
I think we are talking about 2 different things here. My point was that all musical instruments produce harmonics in addition to the fundamental tone. So if the fundamental falls inside the passband it will not be phase shifted and if a harmonic falls outside the passband it will be, or vice versa. I think this phase shift in the harmonic structure will be audible. I haven't conducted any experiments to confirm this hypothesis.