Switching polarity of tweeter in two-way design

The tweeter is wired 'backwards' not to time-align anything but to 'offset' the response spike that occurs in most 2-ways if the tweeter is not reverse-wired. I don't pretend to understand it, but the result is to NONtime-align the system.
.

Not really. That will only work if the crossover frequency's wavelength is exactly twice the distance between the tweeter and midwoofer. And it would only work at that one frequency.

Agree with Jbehr. I always figured the reason for putting the tweeter out of phase was to cancel its response overlap with the woofer. Time aligned designs usually have some slant or tilt thing happening to place the tweeter farther away than the woofer.

I have seen frequency response plots of two way speaker systems with the tweeter hooked up each way. One shows a dramatic downward spike at crossover. Almost complete cancellation. In fact, this is the best way to determine the exact crossover frequency.

However, this effect is probably seen because the microphone is located at a small fixed spot in space, so that the distance to the two drivers is fixed. For real-world listening, polarity of the tweeter does not seem to make a lot of difference. Best idea is to try it both ways.

As for tilting the baffle to align time and phase of the tweeter to the woofer, does the degree of tilting depends on the x-over only or only on the acoustic characteristic of tweeter itself?

"For real-world listening, polarity of the tweeter does not seem to make a lot of difference. Best idea is to try it both ways."

I don't disagree with that, but understand the effect of reversing the tweeter leads from their original backwards orientation. Reversing the tweeter will create a small up-peak in response in the midrange/tweeter crossover region, this ocurring usually around 2.5KHz. I suppose you'd hear that occasionally as added presence or brightness (or maybe 'detail').

What I don't understand is why the designers don't simply pull the crossover frequencies apart to eliminate the spike. But I guess that simply shows how much I don't know.
.

Second order (acoustic) high and low-pass responses are 180 degrees out-of phase.

You get deep notch if you don't invert one (in a perfect world you'd have no output).

Linkwitz Riley filters have Q=.5 with both outputs -6dB at their pole. Inverting one therefore causes the response to sum flat.

2nd order butterworth filters at the same frequency (Q=.707) so you get a 3dB peak when you invert one and combine. Spreading the cross-over frequencies is needed to avoid this.

Sloped baffles accomplish two things:
1. Time alignment of the drivers so the real phase relationship matches theoretical.

2. Having the highest output on-axis rather than off when you don't use a Linkwitz-Riley cross-over.