I can easily roll my own op-amp active xover... is there a particular topology you recommend?

Higher orders also increase the phase shift as you approach the stop band. The rolloff is faster, and accompanying this is a faster phase change. Of course, frequency-dependant attenuation is greater too, so the signal content with the most phase shift is what is most attenuated. The problem the designer has is knowing what frequency and slope to choose given a particular baffle spacing between drivers, or vice versa.

Crossover design is a balancing act, one that requires a mutual effort in loudspeaker layout, so the two are designed together, as a system. Failure to access the interactions properly can (will) cause a cancellation notch in the crossover band. Since there is actually no way to prevent this at all frequencies and all positions, the careful designer chooses where to place the cancellation notch. Certainly, one seeks to prevent it from happening on the forward axis, and the best designs place it far out off-axis, ideally outside the radiation angle of the speaker. This approach requires horn drivers with controlled directivity, of course.

You can't really say one crossover slope is better than another, without knowing all the specifics of a design. The whole goal is to split the signal into frequency bands each driver can safely cover, and to give them all signals that will combine coherently in the acoustic realm. This involves a lot of factors besides electrical phase, including acoustic phase, driver position and desired directivity and coverage angle.

While I understand phase causing a notch at the crossover point, I have another observation.... while in college, as a music major, I spent a lot of time in a sound lab playing with an Arp synthesizer, o-scope, etc... learning what was what in terms of what we hear. (The Arp was an early, crude synth, could make only one note at a time, but you could put together a tone from sine, square, sawtooth waves, add filtering, etc)

As far as phase of overtones in relation to fundamental, which is what we are doing when the signal passes through the crossover from woofer to mid or tweeter, this can all be demonstrated on a synthesizer. You can compare two sawtooth waves, for example, one with the peak on the left (HF leading) and another with the peak on the right (HF lagging)... the sound of both is identical. Now, you can hear it while you are playing with phase, and moving from one to the other, but once the the phase of the higher partials is stable, and the slope completely reversed, the tone quality is the same either way.

Just an observation from actual experience, you guys. Oh, I found some other interesting things, in how we identify and differentiate musical instruments by ear, but that is another chapter...

Paul

To illustrate the issues a little better, here's a chart that shows electrical phase of various crossover slopes:

1st order - 45 degrees at crossover, 90 apart for adjacent drivers
2nd order - 90 degrees at crossover, 180 degrees apart
3rd order - 135 degrees at crossover, 270 degrees apart
4th order - 180 degrees at crossover, 360 degrees apart
5th order - 225 degrees at crossover, 450 degrees apart
6th order - 270 degrees at crossover, 540 degrees apart
7th order - 315 degrees at crossover, 630 degrees apart
8th order - 360 degrees at crossover, 720 degrees apart

This gives you an idea of the amount of phase movement each crossover slope introduces. Combine this with the path length disfferences between each driver and the listener, and you can see how complex summing is in the acoustic realm. At locations where the path length difference plus the phase difference from the crossover combines to make the sound sources any multiple of 180 degrees apart, there is destructive interference which causes a notch. The goal of the designer is to place any notches off-axis, away from the intended listening position. If the speaker is designed for uniform coverage through some angle, then notches must be off-axis far enough to be outside the edge of the coverage angle.

By the way, I agree with you completely on the matter of absolute phase verse moving phase. I made the exact same observation you did with synthesizers, as I'm sure everyone has that has ever been exposed to VCO or any signal generator that can produce a sawtooth wave. I played piano as a boy and got a MOOG synthesizer when I was a teenager. I was initially surprised that a sawtooth sounds the same regardless of its polarity. This made me realize that our ears aren't particularly sensitive to phase by itself - we hear phase change only because of the amplitude response anomalies it creates. I've heard that snakes and reptiles can't see a non-moving object very well, and in a way, we're like that with phase. We cannot hear phase relationships very well unless they're moving.

You would have made a great elec eng prof!

Paul