First Order Crossovers: Pros and Cons

"At the crossover point, for example, one driver is at .707, +45, and the other is at .707, -45, as I stated previously. Due to the fact that this is vector addition, they sum to unity at zero phase. And they do this not only at the crossover frequency, but at every single point from DC to infinity. The first-order is the only crossover that does this."

Karls, thanks for that explanation ... now I completely understand why the first order crossover can work in amplitude and phase terms through the region where both drivers are contributing to the sound. The power output of both driver is 3dB down at this point (amplitude is reduced by 1/(square root of 2), and they are 90 degrees out of phase, but the vector addition of these two waves results in a sine wave that is in phase and 0dB down in amplitude.

Let me explain my porting question on GMA's C-3's relative to time and phase coherence. I have no idea if there is an audible issue with the C-3's design and based on Roy's published specifications there is nothing to suggest what I'm about ask actually takes place, nevertheless I thought I'd throw it out there to elicit a response regarding the porting theory behind this design.

In GMA's C-3 the bass port is firing in an upward direction, directly below and slightly behind both the midrange and tweeter, with a clearance of perhaps 4-5 inches. I'm wondering if conceptually there could be some type of Doppler effect taking place with the placement of the port relative to the midrange and tweeter that could slightly alter the phasing or timing of these drivers? Although there is no high-frequency whizzer cone riding on top the woofer; as in the Tannoy, in theory as the woofer moves backward and air is pushed out of the port, is it possible that this change in air pressure could somehow modulate the midrange and tweeter response by disturbing their wave lengths? Alternatively, when the woofer pushes forward, does the port suck in enough air to also disturb the wave length of the midrange driver and tweeter, thereby throwing off time and phase coherency?

Just to add to the info on vector diagrams, there's a very good explanation of what's going on at the Rane site, particularly in http://www.rane.com/note119.html

The most telling part of that is "The 1st-order case is ideal when summed. It yields a piece of wire. Since the responses are the exact mirror images of each other, they cancel when summed, thus behaving as if neither was there in the first place. Unfortunately, all optimized higher order versions yield flat voltage/power response, group delay or phase shift, but not all at once. Hence, the existence of different alignments and resultant compromises."

Skrivis, great link. As always, a graph is worth a thousand words.

An even more telling part of the article regarding the group delay of a 8th order L-R crossover.
"Is It Audible?

The conservative answer says it is not audible to the overwhelming majority of audio professionals. Under laboratory conditions, some people hear a difference on non-musical tones (clicks and square waves).

The practical answer says it is not audible to anyone for real sound systems reproducing real audio signals."