The "quasi-optimal" french school (post #5) tries to find a compromise between often conflicting requirements. The concept has been discussed here :

http://www.diyaudio.com/forums/mult...sover-high-efficiency-loudspeaker-system.html
Good phase response crossovers are well documented in Jmbee's blog (Jmbee is a DiyAudio member) :

filtre "quasi-optimal" : modèles et variantes - Le blog de jimbee (1)

It appears that, using analog schemes (or their equivalent in digital processors) trying to obtain transient perfection is almost always detrimental to other aspects of crossovers acoustic response.

A good idea of the acoustic response of a crossover can be summarised by knowing the axial response, the propagation delay response of the sum of the two ways and their phase difference.

This phase difference can appreciated by establishing the curve of the sum of the modules of the response of each ways (J-M Le Cleac'h called it the "coincidence response").

Using the post-proecessor of the Tina Spice simulator, this is the formula :

coincid(s) = abs(hi(s)) + abs(lo(s))

I've simulated and listened a lot, if not all, of the schemes of standard (NTM inlcuded) and quasi-optimal crossovers, some of them not documented by Jmbee.

It seems that I consistently prefered the response of third order filters, disliking lower or higher slopes (however Linkwitz-Riley 4th order slopes are a good help to determine an adequate crossover frequency).

It soon appeared to my eyes on the simulator window as well as to my ears in the listening room that the most appealing scheme comes from Herve00.fr (a member of DiyAudio too) :

for a crossover frequency at 1 kHz (-6.1 dB) :

hi-pass: order 1 at 384 Hz, order 2 at 1.170 kHz Q=0.633, delay 180 µs, inverted.

lo-pass: order 1 at 2.604 kHz, order 2 at 855 Hz, Q=0.633.

The corresponding diagrams are attached.

In my system, the resonances of the medium and the tweeter are submitted to transforms, so the real response of the combination of the filters and the drivers are those intended by the theory.

(1) see also Jmbee's chapters :

substrative + delay :

DCX2496 soustractif / delay - Le blog de jimbee
series and Baekgaard topology :

DCX2496 soustractif / delay - Le blog de jimbee