Are first order crossovers best?

Unsound...Where did you (and a lot of other guys)get the idea that a first order (6 dB/oct) crossover has no phase shift? Actually the woofer and tweeter phase varies with frequency, but always differs by 90 degrees. The tweeter can be physically positioned so that at some particular frequency, usually the X/O frequency, the two drivers are in phase. As you get away from the X/O frequency the phase difference between drivers becomes unimportant because one or the other is attenuated. Inverting the polarity of one driver changes the phase discrepancy from plus90 to minus 90...take your choice.

Polarity inversion makes more sense for a second order crossover, where the phase discrepancy is 180 degrees. The selling point for fourth order, apart from the 24dB slopes, is that, with 360 degrees of phase shift the drivers are in phase. Fourth order is difficult and expensive to implement with a passive speaker level X/O, but quite easy for an electronic line level crossover.

Brianmgrarcom...Take a look at the schematics for first and fourth order X/O, and think again about which is more difficult and expensive to design and build. However, your comment about having fewer components in the signal path is very valid. IMHO this, rather than phase issues, is the chief advantage of the first order X/O.

I have a hunch that manufacturers who use first order crossovers, often for very good technical reasons, feel vulnerable to accusations that they are looking to save cost, and respond with marketing hype and the suggestion that their crossover design involves some mysterious art.

Crossovers are a necessary evil. Even the so-called "full range" drivers have crossovers...mechanical crossover that causes only a small section of the cone (sometimes a separate section called a "wizzer") to vibrate at HF. The only truly crossover-free driver is an electrostatic.

Bombaywalla...The link you provided looks interesting, and when I have time to spend I will study it. However, I must dispute your suggestion that the phase difference between drivers in higher order X/O does not remain constant at frequencies away from X/O. A second order X/O is basically a series connection of two first order X/O, and what works the first time does also the second time. A Crown professional electronic X/O that I keep around for experiments is 18 dB/oct, and has a comprehensive manual that shows graphs for both amplitude and phase response for various frequency settings. 270 degree phase difference exists at all frequencies (as I would expect).

My main speakers are Magnepanar MG1.6, and the high pass filter is first order. The low pass is second order, and the break frequencies are significantly different. Of course the Maggie "driver" is quite different from the common cone driver, but it all goes to show that a X/O network can be taylored to the characteristics of the drivers used.

I also use an electronic X/O for subwoofer/main, and it is fourth order. In prior systems, where the main speakers were biamped I have had excellent results with fourth order.

Unsound...We don't separate them. The full range advocates don't like to admit that their drivers break up, and emit different frequencies from different parts of the cone, and this constitutes a mechanical filter. If you think that design of an electrical filter is difficult imagine the work it takes to get a mechanical filter right!

Unsound...I had forgotten the Walsh driver...but, I think that even that had a mechanical X/O of sorts. The top part of the cone for a couple of inches (near the voice coil) was made of metal, while the rest of the cone was some other material.

Blindjim...I think you got your answer in the first couple of responses, but they raised interesting points that have been the basis of ongoing discussion. That's the nature of this forum.
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