Originally Posted by pnw
...CTC from mids to woofer won't be a problem with the relatively low crossover frequency...
That's a good approach for speakers designed to be used outdoors or in a large space, where point source summing is desired. It is also important if the woofer to midrange crossover is above the Schroeder frequency, around 200Hz. That is typical for three-ways that aren't designed with any particular directivity in mind.
But in the uniform-directivity world that Pi Speakers and other similar "waveguide" speakers seek to address, we see a different trend. Our approach is to match the directivities of midwoofer and tweeter, to crossover where the midwoofer beamwidth has collapsed to approximate the horizontal directivity of the waveguide we are using. This approach necessarily favors relatively large diameter midwoofers. The efficiencies are a better match too, but that's a different subject.
This is somewhat counter-intuitive, but as important as close spacing between midwoofer and tweeter is, the distance from midwoofer to subwoofer should be somewhat greater. We aren't looking for point source summing indoors, we are actually looking for spacing on the wavelength scale. The reason is that directivity becomes ambiguous in the modal region, so point-source summing is non-sequitur. There is no way to provide point source summing, because the modes are scattered in space and time. So the next best thing is dense interference, smoothing the sound field by averaging.
The multisub configuration is becoming pretty well understood, but I find sometimes people aren't really thinking about the transition region, which is what helper woofers or "flanking subs
" address. It requires blending of two sound sources in the 80-160Hz region where sound is becoming localizable, so the midwoofer and helper woofer can't be too far apart, but they do need to be far enough apart to smooth the ripple from boundary interference. It's much like the multisub approach, but frequencies are higher so distances are smaller. You put the helper woofer between the nearest boundaries and the main speaker it's flanking, usually just a couple feet away. The main is on a stand a couple feet from the wall, and the flanking sub is on the ground beside the main speaker, pushed back against the wall.
three Pi speakers with flanking subs