{...} a center-cluster end-fire array, {...}
Just to be clear:
end-fire arrays aim to achieve perfect summation in the front, so there should be no on-axis loss of overall level vs. a simple clump, while
gradient arrays aim for perfect cancellation in the back and thus
will have a reduced level vs. a simple clump.
Two subs in cardioid is/was known as the "Ramirez array" - the second sub is basically used only for cancellation to the rear, so you end up with effectively one sub but directional.
IIRC the overall level drop of a two-box gradient array vs. a two-box clump should only be ~3 dB within the array's pass-band. The rear sub is typically attenuated by 3 dB (which results in a ~1.5 dB drop of total output on its own), plus the forward summation is imperfect (although within the pass-band it should still be pretty good, at least for sustained tones), but even a two-box gradient array should result in more output than using a single box on its own (just not as much as if those two boxes were used in some kind of perfect-summation array).
-Russ
