That’s interesting to go with a wide pattern and then combine it with the omni. I’m not quite sure how the distance in spacing fully interplays, but adding the omnis to the subcardioid would cancel out some of the width of the subcardioid. Maybe that’s what he is going for, the ability to control that some.
If you plug the numbers into the Sengpiel visualizer you'll see that the subcard spacing producing about the same image width as the omni spacing.
https://sengpielaudio.com/Visualization-AB60-E.htm
That's why those spacings were settled on; one can have either pair dominate the mix and the stereo image remains essentially the same. The smaller spacing of the directional pair compensates for the fact that they're directional. If one uses a pair that's more directional (card/supercard/hypercard/figure-8) then the spacing is accordingly reduced to keep the stereo width as close to that of the omni pair as possible. (If you experiment with different patterns in the Sengpiel visualizer, set the mic angle to 90 degrees. One could of course try different angles with accordingly different spacings, as long the resulting image width matches that of the omnis fairly closely)
The middle directional pair can be any pattern; Faulkner prefers subcardioid over cardioid not because of the pattern, but because he finds the sound of most SDC cardioids to be "too 'brittle'". I used it many times with hypercardioids with wonderful results.
Your last comment is backwards. Adding omni to subcardioid would widen the the overall pattern, not "cancel out some of the width...". The only 'cancelling out' that would occur when mixing omnis with other patterns would be with supercard, hypercard, and figure-8 because these all have anti-phase rear lobes that would be reduced in amplitude by mixing with an omni - but even in those cases their patterns would be widened, not narrowed.
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Anyone who records acoustic music in reverberent acoustics at 'Classical' distances owes it to themselves to try this dual-pair array. The mix of the two pairs has qualities unobtainable by any single pair alone. It's behavior is quite different from a Straus-Paket, where an omni is strapped to a cardiod and mixed at the same level in order to achieve a subcardioid pattern (that was done before subcardioid SDCs were available).
The Faulkner array is not about 'pattern alteration', but about combing the positive attributes of an omni pair with those of a directional pair. It's really rather magical to slowly mix in the directional pair to the omni; the sound gains three dimentionality and 'focus' without losing any of the richness and bloom of the omni pair. The array also has the property of 'forward gain'; it can pull in instruments from the back of an orchestra such that Faulkner has said he often ends up not using any wind spots in the mix.
None of this will occur unless the spacings are such that the image widths of the two pairs line up well; it's not just a matter of 'mixing some spaced omnis with any old near-coincident cardioid pair' - that's a whole different kettle of fish.