Actually Williams cover omnis, cards, hypercards, hypocards and maybe the other card type.
Right.. and what I'm getting at is this- Take a look at each of his charts. Even though the slope of the curve changes according to the polar pattern, the bottom of each individual curve intersects the base at the same point for any given SRA angle. That is to say, if you point the mics perfectly straight ahead (a 0 degree angle between them), it doesn't matter what polar pattern microphone or what Stereo Zoom chart you use, the charts give the same answer in every case.
The point is that The Stereo Zoom is very useful, especially for directional mics, but it concerns only the
placement of sounds in the playback image. It says nothing about alot of other important aspects that effect the sound of the recording.
For example, using the example above, changing the polar pattern of the microphone and leaving everything else the same (same spacing, 0 degree angle between the mics)
will change the sound of the recording. The sound changes because by changing polar patterns you will be varying the direct/reverberant ratio.. and because different polar patterns have different on-axis responses.. and because the frequency response of each pattern isn't constant off axis. Yet none of those changes are what I was referring to in my post about how adjusting the spacing affects the sound.
And not to be argumentative but I find the angles and distances he gives work fine for bass for me. I use his spacings on omnis and cards and get plenty of bass, and actual honest representation of what is in the hall. I am doing mostly acoustic so it is pretty easy to evaluate that as opposed to rock which can sound like whatever the guy at the soundboard and the band want. Not all soundmen are created equal.
I don't mean to imply that incorrect spacing would cancel out the bass or make it sound wrong or something. It's more a matter of noticing that a subtle change in spacing can sound dramatically different (not that either sound is necessarily wrong) and picking whichever sounds better. I do think that amplified outdoor sound from two widely separated stacks on either side of the stage is a special case and that the effects of mic spacing on both the feel of the bass and also the rest of the spectrum is likely more exaggerated in that case than for acoustic sources. I suspect that effect might be even more exaggerated for a mono board mix played through those widely separated FOH stacks.
For non-house amplified acoustic stuff I'd be more likely to use a smaller spacing.. and be alot closer! The special case of an amplified outdoor festival presents a source that is big and wide like an orchestra. An old general approach for spaced omnis some took was space them 1/2 as wide as the source width. Also consider how far back you'll be. At the FOB spots I record from at festivals, the stacks may be 50 deg apart as viewed from my mics. That would indicate a spacing of 50cm by the Stereo Zoom. But the performers on stage take up an angle of only 20 degrees and that puts me right back to right around my typical 39" if you extend Williams' charts.
I've actually had luck using the NOS spacing and angle with omnis. I've only tried it indoors and ~3'-5' from the stage. YMMV.
Generally the closer you get to the source the narrower you'd space the mics (and the wider the recording angle gets). The Healy method is 7" spacing with 180 degrees between mics and was designed as an onstage technique. So your experience a few feet form the stage is along that continuum.
I am currently doing a lot of MS flanked by a Williams omni array and like the results. I do zero outside rock concert recording but will be doing some in August as we are having a "festival" out here. I'll see what I come up with then.
Are you mixing the mic sources together? If so are you using the omnis just for low end reinforcement or mixing them in full frequency?