Btw, Ken, I am pretty sure you are totally backwards about where midrange dispersion is most noticeable. I'd welcome some correction but I find it harder to tell when I am close up to a cabinet (within 10 feet or so) where exactly polar response falls off. I have always assumed this to be something of the "near field effect" where sound is really different when close to the point source, but I'd be interested to learn more about it. Most discussions of radiation patterns and sound decay I have read have focused on "far field" rather than "near field" whatever that means precisely.
How loud something is, specifically - you'll notice that if you put your head right next to a cabinet and then go 3 feet away, it doesn't sound 6db quieter to you - seems to relate to this.
My experience using cabinets with narrow dispersion patterns (4x10s, single 1x15s or 1x12s with no midrange drivers) has been that it's most noticeable out in the audience, where "hot spots" develop.
I think the reason a lot of people don't notice this is because of midrange reflections around a room. Room modes I think is the term for it, but the sound bounces around off of the ceiling, floor and other obstacles.
Maybe Bill could explain this properly or point us to a discussion if he's got time.