I think you are nitpicking here in order to try to argue that somehow this is not novel and was done before.
I have made no claims regarding the novelty of what Perlisten has done. Just because both designs constitute beamforming doesn't mean they are equivalent. Beamforming can be realized in a very wide variety of ways, and new approaches are developed pretty regularly. From what I've seen, Perlisten has managed a directivity that I believe I would perceive to be superior to what snell accomplished, as the snell beamwidth is too wide to drastically reduce the first reflections from the floor and ceiling.
Again, the way the expanding array works is not the same. I am not sure what part of that you are not seeing.
In fact I understand perfectly well that their implementations vary.
In the expanding array, there is a traditional crossover between the midrange and tweeter. Overlap is typical of the order used. They are symmetric. It is a true crossover. In the Perlisten, the tweeter in the center along with the midrange drivers all have a highpass filter at 1khz so they overlap substantially. There is a point where the midrange is phased out so that eventually the tweeter is the only driver operating. But there is large overlap between those points. Something like 4-5 octaves.
Thanks for the information. I suspect you have mischaracterized the amount of overlap, though. If the mids and tweeter are high pass filtered at 1 kHz, and share 4 octaves of overlap, the mids would be low pass filtered at 16 kHz.
I have never heard beam forming defined like you are.
Well, I'm happy to educate.
All speakers have a forward radiation lobe that is directional.
First of all, this isn't true. Second, it has little if anything to do with what I wrote. For counter examples, consider omni-directional speakers, and speakers that radiate more energy away from the listener than toward them, like the bose 901. Getting back to what I actually said, many speakers have inconsistent angles of maximum response across frequency. For example, odd order crossovers will often result in lobes above or below the design axis that are stronger than the response on the design axis (when paired with asymmetric driver layouts).
MTM and WMTMW designs have created symmetric lobes and also have existed for a long time. But I never considered those beam forming designs. If you want to, that is fine. I think we are just mincing words.
MTM designs don't create "a consistent Maximum Response Axis across the band of interest, with attenuated response at angles away from the MRA. They fail to significantly attenuate off-axis response at frequencies above and below the crossover frequency. In order to make a logical argument that MTM designs constitute beamforming, you'd have to argue that the "band of interest" consisted only of frequencies near the crossover frequency. If operated with such a limited bandwidth, they wouldn't be very good for music reproduction. Also, even at the crossover frequency, many MTM designs suffer from grating lobes, which are generally frowned upon in beamforming, but are sometimes acceptable.
For WMTMW designs, the same assessment applies. Some may have sufficient, wide-band directionality and freedom from extraneous lobes (grating lobes) to constitute beamforming, while others don't. Those that do were almost certainly designed with a strong focus on their dispersion characteristics.
the Snell and Perlisten approach are not similar or related. That remains true. Call them what you want.
I understand that you feel the differences between the Snell and Perlisten approaches are significant, and perhaps under appreciated. However, I think you go too far to say they "are not similar or related". They are both implemented using dynamic drivers consisting of woofers, midranges, and tweeters, arranged in symmetric vertical lines, with passive filters, right? I'd say that constitutes a large amount of similarity. Regarding what we call them, we should use words in ways that are consistent with their definitions, and we should try to be precise with our use of language when having technical discussions.