Here is what I heard in Utah:
1. Siemens Bionor, Lamm ML3, AS2000, big room
2. Vitavox CN 191, Lamm ML2, Micro SX 8000 II, small room
3. JBL M9500, Lamm ML2, Micro SX 8000 II, small room
4. Mitsubishi Diatone, Lamm ML2, AS2000, big room
Four pretty different speakers, one not even horns, all driven by Lamm SET amps and massive belt drive turntables. These four systems sounded different from each other, but they shared a common sound. David calls it "Natural Sound". I heard the same characteristics from all four systems to slightly different degrees, wrote them down in my notebook, listed them, and posted them in two threads. These characteristics describe a sound radically different from the sound I am familiar with in the systems of my local Boston audio friends, and of the systems I have heard at dealers and at shows.
My memory of my former system is that it too sounded radically different from these four systems until I started my long series of experiments to make that system sound more natural. Those experiments mostly involved set up, but also cable and power cord choices and how I supported the gear. I actually thought, as did some musician visitors, that my former Magico Q3s sounded quite natural driven by the Lamm M1.1 hybrid amps. The sound does not seem exclusive to high efficiency speakers and tubes, but I think it helps.
It is clear to me that there are different ways to achieve this type of sound, so I would not subscribe to the idea that it depends on specific gear, though some gear would preclude the system from ever sounding natural. Natural Sound is a specific type of sound that results in the characteristics I heard from those four systems in Utah and wrote on my list. Interestingly, I also heard it from a small digital office system in David's workroom, and from a CD player in his small room.
I suspect that this sound is not unique to vintage speakers. It is a whole-system approach which can include non vintage speakers. I think David would suggest that it has a lot to do with the electronics and that it is easy to kill the whole thing with the wrong power cord or room treatment.