I participated in a blind test between my Neumann KH310 speakers and a prototype speaker from a local hi-end monitor company.
The KH310, while a highly proficient device, hasn't been designed in a way to do anything with time coherence.
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The difference between the two systems, despite having essentially flat AFR, was not subtle. The phase coherent speaker was able to produce louder transients, despite both systems being SPL matched. The other stark difference was in soundstage - both systems could portray almost identical apparent width, however the phase coherent system portrayed depth much better and localisation was more distinct, probably due to point source radiation.
Needless to say, I sold my KH310's shortly after.
Yet we are told by many of the smartest technical people in the industry that there isn't any evidence that time/phase coherency is audible except with respect to achieving a flat response through the crossover regions (in which case it is really the phase coherency that matters and time coherency is merely a means to that end).
For me it is difficult to let go of my early experiences. In the early '70s, when I was 19 or 20, in a big old record store that also sold some loudspeakers, I heard a speaker that I'd never heard of. It was
immediately apparent to me that there was something different about the speaker I was listening to. This was before college, when I was very technically naive. The music that was playing had some
percussion instruments, and to me it was apparent that this speaker was reproducing those sounds in a way that was more realistic than I was used to hearing through amplified loudspeakers. The difference was so stark that my memory of the experience including my reaction remains vivid. Five or six years later I related this experience to a professor that I'd become acquainted with, who had taught electronics and who was a hobbyist, having built several speakers and tube amps. To describe to him what I had heard with this speaker that seemed special, I said that it was able to reproduce the sounds similar to a finger-snap, in a way that most other speakers couldn't. He then introduced me to the concepts of "transient response" and "time domain". Given the chronology of this experience, it is difficult for me to believe that I was just imagining having heard this sound quality, which I identified and understood in an unsophisticated but meaningful way, years before I was the least bit aware of the formalized concepts of transient response and the time domain, or was aware that Kloss had designed these speakers specifically with the intent to achieve these very qualities that I had heard.
We are continually told by some very smart people that steep crossover slops are superior for the various good reasons they give, and they tell us that there are no unwanted consequences of the steep slopes, or of anything else that is harmful to the transient response (i.e., the Helmholtz resonator).
On a few past attempts to discuss this with different people, I have referred to the sound of high quality headphones. I would say something like, "A major reason that these headphones sound so much better than loudspeakers is that there is a single driver with no crossover. The response is also very flat throughout the audible range, such that there is very little phase wandering and thus superior transient response." The typical response I've gotten is something like, "Headphones? I don't listen to headphones." People with a modicum of knowledge will of course mention the avoidance of room effects. But rarely does anyone draw attention to the potential for exceptionally good transient response in a good set of headphones, or to the potential that this is the reason that good headphones sound good (for people who hear a quality in headphones that they don't hear in speakers and who like headphones for this reason). My point is not to suggest headphones as an alternative. My point is that, if in fact this is a property that good headphones have and that isn't shared with most speakers, and if it is detectable to most people (notwithstanding that people don't typically understand why headphones sound different in a way they like), then audibility of good vs. bad transient response is real, contrary to the prevailing expert opinion.
Yet, if it is audible, why are the many learned experts so convinced that it isn't? Is it possible that bias interferes with their ability to conduct a proper test for audibility of differences in transient response fidelity? To conduct a proper test of this hypothesis, it would be necessary to build two speakers that are identical in every respect except that in one, phase undergoes rotation from low to high speaker in a manner like the graph above for the KH310, while in the other, there is very little phase rotation, ideally none at all. This would be a very difficult thing to do, and as such, there may never have been a proper test of this question. Perhaps with a single-driver speaker, listened to close up, digitally equalized to achieve a near-flat response, one without any phase rotation intentionally introduced, the other with phase rotation introduced to mimic speakers like the KH310. Is it possible to do something like this with DSP?