Going back to the start of the thread.
The argument that a frequency response or power response is enough to characterize a sound system is profoundly representative of the state to which some people get, that, while not having been trained in or correctly exposed to the fundamentals of science and epistemology, believe that a sliver of tech information is enough to place them ahead and have a discussion in an ambiguous field with confidence. Confusing information with knowledge is a capital sin in my neighborhood. Fortunately I don't see many people that adept in this way of thinking here. Alas the same can be said the other way around. Just because you have an experience that doesn't map well to any measure or model that you know of, doesn't mean it doesn't exist, that it is unknowable or a branch of black magic. Everything we do here in audio is absurdly simple comparing to even the most trivial tech driven activities today (almost everything involving a microprocessor, making a phone call, checking you mail, driving your car, getting on a plane or making a movie), even taking into account the interaction with our individual auditory and cognitive systems. It is not a trivial problem, but not in the proximity of the list of hard problems we solve everyday as a collective. There are reasons we don't take it seriously tough, that justify the absence of such hard results for audio reproduction, namely the lack of interest and consequently funding. What we know seems to be enough to produce value.
'FR is enough to characterize an audio system'. I always find it useful to apply a bit of reductio ad absurdum to clearly delineate the boundaries of the arguments being put forth, and in this case, it is easy.
- if I play you the same track but backwards, you'll get the same cumulative frequency response. It is an integral, has no topological meaning. I can chop a track in 5 second intervals and introduce 1 sec silence in between. Same FR at the end.
- I do audiograms from time to time. It is pretty clear to me that my hearing is a) not linear and b) not the same sensitivity across the spectrum as anyone else. Yet, apart from crossing clinical thresholds, we all hear what we need to hear, just fine. So either a) our hearing system is able to compensate (within reason) to these variations or b) it is not very relevant (again, within reason)
- a simple FR measurement (that usually is what gets passed to a consumer) doesn't distinguish signal from any type of distortion, it condensates everything into linear distortion. This is not even close to being representative of how our hearing works. I can give you a loudspeaker with insane levels of high order distortion for example, DSP the hell out of it to get a flat FR and all you have in the upper sections of your measurement are carefully crafted and placed distortion products, not even a bit of signal left. But you have your flat FR.
So, it should be clear that FR is a hilariously limited dimension to audio reproduction. It completely disregards time (something we are orders of magnitude more sensitive to) and has limited correlation power to our perception of quality. It is not a good quality metric at all. The extensions to it (a spinorama for example) has a much higher degree of correlation and actually carries useful information, but it is subject to the same critique and it is not reduceable to a number, not even a line. I really don't think these are useful metrics for consumers.
On the one hand I find the ASR crowd interesting and interested, on the other hand the discussions quickly descend into the typical neophyte behavior, completely voiding the value of it. The largest value I get from there is finding out if a given product is electrically hygienic and a look at the build quality and techniques. Most of what tries to relate to performance quality is too far removed from what a hypothetically perfect metric would let us know to be more than noise with an ego, especially when it comes to loudspeakers.
That said, I use FR measurements and low density spinoramas all the time as a tool to design loudspeakers. But it is one tool among many the tool box, and it is not more important than several others.