I was accused to write off topic. But please compare. First your take on your problem. Second my take on your problem. Same, isn't it?
What you discuss is the broadening of the pulse as seen below (courtesy of kimmost). It should come to you easily, that it resembles the signal (a) in my example, namely that the timing of the high frequency part of the "step" signal is preserved, while the low frequency part is shifted in time to later. That is the wiggling tail, the delayed low frequency part. (I hope it isn't necessary to present the original 'pulse' or 'step' here also.) I don't know what you are talking about, if you say, that my take is just nonsense. Nonsense lies in the mind of the beholder, right?
See post #34
See post #297
Something more relevant:
The talk about IMD is an elementary mistake on fineMen's part.
The phase relationship between tones in a general signal is arbitrary.
That is a very good counter argument, thank You, appreciated! But to some degree its "off topic". (I couldn't resist ... ;-) Isn't it so, that the argument, or better to say the requirement for "time correct" speakers is, that the phase relation must not be arbitrary?
I try to exemplify your argument a bit further. The high frequency part occurs independently, going along with the low frequency content without any further correlation that would mean something, right?
It would be perfectly so, if the signal was noise, or an otherwise arbitrary mix of a few frequencies. I argue that this not quite right with music.
- the harmonics of a note are strongly phase-correlated to the base frequency, would you argue that?
- the attack of a note, and I think this is the 'impulse' people are interested in, necessarily contains a broader spectrum than just the harmonics; this part is distinguished by a relatively high amplitude, a rapid decay, especially for the high frequency part making for a strong timely correlation and not the last by its rarity in time - nothing to occur randomly all the time
We could leave it at that, may the reader decide. I think that the proponents of the "time correct" speaker don't want to dig that deep anyway. It is more so, that we want to play around with terms.
Add.: I'm tempted to emphasize that my hint is a "could be" argument, because people never qualify the difference that "time correct" would make in a clear way. So it might be worthwhile to look out for other explanations than the "arrival time at the ear". It may lead to alternative measurements, and Linkwitz already started with burst tests. I also gave a hint to pre- and post-masking effects in the human hearing apparatus.