@mahgister
Then there is a high cost to pay if we TRUST the Fourier linear tools and if we work ONLY in the time independant and frequency domain... The price is we loose contact with the basic of human hearings...
I don't know why you keep bringing up Fourier transform. Most of my tests don't involve any kind of fourier analysis. Take the dashboard I post earlier for that Carver amplifier:

See those THD+N and SINAD numbers? They are computed *without FFT*. The analyzer simply filters out the 1 kHz tone and what is left is noise+distortion. It then simply reports that sum energy of unwanted signal as a ratio to the test signal. No FFT is needed or used.
The problem with that one number, as bad as it is in this case, is that it is not diagnostic. So the analyzer in addition to that shows the fourier transform on top right. Now we see the problems. We have tons and tons of power supply noise and hum which better not be good in any audiophile's mind.
We then look to the right and see copious amount of third harmonic distortion -- not the beloved 2nd harmonic people think tubes output. Using psychacoustics, we can overlay a graph on both the noise and distortion and assess audibility, again based on listening test research.
Fourier transforms then are an invaluable diagnostic tool to assess audibility because much of our knowledge of psychacoustics is in frequency domain, not time. In time domain, we are relative quite deaf. This is by design. When you listen to someone in your home, their voice gets bounced around the room, gets delayed (timing changes) plus attenuated and then mixes with the direct sound creating a "phase soup." So the notion that time matters is non-sequitur in most part.
But again, a lot of our measurements are independent of any kind of Fourier transform. This measurement that I post again has nothing to do with that:

Output power is varied and THD+N extracted per above explanation. It shows that this amplifier is a distortion factory, overlaying its own signature on *everything* you listen to. It is against the very word "high fidelity."
You also keep saying we only use sine waves. We do not and I already explain to you that 32-tone, multitone signal is just that, 32 tones and if you listen to it, it sounds like organ playing. Its waveform in time domain is quite complex looking as well.
My jitter test also uses dual squarewaves which by definition have infinite number of sinewaves:

It looks like a single sine wave but it is not. Everything above other than the 12 kHz spike is unwanted noise and jitter by the way. Using psychoacoustics though, you arrive at what I say above, "not an audible concern." Without the FFT you could do that analysis.
So really I would not keep repeating that the problem with measurements is some random claim about Fourier transform. Plenty of tests don't use them. And when we do, the FFT tells us the very thing we want to know: "how audible is that noise and distortion?" The only people who don't want to see such an FFT is because they are afraid of the story they tell.
They want to claim their gear sounds great despite the flaws found in measurements? That is cool. Just show a controlled test of half a dozen audiophiles with levels matched and blinded. Post that and we can talk. Don't keep writing essays. Essays don't make music. If ears are all that matters, then let's do an ear's only test. Until then, all the rest of what you are quoting is hoped to confuse the regular reader who doesn't understand the topic, hoping to get you to forego proper proofs, that is, with ears only, equipment sounds better.