not only that you distorted the matter saying your sinad tool is not a Fourier tool. This is an half truth. why ?
It is the full truth. Fourier transform takes a time domain signal and converts to fundamental sine waves that created it. This is a proven mathematical relationship. Just like Pythagorean formula. It is not subject to debate. And no experiment whatsoever has disproven it. Again, it is a mathematical proof ("theorem").
There is an observation with respect to such a transform that follows the same in quantum mechanics called Heisenberg uncertainty principle. It says that the more you know about a particles momentum, the less you know about its position and vice versa. The comparable version for Fourier transform is that to get more accuracy in frequency domain, the less you know about its timing and vice versa. Here is a nice video explaining all of this briefly:
The research you put forward says that our hearing system due to its non-linearities, doesn't follow this relationship. That when we trade off timing resolution vs frequency, they don't follow a 1:1 relationship. But this has no bearing whatsoever on audio measurements! In audio measurements, we have a known, usually simple input signal. At no time are we interested in its characteristics with respect to time domain. What we want to know is when it goes into our audio system, does it create noise and distortion that is NOT in the audio signal that was input.
Take my dashboard for example:
On the left is a simple sine wave. In a perfect system, its fourier transform would produce a single spike (on the right) at its frequency and that would be it. Above is not an ideal system so we see harmonic distortion and noise.
The uncertainty principle comes into play in that I had to select large enough number of audio samples to give us the resolution we need on the right to clearly see the spurious tones created by the non-linearities of device under test. For my dashboard, I use 32,000 samples.
It is true then that you don't know where in those 32,000 samples that distortion profile exist from the fourier transform. But you do know that because the above sine wave never changes! It goes on forever producing a single tone at 1 kHz.
I demonstrate all of this in my view on FFT:
Because the number of samples I use is programable, the fourier transforms I show hugely outperform human ear! To wit, I can measure the frequency components of a signal to less than 1 Hz if I want. Human ear has far lower resolution, expressed as ERB:
At 10 KHz, our hearing's frequency discrimination is as poor as 1000 Hz!
All tools in audio directly or indirectly use Fourier mathematics as direct tool or as the only context of interpretation.
No, no, no. Some of the measurements I perform have been around for nearly a century! Way before we have had any audio analyzer had any computing ability to produce fourier transform. You can go on ebay and buy analog THD+N analyzers such as this:
My analyzer produces a more accurate version of these measurements but no fourier analysis is used, and even if it had, it would not matter per my explanation above.
Take this PrimaLuna tube amplifier:
You can take to the bank that it has power supply noise and distortion. There is no uncertainty about that.
Finally, our knowledge of psychoacoustics is strongly based on actual human listening tests. Whatever the ear+brain can do, is already embedded in that science. The experiment you keep citing does not change any of that.
So please, for love of everyone, don't keep repeating what you have been saying about measurements, how they work and their use of fourier transform, or not.