Sergio wrote:
Why is it stated that a chromatic tuner does not work for tuning, even though all models (including the 12 euro ones and non-chromatic guitar tuners that only tune the 6 strings) are in any case already calibrated for equal temperament?
The question arises spontaneously and, in my opinion, deserves an exhaustive answer, because those who are not professionals but are nonetheless curious cannot understand it, even after reading various manuals and now the various tutorials available on the internet. I see that TheSimon has already taken a step and probably provided the answer, but in a way that is still unclear to a novice. Therefore, I want to present what might be the point of view of someone who doesn't understand and attempt to give an answer "from the bottom up," without claiming to interpret the doubts of others.
The simplest question is:
Everything that is read in tuning manuals regarding equal temperament, beats, etc., will surely be reproducible via an electronic chromatic tuner, perhaps even straight from the factory; that is, once the frequencies are established taking into account what is explained in the manuals, I should be set, right?!
The answer is no! Well, then we need to understand why.
Is it perhaps a problem of sensitivity? Is it possible that we are unable to build an instrument, no matter how expensive, that has sufficient sensitivity to fix frequencies in a satisfactory way?!
The answer should be: of course it can! At this point, if the right answer turns out to be wrong, it means the question is wrong!
I believe we must then move into the field of perception, both of the ear and of the electronic instrument, and I believe the devil here is the non-linearity of the auditory system and also that of the "real string" system.
If the electronic instrument were reliable in extracting a fundamental frequency from the sound of each vibrating string, and at the same time the ear were satisfied with having the fundamentals of all strings fixed to precise manual frequencies, we would have no problems.
The problem is therefore perhaps that the ear does not look for the fundamental nor even the simple ratio between fundamentals, but rather the perception of the pitch of a complex sound produced by a "real" string and even more so the ratios between complex sounds. The intelligence of the ear, even before the brain, cannot be reduced to a simple FFT, which an instrument can perform no matter how sophisticated. The perceived pitch would therefore not be that recommended by the instrument and could certainly be different from one piano to another.
Therefore, between one piano and another, the error produced by the electronic instrument certainly varies.
One cannot even think that the error produced by the instrument is constant over time and therefore "photographable" by the instrument for reuse, because obviously the physical characteristics of the piano vary over time.
At this point, one would have to ask: how subjective can tuning be, and how much instead is the quirky fineness of the ear reproducible from one human being to another?!
From personal experience, it seems to me that it is very reproducible, and therefore I also think that the "distance" from one ear to another is typically much smaller than that between an ear and an electronic instrument.
Forgive the length of my attempt, but I perceive and share the need for an answer!
kind regards
p.s. probably, out of ignorance, I have also underestimated the functioning of professional instruments, but I believe the substance does not change.