This post is a follow-up question to this answer:
https://music.stackexchange.com/a/14264/86549
From what I could make of that answer, the need to stretched-tune a piano comes from the strings' less than perfect elasticity, which imperfection is greatest at the two extremities, where the strings are either very thick or thin. Because of that imperfect elasticity, getting the fundamentals exactly right would mean getting the harmonics slightly wrong. By stretching, we get the harmonics that are less wrong but at the expense of fundamentals that have been "stretched." (This may be contrasted with the need, or opportunity, for different temperaments, which to my understanding arises from mathematical reasons.)
Please don't rely on my imperfect summary, but go read the answer itself.
But here comes the question:
If the need for stretched tuning arises from the imperfect nature of the medium the strings are made of, why stretch a (modeled) digital piano? Couldn't the chip generate the frequencies at perfect ratios? By stretching a digital piano, wouldn't you get wrong fundamentals and wrong harmonics?
The only answer I could imagine is that we are so used to stretching in real pianos that we want it replicated in a digital piano. If this were so, could it be that by re-training our ears to octaves without stretching, we could actually begin to hear better music?
By the way, you couldn't replicate a real piano's imperfection in a digital piano simply by multiplying e.g. 0.99 or 1.01 to both the fundamental and all the overtones of a note. You'd have to multiply different factors to the fundamental and each of the overtones, so that, presumably, the fundamental is the most "off" and that the overtones the less off the higher multiple it is of the fundamental (or at least such is the implication of the original answer as I see it).
ADDED LATER
Here I found an explanation for stretching, which if true would apply to a digital piano as much as it does to a real: "I don't see why DPs would benefit less from stretch tuning than acoustics. It's a subjective adjustment meant to compensate for the human ear's relative inefficiency at lower/higher frequencies of the 88-note keyboard."
The same page also includes the following statement, which seems just wrong: "Stretch tuning a piano compensates for two things: 1) the basic fact that our 12 musical intervals are not laid out using perfect fractions (each note is theoretically 1/12 of an octave, but a perfect fifth, which is theoretically at the frequency halfway between the octaves, is actually 6 notes from the lower octave, and only 5 notes from the upper), and . . ." It seems to misunderstand the concept of "half-way." Just because the notes' frequencies are 2:3:4, that doesn't mean the middle note must be "half way" between the other two on a keyboard. And if that were a problem, no "stretching" would fix it.
ADDED STILL LATER
I would also add that the inelastic string and the limited ear ideas are inconsistent and cannot both be right.
The inelastic string idea (by which I mean the answer linked at the top of this post) is committed to saying that stretching only tries to achieve the "right" ratio between the high frequency overtones. For example, if a note and the same note four octaves higher are (meant to be) 1:16, the inelastic string idea says that stretching aims at giving 1:16 to the high overtones rather than to the fundamentals.
In contrast, the limited ear idea is committed to saying that stretching tries to give a ratio other than 1:16, e.g. 1:16.1, to (I suppose) the fundamentals and their respective overtones.
The two ideas are inconsistent, and at least one of them must be wrong. I believe there would be a simple fact of the matter. If you measure the frequencies of well-tuned pianos, fundamentals and overtones, the one or the other idea would prove to be right.
If the inelastic string idea is right, then it would appear that there is in principle no reason for a digital piano to try to emulate a real piano. The piano did not drop down from heaven after all.
If the limited ear idea is right, then even a digital piano must use some sort of stretching.
