Assuming an algorithm could be worked out, would it end up sounding worse due to notes shifting around ever so slightly to make all the ratios work?
* Edited.
Anyway, there's fundamental issues this approach can never solve. An E and G should NEVER EVER be 5/4. That would be E and G-SHARP (or E-flat and G). But this is a good example of the issue. E and G could be 6/5 or 7/6 or 19/16 or… (the first two make the most sense). So, how is the keyboard to know when I play E and G that I wanted it to be part of a C-major 4:5:6 chord versus part of an A7 4:5:6:7 chord? There's no way other than some input that can tell me or the thing adapting after-the-fact when I later add the rest of the chord.
I think the best overall tuning software for keyboards is http://www.tallkite.com/alt-tuner.html by the way, although adaptive stuff isn't the focus.
There's many others though. Cheers
It’s a really unusual experience using it, because the never-quite-tuned sound is part of a piano’s character. With Hermode tuning engaged, every chord has a ringing pure bell-like quality, especially with 7th/diminished chords (which sound immensely satisfying).
Since few instruments in the real world can tune so precisely, Logic amusingly has a slider to make the Hermode tuning “less perfect” if desired.