It seems that we could get our perfect ratios now that we have computers.
As the computer plays, it uses a psychoacoustic model to determine which notes would have significant local tonal impact in the listener's mind. (the automated choices can be overridden as desired) Both past and future notes are considered. Exact ratios are used to determine every note frequency, using nearby significant notes as references.
You'd get nice integer ratios all throughout the music. The pitch standard would slowly vary, such that you could start in A440 and end up in A337. In most music, the pitch wouldn't change all that much, since it is something of a random walk by tiny amounts. There would be the occasional piece of music that causes a continuous unidirectional change in the pitch standard, requiring a few tweaks if that is undesired behavior.
Note that this is already kinda the case for fretless instruments, such as the violin. What you are suggesting to be done by a computer would be done by the player themselves. Obviously deciding exactly what tuning of each note to land on for any part of a song relies on musical intuition which computers are notoriously bad at. But when decided to be appropriate, on the violin perfect 5ths and 4th intervals would be actually (to the limits of the players ability and ear) perfect ratios. The major 3rd itself, which is decidedly enharmonic in equal temperament would sound cleaner and less "beaty".
I've always thought Bach would love the keyboard tools we have today. Simply the ability to switch tunings on the fly, rather than stopping to laboriously change gears on your harpsi/clavichord. I imagine the ability to switch to whatever temperament/tuning you want at the press of a button would have masterfully been taken advantage of by him (to say nothing of arbitrary sound/timbre for each voice/key-range etc. I think he would have loved Switched-On Bach).
Ohh that's a very interesting idea. Wonder if you could actually make something sound significantly better like that. But like you say, people might have rather different ideas on what sounds better.
And after a lifetime of equal temperament, that's what sounds good to me, anything else sounds out of tune. (I haven't experimented to see if even proper perfect 4ths and 5ths sound out of tune to me! That would be weird. Though those notes are very close to their equal temperament versions I think.) I used to have some music software that came with hundreds of different historical temperaments and tunings, from many different traditions, it was fascinating playing around with.
As the computer plays, it uses a psychoacoustic model to determine which notes would have significant local tonal impact in the listener's mind. (the automated choices can be overridden as desired) Both past and future notes are considered. Exact ratios are used to determine every note frequency, using nearby significant notes as references.
You'd get nice integer ratios all throughout the music. The pitch standard would slowly vary, such that you could start in A440 and end up in A337. In most music, the pitch wouldn't change all that much, since it is something of a random walk by tiny amounts. There would be the occasional piece of music that causes a continuous unidirectional change in the pitch standard, requiring a few tweaks if that is undesired behavior.