Comment Wrong question. (Score 1) 111
31-ET, applied correctly, goes a long way to fix the problems 12-ET has rendering pre-20th century music correctly. When this is not a viable option (as with most keyboard instruments), that's what unequal well temperaments are for. Meantone can be very nice for Renaissance and some Baroque but gets to be pretty rancid for Bach and his contemporaries.
If you deny enharmonicity, meaning E-sharp isn't equivalent to F-natural or any other note, and F-sharp is a different pitch from G-flat, then there are essentially an arbitrary number of notes per octave depending on how you want to generate your scale. There are seven uniquely named pitch classes no matter what kind of scale you're working in, meaning diminished scales and other octatonic scales must have a cross-relation in them somewhere (a F-natural and an F-sharp, for example).
So, I'd have to vote for microtonal, the only option that encompasses all of these possibilities simultaneously.