I got to ask The Alexander String Quartet at their Q&A about microtones and whether F# is really the same as Gb (answer: it's not for them).
There IS a notation that they use among themselves about microtones above and below the standard pitch, and they have to agree what pitch, exactly, they're playing at any given note.
Furthermore, the pitch they would use depends on whether the musical line is going up or down; in other words, it could be different in different parts of the same piece.
There are a lot of things that serious musicians know well enough to explain, but almost no one ever asks them.
> whether F# is really the same as Gb (answer: it's not for them).
The reason they're the "same" is because of a limitation of musical instruments in their ability to play in multiple keys that led most Western instruments to be tuned in the 12-tone equal temperament system. If you select a different temperament, or use an instrument that can't be constrained by the 12-tone temperament, such as a computer, they can be different.
Some violin players will also tell you that they're not the same notes.
This may or may not be a disagreement with what you said:
They're the same on an instrument that can only play a defined set of notes, e.g. a piano or fretted instrument. It has nothing to do with the piano being in equal temperament.
If a violinist is playing an F#, his finger isn't necessarily on the exact same spot as when he's playing a Gb. As he explained answering my question, it isn't even in the exact same spot for the same F# every time in the same piece. The string players have very slight variations that they can describe precisely to each other so they sound good together.
I'm not familiar with the minutiae of of piano tuning, but nothing prevents you from tuning your piano keys so that F# and Gb are two different keys. The only reason why they're the same key is because we use an equal temperament tuning. Of course, if you tune the flats and sharps separately, then the range of your piano would be considerably reduced.
And yes, fretless instruments such as violins can be precise enough to differentiate between the two.
There IS a notation that they use among themselves about microtones above and below the standard pitch, and they have to agree what pitch, exactly, they're playing at any given note.
Furthermore, the pitch they would use depends on whether the musical line is going up or down; in other words, it could be different in different parts of the same piece.
There are a lot of things that serious musicians know well enough to explain, but almost no one ever asks them.