Speaking as an engineer:

Surely if you are playing an unfretted instrument - like a violin - sharps and flats can be chosen for their sound.

Guitar, Piano, melodeon, flute etc - you dun gotta go with the available approximations. And they are approximations.

Having said that you can bend a clarinet note or a trombone even a guitar if you are sharpening. And vibrato covers a multitude of sins. Singing - all the possibilities are available, including the wrong ones.

And as Einstein might have said:
E=MF^b