It’s tempting to think that it’s only the domain of modernist composers, theorists and ethnomusicologists to talk of anything but 12 notes in an octave. After all if it was good enough for Mozart and Beethoven it should be good for everyone, right? Well, as it happens, Mozart and Beethoven understood F# and G-flat as different notes. A manuscript survives for example of Mozart’s teaching notes to his English student Thomas Attwood showing the difference between a major semitone (e.g. E to F) and a minor semitone (Fb to F). Almost universally considered as identical today, in his they were pitched slightly differently.
Very few musicians are aware that even into the 19th century fingerboard diagrams and scale exercises existed with two types of accidental (e.g. g# as distinct from a-flat) as well as keyboards with split keys so that the player could choose between accidental types.
It’s remarkable how efficiently this has been filtered out of the system so that even professional classical musicians and teachers – let alone students – are unaware of our microtonal recent history.