I am trying to understand how much of music theory can be done independently of a specific tuning system.
In equal temperament, all semitones have the same size, but that is not the case in other tuning systems. Nevertheless, as far as I understand, we say that between two adjacent notes in a diatonic scale there are either one or two semitones, even if these semitones are of different size for different note combinations.
This means that semitones can be used as an abstract measure of distance between notes, indepent of a specific tuning system.
I am trying to understand how this extends to chromatic notes. According to Wikipedia, an accidental raises/lowers a note by a semitone. Hence E# is one semitone above E.
But how many semitones are there between E# and F? Since both of them are one semitone above E, I am tempted to say that there are zero semitones between them.
In equal temperament, E# and F are enharmonically equivalent, so saying that they are zero semitones apart is fine. In other tuning systems, however, E# and F may very well correspond to different pitches. In these cases, one would need to think of "zero semitones" as an interval of varying (and hence potentially positive) size.
Is this a valid (and common) approach? If not, is there a better way of measuring the distance between notes indepedently of tuning?