Semitone relationships and scales

Look at a guitar, or a piano/synthesizer.

Regardless of where one starts on a guitar, an octave of the note played is found 12 frets above the first fret played. Similarly, in a piano, octaves of notes are separated by 12 semitones.

This leads to the deduction that there is nothing inherently 'special' about the black and white keys on a piano. This is more evident on a guitar, where there are no demarcations for the notes, and all frets bear the same relationships to the adjacent ones.

Essentially, the notes could have just as well been named A through L. There is no reason why 'C#' should be named thus, incorrectly implying that it is in some way related to 'C', and that 'C' has some special significance.

Semitones are mathematically related, however. This is evident by the trained human ear's tendency to 'recognize' a major/minor scale, indicating that the degrees (2212221 in the case of major, 2122122 in the case of minor scales) and the relative frequencies between notes are important for a scale to 'sound' right and for the ear to intuitively identify the root.

The seven modes of a scale (more on this later), however, can be used effectively to 'reprogram'' the ear into accepting something initially unfamiliar as 'correct', making the argument about getting accustomed to set scale degrees null and void.