If you want to get the exact sequence of tones and semitones of the
C major 
scale starting from A, the white keys of the piano are not enough. You would find the semitones between the second and third grade and between the fifth and sixth, and not, as it should be, between the third and fourth and between the seventh and the eighth.
You have to raise by a semitone C, F and G, replacing them with C#, F# and G#: so you generate the
A major 
scale, that reproduces the intervals of the
C major scale starting from A.
In a similar way it is possible to reproduce each of the seven
modes from any black or white key. Since there are seven white keys and five black ones between two C (excluding the second C, that is the repetition of the first), there are twelve major tonalities, twelve minor ones, twelve doric, and so on. To modular means changing from one key to another (for example, from C major to E minor).
