Building the Major Scale

The pattern is the whole thing. Whole, whole, half, whole, whole, whole, half, measured from the tonic back up to itself an octave higher. That sequence of distances is what your ear recognizes as 'major sound,' not any particular set of letter names. Start the pattern on C and you get all white keys, no sharps or flats needed, because C major happens to line up that way naturally. Start anywhere else and some notes have to bend sharp or flat to preserve the same spacing.

Spelling a scale means picking the right letter name and the right accidental for each of the seven degrees, using each letter A through G exactly once. Take D major. D to E is a whole step, fine. E to F needs another whole step, but E to F natural is only a half step, so F must become F sharp. F sharp to G is a half step, matching the pattern's required half there, good. G to A, A to B, B to C sharp are all whole steps, and C sharp to D closes it with the final half step. Two sharps, F sharp and C sharp, forced entirely by the pattern.

This mechanism is what generates every key signature, which is why the next topic, the order of sharps and flats, is not arbitrary either. Once you can spell a scale note by note, you can predict exactly which accidentals its key signature carries, and that same whole-half logic underlies minor scales and modes later on.