Constructing a Major Scale

To construct a major scale, take any note to start, and apply the sequence of whole steps and half steps (WWHWWWH) in ascending order. See the examples below.

The result is the C major scale: C D E F G A B C

Another example

That's the G major scale: G A B C D E F# G

Notice that F# is required to maintain the sequence. This is why different keys have different sharps and flats — they're not arbitrary, they're whatever notes the sequence dictates.