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The Chromatic Scale
The chromatic scale is your friend.
The chromatic scale is constructed entirely of half steps. This makes it a very easy scale to memorize and to play several different ways.
Because the chromatic scale uses consecutive half steps (which happen to be the smallest distance you can move in western music), it contains all of the notes that we use.
Generally, when you ascend the scale you would use sharps, and flats when you descend.