The twelve-tone equally tempered scale tempers , or modifies, the Pythagorean chromatic scale by lowering each fifth slightly less than two cents, thus eliminating the Pythagorean comma of approximately 23.5 cents. Various other temperaments have also been proposed and implemented.
The harmonic chromatic scale therefore has every degree of the scale written twice, apart from the 5th and the key-note or starting note at the top or bottom.
However their form is dependent upon major or minor key signatures and whether the scale is ascending or descending. The image above therefore is only an example of the melodic chromatic scale, as it has no set form. That no scale degree should be used more than twice in succession (for instance G flat - G natural - G sharp) is however a principle upon which most are agreed.
Source: Wikipedia > Chromatic Scale
What is QuickyWiki? QuickyWiki blends the depth of Wikipedia with the ease and speed of Cliffs Notes.