The cells in the skin that are responsible for its colouration are called chromatophores, and they colour the skin because they contain different colour pigments. The distribution of the pigments within these cells isn’t fixed, they can move. If the pigment spreads evenly throughout the entire cell, it becomes evenly and strongly coloured which means that areas of skin containing these chromatophores are also strongly coloured. If colour pigments are concentrated in one small area within the cell, the cell isn’t fully coloured so the skin colouration looks weak. pH and hardness affect colour pigments differently. Melanin, the black pigment, will spread through the cell to a greater extent in hard water and concentrate in smaller areas when the water is soft. On the other hand, the red pigment, astaxanthin, tends to spread throughout the cell in soft, low pH water, and to concentrate in a small area within the cell where the water is hard. In this way, soft, low pH water favours the development of hi (red) and hard, more alkaline water favours the development of sumi (black).

Of course, water parameters can’t possibly turn a poor quality koi into a good one because colouration is primarily determined by genetics and skillful culling but the appropriate parameters can make a good koi just that little bit better.
Reverse osmosis users are trying to emulate water in Japanese ponds by lowering the “hardness” or GH of their pond water to achieve a balance between water that is soft enough to allow red pigment to spread throughout the chromatophores but isn’t so soft that black pigment contracts within the cells and looks weak.
Using reverse osmosis purifiers to lower the mineral content of pond water can have benefits in terms of colour but it isn’t something that should be undertaken lightly. pH is a very important water parameter and the carbonate hardness parameter (KH) is crucial to maintaining a stable pH. Reducing hardness by reducing the calcium and magnesium content will have benefits but RO purifiers also remove carbonate hardness. The lower the KH, the more likely it is that the pH will become unstable. Biological filters consume great quantities of carbonates and, if they become completely exhausted, the pH will suddenly crash to levels that are lethal to koi.
GH may safely be lowered using reverse osmosis but, to avoid a pH crash, the KH should be regularly monitored and topped up as necessary by adding sodium bicarbonate to prevent it from falling below about 3°KH.
(Hobbyists who don't use RO and who prefer a stable pH that doesn't need to be so constantly monitored are advised to keep their KH nearer to 6°KH).