The most famous is the Greek "Golden Mean." This is a mathematical formula of great visual elegance. it is arrived at by bisecting a square and using the diagonal of one half of the square as a radius to extend the dimensions of the square to become a "Golden Rectangle." In the proportion arrived at, a:b=c:a. The "Golden Mean" was used by the Greeks to design most of what they built from the classic Greek amphora to the floor plans of the temples and their elevations.
There are proportional formulas on which scale can be based;
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There are many other scale systems;
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