Van der Waerden's theorem is a theorem of the branch of mathematics called Ramsey theory. The theorem is about the basic structure of the integers. It is named for Dutch mathematician B. L. van der Waerden. [1]

Van der Waerden's theorem states that for any given positive integers C and N, there is some number V(C, N) such that if the integers {1, 2, ..., V(C, N)} are colored, each with one of C different colors, then there are at least N integers in arithmetic progression all of the same color.

The arithmetic progression (red) is based on 1/12 of the octave interval making each step equal to 8.33% of the interval. The arithmetic progression is a linear growth equation with a slope of 0.08333 in the figure