THE MULTIPLICATION TABLE AS A FRAMEWORK FOR THE RATIOS OF RELATIVE PITCH

A multiplication table of 1 to 20 was laid out on a grid. Wherever the numerator and denominator were located, a circle was drawn. Numbers which were cubes (indicated as cubes) show a pattern which I refer to as a "visible three dimensional world". Square numbers always form squares along a diagonal. These form square boundaries for the series. Each series was chosen from that derived by Alain Danielou, based on a circle of fifths, beginning with a base series of C natural.