CIRCLE OF FOURTH AND CIRCLE OF FIFTH (things you must know about them) (part 5)
HERE IS THE MYSTERY SEE MATHEMATICAL ILLUSTRATION OF THE CIRCLE OF FOURTH AND THE CIRCLE OF FIFTH. How to Mathematically Derive the Circle of Fifth The circle of fifths drawn within the chromatic circle as a star ( dodecagram ) To explain the circles, The circle of fifths, or fourths, may be mapped from the chromatic scale by multiplication, and vice versa. between the circle of fifths and the chromatic scale (in integer notation ) multiply by 7 ( M7 ), and for the circle of fourths multiply by 5 (P5). Here is a demonstration of this procedure. Start off with an ordered 12-tuple (tone row ) of integers (0, ...