In summation, the very foundations of music are mathematical. With an understanding of its mathematic origins, we can apply mathematical principals that don’t seem intuitively musical to elevate our knowledge and understanding of music theory. Whether these elevations of harmony take us into visual geometry or aural symmetry and division, harmony would be nothing without mathematics. In the most perfect summation of the harmonic principles discussed today, please enjoy Jacob Collier’s Grammy-Award winning arrangement of “Moon River:”
(for an abridged version, start at 3:22).