Harmony and Natural Order

Harmonies are combinations of elements that resonate in the human perceptual system, and are "understood" without conscious thought. Natural orders are combinations of elements that are easily understood consciously and are typified by gradients and whole-number ratios.

Both types of ordered difference are numerically predictable. They also typically include "mystic" proportions, those which are seldom seen or unique. This has lead to the inclusion of harmonies and ordered difference in most proportional schemes. The resonant characteristic of harmonies, the development of a "new" element that is "more than the original" elements, leads to harmonics being taken as the physical equivalent of the "ampersand."

Natural Order -- Geometric and Linear Progressions

Harmony -- Pythagorean Divisions of the Octave, Musical Scales