A study of basic harmonies

The six images within the header of the introductory article about harmony: Each images represents a different foundation for harmony and these images go from from the most perfect to the most imperfectly perfect (musicians).


10000000 Explanation: Circles and spheres apply the same simple formula in a thousand different ways. You can actually see the emergence of the radius and diameters in the dynamic image that follows.
Sphere to tetrahedron-octahedron couplet Explanation: This perfect stacking of hypothetical cannonballs introduces the perfect space-filling using the hexagons in two dimensions and the tetrahedrons and octahedrons within three dimensions. Imperfections are introduced with the pentastar.  More: Numbers, the Feigenbaum constant.
Octo70 Inside the octahedron are four hexagonal plates around the center-point:  You will be hard-pressed to find this image in any geometry textbook. Follow the four colors, red, white, blue and green and you will actually begin to see the foundations and earliest formations of the basic structure within chemistry.
tetrahedron Tetrahedrons within a tetrahedron with an octahedron in the middle: This image is a key to the UniverseView and to start the process of grappling with basic geometries within the earliest notations. Every tetrahedron has an octahedron in the middle. Every octahedron has six half-size octahedrons in each corner and a tetrahedron in each of the eight faces. One can imagine the progressuion goes on infinitely but here we find it circumscribes the entire universe within 202 notations.
Olympicene2 Olympicene: An organic carbon-based molecule was synthesized with five rings (four benzene rings) to honor the 2012 London Olympics. What makes this especially significant is that in 2012 IBM researchers in Zurich captured this image using non-contact atomic force microscopy. Also, see icosahedron.
choralsinging Teach the world to sing in perfect  harmony: Back in 1971 a Coca-Cola commercial was filmed and it became an instant hit because the image of the entire world singing in harmony is compelling. It is youthful idealism. It gives us hope and imbibes our optimism.  Music should always enrich our sense of self.
Considered: Then rejected:   Not enough harmony here.
5thHarmony Known as Fifth Harmony: In chasing down the wonderfully uplifting name, Fifth Harmony, we discovered that these five are naughty girls. They would blush if their grandmothers saw their performance. And, you can readily imagine each grandmother grabbing their not-so-grand daughter by the ear, arm, hand, nose or neck to read each the riot act! Their YouTube videos include all those gyrations of sexuality that make it  banal and empty. One can imagine their souls are aching for a truly loving person in their life.