What is Harmony?
As we know, the opposites are unified by oscillation. This oscillation is the 'cosmic dance' that constitutes all the flow in the universe. This is the dance of unification, and the universe seems to favor patterns of equilibrium at different levels to 'simulate' the perfect equilibrium of the absolute!
In Sacred Geometry, the hexagonal packing of intersecting circles gives us the FLOWER of LIFE pattern which is also often termed as 'Nature's First Pattern'. From this pattern emerge the 5 Platonic solids which are the only 5 ways of dividing the sphere into perfectly symmetrical segments. These use triangles, squares, and pentagons as building blocks (i.e. numbers 3, 4, and 5). Further, their geometrical properties like vertices, edges, and faces are all measured in ‘regular’ numbers i.e. numbers having only 2, 3, or 5 as prime factors. This is exactly what we need to generate ALL the 12 ratios of the chromatic scale in an octave.
Harmony is the dance of unification between the octaves!
The only 5 perfect shapes of 3D. Also the core of sacred geometry.
Discovery of these 5 solids is hailed as one of the greatest mathematical discoveries of all time.
This is why there can be only 5 Platonic solids in 3D. We need a minimum of 3 faces and a defect (sum of angles < 360) to make a 3D corner.
Incidentally, there are 6 in 4D and then only 3 in 5D and onwards.
Platonic Solids have interesting 'nesting' properties. If you connect the midpoints of all faces, you get a new shape in the inside called a 'dual'. Tetrahedron is a self dual.
Adding up the surface angles of the 5 platonic solids and comparing them, we find the most harmonic music ratios.
Is it possible to generate all the 12 ratios? Give it a go!
Large number of cosmological phenomena related to size and motion of planets in the solar system is also 'harmonic' in nature. Therefore, they correlate with the platonic geometry in many ways.
Paths traced by planets as seen from the earth. The shapes represent the relative relationship between the earth cycle and the cycle of other planets.
The Venus earth relationship is the most famous of all with 13 cycles of venus = 8 cycles of the earth.
13 and 8 being both fibonacci numbers, it is interesting to see a 5 petal flower in the middle.
Music of the spheres!