Explanation of the Inner Octaves Model
This is a color model of octaves in 3 scales, according to the work of G. I. Gurdjieff and Russell Smith, in his book, Gurdjieff: Cosmic Secrets. The central vertical line is Scale-0, starting at the note Re. (The notes are represented by solids: Do, sphere; Re, tetrahedron; Mi, cube; Fa, octahedron; So, dodecahedron; La, cuboctahedron; Ti, icosahedron.) The spirals surrounding the central core octave are the 3 mathematical octaves of Scale-1: these are the 3 inner octaves of the Scale-0 octave. These octaves span the 4 Fundamental Points (Re, Mi, So, and Do) of the Scale-0 octave, and there are spokes connecting the Dos of the Scale-1 octaves to the central octave at these points. The outer spirals are the 9 "Parts of Parts" octaves of Scale-2, also supported on spokes from the 4 Fundamental Points of the inner octaves of Scale-1. The vertical scale of this model is a multiple of the logarithm (base 2) of the frequencies of the notes, so that all doubling octaves in Scale-1 are the same in height.
This is also a physical model of a human being's Centers (Instinctive, Moving, Emotional, and Intellectual), Parts of Centers, and Parts of Parts of Centers, as encoded in the standard deck of 54 cards with 2 jokers. See Chapter 3 of Cosmic Secrets, and in particular, page 48. Diamonds are yellow, Clubs, purple, Hearts, red, and Spades, black. The Extra Joker is orange, the Joker is Indigo, the Major Oscillations are shown as light blue cylinders, and the Minor Oscillations as green cylinders. The remaining stopinders and the connecting spokes between the different scales (at the Fundamental Points) are white, and 3 black supporting spokes have been added for printability.
Because the pattern of the inner octaves is reproduced in the major and minor oscillations (the blue and green cylinders, respectively) of each octave, the 9 pairs of oscillations in this model also reproduce the pattern of the 18 cards consisting of the face cards (12), the aces (4), and the jokers (2).
This is also the pattern of matter atoms and sub-atomic particles (anti-matter is a separate octave).
The Central Core: the Atom
Major oscillation: the nucleus determines the element and isotope
Minor oscillation: the electron orbitals: determines valence, chemical properties
The Central Spiral: Parts of the Atom (or particles released when these parts collide)
The three pairs of oscillations in the central spiral represent the following:
Top Major: the strong and electromagnetic forces that hold the atom together and govern its chemical reactions.
Top minor: the weak and gravitational forces that account for the rest of the atom’s interactions.
Middle Major: the nucleons of the stable matter atom (protons with charge +1, neutrons, with charge 0).
Middle minor: the nucleons of strange matter (found in quark stars and ‘strangelets’ - see Wikipedia).
Bottom Major: electron -like particles (electrons, muon, and tau particles);
Bottom minor: neutrinos (electron neutrinos, muon neutrinos, and tau neutrinos)
The Outer spirals: Parts of Parts of Atoms
The 3 pairs of oscillations in each of the three outer spirals represent the particles that make up the categories of the central spiral oscillations.
Top 3 Octaves: The 3 pairs of particles in the top three octaves are the gauge bosons (particles mediating the strong, electromagnetic, weak, and gravitational forces, all with spin 1).
Top 1 Major: Gluons (mediating the strong force, holding the nucleus together, with charge 0, spin 1) .
Top 1 minor: Photons (mediating the electromagnetic force; charge 0, spin 1 )
Top 2 Major W bosons (mediating the weak force through the absorption or emission of electrons and positrons, causing nuclear transmutation, and absorption or emission of neutrinos; charge +1 or -1, spin 1)
Top 2 minor: Z boson (mediating the weak force through the transfer of spin, momentum, and energy between neutrinos; charge 0, spin 1)
Top 3 Major: Higgs boson (mediating mass; charge 0, spin 1)
Top 3 minor: graviton (mediating gravity; charge 0, spin 1)
Middle 3 Octaves: The nucleons: both stable and unstable; all have spin ½.
Middle 1 Major: Up Quark: found in protons (uud) and neutrons (udd): charge +2/3, spin ½
Middle 1 minor: Down Quark: (found in protons and neutrons, charge -1/3, spin ½)
Middle 2 Major: Charm Quark (unstable, charge +2/3, spin ½)
Middle 2 minor: Strange Quark (unstable, charge -1/3, spin ½)
Middle 3 Major: Top Quark (very unstable, charge +2/3, spin ½)
Middle 3 minor: Bottom Quark (very unstable, charge -1/3, spin ½)
Bottom 3 Octaves: Leptons: electron-like particles and neutrinos, both stable and unstable; all have spin ½ and do not interact with the strong force.
Bottom 1 Major: Electron (found in all matter atoms: charge -1, spin ½)
Bottom 1 minor: Electron Neutrino (does not interact with electromagnetic force: charge 0, spin ½)
Middle 2 Major: Muon (heavy, unstable, charge -1, spin ½)
Middle 2 minor: Muon Neutrino (unstable, charge 0, spin ½)
Middle 3 Major: Tau (very unstable, charge -1/2, spin ½)
Middle 3 minor: Tau Neutrino (very unstable, charge 0, spin ½)
This 3D model and the description of the atom and the subatomic particles was produced with the inspiration, aid, and permission of Russell A. Smith.