Inner Octaves

This is a 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 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. This model is produced with the permission of Russell A. Smith. A colored model will be available soon, with the notes colored to distinguish the 4 suits of cards, and also coloring the cylinders connecting  the appropriate notes to show the major and minor oscillations in each octave.