The fractal enneagram

Commentary

Gurdjieff  explained in some detail that in the enneagram,  every note forms the "do"  for a subordinate octave beneath it.

His original remarks to Ouspensky on this matter are as follows:

“In the study of the law of octaves it must be remembered that octaves in their relation to each other are divided into fundamental and subordinate. The fundamental octave can be likened to the trunk of a tree giving off branches of lateral octaves. The seven fundamental notes of the octave and the two ‘intervals,’ the bearers of new directions, give altogether nine links of a chain, three groups of three links each.

“The fundamental octaves are connected with the secondary or subordinate octaves in a certain definite way. Out of the subordinate octaves of the first order come the subordinate octaves of the second order, and so on. The construction of octaves can be compared with the construction of a tree. From the straight basic trunk there come out boughs on all sides which divide in their turn and pass into branches, becoming smaller and smaller, and finally are covered with leaves. The same process goes on in the construction of the leaves, in the formation of the veins, the serrations, and so on."

...“In order better to understand the significance of the law of octaves it is necessary to have a clear idea of another property of vibrations, namely the so-called ‘inner vibrations.’ This means that within vibrations other vibrations proceed, and that every octave can be resolved into a great number of inner octaves.

“Each note of any octave can be regarded as an octave on another plane.

“Each note of these inner octaves again contains a whole octave and so on, for some considerable way, but not ad infinitum, because there is a definite limit to the development of inner octaves.

“These inner vibrations proceed simultaneously in ‘media’ of different density, interpenetrating one another, they are reflected in one another, give rise to one another; stop, impel, or change one another.

“Let us imagine vibrations in a substance or a medium of a certain definite density. Let us suppose this substance or medium to consist of the comparatively coarse atoms of world 48, each of which is, so to speak, an agglomeration of forty-eight primordial atoms. The vibrations which proceed in this medium are divisible into octaves and the octaves are divisible into notes. Let us imagine that we have taken one octave of these vibrations for the purpose of some kind of investigation. We must realize that within the limits of this octave proceed the vibrations of a still finer substance. The substance of world 48 is saturated with substance of world 24; the vibrations in the substance of world 24 stand in a definite relation to the vibrations in the substance of world 48, namely, each note of the vibrations in the substance of world 48 contains a whole octave of vibrations in the substance of world 24.

“These are the inner octaves.

“The substance of world 24 is, in its turn, permeated with the substance of world 12. In this substance also there are vibrations and each note of the vibrations of world 24 contains a whole octave of the vibrations of world 12. The substance of world 12 is permeated with the substance of world 6. The substance of world 6 is permeated with the substance of world 3. World 3 is permeated with the substance of world 1. Corresponding vibrations exist in each of these worlds and the order remains always the same, namely, each note of the vibrations of a coarser substance contains a whole octave of the vibrations of a finer substance.

“If we begin with vibrations of world 48, we can say that one note of the vibrations in this world contains an octave or seven notes of the vibrations of the planetary world. Each note of the vibrations of the planetary world contains seven notes of the vibrations of the world of the sun. Each vibration of the world of the sun will contain seven notes of the vibrations of the starry world and so on.

“The study of inner octaves, the study of their relation to outer octaves and the possible influence of the former upon the latter, constitute a very important part of the study of the world and of man.”

Excerpt taken from In Search of the Miraculous by P. D. Ouspensky, pub. Paul H. Crompton Ltd, 2004, pp 134-136.

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