Explanation: "In order to understand the meaning of this law it is necessary to regard the universe as consisting of vibrations. These vibrations proceed in all kinds, aspects, and densities of the matter which constitutes the universe, from the finest to the coarsest; they issue from various sources and proceed in various directions, crossing one another, colliding, strengthening, weakening, arresting one another, and so on." " . . . at the base of the understanding of vibrations ancient knowledge places the principle of the discontinuity of vibrations . . . (all vibrations) develop not uniformly but with periodical accelerations and retardations." "The laws which govern the retardation or the deflection of vibrations from their primary direction were known to ancient science. These laws were duly incorporated into a particular formula or diagram which has been preserved up to our times. In this formula the period in which vibrations are doubled was divided into eight unequal steps corresponding to the rate of increase in vibrations. The eighth step repeats the first step with double the number of vibrations. This period of the doubling of vibrations, or the line of the development of vibrations, between a given number of vibrations and double that number, is called on octave, that is to say, composed of eight." "The principle of dividing into eight unequal parts the period, in which the vibrations doubled, is based upon the observation of the non-uniform increase of vibrations in the entire octave, and separate 'steps' of the octave show acceleration and retardation at different moments of its development." "In the guise of this formula ideas of the octave have been handed down from teacher to pupil, from one school to another. In very remote times one of these schools found that it was possible to apply this formula to music. In this way was obtained the seven-tone musical scale which was known in the most distant antiquity, then forgotten, and then discovered or 'found' again." "The seven-tone scale is the formula of a cosmic law which was worked out by ancient schools and applied to music. At the same time, however, if we study the manifestations of the law of octaves in vibrations of other kinds we shall see that the laws are everywhere the same, and that light, heat, chemical, magnetic, and other vibrations are subject to the same laws as sound vibrations. For instance, the light scale is known to physics; in chemistry the periodic system of the elements is without doubt closely connected with the principle of octaves although this connection is still not fully clear to science." George Ivanovitch Gurdjieff in P.D Ouspensky's 'In Search of the Miraculous' (pgs 122-125)