“The principle of the discontinuity of vibration means the definite and necessary

characteristic of all vibrations in nature, whether ascending or descending, to develop

not uniformly but with periodical accelerations and retardations. This principle can be

formulated still more precisely if we say that the force of the original impulse in

vibrations does not act uniformly but, as it were, becomes alternately stronger and

weaker. The force of the impulse acts without changing its nature and vibrations

develop in a regular way only for a certain time which is determined by the nature of

the impulse, the medium, the conditions, and so forth. But at a certain moment a kind

of change takes place in it and the vibrations, so to speak, cease to obey it and for a

short time they slow down and to a certain extent change their nature or direction; for

example, ascending vibrations at a certain moment begin to ascend more slowly, and

descending vibrations begin to descend more slowly. After this temporary retardation,

both in ascending and descending, the vibrations again enter the former channel and

for a certain time ascend or descend uniformly up to a certain moment when a check in

their development again takes place. In this connection, it is significant that the periods

of uniform action of the momentum are not equal and that the moments of retardation

of the vibrations are not symmetrical. One period is shorter, the other is longer.

“In order to determine these moments of retardation, or rather, the checks in the

ascent and descent of vibrations, the lines of development of vibrations are divided into periods corresponding to the doubling or the halving of the number of vibrations in a given space of time.

“Let us imagine a line of increasing vibrations. Let us take them at the moment

when they are vibrating at the rate of one thousand a second. After a certain time the

number of vibrations is doubled, that is, reaches two thousand.

1000 2000

|—————————————————————|

FIG. 7

“It has been found and established that in this interval of vibrations, between the

given number of vibrations and a number twice as large, there are two places where a

retardation in the increase of vibrations takes place. One is near the beginning but not

at the beginning itself. The other occurs almost at the end.

“Approximately:

1000 2000 FIG. 8

|————————|———————————|——|

“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 the vibrations. The eighth step repeats

the first step with double the number of vibrations. This period of the doubling of the

vibrations, or the line of the development of vibrations, between a given number of

vibrations and double that number, is called an octave, that is to say, composed of

eight.

“The principle of dividing into eight unequal parts the period, in which the

vibrations are 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, how-

ever, 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.

“A study of the structure of the seven-tone musical scale gives a very good

foundation for understanding the cosmic law of octaves.”

To continue – P.D.Ouspensky In Search of the Miraculous Chapter 7 page 132 e-book or the book page 125