“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