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.
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. 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.
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. In the guise of this formula ideas of the octave have been handed down from teacher to pupil, from one school to another. The seven-tone scale is the formula of a cosmic law which was worked out by ancient schools and applied to music. A study of the structure of the seven-tone musical scale gives a very good foundation for understanding the cosmic law of octaves...read more>>>...
