In search of the miraculous

first. Together with the two 'additional shocks' which fill the 'intervals' mi-fa and si- do, there are nine elements.

'The complete construction of this symbol which connects it with a complete expression of the law of octaves is more complicated than the construction shown. But even this construction shows the inner laws of one octave and it points out a method of cognizing the essential nature of a thing examined in itself.

Fig. 47

5

9

7

4

2

'The isolated existence of a thing or phenomenon under examination is the closed circle of an eternally returning and uninterruptedly flowing process. The circle symbolizes this process. The separate points in the division of the circumference symbolize the steps of the process. The symbol as a whole is do, that is, something with an orderly and complete existence. It is a circle—a completed cycle. It is the zero of our decimal system; in its inscription it represents a closed cycle. It contains within itself everything necessary for its own existence. It is isolated from its surroundings. The succession of stages in the process must be connected with the succession of the remaining numbers from 1 to 9. The presence of the ninth step filling up the 'interval' si-do, completes the cycle, that is, it closes the circle, which begins anew at this point. The apex of the triangle closes the duality of its base, making possible the manifold forms of its manifestation in the most diverse triangles, in the same way as the point of the apex of the triangle multiplies itself infinitely in the line of its base. Therefore every beginning and completion of the cycle is situated in the apex of the triangle, in the point where the beginning and the end merge, where the circle is closed, and which sounds in the endlessly flowing cycle as the two do's in the octave. But it is the ninth step that closes and again begins a cycle. Therefore in the upper point of the triangle corresponding to do stands the number 9, and among the remaining points are disposed the numbers 1 to 8.

'Passing on to the examination of the complicated figure inside the circle we should understand the laws of its construction. The laws of unity are reflected in all phenomena. The decimal system is constructed on the basis of the same laws. Taking a unit as one note containing within itself a whole octave we must divide this unit into seven unequal parts in order to arrive at the seven notes of this octave. But in the graphic representation the inequality of the parts is not taken into account and for the construction of the diagram there is taken first a seventh part, then two-sevenths, then three-sevenths, four-sevenths, five-sevenths, six-sevenths, and seven-sevenths. Calculating these parts in decimals we get:

1/7=0.142857 . . .

2/7=0.285714 . . .

3/7=0.428571 . . .

4/7=0.571428 . . .

5/7=0.714285 . . .

6/7=0.857142 . . .

7/7=0.999999 . . .

'In examining the series of periodic decimals obtained we at once see that in all except the last the periods consist of exactly the same six digits which run in a definite sequence, so that, knowing the first digit of the period, it is possible to reconstruct the whole period in full.

'If we now place on the circumference all the nine numbers from 1 to 9 and connect those numbers which are included in the period by straight lines in the same sequence in which the numbers stand in the period, according to which number we start from, we shall obtain the figure found inside the circle. The numbers 3, 6, and 9 are not included in the period. They form the separate triangle—the free trinity of the symbol.

'Making use of 'theosophical addition' and taking the sum of the numbers of the period, we obtain nine, that is, a whole octave. Again in each separate note there will be included a whole octave subject to the same laws as the first. The positions of the notes will correspond to the numbers of the period and the drawing of an octave will look like the following:

'The triangle 9-3-6, which unites into one whole the three points on the circumference not included in the period, connects together the law of seven and the law of three. The numbers 3-6-9 are not included in the period; two of them, 3 and 6, correspond to the two 'intervals' in the octave, the third is, so to speak, superfluous and at the same time it replaces the fundamental note which does not enter the period. Moreover, any phenomenon which is able to act reciprocally with a phenomenon similar to it sounds as the note do in a corresponding octave. Therefore do can emerge from its circle and enter into orderly correlation with another circle, that is, play that role in another cycle which, in the cycle under consideration, is played by the 'shocks* filling the 'intervals' in the octave. Therefore, here also, by having this possibility do is connected by the triangle 3-6-9 with those places in the octave where the shocks from outside sources occur, where the octave can be penetrated to make connection with what exists outside it. The law of three stands out, so to speak, from the law of seven, the triangle penetrates through the period and these two figures in combination give the inner structure of the octave and its notes.

'At this point in our reasoning it would be entirely right to raise the question: Why is one of the 'intervals' which is designated by the number 3 found in its right place between the notes mi and fa, and the other, which is designated by the number 6, found between sol and la, when its right place is between si and do.

'If the conditions had been observed as to the appearance of the second interval (6) in its own place, we should have had the following circle:

And the nine elements of the closed cycle would have been grouped symmetrically together in the following way: