“The octave is the means by which the three mothers set up the process of rhythmic response. It is the law that to each action there is an equal and opposite reaction.”
Book of Jubilee, Chapter 5
The octave arises from the internal structure of the fourth world cosmoses. The cosmoses are described in an earlier post, and are each formed as a cycle of constructors, the 3rd force in one constructor becoming the first force of the next. For example, the fifth cosmos dependant from UAD is:
In this pattern there are a total of 6 x 3=18 forces, but a more compact way of writing the pattern is to only write the repeating forces once, so that UAD-DAU would become UADAU, with the D in the middle serving as the last force in UAD and the first in DAU. Doing this to the entire cosmos gives the sequence:
U A D A U D A U D U A D
The process is more clearly shown in a circular figure, since it runs in cycles. In the figure below, the same cosmos is illustrated, with the forces arranged around a circle, moving clockwise from the right hand side, starting with UAD, which is numbered 1, 2, 3, and ending with ADU, numbered 11,12,1.
Energy steps within the octave
There are patterns within the cycle of twelve mothers. For example, the unifying mother appears in position 1, 5, 8 and 10, separated from each other by steps of 3 then 2 and then 1. The pattern is reversed for the affirming mother, which takes increasing steps, whilst the denying mother is evenly spaced in the cycle. These patterns are illustrated below:
“The mother which starts each octave, the first in the initiating constructor, possesses the greatest energy, and this energy runs down in jumps of three, two, and one steps. The second mother in the initiating constructor starts slowly and builds up to higher energies by one, two and three steps. The mother in the third place maintains the same strength throughout the six constructors in steps of two, two and two.”
The Notes of the Octave
The pattern of the octave is the same as a musical octave, with seven notes progressing from the note do to the same note at a higher frequency:
do – re – mi – fa – sol – la – si – do
The spacing of the notes in an octave is not constant. The mi-fa interval and the si-do interval are half as wide as the others (semi-tones rather than full tones). This same pattern is seen in the octave embedded in the sequence of twelve mothers.
The full tone intervals appears with another mother between the two notes. For example, the first two notes of the octave (do-re) are formed by the first three mothers in the sequence:
U (the do note) – A (the interval) – D (the re note)
The semi-tone intervals appear with no third mother between the notes. For example, the first shortened interval (mi-fa) is formed by:
U (the mi note) – D (the fa note)
In many traditions the octave is seen as a model of cosmological processes, with the shortened intervals indicative of places where a change of pace or direction might occur.
These are explained in the Book of Jubilee as a consequence of the way the mothers are arranged:
“When the third mother follows the first mother, the effect is to slow down process; when it leads the first mother, process is speeded up. The places where the third mother stands next to the first mother are the sixth, the ninth and the twelfth. In the sixth position it slows process down; in the ninth it both speeds up and slows down, so there is no effect; but in the twelfth process speeds up to start the next octave.”
One way to think about this is as follows:
This particular octave is about the interaction of two mothers, U and D; all of the notes are centred on these two.
Where the interaction between the two is mediated by the third mother, a smooth interaction takes place, and we get the full tone steps UAD (at do-re and la-si) and DAU (at re-mi and fa-sol).
Where the two mother meet without the mediation of the third, we get a different type of interaction: the UD at mi-fa slows the process, and the DU at si-do speeds up the process. In the centre of the octave we get both occurring together: UDU at sol-la.
Mutually Maintaining Octave
Each fourth world cosmos contains two octaves. The one we have just looked at is complemented by a second octave starting halfway round the circle in position 7:
This octave has the same pattern, but is about the interaction of A and D, mediated this time by U. The two octaves within the cosmos interlock and maintain each other.
Some questions to ponder: How many octave patterns are there all together, taking into account all of the fourth world cosmoses? How do the two octaves maintain each other? What would they sound like? If there was a movement for the octave, a dance perhaps, what would it be like?