The word ‘octave’ itself is derived from Latin, meaning “the eighth”—although octave law itself is as much about the number seven. At its simplest level, octave law basically posits that everything in existence is built on a structure of seven distinct parts, with the eighth part being a reiteration or variation of the first part. This is most clearly expressed in terms of music: in your basic diatonic scale, there are seven notes—do, re, mi, fa, so, la, ti—with the eighth note, another do, completing the octave and functioning as both the last part of this first scale and the first part of the next. The eighth note doubles the frequency of the first note, thus echoing the prior scale while subtly altering the tone of the next.
In other words, once you get past the first seven notes, it’s all fundamentally the same music. Or, as Hermes Trismegistus is reputed to have expressed it in his Emerald Tablet: “That which is above is like to that which is below, and that which is below is like to that which is above, to accomplish the miracles of the one thing.”
Of course, inherent in the concept is that while all these progressions of eight are essentially the same, they are also significantly differentiated as you either ascend or descend a given series of octaves. As is said in Meditations on the Tarot: “Since at the root of the diversity of phenomena their unity is found—in such a way that they are at one and the same time different and one—they are neither identical nor heterogeneous, but are analogous in so far as they manifest their essential kinship.”
This is taken to apply to everything from planetary orbits to the intrinsic nature of Man. At one point or another, under various names, Egyptians, Zoroastrians, Buddhists, and Christians have all enumerated the seven “principles of Man” as follows:
1. physical body
2. vital force
3. astral body (the etheric duplicate of the body, a sort of template or blueprint)
4. animal soul (passion or emotion)
5. human soul (intellect or will)
6. spiritual soul
7. universal spirit
Some cultures see these as stages through which every individual must progress in order to achieve perfection, which of course is perceived as the eighth and integrating principle.
No, I have not abandoned my customary cynicism for New Age (or in this case, Old Age, really) mysticism. The preceding 'treatisette' is actually the result of some research I did for the role-playing game I'm in under Dean. Which means that only K8, Alex, and Dean himself will understand the relevance of the topic, but I figured it was interesting enough to share with y'all anyway.