Harmonic Law, at it's most basic essence, is an adherence to progressive whole-number divisions of some whole structure. The entirety of that "whole" is regarded as the "fundamental", or the "first harmonic". If we take the structure and effectively "fold it in half" - so we have two equal divisions (i.e. the fundamental divided by two) - we arrive at the "second harmonic". If we instead fold it in thirds - for three equal divisions - this becomes the "third harmonic". This "harmonic progression" holds true for each whole-numbered division of our fundamental structure.
Every manifold structure - from a thought or event to a manifest object and its surrounding environment - can be broken down into and fully represented by its harmonic components (which we refer to as "partials")...and each of these partials is nothing more than the specific nature and behaviour of some whole-numbered division of the complete structure. By merely summing these harmonic partials together, we are able to flawlessly reconstruct that which they represent.
When we observe an object or event using the sensory tools of our perception, we quickly conclude that these are formed from a vast array of heterogenous components - each intertwined with the others to make manifest both the form and dynamics of our observed subject. With so many diverse elements contributing to the composition of our subject - and our conventional inability to effectively deal with all of these at once - it becomes impossible to fully interact with, let alone understand, our subject for the purposes of transformation.
Whilst our subject is in "partial form", however, we gain a unique perspective unattainable by other conventional means. Rather than dealing with some complex interplay of diverse elements, we have, in partials, a homogenous manifestation of our "whole". Thus, we see the diversity of our endlessly-variable subject condensed into a coherent collection of uniform partials - reducing many things to oneness. This allows us not only to observe the manifold composition and dynamics of our subject all at once, but also to effect change upon it as a singular, unified whole.
Adhering to the precepts of Harmonic Law is critical in achieving this "resynthesis". If the partials of our subject were not gathered as whole-numbered ratios of the whole, then the representation and resulting transformation would be incomplete and fractionated. Gathering and redistributing the partials strictly in whole-numbered ratios ensures that we not only have the right number of "pieces to the puzzle", but that each piece fits in perfectly with all the others without gaps or overlap.
In our diagram of the expression of harmony, we show a series up through the fourth harmonic, using coloured spheres to represent the partials. Each successive set fits perfectly within the whole, without gaps or overlap. This provides a genuine expression of the essence of Harmonic Law.
There is one further component that bears mention here: the "Origin". While we often think of the harmonic series as being whole-numbered ratio divisions of the fundamental (i.e. 1/2, 1/3, 1/4, etc - with the fundamental being 1/1), there is also a component which is antecedent to the fundamental of the whole. Placed within the harmonic series, this would constitute a mathematical impossibility - conventionally seen as an "undefinable" value (1/0) - but it is nonetheless a crucial ingredient of our formula. The Origin embodies the relationship between our subject and its environment (i.e. "the fundamental interconnectedness of all things"), as well as the relationship with its Source.